Finite Group Databasebeta

← C3×#74393 #11805413

Subgroups — C3×#74393 #11805413

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic
5C2×C3×#67⋊C4C211yesmaximal, characteristic
6C32×#385C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8C3×#4976C211yesmaximal, characteristic, complemented
9C3×#4975C211yesmaximal, characteristic, complemented
10C3×#4950C211yesmaximal, characteristic, complemented
11C3×#4942C211yesmaximal, characteristic, complemented
12C3×#4668C211yesmaximal, characteristic, complemented
13C3×#4667C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4647C211yesmaximal, characteristic, complemented
16C3×D4×C4⋊C4—31nomaximal
17#74393C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C3×C4×#67—24no—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4—24no—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C2×C3×C4×Dic3C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C3×D3×C4⋊C4—24no—
50C3×#67⋊C4—24no—
51C3×#67⋊C4C418yescomplemented
52C32×#95C2211yescharacteristic
53C32×#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C3×C3⋊#95C2211yescharacteristic
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C22×C3×C4⋊C4—31no—
62C22×C3×C4⋊C4—31no—
63C2×C4×#67C2×C311yescharacteristic
64C22×Dic3⋊C4C2×C311yescharacteristic, complemented
65C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
66C2×#67⋊C4C2×C311yescharacteristic
67C2×#67⋊C4C2×C311yescharacteristic
68C3×#389—31no—
69C3×#389—31no—
70C3×#385—21no—
71C3×#385—31no—
72C3×#385—31no—
73C3×#385—31no—
74C3×#385D311yescharacteristic, complemented
75C3×#385C2×C311yescharacteristic, complemented
76C3×#384—31no—
77C3×#380—31no—
78C3×#380—31no—
79C3×C4×C4⋊C4—31no—
80#4989C2×C311yescharacteristic, complemented
81#4976C2×C311yescharacteristic, complemented
82#4975C2×C311yescharacteristic, complemented
83#4950C2×C311yescharacteristic, complemented
84#4942C2×C311yescharacteristic, complemented
85#4668C2×C311yescharacteristic, complemented
86#4667C2×C311yescharacteristic, complemented
87#4649C2×C311yescharacteristic, complemented
88#4647C2×C311yescharacteristic, complemented
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67C2×C414yes—
101C2×C3×#67D414yes—
102C2×C3×#67Q814yes—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2×C414yescomplemented
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—41no—
123C2×C3×C4×D3—41no—
124C2×C3×C4×D3C2×C414yescomplemented
125C32×C4⋊C4—22no—
126C32×C4⋊C4—41no—
127C32×C22⋊C4—22no—
128C32×C22⋊C4C2×C414yescomplemented
129C3×#217—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4C2×C414yescomplemented
133C3×C4⋊Dic3—22no—
134C3×C4⋊Dic3—41no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—22no—
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141C3×Dic3⋊C4—22no—
142C3×Dic3⋊C4C2×C414yescomplemented
143C3×Dic3⋊C4D414yescomplemented
144C3×C4×Dic3—22no—
145C3×C4×Dic3—22no—
146C3×C4×Dic3C2×C414yescomplemented
147D4×C4⋊C4—31noSylow
148C22×C3×D4—31no—
149C23×C3×C4—21no—
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C23×C3×C4C2×D311yescharacteristic
156C23×C3×C4C22×C311yescharacteristic
157C22×#67C22×C311yescharacteristic
158C23×Dic3C22×C311yescharacteristic
159C23×Dic3C22×C311yescharacteristic
160C22×C4×D3C22×C311yescharacteristic
161C22×C4×D3C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C3×C4×D4—38no—
164C3×C4×D4—64no—
165C3×C4×D4—64no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—64no—
