Finite Group Databasebeta

← C3×#80494 #11889829

Subgroups — C3×#80494 #11889829

Order 1152.

818 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic
2C3×#5581C211yesmaximal, characteristic, complemented
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5189C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5026C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4815C211yesmaximal, characteristic, complemented
13C3×#4811C211yesmaximal, characteristic, complemented
14C3×#4804C211yesmaximal, characteristic, complemented
15C3×#4803C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#80494C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#895—21no—
32C3×#894—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#889—21no—
39C3×#876—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#872—21no—
43C3×#870C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×#818C2211yescharacteristic
57C3×#817C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×#547—31no—
63#5726C2×C311yescharacteristic
64#5581C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#484—31no—
68C3×#478—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—21no—
72C3×#462D311yescharacteristic, complemented
73C3×#462C2×C311yescharacteristic, complemented
74C3×#452—31no—
75C3×#452—31no—
76C3×#440—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5189C2×C311yescharacteristic, complemented
81#5188C2×C311yescharacteristic, complemented
82#5187C2×C311yescharacteristic, complemented
83#5187C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5026C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4836C2×C311yescharacteristic, complemented
88#4815C2×C311yescharacteristic, complemented
89#4811C2×C311yescharacteristic, complemented
90#4804C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×#239—22no—
96C3×#239—22no—
97C3×#239—41no—
98C3×#239—41no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C32×Q16—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C42—21no—
118C32×C42C2311yescharacteristic
119C3×#215—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3315—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#239C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—21no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C22×C311yescharacteristic
154C2×C3×Q16C22×C311yescharacteristic
155C2×C3×SD16—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C4⋊Q8—21no—
159C3×C4⋊Q8C2×D311yescharacteristic
160C3×C4⋊Q8C22×C311yescharacteristic
161C3×#126—61no—
162C3×#125—31no—
163C3×#125—61no—
164C3×#123—61no—
165C3×#123—61no—
166C3×#123—61no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×#121—61no—
172C3×C4×Q8—21no—
173C3×C4×Q8C2×D311yescharacteristic
174C3×C4×Q8C22×C311yescharacteristic
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—61no—
181#946C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183#946C22×C311yescharacteristic
184#946C22×C311yescharacteristic
185C2×#215C22×C311yescharacteristic
186C2×ΓL(1,𝔽25)C22×C311yescharacteristic
187C2×D3×C8C22×C311yescharacteristic
188#895—21no—
189#894—21no—
190#894—21no—
191#894—21no—
192#892C22×C311yescharacteristic
193D3×C4⋊C4—21no—
194D3×C4⋊C4C22×C311yescharacteristic
195#889—21no—
196#876—21no—
197C4×D12C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic
199#872—21no—
200#870C22×C311yescharacteristic
201C3×#107—31no—
202C3×#107—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×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
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#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232(C2×D3)⋊C8C22×C311yescharacteristic
233#818C22×C311yescharacteristic
234#817C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—41no—
261C3×D12—42no—
262C3×D12—42no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#547—31no—
278#491—31no—
279#485—31no—
280#484—31no—
281#478—31no—
282#470—31no—
283#467—31no—
284#462C3×D311yescharacteristic, complemented
285#452—31no—
286#452—31no—
287#440—31no—
288#435—31no—
289#417—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—121no—
294C3×#41—121no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314#239—22no—
315#239—22no—
316#239—41no—
317#239—41no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12C3×D411yescharacteristic
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3C23×C311yescharacteristic
327C2×C4×D3C23×C311yescharacteristic
328C3×Q16—41no—
329C3×Q16—41no—
330C3×Q16—41no—
331C3×Q16—41no—
332C3×Q16—42no—
333C3×Q16—42no—
334C3×SD16—62no—
335C3×M16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—41no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C23×C311yescharacteristic
383#215—22no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4C3×D411yescharacteristic
391(C2×D3)⋊C4C3×D411yescharacteristic
392C4⋊Dic3C3×D411yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403C4×Dic3—21no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406ΓL(1,𝔽25)—41no—
407D3×C8—41no—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C2×#41—31no—
432C2×#41—31no—
433C2×Q16C2×C3×D311yescharacteristic
434C2×Q16C2×C3×D311yescharacteristic
