Finite Group Databasebeta

← C3×C4×D3×#67 #13174652

Subgroups — C3×C4×D3×#67 #13174652

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic
3C2×C3×C4×D32C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×D3×#217C211yesmaximal, characteristic, complemented
8C3×#63952C211yesmaximal, characteristic, complemented
9C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×#63904C211yesmaximal, characteristic, complemented
11C3×C4×#626C211yesmaximal, characteristic, complemented
12C3×C4×#625C211yesmaximal, characteristic, complemented
13C3×#63879C211yesmaximal, characteristic, complemented
14C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
16C2×C3×C4×#67—31nomaximal
17C3×C4×D3×D4—31nomaximal
18C4×D3×#67C311yesmaximal, characteristic, direct product factor
19C23×C32×D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×C32×C4×D3—24no—
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C2×C32×C4×D3C2211yescharacteristic, complemented
32C3×D3×#67C418yesdirect product factor
33C2×C3×#626C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic
38C2×C3×D3×Dic3C2211yescharacteristic
39C2×C3×D3×Dic3C2211yescharacteristic, complemented
40C3×C4×D32—24no—
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48C32×C4×Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C3×Dic32C2211yescharacteristic, complemented
57C23×C32×C4—31no—
58C22×C3×#67—31no—
59C2×C3×D3×D4—31no—
60C22×C3×C4×D3—21no—
61C22×C3×C4×D3—31no—
62C22×C3×C4×D3—31no—
63C22×C3×C4×D3D311yescharacteristic, complemented
64C22×C3×C4×D3C2×C311yescharacteristic, complemented
65C2×D3×#67C2×C311yescharacteristic
66C2×C4×D32C2×C311yescharacteristic, complemented
67C32×C4×D4—31no—
68C4×#638C2×C311yescharacteristic, complemented
69C2×C3×#217—31no—
70C3×D4×Dic3—31no—
71C3×C4×#67—21no—
72C3×C4×#67—31no—
73C3×C4×#67—31no—
74C3×C4×#67—31no—
75C3×C4×#67—31no—
76C3×C4×#67—31no—
77C3×C4×#67—31no—
78C3×C4×#67—31no—
79C3×C4×#67—31no—
80C3×C4×#67—31no—
81C3×C4×#67—61no—
82C3×C4×#67D311yescharacteristic, direct product factor
83C3×C4×#67C2×C311yescharacteristic, complemented
84C2×C3×(C2×D3)⋊C4—31no—
85C2×C3×Dic3⋊C4—31no—
86C2×C3×C4×Dic3—31no—
87C3×#893—31no—
88C3×D3×C4⋊C4—31no—
89C3×#67⋊C4—31no—
90C3×#67⋊C4—31no—
91C3×D3×C22⋊C4—31no—
92C3×D3×C22⋊C4—31no—
93C3×C4×D12—31no—
94C3×C42×D3—31no—
95Dic3×#67C2×C311yescharacteristic, complemented
96D3×#217C2×C311yescharacteristic, complemented
97#63952C2×C311yescharacteristic, complemented
98D3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
99#63904C2×C311yescharacteristic, complemented
100C4×#626C2×C311yescharacteristic, complemented
101C4×#625C2×C311yescharacteristic, complemented
102#63879C2×C311yescharacteristic, complemented
103D3×Dic3⋊C4C2×C311yescharacteristic, complemented
104C4×D3×Dic3C2×C311yescharacteristic, complemented
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3—22no—
108C22×C32×D3—22no—
109C22×C32×D3C2×C414yescomplemented
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×C3×D32—22no—
114C2×C3×D32—22no—
115C2×C3×D32C2×C414yescomplemented
116C2×C33×C4—22no—
117C2×C33×C4C2311yescharacteristic
118C2×C33×C4C2311yescharacteristic
119C3×#638C2×C414yescomplemented
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C3×C4×C3⋊D3—22no—
124C32×#67C2×C414yescomplemented
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C32×C4×D3—22no—
132C32×C4×D3—22no—
133C32×C4×D3—22no—
134C32×C4×D3—22no—
135C32×C4×D3D414yescomplemented
136C3×#626C2×C414yescomplemented
137C3×#625C2×C414yescomplemented
138C3×#624—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—22no—
141C3×D3×Dic3—22no—
142C3×D3×Dic3C2×C414yescomplemented
143C2×C3×C4×D4—91no—
144C2×C4×#67—31no—
145C4×D3×D4—31no—
146C24×C32—31no—
147C23×C3×D3—21no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3C2×D311yescharacteristic
151C23×C3×D3C22×C311yescharacteristic
152C22×D32C22×C311yescharacteristic
153C2×C32×D4—31no—
154C22×C32×C4—21no—
155C22×C32×C4—21no—
156C22×C32×C4—21no—
157C22×C32×C4—31no—
158C22×C32×C4—31no—
159C22×C32×C4—31no—
160C22×C32×C4—31no—
161C22×C32×C4—31no—
162C22×C32×C4—31no—
163C22×C32×C4—41no—
164C22×C32×C4—64no—
165C22×C32×C4C2×D311yescharacteristic, complemented
