Finite Group Databasebeta

← C3×#80915 #11889331

Subgroups — C3×#80915 #11889331

Order 1152.

807 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5639C211yesmaximal, characteristic
2C3×#5632C211yesmaximal, characteristic
3C32×#470C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic
7C3×#5120C211yesmaximal, characteristic, complemented
8C3×#5050C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4862C211yesmaximal, characteristic, complemented
11C3×#4857C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×#4797C211yesmaximal, characteristic, complemented
15C3×#4789C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#80915C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#896—21no—
34C3×#892—21no—
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#890C2211yescharacteristic
37C3×#889—21no—
38C3×#888—21no—
39C3×#887C2211yescharacteristic
40C3×#883—21no—
41C3×#67⋊C4—21no—
42C3×#879—21no—
43C3×#878—21no—
44C32×#106C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5639C2×C311yescharacteristic
64#5632C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#470—21no—
70C3×#470D311yescharacteristic, complemented
71C3×#470C2×C311yescharacteristic, complemented
72C3×#467—31no—
73C3×#462—31no—
74C3×#451—31no—
75C3×#451—31no—
76C3×#441—31no—
77C3×#435—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5186C2×C311yescharacteristic, complemented
81#5182C2×C311yescharacteristic, complemented
82#5127C2×C311yescharacteristic
83#5120C2×C311yescharacteristic, complemented
84#5050C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4862C2×C311yescharacteristic, complemented
87#4857C2×C311yescharacteristic, complemented
88#4813C2×C311yescharacteristic, complemented
89D3×#103C2×C311yescharacteristic, complemented
90#4797C2×C311yescharacteristic, complemented
91#4789C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—41no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—22no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—41no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C32×Q16—41no—
109C32×M16—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—22no—
121C3×#216—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
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⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C22×C311yescharacteristic
154C2×C3×M16—21no—
155C2×C3×M16C2×D311yescharacteristic
156C2×C3×M16C22×C311yescharacteristic
157C22×C3×C8—31no—
158C3×C4⋊Q8—31no—
159C3×C4⋊Q8—61no—
160C3×#126—61no—
161C3×#125—31no—
162C3×#125—61no—
163C3×#123—61no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C22⋊Q8C22×C311yescharacteristic
174C3×C4×Q8—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C3×#117—61no—
180C2×C3×C4⋊C4—31no—
181#946C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic
183#944C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185C2×#216C22×C311yescharacteristic
186C4×#67C22×C311yescharacteristic
187#926C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic
189#897C22×C311yescharacteristic
190#896—21no—
191#892—21no—
192D3×C4⋊C4C22×C311yescharacteristic
193#890C22×C311yescharacteristic
194#889—21no—
195#888—21no—
196#887C22×C311yescharacteristic
197#883—21no—
198#67⋊C4—21no—
199#879—21no—
200#878—21no—
201C3×#107—31no—
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×#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#830C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#815C22×C311yescharacteristic
233Dic3⋊C8C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
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—22no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
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#470C3×D311yescharacteristic, complemented
282#467—31no—
283#462—31no—
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—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C2×#67C3×D411yescharacteristic
313C22×Dic3—21no—
314D3×Q8—22no—
315D3×Q8—41no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3C23×C311yescharacteristic
319C2×Dic6—22no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—41no—
323C2×Dic6C23×C311yescharacteristic
324C2×Dic6C23×C311yescharacteristic
325C3×Q16—41no—
326C3×Q16—41no—
327C3×Q16—42no—
328C3×Q16—62no—
329C3×Q16—121no—
330C3×M16—41no—
331C3×M16—41no—
332C3×M16—42no—
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—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—41no—
373C3×C22⋊C4—41no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42—61no—
381#217—21no—
382#217C3×D411yescharacteristic
383#216—22no—
384#216—41no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4C3×D411yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
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⋊C4C3×D411yescharacteristic
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406D3×C8—41no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3#13712yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3×Dic3—22no—
