Finite Group Databasebeta

← C3×#81546 #11888570

Subgroups — C3×#81546 #11888570

Order 1152.

836 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C3×#5530C211yesmaximal, characteristic, complemented
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4886C211yesmaximal, characteristic, complemented
8C3×#4869C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4810C211yesmaximal, characteristic, complemented
12C3×#4803C211yesmaximal, characteristic, complemented
13C3×#4797C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#81546C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#893C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×D3×C4⋊C4—21no—
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#890C2211yescharacteristic
38C3×#884—21no—
39C3×#884—21no—
40C3×#883—21no—
41C3×#883—21no—
42C3×#876—21no—
43C3×C4×D12—21no—
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5631C2×C311yescharacteristic, complemented
64#5530C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—21no—
67C3×#485D311yescharacteristic, complemented
68C3×#485C2×C311yescharacteristic, complemented
69C3×#483—31no—
70C3×#478—31no—
71C3×#468—31no—
72C3×#465—31no—
73C3×#461—31no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#442—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5048C2×C311yescharacteristic, complemented
81#5002C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4886C2×C311yescharacteristic, complemented
84#4869C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4818C2×C311yescharacteristic, complemented
87#4810C2×C311yescharacteristic, complemented
88#4803C2×C311yescharacteristic, complemented
89#4797C2×C311yescharacteristic, complemented
90#4734C2×C311yescharacteristic, complemented
91#4730C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C3×#239—22no—
98C3×#239—41no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C42—21no—
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×#204—41no—
143C3×ΓL(1,𝔽25)—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×#126—61no—
156C3×#125—31no—
157C3×#123—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8C2×D311yescharacteristic
163C3×C22⋊Q8C22×C311yescharacteristic
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121—61no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×#117—21no—
173C3×#117C2×D311yescharacteristic
174C3×#117C22×C311yescharacteristic
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—61no—
177#944C22×C311yescharacteristic
178C2×#215C22×C311yescharacteristic
179#930C22×C311yescharacteristic
180C4×#67C22×C311yescharacteristic
181C22×C3⋊C8C22×C311yescharacteristic
182C2×D24C22×C311yescharacteristic
183C2×#204C22×C311yescharacteristic
184C2×ΓL(1,𝔽25)C22×C311yescharacteristic
185#897C22×C311yescharacteristic
186#895C22×C311yescharacteristic
187#894—21no—
188#893C22×C311yescharacteristic
189#893C22×C311yescharacteristic
190D3×C4⋊C4—21no—
191D3×C4⋊C4C22×C311yescharacteristic
192#890C22×C311yescharacteristic
193#884—21no—
194#884—21no—
195#883—21no—
196#883—21no—
197#876—21no—
198C4×D12—21no—
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic
201C3×#107C22×C311yescharacteristic
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103C2×D311yescharacteristic
214C3×#103C2×D311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×#97—31no—
226#835C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#815C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—41no—
253C3×#67—42no—
254C3×#67—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—42no—
264C3×D12—42no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491—31no—
282#485C3×D311yescharacteristic, complemented
283#483—31no—
284#478—31no—
285#468—31no—
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67C3×D411yescharacteristic
321#239—22no—
322#239—41no—
323#235—22no—
324#235—41no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12C23×C311yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3C23×C311yescharacteristic
335C2×Dic6C23×C311yescharacteristic
336C3×SD16—121no—
337C3×SD16—121no—
338C3×D8—62no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42—31no—
385C3×C42—41no—
386#217C3×D411yescharacteristic
387#215—41no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4C3×D411yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3C23×C311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4C3×D411yescharacteristic
402C4×Dic3C23×C311yescharacteristic
403C2×C3⋊C8—41no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406D24—22no—
407#204—41no—
408ΓL(1,𝔽25)—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—31no—
436C2×SD16—31no—
437C2×SD16—31no—
438C2×D8—31no—
439C2×M16—31no—
440C22×C8—31no—
441C4⋊Q8—31no—
442#126—61no—
443#125—31no—
444#123—61no—
445#123—61no—
446#123—61no—
