Finite Group Databasebeta

← C3×#80493 #11889367

Subgroups — C3×#80493 #11889367

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C3×#5581C211yesmaximal, characteristic
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5189C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5030C211yesmaximal, characteristic, complemented
10C3×#4836C211yesmaximal, characteristic
11C3×#4829C211yesmaximal, characteristic, complemented
12C3×#4814C211yesmaximal, characteristic, complemented
13C3×#4805C211yesmaximal, characteristic, complemented
14C3×#4802C211yesmaximal, characteristic, complemented
15C3×D3×#103C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#80493C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#896—21no—
32C3×#896—21no—
33C3×#894—21no—
34C3×#893—21no—
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#889—21no—
38C3×#888—21no—
39C3×#876—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872—21no—
42C3×#870C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#818C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5727C2×C311yescharacteristic
64#5581C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—21no—
72C3×#462D311yescharacteristic, complemented
73C3×#462C2×C311yescharacteristic, complemented
74C3×#451—31no—
75C3×#451—31no—
76C3×#441—31no—
77C3×#435—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5189C2×C311yescharacteristic, complemented
81#5188C2×C311yescharacteristic, complemented
82#5186C2×C311yescharacteristic, complemented
83#5186C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5030C2×C311yescharacteristic, complemented
86#4836C2×C311yescharacteristic
87#4829C2×C311yescharacteristic, complemented
88#4814C2×C311yescharacteristic, complemented
89#4805C2×C311yescharacteristic, complemented
90#4802C2×C311yescharacteristic, complemented
91D3×#103C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C2×C3×D12D411yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×Q16—41no—
109C32×Q16—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C3×#216—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C2×D3×Q8C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—21no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C2×C3×Q16C22×C311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C4⋊Q8—21no—
159C3×C4⋊Q8—61no—
160C3×C4⋊Q8C2×D311yescharacteristic
161C3×C4⋊Q8C22×C311yescharacteristic
162C3×#126—61no—
163C3×#125—31no—
164C3×#125—61no—
165C3×#123—61no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8—61no—
172C3×C4×Q8—21no—
173C3×C4×Q8—31no—
174C3×C4×Q8C2×D311yescharacteristic
175C3×C4×Q8C22×C311yescharacteristic
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C3×#117—61no—
180C2×C3×C4⋊C4—31no—
181#946C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183#946C22×C311yescharacteristic
184#946C22×C311yescharacteristic
185C2×#216C22×C311yescharacteristic
186C2×ΓL(1,𝔽25)C22×C311yescharacteristic
187C2×D3×C8C22×C311yescharacteristic
188#896—21no—
189#896—21no—
190#894—21no—
191#893—21no—
192#892C22×C311yescharacteristic
193D3×C4⋊C4C22×C311yescharacteristic
194#889—21no—
195#888—21no—
196#876—21no—
197C4×D12C22×C311yescharacteristic
198#872—21no—
199#870C22×C311yescharacteristic
200C4×Dic6C22×C311yescharacteristic
201C3×#107—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—21no—
205C3×C4⋊C8C2×D311yescharacteristic
206C3×C4⋊C8C22×C311yescharacteristic
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103C2×D311yescharacteristic
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×#97—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic
231#818C22×C311yescharacteristic
232#817C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—31no—
277#491—31no—
278#485—31no—
279#483—31no—
280#479—31no—
281#470—31no—
282#467—31no—
283#462C3×D311yescharacteristic, complemented
284#451—31no—
285#451—31no—
286#441—31no—
287#435—31no—
288#419—31no—
289C2×#103—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×D4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312D3×Q8—22no—
313D3×Q8—22no—
314D3×Q8—41no—
315D3×Q8—41no—
316C2×D12C3×D411yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3C23×C311yescharacteristic
321C2×C4×D3C23×C311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6C23×C311yescharacteristic
325C3×Q16—41no—
326C3×Q16—41no—
327C3×Q16—41no—
328C3×Q16—41no—
329C3×Q16—42no—
330C3×Q16—42no—
331C3×Q16—62no—
332C3×M16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—41no—
377C3×C42—61no—
378C3×C42—61no—
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381#216—22no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4C3×D411yescharacteristic
388(C2×D3)⋊C4C3×D411yescharacteristic
389C4⋊Dic3C3×D411yescharacteristic
390C4⋊Dic3C23×C311yescharacteristic
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C2×C3⋊C8C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405ΓL(1,𝔽25)—41no—