166C22×C32×C4C2×D311yescharacteristic, complemented
167C22×C32×C4C22×C311yescharacteristic, complemented
168C2×#638C22×C311yescharacteristic
169C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
170C2×C3×#67—21no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—38no—
176C2×C3×#67—31no—
177C2×C3×#67—61no—
178C2×C3×#67C2×D311yescharacteristic
179C2×C3×#67C22×C311yescharacteristic
180C22×C3×Dic3—21no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C22×C3×Dic3C22×C311yescharacteristic, complemented
187C3×D3×D4—38no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—28no—
190C2×C3×C4×D3—21no—
191C2×C3×C4×D3—21no—
192C2×C3×C4×D3—21no—
193C2×C3×C4×D3—21no—
194C2×C3×C4×D3—24no—
195C2×C3×C4×D3—24no—
196C2×C3×C4×D3—21no—
197C2×C3×C4×D3—31no—
198C2×C3×C4×D3—31no—
199C2×C3×C4×D3—31no—
200C2×C3×C4×D3—31no—
201C2×C3×C4×D3—31no—
202C2×C3×C4×D3—31no—
203C2×C3×C4×D3—31no—
204C2×C3×C4×D3—31no—
205C2×C3×C4×D3—64no—
206C2×C3×C4×D3—64no—
207C2×C3×C4×D3—61no—
208C2×C3×C4×D3C2×D311yescharacteristic
209C2×C3×C4×D3C2×D311yescharacteristic
210C2×C3×C4×D3C2×D311yescharacteristic, complemented
211C2×C3×C4×D3C2×D311yescharacteristic, complemented
212C2×C3×C4×D3C2×D311yescharacteristic, complemented
213C2×C3×C4×D3C22×C311yescharacteristic
214C2×C3×C4×D3C22×C311yescharacteristic
215C2×C3×C4×D3C22×C311yescharacteristic, complemented
216C2×C3×C4×D3C22×C311yescharacteristic, complemented
217C2×C3×C4×D3C22×C311yescharacteristic, complemented
218D3×#67C3×C418yesdirect product factor
219C2×#626C22×C311yescharacteristic
220C2×#625C22×C311yescharacteristic
221C2×#624C22×C311yescharacteristic, complemented
222C2×D3×Dic3C22×C311yescharacteristic
223C2×D3×Dic3C22×C311yescharacteristic
224C2×D3×Dic3C22×C311yescharacteristic
225C2×D3×Dic3C22×C311yescharacteristic, complemented
226C4×D32—24no—
227C32×C4⋊C4—31no—
228C32×C22⋊C4—31no—
229C32×C22⋊C4—31no—
230C32×C42—31no—
231#3757C22×C311yescharacteristic, complemented
232#3752C22×C311yescharacteristic, complemented
233#3750C22×C311yescharacteristic, complemented
234C4×C3⋊Dic3C22×C311yescharacteristic, complemented
235C3×#217—21no—
236C3×#217—31no—
237C3×#217—31no—
238C3×#217—31no—
239C3×#217—31no—
240C3×#217—31no—
241C3×#217—61no—
242C3×#217C2×D311yescharacteristic, complemented
243C3×#217C22×C311yescharacteristic, complemented
244C3×(C2×D3)⋊C4—21no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248C3×(C2×D3)⋊C4—31no—
249C3×(C2×D3)⋊C4—31no—
250C3×(C2×D3)⋊C4—31no—
251C3×(C2×D3)⋊C4—31no—
252C3×(C2×D3)⋊C4—61no—
253C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
254C3×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
255C3×C4⋊Dic3—31no—
256C3×Dic3⋊C4—21no—
257C3×Dic3⋊C4—31no—
258C3×Dic3⋊C4—31no—
259C3×Dic3⋊C4—31no—
260C3×Dic3⋊C4—31no—
261C3×Dic3⋊C4—31no—
262C3×Dic3⋊C4—61no—
263C3×Dic3⋊C4C2×D311yescharacteristic, complemented
264C3×Dic3⋊C4C22×C311yescharacteristic, complemented
265C3×C4×Dic3—21no—
266C3×C4×Dic3—31no—
267C3×C4×Dic3—31no—
268C3×C4×Dic3—31no—
269C3×C4×Dic3—31no—
270C3×C4×Dic3—31no—
271C3×C4×Dic3—31no—
272C3×C4×Dic3—61no—
273C3×C4×Dic3C2×D311yescharacteristic, complemented
274C3×C4×Dic3C22×C311yescharacteristic, complemented
275#3724C22×C311yescharacteristic, complemented
276Dic3⋊Dic3C22×C311yescharacteristic, complemented
277#3722C22×C311yescharacteristic, complemented
278(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
279(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
280(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
281Dic32C22×C311yescharacteristic, complemented
282Dic32C22×C311yescharacteristic, complemented
283C22×C33—21no—
284C22×C33—21no—
285C22×C33C22×C412yescomplemented
286C22×C33C2411yescharacteristic
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3C22×C412yescomplemented
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—28no—
295C2×C32×D3C22×C412yes—
296C2×C32×D3C22×C412yescomplemented
297C2×C32×D3C22×C412yescomplemented
298C2×C32×D3C2×D412yes—
299C2×C32×D3#4112yes—
300C3×D32—28no—
301C33×C4—21no—
302C33×C4C2×D412yescomplemented
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3C22×C412yescomplemented
306C32×Dic3—21no—
307C32×Dic3—21no—
308C32×Dic3—21no—
