Finite Group Databasebeta

← C3×C4×#3804 #13174439

Subgroups — C3×C4×#3804 #13174439

Order 1728.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×#63955C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8C3×C4×#627C211yesmaximal, characteristic, complemented
9C3×C4×#626C211yesmaximal, characteristic, complemented
10C3×C4×#624C211yesmaximal, characteristic, complemented
11C3×#63880C211yesmaximal, characteristic, complemented
12C3×#63877C211yesmaximal, characteristic, complemented
13C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
14C3×#63837C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×C4×#237—31nomaximal
17C3×C4×#235—31nomaximal
18C4×#3804C311yesmaximal, characteristic, direct product factor
19C22×C33×C4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C3×#3804C418yesdirect product factor
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×C4×C3⋊Dic3C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic
44C32×C4×Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C2×C3×#237—31no—
56C2×C3×#235—31no—
57C2×#3804C2×C311yescharacteristic
58C32×C4×D4—31no—
59C2×C32×C42—31no—
60C4×#638C2×C311yescharacteristic, complemented
61C3×D4×Dic3—31no—
62C3×C4×#67—21no—
63C3×C4×#67—31no—
64C3×C4×#67—31no—
65C3×C4×#67—31no—
66C3×C4×#67—31no—
67C3×C4×#67—31no—
68C3×C4×#67—61no—
69C3×C4×#67D311yescharacteristic, complemented
70C3×C4×#67C2×C311yescharacteristic, complemented
71C3×#926—31no—
72C2×C3×C4×Dic3—21no—
73C2×C3×C4×Dic3—31no—
74C2×C3×C4×Dic3D311yescharacteristic, complemented
75C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
76C3×#892—31no—
77C3×#887—31no—
78C3×#67⋊C4—31no—
79C3×#67⋊C4—31no—
80C3×#877—31no—
81C3×#877—31no—
82C3×C4×D12—31no—
83C3×C4×D12—31no—
84C3×#872—31no—
85C3×#872—31no—
86C3×C42×D3—31no—
87C3×C42×D3—31no—
88C3×C42×D3—31no—
89C3×C4×Dic6—31no—
90C3×C4×Dic6—31no—
91C3×C4×Dic6—31no—
92Dic3×#67C2×C311yescharacteristic, complemented
93#63955C2×C311yescharacteristic, complemented
94#63952C2×C311yescharacteristic, complemented
95C4×#627C2×C311yescharacteristic, complemented
96C4×#626C2×C311yescharacteristic, complemented
97C4×#624C2×C311yescharacteristic, complemented
98#63880C2×C311yescharacteristic, complemented
99#63877C2×C311yescharacteristic, complemented
100C4×D3×Dic3C2×C311yescharacteristic, complemented
101#63837C2×C311yescharacteristic, complemented
102#63836C2×C311yescharacteristic, complemented
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4—22no—
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C3×#638C2×C414yescomplemented
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4×C3⋊D3—22no—
114C32×#67C2×C414yescomplemented
115C2×C32×Dic3—22no—
116C2×C32×Dic3C2×C414yescomplemented
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×C4×D3—22no—
125C3×#627C2×C414yescomplemented
126C3×#626C2×C414yescomplemented
127C3×#624—22no—
128C3×#624C2×C414yescomplemented
129C3×D3×Dic3—22no—
130C3×D3×Dic3C2×C414yescomplemented
131C3×C4×#41—91no—
132C4×#237—31no—
133C4×#235—31no—
134C2×C32×D4—31no—
135C22×C32×C4—21no—
136C22×C32×C4—21no—
137C22×C32×C4—21no—
138C22×C32×C4—31no—
139C22×C32×C4—31no—
140C22×C32×C4—31no—
141C22×C32×C4—41no—
142C22×C32×C4C2×D311yescharacteristic
143C22×C32×C4C2×D311yescharacteristic
144C22×C32×C4C22×C311yescharacteristic