435C2×SD16—31no—
436C2×M16—31no—
437C22×C8—31no—
438C4⋊Q8C2×C3×D311yescharacteristic
439#126—61no—
440#125—31no—
441#125—61no—
442#123—61no—
443#123—61no—
444#123—61no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449#121—61no—
450C4×Q8C2×C3×D311yescharacteristic
451C4×D4—31no—
452C4×D4—31no—
453#117—31no—
454#117—61no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—61no—
457#107—31no—
458#107—31no—
459#106—31no—
460C4⋊C8C2×C3×D311yescharacteristic
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103C2×C3×D311yescharacteristic
467#103C2×C3×D311yescharacteristic
468#102—31no—
469#102—31no—
470#102—31no—
471C22⋊C8—31no—
472C22⋊C8—31no—
473#97—31no—
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3C2×C3×D411yescharacteristic
479C22×D3C2×C3×D411yescharacteristic
480C3×Q8—22no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—32no—
499C3×D4—61no—
500C3×D4—121no—
501C3×D4—122no—
502C3×D4—122no—
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—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C2×C3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C24×C311yescharacteristic
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3C2×C3×D411yescharacteristic
541C2×Dic3C2×C3×D411yescharacteristic
542D12—21no—
543D12—41no—
544D12—42no—
545D12—42no—
546D12C3×#4112yes—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—42no—
553C4×D3—42no—
554C4×D3—42no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—41no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32#54611yescharacteristic
566C2×C32#57511yescharacteristic
567C2×C32#57811yescharacteristic
568C3×D3—41no—
569C3×D3—41no—
570C3×D3—42no—
571#41—62no—
572#41—62no—
573#41—121no—
574#41—121no—
575C2×Q8C22×C3×D311yescharacteristic
576C2×Q8C22×C3×D311yescharacteristic
577C2×Q8C22×C3×D311yescharacteristic
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588Q16—41no—
589Q16—41no—
590SD16—62no—
591M16—121no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—121no—
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4C22×C3×D311yescharacteristic
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C42—21no—
621C42—61no—
622C42C22×C3×D311yescharacteristic
623C22×C3—21no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×C3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—22no—
642C2×D3—41no—
643C2×D3—41no—
644C3×C4—22no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—42no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4#100411yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672C3×C4C3×H(5,𝔽2)11yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678C32#331511yescharacteristic, complemented, Sylow
679C23—31no—
680C23—31no—
681C23—61no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688D4—32no—
689D4—61no—
690D4—121no—
691D4—122no—
692D4—122no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4C3×D3×D411yescharacteristic
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C23×C3×D311yescharacteristic
713C8—21no—
714C8—21no—
715C8—61no—
716C8—61no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—121no—
721C2×C3—121no—
722C2×C3—122no—
723C2×C3#561211yescharacteristic
724C2×C3#576611yescharacteristic
725C2×C3#577711yescharacteristic
726C2×C3C3×#54611yescharacteristic
727C2×C3C3×#57511yescharacteristic
728C2×C3C3×#57811yescharacteristic
729D3—41no—
730D3—41no—
731D3—42no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—62no—
739C22—121no—
740C22—121no—
741C22C2×C3×D3×D411yescharacteristic
742C4—21no—
743C4—21no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—61no—
749C4—61no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4C3×#100411yescharacteristic
754C4C3×D3×#4111yescharacteristic
755C3—21no—
756C3#8049411yescharacteristic, direct product factor
757C3C3×#331511yescharacteristic, complemented
758C2—121no—
759C2—121no—
760C2—122no—
761C2C3×#561211yescharacteristic
762C2C3×#576611yescharacteristic
763C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC3×#5726C2
hypercenterC3×#462D3
hypocenterC3C3×#3315
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
2. C3×#5581C2semidirect
3. C32×#462C2semidirect
4. C3×#5189C2semidirect
5. C3×#5188C2semidirect
6. C3×#5187C2semidirect
7. C3×#5187C2semidirect
8. C3×#5082C2semidirect
9. C3×#5026C2semidirect
10. C3×#4847C2semidirect
11. C3×#4836C2semidirect
12. C3×#4815C2semidirect
13. C3×#4811C2semidirect
14. C3×#4804C2semidirect
15. C3×#4803C2semidirect
17. #80494C3direct (N × H)
64. #5581C2×C3semidirect
72. C3×#462D3semidirect
73. C3×#462C2×C3semidirect
80. #5189C2×C3semidirect
81. #5188C2×C3semidirect
82. #5187C2×C3semidirect
83. #5187C2×C3semidirect
84. #5082C2×C3semidirect
85. #5026C2×C3semidirect
86. #4847C2×C3semidirect
87. #4836C2×C3semidirect
88. #4815C2×C3semidirect
89. #4811C2×C3semidirect
90. #4804C2×C3semidirect
91. #4803C2×C3semidirect
284. #462C3×D3semidirect
678. C32#3315semidirect
756. C3#80494direct (N × H)
757. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C3×#55812
C32×#4622
C3×#51892
C3×#51882
C3×#51872
C3×#50822
C3×#50262
C3×#48472
C3×#48362
C3×#48152
C3×#48112
C3×#48042
C3×#48032
C3×#33153
#804943