309C32×Dic3C22×C412yescomplemented
310C32×Dic3C2×D412yescomplemented
311C22×C3×D4—91no—
312C23×C3×C4—31no—
313C23×C3×C4—31no—
314C23×C3×C4—61no—
315C23×C3×C4—91no—
316C22×#67—31no—
317C2×D3×D4—31no—
318C22×C4×D3—31no—
319C22×C4×D3—31no—
320C22×C4×D3C3×D311yescharacteristic, complemented
321C3×C4×D4—31no—
322C3×C4×D4—31no—
323C3×C4×D4—61no—
324C3×C4×D4—91no—
325C3×C4×D4—91no—
326C3×C4×D4—91no—
327C3×C4×D4—91no—
328C3×C4×D4—91no—
329C3×C4×D4—91no—
330C3×C4×D4—91no—
331C2×C3×C4⋊C4—91no—
332C2×C3×C22⋊C4—91no—
333C2×C3×C22⋊C4—91no—
334C2×C3×C42—91no—
335C2×#217—31no—
336D4×Dic3—31no—
337C4×#67—31no—
338C4×#67—31no—
339C4×#67—31no—
340C4×#67—31no—
341C4×#67—31no—
342C4×#67—31no—
343C4×#67—31no—
344C4×#67—31no—
345C4×#67—31no—
346C4×#67—61no—
347C4×#67C3×D311yescharacteristic, direct product factor
348C2×(C2×D3)⋊C4—31no—
349C2×Dic3⋊C4—31no—
350C2×C4×Dic3—31no—
351#893—31no—
352D3×C4⋊C4—31no—
353#67⋊C4—31no—
354#67⋊C4—31no—
355D3×C22⋊C4—31no—
356D3×C22⋊C4—31no—
357C4×D12—31no—
358C42×D3—31no—
359C23×C32—21no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—31no—
363C23×C32—34no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—41no—
367C23×C32—62no—
368C23×C32—62no—
369C23×C32C22×D311yescharacteristic
370C23×C32C22×D311yescharacteristic
371C23×C32C23×C311yescharacteristic
372C22×C3⋊D3C23×C311yescharacteristic
373C22×C3×D3—24no—
374C22×C3×D3—24no—
375C22×C3×D3—22no—
376C22×C3×D3—22no—
377C22×C3×D3—22no—
378C22×C3×D3—22no—
379C22×C3×D3—24no—
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—21no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—34no—
386C22×C3×D3—34no—
387C22×C3×D3—61no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3C4×D314yescomplemented
393C22×C3×D3C2×C3×C414yescomplemented
394C22×C3×D3C22×D311yescharacteristic
395C22×C3×D3C22×D311yescharacteristic
396C22×C3×D3C22×D311yescharacteristic
397C22×C3×D3C23×C311yescharacteristic
398C22×C3×D3C23×C311yescharacteristic
399C22×C3×D3C23×C311yescharacteristic
400C2×D32—22no—
401C2×D32—22no—
402C2×D32C2×C3×C414yescomplemented
403C32×D4—34no—
404C2×C32×C4—22no—
405C2×C32×C4—24no—
406C2×C32×C4—22no—
407C2×C32×C4—22no—
408C2×C32×C4—21no—
409C2×C32×C4—21no—
410C2×C32×C4—21no—
411C2×C32×C4—21no—
412C2×C32×C4—21no—
413C2×C32×C4—21no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416C2×C32×C4—34no—
417C2×C32×C4—31no—
418C2×C32×C4—31no—
419C2×C32×C4—31no—
420C2×C32×C4—41no—
421C2×C32×C4—41no—
422C2×C32×C4—42no—
423C2×C32×C4—42no—
424C2×C32×C4—44no—
425C2×C32×C4—62no—
426C2×C32×C4—62no—
427C2×C32×C4—62no—
428C2×C32×C4—62no—
429C2×C32×C4—62no—
430C2×C32×C4C22×D311yescharacteristic
431C2×C32×C4C22×D311yescharacteristic
432C2×C32×C4C22×D311yescharacteristic
433C2×C32×C4C22×D311yescharacteristic
434C2×C32×C4C23×C311yescharacteristic
435C2×C32×C4C23×C311yescharacteristic
436#638C2×C3×C414yescomplemented
437C2×C3⋊Dic3C23×C311yescharacteristic
438C2×C3⋊Dic3C23×C311yescharacteristic
439C2×C3⋊Dic3C23×C311yescharacteristic
440C4×C3⋊D3—22no—
441C3×#67—24no—
442C3×#67—34no—
443C3×#67—34no—
444C3×#67—34no—
445C3×#67—34no—
446C3×#67—34no—
447C3×#67—64no—
448C3×#67C4×D314yesdirect product factor
449C3×#67C2×C3×C414yescomplemented
450C2×C3×Dic3—24no—
451C2×C3×Dic3—22no—
452C2×C3×Dic3—22no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—34no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—61no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—62no—
469C2×C3×Dic3—62no—
470C2×C3×Dic3—62no—
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C23×C311yescharacteristic
477C2×C3×Dic3C23×C311yescharacteristic
478C2×C3×Dic3C23×C311yescharacteristic
479C2×C3×Dic3C23×C311yescharacteristic
480C2×C3×Dic3C23×C311yescharacteristic
481C3×D12—34no—
482C3×C4×D3—24no—
483C3×C4×D3—24no—
484C3×C4×D3—24no—
485C3×C4×D3—22no—
486C3×C4×D3—22no—
487C3×C4×D3—22no—
488C3×C4×D3—22no—
489C3×C4×D3—22no—
490C3×C4×D3—22no—
491C3×C4×D3—22no—
492C3×C4×D3—22no—
493C3×C4×D3—24no—
494C3×C4×D3—34no—
495C3×C4×D3—42no—
496C3×C4×D3—62no—
497C3×C4×D3—62no—
498C3×C4×D3—62no—
499C3×C4×D3—62no—
500C3×C4×D3—62no—
501C3×C4×D3—62no—
502C3×C4×D3—62no—
503C3×C4×D3—122no—
504C3×C4×D3#6714yesdirect product factor