145C2×#638C22×C311yescharacteristic
146C2×C4×C3⋊D3C22×C311yescharacteristic
147C2×C3×#67—21no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—61no—
152C2×C3×#67C2×D311yescharacteristic
153C2×C3×#67C22×C311yescharacteristic
154C22×C3×Dic3—21no—
155C22×C3×Dic3—21no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3C2×D311yescharacteristic
159C22×C3×Dic3C2×D311yescharacteristic
160C22×C3×Dic3C22×C311yescharacteristic
161C22×C3×Dic3C22×C311yescharacteristic
162C3×#237—38no—
163C3×#235—38no—
164C2×C3×D12—31no—
165C2×C3×C4×D3—21no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—61no—
175C2×C3×C4×D3C2×D311yescharacteristic
176C2×C3×C4×D3C22×C311yescharacteristic
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×#627C22×C311yescharacteristic
180C2×#626C22×C311yescharacteristic
181C2×#624C22×C311yescharacteristic
182C2×#624C22×C311yescharacteristic
183#3804C3×C418yesdirect product factor
184C2×D3×Dic3C22×C311yescharacteristic
185C2×D3×Dic3C22×C311yescharacteristic
186C32×C4⋊C4—31no—
187C32×C22⋊C4—31no—
188C32×C22⋊C4—31no—
189C32×C42—31no—
190C32×C42—31no—
191C32×C42—31no—
192C32×C42—31no—
193C32×C42—31no—
194#3757C22×C311yescharacteristic
195#3752C22×C311yescharacteristic
196#3750C22×C311yescharacteristic
197C4×C3⋊Dic3C22×C311yescharacteristic
198C3×#217—21no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217C2×D311yescharacteristic
204C3×#217C22×C311yescharacteristic
205C3×(C2×D3)⋊C4—21no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—61no—
212C3×(C2×D3)⋊C4C2×D311yescharacteristic
213C3×(C2×D3)⋊C4C22×C311yescharacteristic
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—61no—
226C3×Dic3⋊C4C2×D311yescharacteristic
227C3×Dic3⋊C4C22×C311yescharacteristic
228C3×C4×Dic3—21no—
229C3×C4×Dic3—21no—
230C3×C4×Dic3—21no—
231C3×C4×Dic3—21no—
232C3×C4×Dic3—21no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—61no—
244C3×C4×Dic3C2×D311yescharacteristic
245C3×C4×Dic3C2×D311yescharacteristic
246C3×C4×Dic3C2×D311yescharacteristic
247C3×C4×Dic3C2×D311yescharacteristic
248C3×C4×Dic3C2×D311yescharacteristic
249C3×C4×Dic3C22×C311yescharacteristic
250C3×C4×Dic3C22×C311yescharacteristic
251C3×C4×Dic3C22×C311yescharacteristic
252C3×C4×Dic3C22×C311yescharacteristic
253C3×C4×Dic3C22×C311yescharacteristic
254#3724C22×C311yescharacteristic
255Dic3⋊Dic3C22×C311yescharacteristic
256Dic3⋊Dic3C22×C311yescharacteristic
257Dic3⋊Dic3C22×C311yescharacteristic
258#3722C22×C311yescharacteristic
259(C2×D3)⋊Dic3C22×C311yescharacteristic
260Dic32C22×C311yescharacteristic
261Dic32C22×C311yescharacteristic
262Dic32C22×C311yescharacteristic
263Dic32C22×C311yescharacteristic
264C22×C33—21no—
265C22×C33—21no—
266C22×C33C22×C412yes—
267C22×C33C2411yescharacteristic
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3C22×C412yes—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3C22×C412yes—
274C33×C4—21no—
275C33×C4#4112yescomplemented
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3C22×C412yes—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3C22×C412yes—
283C32×Dic3C22×C412yes—
284C32×Dic3C22×C412yes—
285C32×Dic3#4112yescomplemented
286C2×C3×#41—91no—
287C2×#237—31no—
288C2×#235—31no—
289C3×C4×Q8—91no—
290C3×C4×Q8—91no—
291C3×C4×D4—31no—
292C3×C4×D4—31no—
293C3×C4×D4—61no—
294C3×C4×D4—91no—