180C2×C3×C4⋊C4—64no—
181C2×C3×C4⋊C4C2×D311yescharacteristic
182C2×C3×C4⋊C4C2×D311yescharacteristic
183C2×C3×C4⋊C4C22×C311yescharacteristic
184C2×C3×C4⋊C4C22×C311yescharacteristic
185C2×C3×C22⋊C4—21no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C22×C311yescharacteristic
194C2×C3×C22⋊C4C22×C311yescharacteristic
195C2×C3×C42—31no—
196C2×C3×C42—31no—
197C2×C3×C42—31no—
198C2×#217C22×C311yescharacteristic
199C4×#67—24no—
200C2×(C2×D3)⋊C4C22×C311yescharacteristic
201C2×(C2×D3)⋊C4C22×C311yescharacteristic
202C2×(C2×D3)⋊C4C22×C311yescharacteristic
203C2×C4⋊Dic3C22×C311yescharacteristic
204C2×C4⋊Dic3C22×C311yescharacteristic
205C2×Dic3⋊C4—24no—
206C2×Dic3⋊C4C22×C311yescharacteristic
207C2×Dic3⋊C4C22×C311yescharacteristic
208C2×Dic3⋊C4C22×C311yescharacteristic
209C2×Dic3⋊C4C22×C311yescharacteristic
210C2×Dic3⋊C4C22×C311yescharacteristic
211C2×Dic3⋊C4C22×C311yescharacteristic
212C2×Dic3⋊C4C22×C311yescharacteristic
213C2×Dic3⋊C4C22×C311yescharacteristic
214C2×Dic3⋊C4C22×C311yescharacteristic
215C2×C4×Dic3C22×C311yescharacteristic
216C2×C4×Dic3C22×C311yescharacteristic
217C2×C4×Dic3C22×C311yescharacteristic
218D3×C4⋊C4—24no—
219#67⋊C4—24no—
220#67⋊C4C3×C418yescomplemented
221C3×#95—21no—
222C3×#95—21no—
223C3×#95—31no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95C2×D311yescharacteristic
228C3×#95C2×D311yescharacteristic
229C3×#95C22×C311yescharacteristic
230C3×#95C22×C311yescharacteristic
231C3⋊#95C22×C311yescharacteristic
232C3⋊#95C22×C311yescharacteristic
233C3⋊#95C22×C311yescharacteristic
234C3⋊#95C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2×D412yes—
241C23×C32C2×Q812yes—
242C23×C32C2411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×Q812yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—44no—
266C2×C32×C4C22×C412yes—
267C2×C32×C4C22×C412yes—
268C2×C32×C4C2×D412yes—
269C3×#67C4⋊C4116yescomplemented
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—28no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—44no—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C22×C412yes—
287C2×C3×Dic3C22×C412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×Q812yes—
292C2×C3×Dic3#4112yes—
293C3×C4×D3—28no—
294C3×C4×D3—44no—
295C3×C4×D3—44no—
296C2×C4×D4—31no—
297C2×C4×D4—31no—
298C2×C4×D4—31no—
299C22×C4⋊C4—31no—
300C22×C4⋊C4—31no—
301#389—31no—
302#389—31no—
303#385—31no—
304#385—31no—
305#385—31no—
306#385C3×D311yescharacteristic, complemented
307#384—31no—
308#380—31no—
309#380—31no—
310C4×C4⋊C4—31no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C23×C311yescharacteristic
315C23×D3C23×C311yescharacteristic
316C2×C3×D4—34no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—34no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—34no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—42no—
339C22×C3×C4—42no—
340C22×C3×C4—41no—
341C22×C3×C4—41no—
342C22×C3×C4—42no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—62no—
349C22×C3×C4—62no—
350C22×C3×C4—62no—
351C22×C3×C4—62no—
352C22×C3×C4—62no—
353C22×C3×C4—121no—
354C22×C3×C4—121no—
355C22×C3×C4—121no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C22×C3×C4C23×C311yescharacteristic
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C22×C3×C4C23×C311yescharacteristic
368C2×#67C2×C3×C414yes—
369C2×#67C3×D414yes—
370C2×#67C3×Q814yes—
371C22×Dic3—22no—
372C22×Dic3—22no—
373C22×Dic3—22no—
374C22×Dic3—22no—