505C3×C4×D3C3×D414yescomplemented
506#626C2×C3×C414yescomplemented
507#625C2×C3×C414yescomplemented
508#624—22no—
509D3×Dic3—22no—
510D3×Dic3—22no—
511D3×Dic3—22no—
512D3×Dic3C2×C3×C414yescomplemented
513C2×C4×D4—91noSylow
514C2×C33—22no—
515C2×C33C23×C411yescharacteristic
516C2×C33C22×D411yescharacteristic
517C2×C33C2×#4111yescharacteristic
518C3×C3⋊D3—22no—
519C32×D3—22no—
520C32×D3—22no—
521C32×D3C4×D414yescomplemented
522C24×C3—31no—
523C24×C3—31no—
524C24×C3—61no—
525C24×C3—91no—
526C23×D3—31no—
527C23×D3—31no—
528C23×D3C2×C3×D311yescharacteristic
529C2×C3×D4—31no—
530C2×C3×D4—31no—
531C2×C3×D4—61no—
532C2×C3×D4—91no—
533C2×C3×D4—98no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C22×C3×C4—21no—
537C22×C3×C4—21no—
538C22×C3×C4—21no—
539C22×C3×C4—31no—
540C22×C3×C4—31no—
541C22×C3×C4—31no—
542C22×C3×C4—31no—
543C22×C3×C4—31no—
544C22×C3×C4—31no—
545C22×C3×C4—31no—
546C22×C3×C4—31no—
547C22×C3×C4—31no—
548C22×C3×C4—31no—
549C22×C3×C4—31no—
550C22×C3×C4—31no—
551C22×C3×C4—41no—
552C22×C3×C4—61no—
553C22×C3×C4—61no—
554C22×C3×C4—61no—
555C22×C3×C4—61no—
556C22×C3×C4—61no—
557C22×C3×C4—61no—
558C22×C3×C4—64no—
559C22×C3×C4—64no—
560C22×C3×C4—68no—
561C22×C3×C4—91no—
562C22×C3×C4—91no—
563C22×C3×C4—91no—
564C22×C3×C4—91no—
565C22×C3×C4—91no—
566C22×C3×C4—91no—
567C22×C3×C4—184no—
568C22×C3×C4D3211yescharacteristic, complemented
569C22×C3×C4C2×C3×D311yescharacteristic, complemented
570C22×C3×C4C2×C3×D311yescharacteristic, complemented
571C2×#67—31no—
572C2×#67—31no—
573C2×#67—31no—
574C2×#67—31no—
575C2×#67—38no—
576C2×#67—31no—
577C2×#67—61no—
578C2×#67C2×C3×D311yescharacteristic
579C22×Dic3—31no—
580C22×Dic3—31no—
581C22×Dic3—31no—
582C22×Dic3—31no—
583C22×Dic3C2×C3×D311yescharacteristic, complemented
584D3×D4—38no—
585C2×D12—31no—
586C2×C4×D3—24no—
587C2×C4×D3—31no—
588C2×C4×D3—31no—
589C2×C4×D3—31no—
590C2×C4×D3—31no—
591C2×C4×D3—31no—
592C2×C4×D3—31no—
593C2×C4×D3—31no—
594C2×C4×D3—31no—
595C2×C4×D3—61no—
596C2×C4×D3—64no—
597C2×C4×D3—64no—
598C2×C4×D3C2×C3×D311yescharacteristic
599C2×C4×D3C2×C3×D311yescharacteristic
600C2×C4×D3C2×C3×D311yescharacteristic, complemented
601C2×C4×D3C2×C3×D311yescharacteristic, complemented
602C2×C4×D3C2×C3×D311yescharacteristic, complemented
603C3×C4⋊C4—31no—
604C3×C4⋊C4—31no—
605C3×C4⋊C4—61no—
606C3×C4⋊C4—91no—
607C3×C4⋊C4—91no—
608C3×C4⋊C4—91no—
609C3×C22⋊C4—31no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—31no—
612C3×C22⋊C4—31no—
613C3×C22⋊C4—61no—
614C3×C22⋊C4—61no—
615C3×C22⋊C4—91no—
616C3×C22⋊C4—91no—
617C3×C22⋊C4—91no—
618C3×C22⋊C4—91no—
619C3×C22⋊C4—91no—
620C3×C22⋊C4—91no—
621C3×C42—31no—
622C3×C42—31no—
623C3×C42—61no—
624C3×C42—91no—
625C3×C42—91no—
626C3×C42—91no—
627#217—31no—
628#217—31no—
629#217—31no—
630#217—31no—
631#217—31no—
632#217—61no—
633#217C2×C3×D311yescharacteristic, complemented
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—31no—
637(C2×D3)⋊C4—31no—
638(C2×D3)⋊C4—31no—
639(C2×D3)⋊C4—31no—
640(C2×D3)⋊C4—31no—
641(C2×D3)⋊C4—61no—
642(C2×D3)⋊C4C2×C3×D311yescharacteristic, complemented
643C4⋊Dic3—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—31no—
646Dic3⋊C4—31no—
647Dic3⋊C4—31no—
648Dic3⋊C4—31no—
649Dic3⋊C4—61no—
650Dic3⋊C4C2×C3×D311yescharacteristic, complemented
651C4×Dic3—31no—
652C4×Dic3—31no—
653C4×Dic3—31no—
654C4×Dic3—31no—
655C4×Dic3—31no—
656C4×Dic3—31no—
657C4×Dic3—61no—
658C4×Dic3C2×C3×D311yescharacteristic, complemented
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—22no—
662C22×C32—22no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—22no—
671C22×C32—22no—
672C22×C32—22no—
673C22×C32—32no—
674C22×C32—32no—
675C22×C32—32no—
676C22×C32—32no—
677C22×C32—32no—
678C22×C32—42no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—42no—
685C22×C32—42no—
686C22×C32—68no—
687C22×C32—61no—
688C22×C32—61no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32C2×C4×D312yescomplemented
692C22×C32C2×C4×D312yescomplemented
693C22×C32C22×C3×C412yescomplemented
694C22×C32C23×D311yescharacteristic
695C22×C32C23×D311yescharacteristic
696C22×C32C24×C311yescharacteristic
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3C22×C3×C412yescomplemented
700C2×C3×D3—22no—