295C3×C4×D4—91no—
296C3×C4×D4—91no—
297C3×C4×D4—91no—
298C3×C4×D4—91no—
299C3×#117—91no—
300C3×#117—91no—
301C3×#117—91no—
302C2×C3×C42—31no—
303C2×C3×C42—31no—
304C2×C3×C42—61no—
305C2×C3×C42—91no—
306C2×C3×C42—91no—
307D4×Dic3—31no—
308C4×#67—31no—
309C4×#67—31no—
310C4×#67—31no—
311C4×#67—31no—
312C4×#67—31no—
313C4×#67—61no—
314C4×#67C3×D311yescharacteristic, complemented
315#926—31no—
316C2×C4×Dic3—31no—
317C2×C4×Dic3C3×D311yescharacteristic, complemented
318#892—31no—
319#887—31no—
320#67⋊C4—31no—
321#67⋊C4—31no—
322#877—31no—
323#877—31no—
324C4×D12—31no—
325C4×D12—31no—
326#872—31no—
327#872—31no—
328C42×D3—31no—
329C42×D3—31no—
330C42×D3—31no—
331C4×Dic6—31no—
332C4×Dic6—31no—
333C4×Dic6—31no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—31no—
338C23×C32—41no—
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C23×C32C23×C311yescharacteristic
342C22×C3⋊D3C23×C311yescharacteristic
343C22×C3×D3—21no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C23×C311yescharacteristic
349C32×D4—34no—
350C2×C32×C4—22no—
351C2×C32×C4—24no—
352C2×C32×C4—22no—
353C2×C32×C4—22no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—34no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—41no—
369C2×C32×C4—41no—
370C2×C32×C4—42no—
371C2×C32×C4—42no—
372C2×C32×C4—44no—
373C2×C32×C4—62no—
374C2×C32×C4—62no—
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C23×C311yescharacteristic
380C2×C32×C4C23×C311yescharacteristic
381#638C2×C3×C414yescomplemented
382C2×C3⋊Dic3C23×C311yescharacteristic
383C2×C3⋊Dic3C23×C311yescharacteristic
384C2×C3⋊Dic3C23×C311yescharacteristic
385C4×C3⋊D3—22no—
386C3×#67—24no—
387C3×#67—34no—
388C3×#67—34no—
389C3×#67—34no—
390C3×#67—64no—
391C3×#67C4×D314yescomplemented
392C3×#67C2×C3×C414yescomplemented
393C2×C3×Dic3—24no—
394C2×C3×Dic3—22no—
395C2×C3×Dic3—22no—
396C2×C3×Dic3—24no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—34no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3C4×D314yescomplemented
416C2×C3×Dic3C2×C3×C414yescomplemented
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C23×C311yescharacteristic
425C2×C3×Dic3C23×C311yescharacteristic
426C2×C3×Dic3C23×C311yescharacteristic
427C2×C3×Dic3C23×C311yescharacteristic
428C2×C3×Dic3C23×C311yescharacteristic
429C2×C3×Dic3C23×C311yescharacteristic
430C2×C3×Dic3C23×C311yescharacteristic
431C3×D12—34no—
432C3×C4×D3—22no—
433C3×C4×D3—22no—
434C3×C4×D3—34no—
435C3×C4×D3—34no—
436C3×C4×D3—34no—
437C3×C4×D3—42no—
438C3×C4×D3—62no—
439C3×C4×D3—62no—
440C3×C4×D3—62no—
441C3×C4×D3—62no—
442C3×C4×D3—62no—
443C3×C4×D3—122no—
444C3×Dic6—34no—
445C3×Dic6—34no—
446#627C2×C3×C414yescomplemented
447#626C2×C3×C414yescomplemented
448#624—22no—
449#624C2×C3×C414yescomplemented
450D3×Dic3—22no—
451D3×Dic3C2×C3×C414yescomplemented
452C4×#41—91noSylow
453C2×C33—22no—
454C2×C33C23×C411yescharacteristic
455C2×C33C2×#4111yescharacteristic
456C2×C33C2×#4111yescharacteristic
457C3×C3⋊D3—22no—
458C32×D3—22no—
459C3×#41—98no—
460C2×C3×Q8—91no—
461C2×C3×D4—31no—
462C2×C3×D4—31no—
463C2×C3×D4—61no—
464C2×C3×D4—91no—
465C2×C3×D4—91no—
466C22×C3×C4—21no—
467C22×C3×C4—21no—
468C22×C3×C4—21no—
469C22×C3×C4—31no—
470C22×C3×C4—31no—
471C22×C3×C4—31no—
472C22×C3×C4—31no—
473C22×C3×C4—31no—
474C22×C3×C4—31no—
475C22×C3×C4—41no—