375C22×Dic3—41no—
376C22×Dic3C2×C3×C414yescomplemented
377C22×Dic3C23×C311yescharacteristic
378C22×Dic3C23×C311yescharacteristic
379C22×Dic3C23×C311yescharacteristic
380C22×Dic3C23×C311yescharacteristic
381C22×Dic3C23×C311yescharacteristic
382C22×Dic3C23×C311yescharacteristic
383C22×Dic3C23×C311yescharacteristic
384C2×C4×D3—22no—
385C2×C4×D3—22no—
386C2×C4×D3—22no—
387C2×C4×D3—22no—
388C2×C4×D3—22no—
389C2×C4×D3—22no—
390C2×C4×D3—41no—
391C2×C4×D3—41no—
392C2×C4×D3C2×C3×C414yescomplemented
393C3×C4⋊C4—22no—
394C3×C4⋊C4—22no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—42no—
398C3×C4⋊C4—41no—
399C3×C4⋊C4—41no—
400C3×C4⋊C4—42no—
401C3×C4⋊C4—62no—
402C3×C4⋊C4—62no—
403C3×C4⋊C4—62no—
404C3×C4⋊C4—62no—
405C3×C4⋊C4—62no—
406C3×C4⋊C4—62no—
407C3×C4⋊C4—62no—
408C3×C4⋊C4—62no—
409C3×C4⋊C4—121no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—22no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—42no—
415C3×C22⋊C4—62no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4C4×D314yescomplemented
419C3×C22⋊C4C2×C3×C414yescomplemented
420C3×C42—34no—
421C3×C42—62no—
422C3×C42—62no—
423#217—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—22no—
426(C2×D3)⋊C4C2×C3×C414yescomplemented
427C4⋊Dic3—22no—
428C4⋊Dic3—41no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—22no—
433Dic3⋊C4—22no—
434Dic3⋊C4—22no—
435Dic3⋊C4—22no—
436Dic3⋊C4C2×C3×C414yescomplemented
437Dic3⋊C4C3×D414yescomplemented
438C4×Dic3—22no—
439C4×Dic3—22no—
440C4×Dic3C2×C3×C414yescomplemented
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32C2×C4⋊C414yescomplemented
448C22×C32C23×C411yescharacteristic
449C22×C32C22×D411yescharacteristic
450C22×C32C22×D411yescharacteristic
451C22×C32C22×Q811yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C322−1+411yescharacteristic
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3C2×C4⋊C414yescomplemented
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—41no—
466C32×C4—41no—
467C32×C4—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C2×C4⋊C414yescomplemented
474C3×Dic3C4×D414yescomplemented
475C22×D4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4C2×C3×D311yescharacteristic
482C4×D4—38no—
483C4×D4—64no—
484C4×D4—64no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—64no—
497C2×C4⋊C4—64no—
498C2×C4⋊C4C2×C3×D311yescharacteristic
499C2×C4⋊C4C2×C3×D311yescharacteristic
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4C2×C3×D311yescharacteristic
505C2×C22⋊C4C2×C3×D311yescharacteristic
506C2×C42—31no—
507C2×C42—31no—
508C2×C42—31no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—31no—
513#95C2×C3×D311yescharacteristic
514#95C2×C3×D311yescharacteristic
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3C2×C4×D312yes—
539C23×C3D3×D412yes—
540C23×C3D3×Q812yes—
541C23×C3C22×C3×C412yes—
542C23×C3C2×C3×D412yes—
543C23×C3C2×C3×Q812yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C24×C311yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3C22×C3×C412yes—
551C22×D3C2×C3×D412yes—
552C22×D3C2×C3×Q812yes—
553C3×D4—316no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—44no—
611C2×C3×C4—44no—
612C2×C3×C4—48no—
613C2×C3×C4—68no—
614C2×C3×C4—68no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—124no—
629C2×C3×C4—124no—
630C2×C3×C4—124no—
631C2×C3×C4C2×C4×D312yes—
632C2×C3×C4C2×C4×D312yes—
633C2×C3×C4D3×D412yes—
634C2×C3×C4C22×C3×C412yes—