701C2×C3×D3—22no—
702C2×C3×D3—216no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—21no—
706C2×C3×D3—21no—
707C2×C3×D3—21no—
708C2×C3×D3—21no—
709C2×C3×D3—21no—
710C2×C3×D3—21no—
711C2×C3×D3—28no—
712C2×C3×D3—28no—
713C2×C3×D3—22no—
714C2×C3×D3—22no—
715C2×C3×D3—22no—
716C2×C3×D3—22no—
717C2×C3×D3—22no—
718C2×C3×D3—32no—
719C2×C3×D3—32no—
720C2×C3×D3—41no—
721C2×C3×D3—41no—
722C2×C3×D3—62no—
723C2×C3×D3—68no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—68no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3C2×C4×D312yes—
732C2×C3×D3C2×C4×D312yescomplemented
733C2×C3×D3C2×C4×D312yescomplemented
734C2×C3×D3#23512yes—
735C2×C3×D3C2×#6712yes—
736C2×C3×D3C22×C3×C412yes—
737C2×C3×D3C22×C3×C412yescomplemented
738C2×C3×D3C22×C3×C412yescomplemented
739C2×C3×D3C2×C3×D412yes—
740C2×C3×D3C3×#4112yes—
741D32—28no—
742C32×C4—21no—
743C32×C4—22no—
744C32×C4—21no—
745C32×C4—21no—
746C32×C4—22no—
747C32×C4—22no—
748C32×C4—22no—
749C32×C4—32no—
750C32×C4—32no—
751C32×C4—42no—
752C32×C4—41no—
753C32×C4—41no—
754C32×C4—42no—
755C32×C4—61no—
756C32×C4—61no—
757C32×C4—61no—
758C32×C4D3×D412yescomplemented
759C32×C4C2×#6712yescomplemented
760C32×C4C2×C3×D412yescomplemented
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3C22×C3×C412yescomplemented
764C3×Dic3—22no—
765C3×Dic3—21no—
766C3×Dic3—21no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—22no—
772C3×Dic3—22no—
773C3×Dic3—32no—
774C3×Dic3—32no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—62no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—121no—
783C3×Dic3—121no—
784C3×Dic3C2×C4×D312yescomplemented
785C3×Dic3C2×#6712yescomplemented
786C3×Dic3C22×C3×C412yescomplemented
787C3×Dic3C2×C3×D412yescomplemented
788C22×D4—91no—
789C23×C4—31no—
790C23×C4—91no—
791C4×D4—31no—
792C4×D4—91no—
793C4×D4—91no—
794C4×D4—91no—
795C4×D4—91no—
796C4×D4—91no—
797C4×D4—91no—
798C4×D4—91no—
799C2×C4⋊C4—91no—
800C2×C22⋊C4—91no—
801C2×C22⋊C4—91no—
802C2×C42—91no—
803C33C2×C4×D411yescharacteristic, complemented, Sylow
804C23×C3—21no—
805C23×C3—21no—
806C23×C3—21no—
807C23×C3—31no—
808C23×C3—31no—
809C23×C3—31no—
810C23×C3—31no—
811C23×C3—31no—
812C23×C3—31no—
813C23×C3—34no—
814C23×C3—34no—
815C23×C3—41no—
816C23×C3—61no—
817C23×C3—61no—
818C23×C3—64no—
819C23×C3—61no—
820C23×C3—62no—
821C23×C3—62no—
822C23×C3—62no—
823C23×C3—62no—
824C23×C3—64no—
825C23×C3—64no—
826C23×C3—94no—
827C23×C3—91no—
828C23×C3—182no—
829C23×C3—182no—
830C23×C3C2×D3211yescharacteristic
831C23×C3C22×C3×D311yescharacteristic
832C23×C3C22×C3×D311yescharacteristic
833C22×D3—22no—
834C22×D3—22no—
835C22×D3—31no—
836C22×D3—31no—
837C22×D3—34no—
838C22×D3—34no—
839C22×D3—61no—
840C22×D3—62no—
841C22×D3—62no—
842C22×D3—62no—
843C22×D3—62no—
844C22×D3C3×C4×D314yescomplemented
845C22×D3C22×C3×D311yescharacteristic
846C22×D3C22×C3×D311yescharacteristic
847C22×D3C22×C3×D311yescharacteristic
848C3×D4—34no—
849C3×D4—34no—
850C3×D4—64no—
851C3×D4—94no—
852C3×D4—94no—
853C3×D4—94no—
854C2×C3×C4—24no—
855C2×C3×C4—22no—
856C2×C3×C4—22no—
857C2×C3×C4—22no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—31no—
867C2×C3×C4—31no—
868C2×C3×C4—34no—
869C2×C3×C4—34no—
870C2×C3×C4—31no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—42no—
877C2×C3×C4—42no—
878C2×C3×C4—44no—
879C2×C3×C4—41no—
880C2×C3×C4—41no—
881C2×C3×C4—64no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—61no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—62no—
888C2×C3×C4—62no—
889C2×C3×C4—62no—
890C2×C3×C4—62no—
891C2×C3×C4—64no—
892C2×C3×C4—64no—
893C2×C3×C4—64no—
894C2×C3×C4—62no—
895C2×C3×C4—62no—
896C2×C3×C4—64no—
897C2×C3×C4—62no—
898C2×C3×C4—62no—
899C2×C3×C4—62no—
900C2×C3×C4—62no—
901C2×C3×C4—94no—
902C2×C3×C4—91no—
903C2×C3×C4—91no—
904C2×C3×C4—91no—
905C2×C3×C4—122no—
906C2×C3×C4—182no—
907C2×C3×C4—182no—
908C2×C3×C4—182no—
909C2×C3×C4—182no—
910C2×C3×C4—182no—
911C2×C3×C4C2×D3211yescharacteristic
912C2×C3×C4C2×D3211yescharacteristic
913C2×C3×C4C22×C3×D311yescharacteristic
914C2×C3×C4C22×C3×D311yescharacteristic
915C2×C3×C4C22×C3×D311yescharacteristic
916C2×C3×C4C22×C3×D311yescharacteristic
917#67—34no—
918#67—34no—
919#67—34no—
920#67—34no—