476C22×C3×C4—61no—
477C22×C3×C4—61no—
478C22×C3×C4—61no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C22×C3×C4—91no—
483C22×C3×C4—91no—
484C22×C3×C4D3211yescharacteristic
485C22×C3×C4C2×C3×D311yescharacteristic
486C22×C3×C4C2×C3×D311yescharacteristic
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—61no—
491C2×#67C2×C3×D311yescharacteristic
492C22×Dic3—31no—
493C22×Dic3—31no—
494C22×Dic3C2×C3×D311yescharacteristic
495C22×Dic3C2×C3×D311yescharacteristic
496#237—38no—
497#235—38no—
498C2×D12—31no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—31no—
504C2×C4×D3—31no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—61no—
508C2×C4×D3C2×C3×D311yescharacteristic
509C2×Dic6—31no—
510C2×Dic6—31no—
511C3×C4⋊C4—31no—
512C3×C4⋊C4—31no—
513C3×C4⋊C4—61no—
514C3×C4⋊C4—91no—
515C3×C4⋊C4—91no—
516C3×C4⋊C4—91no—
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
519C3×C22⋊C4—31no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—61no—
524C3×C22⋊C4—61no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C42—31no—
530C3×C42—31no—
531C3×C42—31no—
532C3×C42—31no—
533C3×C42—31no—
534C3×C42—31no—
535C3×C42—31no—
536C3×C42—31no—
537C3×C42—31no—
538C3×C42—31no—
539C3×C42—61no—
540C3×C42—61no—
541C3×C42—61no—
542C3×C42—61no—
543C3×C42—61no—
544C3×C42—91no—
545C3×C42—91no—
546C3×C42—91no—
547C3×C42—91no—
548C3×C42—91no—
549#217—31no—
550#217—31no—
551#217—31no—
552#217—61no—
553#217C2×C3×D311yescharacteristic
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—61no—
560(C2×D3)⋊C4C2×C3×D311yescharacteristic
561C4⋊Dic3—31no—
562C4⋊Dic3—31no—
563C4⋊Dic3—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—61no—
572Dic3⋊C4C2×C3×D311yescharacteristic
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—31no—
581C4×Dic3—31no—
582C4×Dic3—31no—
583C4×Dic3—61no—
584C4×Dic3C2×C3×D311yescharacteristic
585C4×Dic3C2×C3×D311yescharacteristic
586C4×Dic3C2×C3×D311yescharacteristic
587C4×Dic3C2×C3×D311yescharacteristic
588C4×Dic3C2×C3×D311yescharacteristic
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—22no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—32no—
604C22×C32—42no—
605C22×C32—41no—
606C22×C32—41no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
611C22×C32—42no—
612C22×C32—61no—
613C22×C32—61no—
614C22×C32C2×C4×D312yes—
615C22×C32C2×C4×D312yes—
616C22×C32C22×C3×C412yes—
617C22×C32C23×D311yescharacteristic
618C22×C32C23×D311yescharacteristic
619C22×C32C24×C311yescharacteristic
620C2×C3⋊D3—21no—
621C2×C3⋊D3—21no—
622C2×C3⋊D3C22×C3×C412yes—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—22no—
628C2×C3×D3—32no—
629C2×C3×D3—32no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—62no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3C2×C4×D312yes—
640C2×C3×D3C22×C3×C412yes—
641C32×C4—21no—
642C32×C4—22no—
643C32×C4—21no—
644C32×C4—21no—
645C32×C4—22no—
646C32×C4—22no—
647C32×C4—22no—
648C32×C4—32no—
649C32×C4—32no—
650C32×C4—32no—
651C32×C4—32no—
652C32×C4—42no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—42no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4#23512yescomplemented
660C32×C4#23712yescomplemented
661C32×C4C3×#4112yescomplemented
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3C22×C3×C412yes—
665C3×Dic3—22no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—22no—