447C22⋊Q8—31no—
448C22⋊Q8C2×C3×D311yescharacteristic
449#121—31no—
450#121—31no—
451#121—61no—
452#121—61no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457#117C2×C3×D311yescharacteristic
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460#107C2×C3×D311yescharacteristic
461#106—31no—
462#106C2×C3×D311yescharacteristic
463C4⋊C8—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474C22⋊C8—31no—
475C22⋊C8C2×C3×D311yescharacteristic
476#97—31no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×C3×D411yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3C2×C3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—32no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C3×D4—122no—
500C3×D4—121no—
501C3×D4—122no—
502C3×D4—241no—
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—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4—122no—
533C2×C3×C4—241no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—41no—
540#67—42no—
541#67—81no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546C2×Dic3C2×C3×D411yescharacteristic
547D12—21no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12—42no—
552D12C3×#4112yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—42no—
556C4×D3—42no—
557C4×D3—42no—
558C4×D3—81no—
559C4×D3—81no—
560Dic6—21no—
561Dic6—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—41no—
573C2×C32#54611yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—41no—
577C3×D3—42no—
578C3×D3—81no—
579#41—62no—
580#41—62no—
581#41—121no—
582#41—121no—
583C2×Q8—31no—
584C2×Q8C22×C3×D311yescharacteristic
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4C22×C3×D311yescharacteristic
599SD16—121no—
600SD16—121no—
601D8—62no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—121no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4C22×C3×D311yescharacteristic
618C4⋊C4C22×C3×D311yescharacteristic
619C4⋊C4C22×C3×D311yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C42—21no—
630C42—31no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685C3×C4C2×C3×#4111yescharacteristic
686C3×C4C3×H(5,𝔽2)11yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692C32#330711yescharacteristic, complemented, Sylow
693C23—31no—
694C23—61no—
695C23—61no—
696C23C3×D3×D411yescharacteristic
697Q8—21no—
698Q8—21no—
699Q8—61no—
700Q8—61no—
701D4—32no—
702D4—61no—
703D4—61no—
704D4—61no—
705D4—122no—
706D4—122no—
707D4—121no—
708D4—122no—
709D4—241no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—241no—
727C2×C4—241no—
728C2×C4C3×D3×D411yescharacteristic
729C2×C4C23×C3×D311yescharacteristic
730C8—21no—
731C8—21no—
732C8—61no—
733C8—61no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—81no—
740C2×C3—121no—
741C2×C3—122no—
742C2×C3—241no—
743C2×C3#565411yescharacteristic
744C2×C3#576811yescharacteristic
745C2×C3#577811yescharacteristic
746C2×C3C3×#54611yescharacteristic
747C2×C3C3×#57511yescharacteristic
748C2×C3C3×#57711yescharacteristic
749D3—41no—
750D3—42no—
751D3—81no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—62no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22C2×C3×D3×D411yescharacteristic
765C4—21no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—61no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4C3×D3×#4111yescharacteristic
776C4C3×#100911yescharacteristic
777C3—21no—
778C3#8154611yescharacteristic, direct product factor
779C3C3×#330711yescharacteristic, complemented
780C2—41no—
781C2—121no—
782C2—122no—
783C2—241no—
784C2C3×#565411yescharacteristic
785C2C3×#576811yescharacteristic
786C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
hypercenterC3×#485D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
1. C3×#5631C2semidirect
2. C3×#5530C2semidirect
3. C32×#485C2semidirect
4. C3×#5048C2semidirect
5. C3×#5002C2semidirect
6. C3×#4891C2semidirect
7. C3×#4886C2semidirect
8. C3×#4869C2semidirect
9. C3×#4862C2semidirect
10. C3×#4818C2semidirect
11. C3×#4810C2semidirect
12. C3×#4803C2semidirect
13. C3×#4797C2semidirect
14. C3×#4734C2semidirect
15. C3×#4730C2semidirect
17. #81546C3direct (N × H)
63. #5631C2×C3semidirect
64. #5530C2×C3semidirect
67. C3×#485D3semidirect
68. C3×#485C2×C3semidirect
80. #5048C2×C3semidirect
81. #5002C2×C3semidirect
82. #4891C2×C3semidirect
83. #4886C2×C3semidirect
84. #4869C2×C3semidirect
85. #4862C2×C3semidirect
86. #4818C2×C3semidirect
87. #4810C2×C3semidirect
88. #4803C2×C3semidirect
89. #4797C2×C3semidirect
90. #4734C2×C3semidirect
91. #4730C2×C3semidirect
282. #485C3×D3semidirect
692. C32#3307semidirect
778. C3#81546direct (N × H)
779. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C3×#55302
C32×#4852
C3×#50482
C3×#50022
C3×#48912
C3×#48862
C3×#48692
C3×#48622
C3×#48182
C3×#48102
C3×#48032
C3×#47972
C3×#47342
C3×#47302
C3×#33073
#815463