921#67—34no—
922#67—64no—
923#67C3×C4×D314yesdirect product factor
924C2×Dic3—22no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—34no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—31no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—61no—
935C2×Dic3—62no—
936C2×Dic3—62no—
937C2×Dic3—62no—
938C2×Dic3C22×C3×D311yescharacteristic
939C2×Dic3C22×C3×D311yescharacteristic
940C2×Dic3C22×C3×D311yescharacteristic
941C2×Dic3C22×C3×D311yescharacteristic
942C2×Dic3C22×C3×D311yescharacteristic
943D12—34no—
944C4×D3—22no—
945C4×D3—22no—
946C4×D3—22no—
947C4×D3—22no—
948C4×D3—34no—
949C4×D3—62no—
950C4×D3—62no—
951C4×D3—62no—
952C4×D3—62no—
953C4×D3—62no—
954C4×D3—62no—
955C4×D3—62no—
956C4×D3—122no—
957C4×D3C3×#6714yesdirect product factor
958C2×C32—22no—
959C2×C32—24no—
960C2×C32—22no—
961C2×C32—22no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—34no—
972C2×C32—41no—
973C2×C32—41no—
974C2×C32—41no—
975C2×C32—42no—
976C2×C32—42no—
977C2×C32—44no—
978C2×C32—62no—
979C2×C32—62no—
980C2×C32C22×C4×D311yescharacteristic
981C2×C32C22×C4×D311yescharacteristic
982C2×C32C2×#23511yescharacteristic
983C2×C32C2×D3×D411yescharacteristic
984C2×C32D3×#4111yescharacteristic
985C2×C32C22×#6711yescharacteristic
986C2×C32C23×C3×C411yescharacteristic
987C2×C32C22×C3×D411yescharacteristic
988C2×C32C2×C3×#4111yescharacteristic
989C3⋊D3—22no—
990C3×D3—24no—
991C3×D3—22no—
992C3×D3—22no—
993C3×D3—22no—
994C3×D3—22no—
995C3×D3—24no—
996C3×D3—42no—
997C3×D3—62no—
998C3×D3—62no—
999C3×D3—122no—
1000C3×D3C4×#6714yesdirect product factor
1001C3×D3C3×C4×D414yescomplemented
1002C24—31no—
1003C24—91no—
1004C2×D4—31no—
1005C2×D4—91no—
1006C2×D4—98no—
1007C2×D4—91no—
1008C2×D4—91no—
1009C22×C4—31no—
1010C22×C4—31no—
1011C22×C4—31no—
1012C22×C4—31no—
1013C22×C4—31no—
1014C22×C4—31no—
1015C22×C4—64no—
1016C22×C4—91no—
1017C22×C4—91no—
1018C22×C4—91no—
1019C22×C4—91no—
1020C22×C4—91no—
1021C22×C4—91no—
1022C22×C4—184no—
1023C22×C4C3×D3211yescharacteristic, complemented
1024C4⋊C4—31no—
1025C4⋊C4—91no—
1026C4⋊C4—91no—
1027C4⋊C4—91no—
1028C22⋊C4—31no—
1029C22⋊C4—31no—
1030C22⋊C4—91no—
1031C22⋊C4—91no—
1032C22⋊C4—91no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C42—31no—
1037C42—91no—
1038C42—91no—
1039C42—91no—
1040C22×C3—22no—
1041C22×C3—22no—
1042C22×C3—21no—
1043C22×C3—21no—
1044C22×C3—21no—
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—22no—
1052C22×C3—22no—
1053C22×C3—22no—
1054C22×C3—32no—
1055C22×C3—32no—
1056C22×C3—32no—
1057C22×C3—32no—
1058C22×C3—32no—
1059C22×C3—32no—
1060C22×C3—32no—
1061C22×C3—32no—
1062C22×C3—32no—
1063C22×C3—32no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—42no—
1069C22×C3—42no—
1070C22×C3—41no—
1071C22×C3—42no—
1072C22×C3—62no—
1073C22×C3—62no—
1074C22×C3—62no—
1075C22×C3—62no—
1076C22×C3—62no—
1077C22×C3—68no—
1078C22×C3—68no—
1079C22×C3—62no—
1080C22×C3—616no—
1081C22×C3—62no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—92no—
1091C22×C3—121no—
1092C22×C3—121no—
1093C22×C3—188no—
1094C22×C3—181no—
1095C22×C3—181no—
1096C22×C3C4×D3212yescomplemented
1097C22×C3C2×C3×C4×D312yescomplemented
1098C22×C3C2×C3×C4×D312yescomplemented
1099C22×C3C22×D3211yescharacteristic
1100C22×C3C23×C3×D311yescharacteristic
1101C22×C3C23×C3×D311yescharacteristic
1102C2×D3—21no—
1103C2×D3—21no—
1104C2×D3—21no—
1105C2×D3—21no—
1106C2×D3—28no—
1107C2×D3—32no—
1108C2×D3—32no—
1109C2×D3—62no—
1110C2×D3—68no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—68no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3C2×C3×C4×D312yes—
1119C2×D3C2×C3×C4×D312yescomplemented
1120C2×D3C2×C3×C4×D312yescomplemented
1121C2×D3C3×#23512yes—
1122C2×D3C2×C3×#6712yes—
1123C3×C4—22no—
1124C3×C4—21no—
1125C3×C4—21no—
1126C3×C4—21no—
1127C3×C4—22no—
1128C3×C4—22no—
1129C3×C4—22no—
1130C3×C4—32no—
1131C3×C4—32no—
1132C3×C4—32no—
1133C3×C4—32no—
1134C3×C4—41no—
1135C3×C4—41no—
1136C3×C4—42no—
1137C3×C4—42no—
1138C3×C4—62no—
1139C3×C4—62no—
1140C3×C4—62no—
1141C3×C4—61no—
1142C3×C4—61no—
1143C3×C4—61no—
1144C3×C4—61no—
1145C3×C4—61no—
1146C3×C4—61no—
1147C3×C4—92no—
1148C3×C4—121no—
1149C3×C4—121no—
1150C3×C4—181no—
1151C3×C4—181no—