673C3×Dic3—22no—
674C3×Dic3—22no—
675C3×Dic3—22no—
676C3×Dic3—32no—
677C3×Dic3—32no—
678C3×Dic3—41no—
679C3×Dic3—41no—
680C3×Dic3—62no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3C2×C4×D312yes—
688C3×Dic3C2×C4×D312yes—
689C3×Dic3C2×C4×D312yes—
690C3×Dic3#23512yescomplemented
691C3×Dic3C22×C3×C412yes—
692C3×Dic3C22×C3×C412yes—
693C3×Dic3C22×C3×C412yes—
694C3×Dic3C3×#4112yescomplemented
695C2×#41—91no—
696C4×Q8—91no—
697C4×Q8—91no—
698C4×D4—31no—
699C4×D4—91no—
700C4×D4—91no—
701C4×D4—91no—
702C4×D4—91no—
703C4×D4—91no—
704#117—91no—
705#117—91no—
706#117—91no—
707C2×C42—31no—
708C2×C42—91no—
709C2×C42—91no—
710C33C4×#4111yescharacteristic, complemented, Sylow
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—41no—
717C23×C3—61no—
718C23×C3—91no—
719C23×C3C2×D3211yescharacteristic
720C23×C3C22×C3×D311yescharacteristic
721C23×C3C22×C3×D311yescharacteristic
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3C22×C3×D311yescharacteristic
726C3×Q8—94no—
727C3×D4—34no—
728C3×D4—34no—
729C3×D4—64no—
730C3×D4—94no—
731C3×D4—94no—
732C2×C3×C4—24no—
733C2×C3×C4—22no—
734C2×C3×C4—22no—
735C2×C3×C4—22no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—34no—
751C2×C3×C4—34no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—42no—
759C2×C3×C4—42no—
760C2×C3×C4—44no—
761C2×C3×C4—41no—
762C2×C3×C4—41no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—61no—
768C2×C3×C4—64no—
769C2×C3×C4—61no—
770C2×C3×C4—61no—
771C2×C3×C4—62no—
772C2×C3×C4—62no—
773C2×C3×C4—64no—
774C2×C3×C4—62no—
775C2×C3×C4—62no—
776C2×C3×C4—94no—
777C2×C3×C4—94no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—122no—
782C2×C3×C4—182no—
783C2×C3×C4—182no—
784C2×C3×C4—182no—
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C22×C3×D311yescharacteristic
788C2×C3×C4C22×C3×D311yescharacteristic
789C2×C3×C4C22×C3×D311yescharacteristic
790C2×C3×C4C22×C3×D311yescharacteristic
791#67—34no—
792#67—34no—
793#67—34no—
794#67—64no—
795#67C3×C4×D314yescomplemented
796C2×Dic3—22no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—34no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—62no—
808C2×Dic3C3×C4×D314yescomplemented
809C2×Dic3C22×C3×D311yescharacteristic
810C2×Dic3C22×C3×D311yescharacteristic
811C2×Dic3C22×C3×D311yescharacteristic
812C2×Dic3C22×C3×D311yescharacteristic
813C2×Dic3C22×C3×D311yescharacteristic
814C2×Dic3C22×C3×D311yescharacteristic
815C2×Dic3C22×C3×D311yescharacteristic
816D12—34no—
817C4×D3—22no—
818C4×D3—34no—
819C4×D3—34no—
820C4×D3—34no—
821C4×D3—62no—
822C4×D3—62no—
823C4×D3—62no—
824C4×D3—62no—
825C4×D3—62no—
826C4×D3—122no—
827Dic6—34no—
828Dic6—34no—
829C2×C32—22no—
830C2×C32—24no—
831C2×C32—22no—
832C2×C32—22no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—41no—
845C2×C32—42no—
846C2×C32—42no—
847C2×C32—44no—
848C2×C32—62no—
849C2×C32C22×C4×D311yescharacteristic
850C2×C32C22×C4×D311yescharacteristic
851C2×C32C2×#23511yescharacteristic
852C2×C32C2×#23511yescharacteristic
853C2×C32C2×#23711yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32C23×C3×C411yescharacteristic
856C2×C32C2×C3×#4111yescharacteristic
857C2×C32C2×C3×#4111yescharacteristic
858C3⋊D3—22no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—62no—
863C3×D3—62no—
864C3×D3—122no—
865#41—98no—