635C2×C3×C4C22×C3×C412yes—
636C2×C3×C4C2×C3×D412yes—
637#67C3×C4⋊C4116yescomplemented
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—28no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—44no—
653C2×Dic3C22×C3×C412yes—
654C2×Dic3C22×C3×C412yes—
655C2×Dic3C22×C3×C412yes—
656C2×Dic3C2×C3×D412yes—
657C2×Dic3C2×C3×D412yes—
658C2×Dic3C2×C3×D412yes—
659C2×Dic3C2×C3×Q812yes—
660C2×Dic3C3×#4112yes—
661C4×D3—28no—
662C4×D3—44no—
663C4×D3—44no—
664C2×C32—24no—
665C2×C32C22×C4⋊C411yescharacteristic
666C2×C32C2×C4×D411yescharacteristic
667C2×C32#52011yescharacteristic
668C2×C32D4211yescharacteristic
669C2×C32#54711yescharacteristic
670C2×C32D4×Q811yescharacteristic
671C2×C32#55411yescharacteristic
672C3×D3—24no—
673C24—31no—
674C24C22×C3×D311yescharacteristic
675C2×D4—34no—
676C2×D4—34no—
677C2×D4—34no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—34no—
685C22×C4—34no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—41no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—121no—
701C22×C4—121no—
702C22×C4—121no—
703C22×C4C22×C3×D311yescharacteristic
704C22×C4C22×C3×D311yescharacteristic
705C22×C4C22×C3×D311yescharacteristic
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D311yescharacteristic
708C22×C4C22×C3×D311yescharacteristic
709C4⋊C4—22no—
710C4⋊C4—34no—
711C4⋊C4—34no—
712C4⋊C4—41no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—121no—
722C22⋊C4—22no—
723C22⋊C4—34no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4C3×C4×D314yescomplemented
728C42—34no—
729C42—62no—
730C42—62no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—24no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—34no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3D3×C4⋊C414yescomplemented
765C22×C3C2×C3×C4⋊C414yescomplemented
766C22×C3C22×C4×D311yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×D411yescharacteristic
769C22×C3#100411yescharacteristic
770C22×C3C2×D3×Q811yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3#101011yescharacteristic
773C22×C3C23×C3×C411yescharacteristic
774C22×C3C22×C3×D411yescharacteristic
775C22×C3C22×C3×D411yescharacteristic
776C22×C3C22×C3×Q811yescharacteristic
777C22×C3C2×C3×#4111yescharacteristic
778C22×C3C3×H(5,𝔽2)11yescharacteristic
779C22×C3C3×2−1+411yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3C2×C3×C4⋊C414yescomplemented
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—34no—
794C3×C4—34no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—42no—
798C3×C4—42no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—81no—
808C3×C4—81no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812Dic3—22no—
813Dic3—22no—
814Dic3—41no—
815Dic3—41no—
816Dic3—41no—
817Dic3C2×C3×C4⋊C414yescomplemented
818Dic3C3×C4×D414yescomplemented
819C32D4×C4⋊C411yescharacteristic, complemented, Sylow
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—32no—
825C23—32no—
826C23—32no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23C2×C3×C4×D312yes—
832C23C3×D3×D412yes—
833C23C3×D3×Q812yes—
834C23C23×C3×D311yescharacteristic
835D4—316no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—44no—
860C2×C4—68no—
861C2×C4—68no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4—124no—
878C2×C4C2×C3×C4×D312yes—
879C2×C4C2×C3×C4×D312yes—
880C2×C4C3×D3×D412yes—
881C2×C3—24no—
882C2×C3—24no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—44no—
891C2×C3—64no—