1152C3×C4D3×#6712yesdirect product factor
1153C3×C4C3×D3×D412yescomplemented
1154C3×C4C2×C3×#6712yescomplemented
1155Dic3—21no—
1156Dic3—21no—
1157Dic3—21no—
1158Dic3—32no—
1159Dic3—32no—
1160Dic3—62no—
1161Dic3—61no—
1162Dic3—61no—
1163Dic3—61no—
1164Dic3—61no—
1165Dic3—121no—
1166Dic3—121no—
1167Dic3C2×C3×C4×D312yescomplemented
1168Dic3C2×C3×#6712yescomplemented
1169C32—21no—
1170C32—21no—
1171C32—21no—
1172C32—41no—
1173C32C4×D3×D411yescharacteristic, complemented
1174C32C2×C4×#6711yescharacteristic, complemented
1175C32C2×C3×C4×D411yescharacteristic, complemented
1176C23—31no—
1177C23—31no—
1178C23—31no—
1179C23—34no—
1180C23—62no—
1181C23—62no—
1182C23—94no—
1183C23—91no—
1184C23—182no—
1185C23—182no—
1186C23C2×C3×D3211yescharacteristic
1187D4—34no—
1188D4—94no—
1189D4—94no—
1190D4—94no—
1191C2×C4—22no—
1192C2×C4—31no—
1193C2×C4—31no—
1194C2×C4—34no—
1195C2×C4—31no—
1196C2×C4—31no—
1197C2×C4—31no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—94no—
1204C2×C4—91no—
1205C2×C4—91no—
1206C2×C4—91no—
1207C2×C4—182no—
1208C2×C4—182no—
1209C2×C4—182no—
1210C2×C4—182no—
1211C2×C4—182no—
1212C2×C4C2×C3×D3211yescharacteristic
1213C2×C4C2×C3×D3211yescharacteristic
1214C2×C3—24no—
1215C2×C3—22no—
1216C2×C3—22no—
1217C2×C3—22no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—21no—
1222C2×C3—21no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—21no—
1227C2×C3—34no—
1228C2×C3—34no—
1229C2×C3—42no—
1230C2×C3—42no—
1231C2×C3—44no—
1232C2×C3—41no—
1233C2×C3—41no—
1234C2×C3—41no—
1235C2×C3—64no—
1236C2×C3—64no—
1237C2×C3—62no—
1238C2×C3—62no—
1239C2×C3—62no—
1240C2×C3—62no—
1241C2×C3—122no—
1242C2×C3—182no—
1243C2×C3C2×C4×D3211yescharacteristic
1244C2×C3D3×#23511yescharacteristic
1245C2×C3C2×D3×#6711yescharacteristic
1246C2×C3C22×C3×C4×D311yescharacteristic
1247C2×C3C22×C3×C4×D311yescharacteristic
1248C2×C3C2×C3×#23511yescharacteristic
1249C2×C3C2×C3×D3×D411yescharacteristic
1250C2×C3C3×D3×#4111yescharacteristic
1251C2×C3C22×C3×#6711yescharacteristic
1252D3—22no—
1253D3—22no—
1254D3—62no—
1255D3—62no—
1256D3—122no—
1257D3C3×C4×#6714yesdirect product factor
1258C22—21no—
1259C22—21no—
1260C22—32no—
1261C22—32no—
1262C22—32no—
1263C22—32no—
1264C22—32no—
1265C22—68no—
1266C22—61no—
1267C22—61no—
1268C22—61no—
1269C22—61no—
1270C22—92no—
1271C22—188no—
1272C22—181no—
1273C22—181no—
1274C22C3×C4×D3212yescomplemented
1275C22C22×C3×D3211yescharacteristic
1276C4—21no—
1277C4—32no—
1278C4—32no—
1279C4—61no—
1280C4—61no—
1281C4—61no—
1282C4—92no—
1283C4—181no—
1284C4—181no—
1285C4C3×D3×#6712yesdirect product factor
1286C3—21no—
1287C3—21no—
1288C3—21no—
1289C3—41no—
1290C3C4×D3×#6711yescharacteristic, direct product factor
1291C3C3×C4×D3×D411yescharacteristic, complemented
1292C3C2×C3×C4×#6711yescharacteristic, complemented
1293C2—22no—
1294C2—34no—
1295C2—62no—
1296C2—62no—
1297C2—182no—
1298C2C2×C3×C4×D3211yescharacteristic
1299C2C3×D3×#23511yescharacteristic
1300C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C3×D3×#67C2
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
3. C2×C3×C4×D32C2semidirect
4. C3×C4×#638C2semidirect
5. C32×C4×#67C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×D3×#217C2semidirect
8. C3×#63952C2semidirect
9. C3×D3×(C2×D3)⋊C4C2semidirect
10. C3×#63904C2semidirect
11. C3×C4×#626C2semidirect
12. C3×C4×#625C2semidirect
13. C3×#63879C2semidirect
14. C3×D3×Dic3⋊C4C2semidirect
15. C3×C4×D3×Dic3C2semidirect
18. C4×D3×#67C3direct (N × H)
21. C22×C33×C4C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
25. C22×C32×Dic3C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×C4×D3C22semidirect
31. C2×C32×C4×D3C22semidirect
32. C3×D3×#67C4direct (N × H)
35. C2×C3×#624C22semidirect
39. C2×C3×D3×Dic3C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
45. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. C32×C4×Dic3C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
56. C3×Dic32C22semidirect
63. C22×C3×C4×D3D3semidirect
64. C22×C3×C4×D3C2×C3semidirect
66. C2×C4×D32C2×C3semidirect
68. C4×#638C2×C3semidirect
82. C3×C4×#67D3direct (N × H)
83. C3×C4×#67C2×C3semidirect
95. Dic3×#67C2×C3semidirect
96. D3×#217C2×C3semidirect