422C3×Dic3—21no—
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×Q16—31no—
432C2×Q16C2×C3×D311yescharacteristic
433C2×M16C2×C3×D311yescharacteristic
434C22×C8—31no—
435C4⋊Q8—31no—
436C4⋊Q8—61no—
437#126—61no—
438#125—31no—
439#125—61no—
440#123—61no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444C22⋊Q8—61no—
445C22⋊Q8C2×C3×D311yescharacteristic
446C22⋊Q8C2×C3×D311yescharacteristic
447C4×Q8—31no—
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4—61no—
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454#107—31no—
455#106—31no—
456#106C2×C3×D311yescharacteristic
457C4⋊C8—31no—
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—21no—
472C23×C3—31no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×C3×D411yescharacteristic
475C22×D3C2×C3×D411yescharacteristic
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—32no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—122no—
493C3×Q8—122no—
494C3×D4—62no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
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—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67—22no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—42no—
537C2×Dic3C2×C3×D411yescharacteristic
538C2×Dic3C2×C3×D411yescharacteristic
539C2×Dic3C2×C3×D411yescharacteristic
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—42no—
543C4×D3—42no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—42no—
548Dic6—42no—
549Dic6C3×#4112yes—
550C3×C8—22no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C2×C32—41no—
561C2×C32#54611yescharacteristic
562C2×C32C2×#13711yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—22no—
565C2×Q8—31no—
566C2×Q8—31no—
567C2×Q8—61no—
568C2×Q8—62no—
569C2×Q8—61no—
570C2×Q8—62no—
571C2×Q8—121no—
572C2×Q8—121no—
573C2×Q8C22×C3×D311yescharacteristic
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—31no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4C22×C3×D311yescharacteristic
581Q16—41no—
582Q16—62no—
583Q16—121no—
584M16—41no—
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—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4C22×C3×D311yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C42—31no—
614C42—61no—
615C42—61no—
616C42—61no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C22×C3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3C3×#13712yes—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—62no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4#100411yescharacteristic
660C3×C4D3×#4111yescharacteristic
661C3×C4C2×C3×#4111yescharacteristic
662C3×C4C3×H(5,𝔽2)11yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—22no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670C32#331211yescharacteristic, complemented, Sylow
671C23—31no—
672C23C3×D3×D411yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—21no—
677Q8—32no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—122no—
682Q8—122no—
683D4—62no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4C3×D3×D411yescharacteristic
703C2×C4C23×C3×D311yescharacteristic
704C8—21no—
705C8—21no—
706C8—61no—
707C8—61no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—62no—
714C2×C3—81no—
715C2×C3#561011yescharacteristic
716C2×C3D3×#13711yescharacteristic
717C2×C3#577911yescharacteristic
718C2×C3C3×#54611yescharacteristic
719C2×C3C2×C3×#13711yescharacteristic
720C2×C3C3×#57811yescharacteristic
721D3—22no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22C2×C3×D3×D411yescharacteristic
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4C3×#100411yescharacteristic
742C4C3×D3×#4111yescharacteristic
743C3—21no—
744C3#8091511yescharacteristic, direct product factor
745C3C3×#331211yescharacteristic, complemented
746C2—41no—
747C2—62no—
748C2C3×#561011yescharacteristic
749C2C3×D3×#13711yescharacteristic
750C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#470D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
3. C32×#470C2semidirect
4. C3×#5186C2semidirect
5. C3×#5182C2semidirect
7. C3×#5120C2semidirect
8. C3×#5050C2semidirect
9. C3×#5045C2semidirect
10. C3×#4862C2semidirect
11. C3×#4857C2semidirect
12. C3×#4813C2semidirect
13. C3×D3×#103C2semidirect
14. C3×#4797C2semidirect
15. C3×#4789C2semidirect
17. #80915C3direct (N × H)
70. C3×#470D3semidirect
71. C3×#470C2×C3semidirect
80. #5186C2×C3semidirect
81. #5182C2×C3semidirect
83. #5120C2×C3semidirect
84. #5050C2×C3semidirect
85. #5045C2×C3semidirect
86. #4862C2×C3semidirect
87. #4857C2×C3semidirect
88. #4813C2×C3semidirect
89. D3×#103C2×C3semidirect
90. #4797C2×C3semidirect
91. #4789C2×C3semidirect
281. #470C3×D3semidirect
670. C32#3312semidirect
744. C3#80915direct (N × H)
745. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×#56392
C3×#56322
C32×#4702
C3×#51862
C3×#51822
C3×#51272
C3×#51202
C3×#50502
C3×#50452
C3×#48622
C3×#48572
C3×#48132
C3×D3×#1032
C3×#47972
C3×#47892
C3×#33123
#809153