866C2×Q8—91no—
867C2×D4—31no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—31no—
871C22×C4—31no—
872C22×C4—31no—
873C22×C4—91no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—91no—
878C22×C4C3×D3211yescharacteristic
879C4⋊C4—31no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C22⋊C4—31no—
886C22⋊C4—31no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C42—31no—
892C42—31no—
893C42—31no—
894C42—31no—
895C42—31no—
896C42—91no—
897C42—91no—
898C42—91no—
899C42—91no—
900C42—91no—
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—22no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—32no—
916C22×C3—32no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—41no—
924C22×C3—42no—
925C22×C3—62no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—92no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3C4×D3212yes—
936C22×C3C2×C3×C4×D312yes—
937C22×C3C2×C3×C4×D312yes—
938C22×C3C22×D3211yescharacteristic
939C22×C3C23×C3×D311yescharacteristic
940C22×C3C23×C3×D311yescharacteristic
941C2×D3—21no—
942C2×D3—21no—
943C2×D3—32no—
944C2×D3—32no—
945C2×D3—62no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3C2×C3×C4×D312yes—
953C3×C4—22no—
954C3×C4—21no—
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—22no—
958C3×C4—22no—
959C3×C4—22no—
960C3×C4—32no—
961C3×C4—32no—
962C3×C4—32no—
963C3×C4—32no—
964C3×C4—32no—
965C3×C4—32no—
966C3×C4—32no—
967C3×C4—32no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—62no—
973C3×C4—62no—
974C3×C4—62no—
975C3×C4—62no—
976C3×C4—62no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—92no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4#380412yesdirect product factor
989C3×C4C3×#23512yescomplemented
990C3×C4C3×#23712yescomplemented
991Dic3—21no—
992Dic3—21no—
993Dic3—21no—
994Dic3—32no—
995Dic3—32no—
996Dic3—62no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—121no—
1002Dic3—121no—
1003Dic3C2×C3×C4×D312yes—
1004Dic3C2×C3×C4×D312yes—
1005Dic3C2×C3×C4×D312yes—
1006Dic3C3×#23512yescomplemented
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32C4×#23511yescharacteristic, complemented
1012C32C4×#23711yescharacteristic, complemented
1013C32C3×C4×#4111yescharacteristic, complemented
1014C23—31no—
1015C23—91no—
1016C23C2×C3×D3211yescharacteristic
1017Q8—94no—
1018D4—34no—
1019D4—94no—
1020D4—94no—
1021C2×C4—22no—
1022C2×C4—31no—
1023C2×C4—31no—
1024C2×C4—31no—
1025C2×C4—31no—
1026C2×C4—34no—
1027C2×C4—31no—
1028C2×C4—31no—
1029C2×C4—31no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—94no—
1033C2×C4—94no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—182no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4C2×C3×D3211yescharacteristic
1041C2×C4C2×C3×D3211yescharacteristic
1042C2×C3—24no—
1043C2×C3—22no—
1044C2×C3—22no—
1045C2×C3—22no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—42no—
1056C2×C3—42no—
1057C2×C3—44no—
1058C2×C3—41no—
1059C2×C3—41no—
1060C2×C3—41no—
1061C2×C3—62no—
1062C2×C3—62no—
1063C2×C3—122no—
1064C2×C3—182no—
1065C2×C3C2×C4×D3211yescharacteristic
1066C2×C3D3×#23511yescharacteristic
1067C2×C3C2×#380411yescharacteristic
1068C2×C3C22×C3×C4×D311yescharacteristic
1069C2×C3C22×C3×C4×D311yescharacteristic
1070C2×C3C2×C3×#23511yescharacteristic
1071C2×C3C2×C3×#23511yescharacteristic