97. #63952C2×C3semidirect
98. D3×(C2×D3)⋊C4C2×C3semidirect
99. #63904C2×C3semidirect
100. C4×#626C2×C3semidirect
101. C4×#625C2×C3semidirect
102. #63879C2×C3semidirect
103. D3×Dic3⋊C4C2×C3semidirect
104. C4×D3×Dic3C2×C3semidirect
109. C22×C32×D3C2×C4semidirect
115. C2×C3×D32C2×C4semidirect
119. C3×#638C2×C4semidirect
124. C32×#67C2×C4semidirect
135. C32×C4×D3D4semidirect
136. C3×#626C2×C4semidirect
137. C3×#625C2×C4semidirect
142. C3×D3×Dic3C2×C4semidirect
165. C22×C32×C4C2×D3semidirect
166. C22×C32×C4C2×D3semidirect
167. C22×C32×C4C22×C3semidirect
169. C2×C4×C3⋊D3C22×C3semidirect
185. C22×C3×Dic3C2×D3semidirect
186. C22×C3×Dic3C22×C3semidirect
210. C2×C3×C4×D3C2×D3semidirect
211. C2×C3×C4×D3C2×D3semidirect
212. C2×C3×C4×D3C2×D3semidirect
215. C2×C3×C4×D3C22×C3semidirect
216. C2×C3×C4×D3C22×C3semidirect
217. C2×C3×C4×D3C22×C3semidirect
218. D3×#67C3×C4direct (N × H)
221. C2×#624C22×C3semidirect
225. C2×D3×Dic3C22×C3semidirect
231. #3757C22×C3semidirect
232. #3752C22×C3semidirect
233. #3750C22×C3semidirect
234. C4×C3⋊Dic3C22×C3semidirect
242. C3×#217C2×D3semidirect
243. C3×#217C22×C3semidirect
253. C3×(C2×D3)⋊C4C2×D3semidirect
254. C3×(C2×D3)⋊C4C22×C3semidirect
263. C3×Dic3⋊C4C2×D3semidirect
264. C3×Dic3⋊C4C22×C3semidirect
273. C3×C4×Dic3C2×D3semidirect
274. C3×C4×Dic3C22×C3semidirect
275. #3724C22×C3semidirect
276. Dic3⋊Dic3C22×C3semidirect
277. #3722C22×C3semidirect
278. (C2×D3)⋊Dic3C22×C3semidirect
279. (C2×D3)⋊Dic3C22×C3semidirect
280. (C2×D3)⋊Dic3C22×C3semidirect
281. Dic32C22×C3semidirect
282. Dic32C22×C3semidirect
285. C22×C33C22×C4semidirect
289. C2×C3×C3⋊D3C22×C4semidirect
296. C2×C32×D3C22×C4semidirect
297. C2×C32×D3C22×C4semidirect
302. C33×C4C2×D4semidirect
305. C3×C3⋊Dic3C22×C4semidirect
309. C32×Dic3C22×C4semidirect
310. C32×Dic3C2×D4semidirect
320. C22×C4×D3C3×D3semidirect
347. C4×#67C3×D3direct (N × H)
392. C22×C3×D3C4×D3semidirect
393. C22×C3×D3C2×C3×C4semidirect
402. C2×D32C2×C3×C4semidirect
436. #638C2×C3×C4semidirect
448. C3×#67C4×D3direct (N × H)
449. C3×#67C2×C3×C4semidirect
504. C3×C4×D3#67direct (N × H)
505. C3×C4×D3C3×D4semidirect
506. #626C2×C3×C4semidirect
507. #625C2×C3×C4semidirect
512. D3×Dic3C2×C3×C4semidirect
521. C32×D3C4×D4semidirect
568. C22×C3×C4D32semidirect
569. C22×C3×C4C2×C3×D3semidirect
570. C22×C3×C4C2×C3×D3semidirect
583. C22×Dic3C2×C3×D3semidirect
600. C2×C4×D3C2×C3×D3semidirect
601. C2×C4×D3C2×C3×D3semidirect
602. C2×C4×D3C2×C3×D3semidirect
633. #217C2×C3×D3semidirect
642. (C2×D3)⋊C4C2×C3×D3semidirect
650. Dic3⋊C4C2×C3×D3semidirect
658. C4×Dic3C2×C3×D3semidirect
691. C22×C32C2×C4×D3semidirect
692. C22×C32C2×C4×D3semidirect
693. C22×C32C22×C3×C4semidirect
699. C2×C3⋊D3C22×C3×C4semidirect
732. C2×C3×D3C2×C4×D3semidirect
733. C2×C3×D3C2×C4×D3semidirect
737. C2×C3×D3C22×C3×C4semidirect
738. C2×C3×D3C22×C3×C4semidirect
758. C32×C4D3×D4semidirect
759. C32×C4C2×#67semidirect
760. C32×C4C2×C3×D4semidirect
763. C3⋊Dic3C22×C3×C4semidirect
784. C3×Dic3C2×C4×D3semidirect
785. C3×Dic3C2×#67semidirect
786. C3×Dic3C22×C3×C4semidirect
787. C3×Dic3C2×C3×D4semidirect
803. C33C2×C4×D4semidirect
844. C22×D3C3×C4×D3semidirect
923. #67C3×C4×D3direct (N × H)
957. C4×D3C3×#67direct (N × H)
1000. C3×D3C4×#67direct (N × H)
1001. C3×D3C3×C4×D4semidirect
1023. C22×C4C3×D32semidirect
1096. C22×C3C4×D32semidirect
1097. C22×C3C2×C3×C4×D3semidirect
1098. C22×C3C2×C3×C4×D3semidirect
1119. C2×D3C2×C3×C4×D3semidirect
1120. C2×D3C2×C3×C4×D3semidirect
1152. C3×C4D3×#67direct (N × H)
1153. C3×C4C3×D3×D4semidirect
1154. C3×C4C2×C3×#67semidirect
1167. Dic3C2×C3×C4×D3semidirect
1168. Dic3C2×C3×#67semidirect
1173. C32C4×D3×D4semidirect
1174. C32C2×C4×#67semidirect
1175. C32C2×C3×C4×D4semidirect
1257. D3C3×C4×#67direct (N × H)
1274. C22C3×C4×D32semidirect
1285. C4C3×D3×#67direct (N × H)
1290. C3C4×D3×#67direct (N × H)
1291. C3C3×C4×D3×D4semidirect
1292. C3C2×C3×C4×#67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C32×C4×D32
C2×C3×D3×#672
C2×C3×C4×D322
C3×C4×#6382
C32×C4×#672
C3×Dic3×#672
C3×D3×#2172
C3×#639522
C3×D3×(C2×D3)⋊C42
C3×#639042
C3×C4×#6262
C3×C4×#6252
C3×#638792
C3×D3×Dic3⋊C42
C3×C4×D3×Dic32
C2×C3×C4×#673
C3×C4×D3×D43
C4×D3×#673