892C2×C3C2×D3×C4⋊C411yescharacteristic
893C2×C3C4×D3×D411yescharacteristic
894C2×C3#554611yescharacteristic
895C2×C3#559011yescharacteristic
896C2×C3#563211yescharacteristic
897C2×C3#563611yescharacteristic
898C2×C3#565511yescharacteristic
899C2×C3C22×C3×C4⋊C411yescharacteristic
900C2×C3C2×C3×C4×D411yescharacteristic
901C2×C3C3×#52011yescharacteristic
902C2×C3C3×D4211yescharacteristic
903C2×C3C3×#54711yescharacteristic
904C2×C3C3×D4×Q811yescharacteristic
905C2×C3C3×#55411yescharacteristic
906D3—24no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—34no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22C3×D3×C4⋊C414yescomplemented
921C22C22×C3×C4×D311yescharacteristic
922C22C2×C3×D3×D411yescharacteristic
923C22C2×C3×D3×D411yescharacteristic
924C22C3×#100411yescharacteristic
925C22C2×C3×D3×Q811yescharacteristic
926C22C3×D3×#4111yescharacteristic
927C22C3×#101011yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—34no—
932C4—34no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—62no—
937C4—62no—
938C4—121no—
939C4—121no—
940C4—121no—
941C3—21no—
942C3#7439311yescharacteristic, direct product factor
943C3C3×D4×C4⋊C411yescharacteristic, complemented
944C2—24no—
945C2—64no—
946C2C2×C3×D3×C4⋊C411yescharacteristic
947C2C3×C4×D3×D411yescharacteristic
948C2C3×#554611yescharacteristic
949C2C3×#559011yescharacteristic
950C2C3×#563211yescharacteristic
951C2C3×#563611yescharacteristic
952C2C3×#565511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×#385D3
hypocenterC3C3×D4×C4⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
6. C32×#385C2semidirect
7. C3×#4989C2semidirect
8. C3×#4976C2semidirect
9. C3×#4975C2semidirect
10. C3×#4950C2semidirect
11. C3×#4942C2semidirect
12. C3×#4668C2semidirect
13. C3×#4667C2semidirect
14. C3×#4649C2semidirect
15. C3×#4647C2semidirect
17. #74393C3direct (N × H)
51. C3×#67⋊C4C4semidirect
64. C22×Dic3⋊C4C2×C3semidirect
65. C2×D3×C4⋊C4C2×C3semidirect
74. C3×#385D3semidirect
75. C3×#385C2×C3semidirect
80. #4989C2×C3semidirect
81. #4976C2×C3semidirect
82. #4975C2×C3semidirect
83. #4950C2×C3semidirect
84. #4942C2×C3semidirect
85. #4668C2×C3semidirect
86. #4667C2×C3semidirect
87. #4649C2×C3semidirect
88. #4647C2×C3semidirect
108. C22×C3×Dic3C2×C4semidirect
124. C2×C3×C4×D3C2×C4semidirect
128. C32×C22⋊C4C2×C4semidirect
132. C3×(C2×D3)⋊C4C2×C4semidirect
142. C3×Dic3⋊C4C2×C4semidirect
143. C3×Dic3⋊C4D4semidirect
146. C3×C4×Dic3C2×C4semidirect
220. #67⋊C4C3×C4semidirect
269. C3×#67C4⋊C4semidirect
306. #385C3×D3semidirect
376. C22×Dic3C2×C3×C4semidirect
392. C2×C4×D3C2×C3×C4semidirect
418. C3×C22⋊C4C4×D3semidirect
419. C3×C22⋊C4C2×C3×C4semidirect
426. (C2×D3)⋊C4C2×C3×C4semidirect
436. Dic3⋊C4C2×C3×C4semidirect
437. Dic3⋊C4C3×D4semidirect
440. C4×Dic3C2×C3×C4semidirect
447. C22×C32C2×C4⋊C4semidirect
461. C2×C3×D3C2×C4⋊C4semidirect
473. C3×Dic3C2×C4⋊C4semidirect
474. C3×Dic3C4×D4semidirect
637. #67C3×C4⋊C4semidirect
727. C22⋊C4C3×C4×D3semidirect
764. C22×C3D3×C4⋊C4semidirect
765. C22×C3C2×C3×C4⋊C4semidirect
786. C2×D3C2×C3×C4⋊C4semidirect
817. Dic3C2×C3×C4⋊C4semidirect
818. Dic3C3×C4×D4semidirect
819. C32D4×C4⋊C4semidirect
920. C22C3×D3×C4⋊C4semidirect
942. C3#74393direct (N × H)
943. C3C3×D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×Dic3⋊C42
C2×C3×D3×C4⋊C42
C2×C3×#67⋊C42
C32×#3852
C3×#49892
C3×#49762
C3×#49752
C3×#49502
C3×#49422
C3×#46682
C3×#46672
C3×#46492
C3×#46472
C3×D4×C4⋊C43
#743933