1072C2×C3C2×C3×#23711yescharacteristic
1073C2×C3C3×D3×#4111yescharacteristic
1074D3—22no—
1075D3—62no—
1076D3—62no—
1077D3—122no—
1078C22—21no—
1079C22—21no—
1080C22—32no—
1081C22—61no—
1082C22—61no—
1083C22—92no—
1084C22—181no—
1085C22—181no—
1086C22C3×C4×D3212yes—
1087C22C22×C3×D3211yescharacteristic
1088C4—21no—
1089C4—32no—
1090C4—32no—
1091C4—32no—
1092C4—32no—
1093C4—61no—
1094C4—61no—
1095C4—61no—
1096C4—92no—
1097C4—181no—
1098C4—181no—
1099C4C3×#380412yesdirect product factor
1100C3—21no—
1101C3—21no—
1102C3—21no—
1103C3—41no—
1104C3C4×#380411yescharacteristic, direct product factor
1105C3C3×C4×#23511yescharacteristic, complemented
1106C3C3×C4×#23711yescharacteristic, complemented
1107C2—22no—
1108C2—62no—
1109C2—182no—
1110C2C2×C3×C4×D3211yescharacteristic
1111C2C3×D3×#23511yescharacteristic
1112C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C3×#3804C2
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×C4×#41
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
2. C3×C4×#638C2semidirect
3. C32×C4×#67C2semidirect
4. C2×C32×C4×Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63955C2semidirect
7. C3×#63952C2semidirect
8. C3×C4×#627C2semidirect
9. C3×C4×#626C2semidirect
10. C3×C4×#624C2semidirect
11. C3×#63880C2semidirect
12. C3×#63877C2semidirect
13. C3×C4×D3×Dic3C2semidirect
14. C3×#63837C2semidirect
15. C3×#63836C2semidirect
18. C4×#3804C3direct (N × H)
30. C3×#3804C4direct (N × H)
60. C4×#638C2×C3semidirect
69. C3×C4×#67D3semidirect
70. C3×C4×#67C2×C3semidirect
74. C2×C3×C4×Dic3D3semidirect
75. C2×C3×C4×Dic3C2×C3semidirect
92. Dic3×#67C2×C3semidirect
93. #63955C2×C3semidirect
94. #63952C2×C3semidirect
95. C4×#627C2×C3semidirect
96. C4×#626C2×C3semidirect
97. C4×#624C2×C3semidirect
98. #63880C2×C3semidirect
99. #63877C2×C3semidirect
100. C4×D3×Dic3C2×C3semidirect
101. #63837C2×C3semidirect
102. #63836C2×C3semidirect
109. C3×#638C2×C4semidirect
114. C32×#67C2×C4semidirect
116. C2×C32×Dic3C2×C4semidirect
125. C3×#627C2×C4semidirect
126. C3×#626C2×C4semidirect
128. C3×#624C2×C4semidirect
130. C3×D3×Dic3C2×C4semidirect
183. #3804C3×C4direct (N × H)
275. C33×C4#41semidirect
285. C32×Dic3#41semidirect
314. C4×#67C3×D3semidirect
317. C2×C4×Dic3C3×D3semidirect
381. #638C2×C3×C4semidirect
391. C3×#67C4×D3semidirect
392. C3×#67C2×C3×C4semidirect
415. C2×C3×Dic3C4×D3semidirect
416. C2×C3×Dic3C2×C3×C4semidirect
446. #627C2×C3×C4semidirect
447. #626C2×C3×C4semidirect
449. #624C2×C3×C4semidirect
451. D3×Dic3C2×C3×C4semidirect
659. C32×C4#235semidirect
660. C32×C4#237semidirect
661. C32×C4C3×#41semidirect
690. C3×Dic3#235semidirect
694. C3×Dic3C3×#41semidirect
710. C33C4×#41semidirect
795. #67C3×C4×D3semidirect
808. C2×Dic3C3×C4×D3semidirect
988. C3×C4#3804direct (N × H)
989. C3×C4C3×#235semidirect
990. C3×C4C3×#237semidirect
1006. Dic3C3×#235semidirect
1011. C32C4×#235semidirect
1012. C32C4×#237semidirect
1013. C32C3×C4×#41semidirect
1099. C4C3×#3804direct (N × H)
1104. C3C4×#3804direct (N × H)
1105. C3C3×C4×#235semidirect
1106. C3C3×C4×#237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C3×C4×#6382
C32×C4×#672
C2×C32×C4×Dic32
C3×Dic3×#672
C3×#639552
C3×#639522
C3×C4×#6272
C3×C4×#6262
C3×C4×#6242
C3×#638802
C3×#638772
C3×C4×D3×Dic32
C3×#638372
C3×#638362
C3×C4×#2373
C3×C4×#2353
C4×#38043