406D3×C8—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3#13712yes—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—31no—
431C2×Q16C2×C3×D311yescharacteristic
432C2×Q16C2×C3×D311yescharacteristic
433C2×M16—31no—
434C22×C8—31no—
435C4⋊Q8—61no—
436C4⋊Q8C2×C3×D311yescharacteristic
437#126—61no—
438#125—31no—
439#125—61no—
440#123—61no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C4×Q8—31no—
448C4×Q8C2×C3×D311yescharacteristic
449C4×D4—31no—
450C4×D4—61no—
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454#107—31no—
455#106—31no—
456#106—31no—
457C4⋊C8C2×C3×D311yescharacteristic
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103C2×C3×D311yescharacteristic
467#103C2×C3×D311yescharacteristic
468C22⋊C8—31no—
469C22⋊C8—31no—
470#97—31no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3C2×C3×D411yescharacteristic
474C22×D3C2×C3×D411yescharacteristic
475C3×Q8—22no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—32no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—61no—
495C3×Q8—122no—
496C3×Q8—122no—
497C3×D4—62no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C24×C311yescharacteristic
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538D12—22no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—42no—
546Dic6—21no—
547Dic6—42no—
548Dic6—42no—
549Dic6C3×#4112yes—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C2×C32#54611yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C2×C32#57811yescharacteristic
563C3×D3—22no—
564C3×D3—41no—
565C2×Q8—31no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—62no—
569C2×Q8—62no—
570C2×Q8—121no—
571C2×Q8—121no—
572C2×Q8C22×C3×D311yescharacteristic
573C2×Q8C22×C3×D311yescharacteristic
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581Q16—41no—
582Q16—41no—
583Q16—62no—
584M16—121no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—121no—
588C2×C8C22×C3×D311yescharacteristic
589C2×C8C22×C3×D311yescharacteristic
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C42—21no—
614C42—61no—
615C42—61no—
616C42C22×C3×D311yescharacteristic
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×C3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3C3×#13712yes—
632C3×C4—22no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—62no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4#100411yescharacteristic
659C3×C4D3×#4111yescharacteristic
660C3×C4C2×C3×#4111yescharacteristic
661C3×C4C3×H(5,𝔽2)11yescharacteristic
662Dic3—22no—
663Dic3—21no—
664Dic3—21no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668C32#331211yescharacteristic, complemented, Sylow
669C23—31no—
670C23—31no—
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—21no—
677Q8—32no—
678Q8—61no—
679Q8—122no—
680Q8—122no—
681D4—62no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4C3×D3×D411yescharacteristic
700C2×C4C3×D3×D411yescharacteristic
701C2×C4C23×C3×D311yescharacteristic
702C8—21no—
703C8—21no—
704C8—61no—
705C8—61no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—62no—
710C2×C3—121no—
711C2×C3#561211yescharacteristic
712C2×C3#576611yescharacteristic
713C2×C3D3×#13711yescharacteristic
714C2×C3C3×#54611yescharacteristic
715C2×C3C2×C3×#13711yescharacteristic
716C2×C3C3×#57811yescharacteristic
717D3—22no—
718D3—41no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22C2×C3×D3×D411yescharacteristic
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—62no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4C3×#100411yescharacteristic
739C4C3×D3×#4111yescharacteristic
740C3—21no—
741C3#8049311yescharacteristic, direct product factor
742C3C3×#331211yescharacteristic, complemented
743C2—62no—
744C2—121no—
745C2C3×#561211yescharacteristic
746C2C3×#576611yescharacteristic
747C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×#462D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
3. C32×#462C2semidirect
4. C3×#5189C2semidirect
5. C3×#5188C2semidirect
6. C3×#5186C2semidirect
7. C3×#5186C2semidirect
8. C3×#5082C2semidirect
9. C3×#5030C2semidirect
11. C3×#4829C2semidirect
12. C3×#4814C2semidirect
13. C3×#4805C2semidirect
14. C3×#4802C2semidirect
15. C3×D3×#103C2semidirect
17. #80493C3direct (N × H)
72. C3×#462D3semidirect
73. C3×#462C2×C3semidirect
80. #5189C2×C3semidirect
81. #5188C2×C3semidirect
82. #5186C2×C3semidirect
83. #5186C2×C3semidirect
84. #5082C2×C3semidirect
85. #5030C2×C3semidirect
87. #4829C2×C3semidirect
88. #4814C2×C3semidirect
89. #4805C2×C3semidirect
90. #4802C2×C3semidirect
91. D3×#103C2×C3semidirect
283. #462C3×D3semidirect
668. C32#3312semidirect
741. C3#80493direct (N × H)
742. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55812
C32×#4622
C3×#51892
C3×#51882
C3×#51862
C3×#50822
C3×#50302
C3×#48362
C3×#48292
C3×#48142
C3×#48052
C3×#48022
C3×D3×#1032
C3×#33123
#804933