Finite Group Databasebeta

← C3×#80196 #11889325

Subgroups — C3×#80196 #11889325

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2C3×#5639C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7C3×#5184C211yesmaximal, characteristic, complemented
8C3×#5182C211yesmaximal, characteristic, complemented
9C3×#5052C211yesmaximal, characteristic, complemented
10C3×#4805C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4797C211yesmaximal, characteristic, complemented
13C3×#4796C211yesmaximal, characteristic, complemented
14C3×#4728C211yesmaximal, characteristic
15C3×#4723C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#80196C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C3×#946—21no—
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×#944—21no—
29C3×#944C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C3×C4×#67—21no—
32C3×C4×#67C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#924—21no—
35C3×#924C2211yescharacteristic
36C2×C3×#208C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#892—21no—
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#890C2211yescharacteristic
41C3×#889—21no—
42C3×#883—21no—
43C3×#879—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#815C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63Q8×#67C2×C311yescharacteristic
64#5639C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#451—21no—
73C3×#451—31no—
74C3×#451D311yescharacteristic, complemented
75C3×#451C2×C311yescharacteristic, complemented
76C3×#441—31no—
77C3×#435—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5225C2×C311yescharacteristic, complemented
81#5188C2×C311yescharacteristic, complemented
82#5186C2×C311yescharacteristic, complemented
83#5184C2×C311yescharacteristic, complemented
84#5182C2×C311yescharacteristic, complemented
85#5052C2×C311yescharacteristic, complemented
86#4805C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4797C2×C311yescharacteristic, complemented
89#4796C2×C311yescharacteristic, complemented
90#4728C2×C311yescharacteristic
91#4723C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×Q16—22no—
109C32×Q16—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#216—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C3×#208—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C22×C311yescharacteristic
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×Q16—21no—
151C2×C3×Q16—21no—
152C2×C3×Q16—31no—
153C2×C3×Q16C2×D311yescharacteristic
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×Q16C22×C311yescharacteristic
157C2×C3×M16—31no—
158C22×C3×C8—31no—
159C3×C4⋊Q8—31no—
160C3×C4⋊Q8—61no—
161C3×#126—61no—
162C3×#125—31no—
163C3×#125—61no—
164C3×#123—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C4×Q8—31no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180#946—21no—
181#946C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183Q8×Dic3C22×C311yescharacteristic
184Q8×Dic3C22×C311yescharacteristic
185#944—21no—
186#944C22×C311yescharacteristic
187C2×#216C22×C311yescharacteristic
188C4×#67—21no—
189C4×#67C22×C311yescharacteristic
190#926C22×C311yescharacteristic
191#924—21no—
192#924C22×C311yescharacteristic
193C2×#208C22×C311yescharacteristic
194C2×D3×C8C22×C311yescharacteristic
195#892—21no—
196D3×C4⋊C4C22×C311yescharacteristic
197#890C22×C311yescharacteristic
198#889—21no—
199#883—21no—
200#879—21no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103C2×D311yescharacteristic
216C3×#103C2×D311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×#97—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#818C22×C311yescharacteristic
231#817C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#815C22×C311yescharacteristic
235Dic3⋊C8C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—42no—
246C32×Q8#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
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#462—31no—
284#451—31no—
285#451C3×D311yescharacteristic, complemented
286#441—31no—
287#435—31no—
288#419—31no—
289C2×#103—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—41no—
299C2×C3×Q8—42no—
300C2×C3×Q8—41no—
301C2×C3×Q8—41no—
302C2×C3×Q8—42no—
303C2×C3×Q8—61no—
304C2×C3×Q8—62no—
305C2×C3×Q8—121no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C23×C311yescharacteristic
310C2×C3×Q8C23×C311yescharacteristic
311C2×C3×Q8C23×C311yescharacteristic
312C2×C3×D4—31no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67C3×D411yescharacteristic
323D3×Q8—22no—
324D3×Q8—41no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3C23×C311yescharacteristic
328C2×Dic6—21no—
329C2×Dic6C23×C311yescharacteristic
330C3×Q16—22no—
331C3×Q16—22no—
332C3×Q16—42no—
333C3×Q16—41no—
334C3×Q16—41no—
335C3×Q16—42no—
336C3×Q16—121no—
337C3×M16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—41no—
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⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—41no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—31no—
377C3×C42—61no—
378C3×C42—61no—
379C3×C42—61no—
380#217—21no—
381#217—21no—
382#217C3×D411yescharacteristic
383#216—41no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
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⋊C4C3×D411yescharacteristic
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3C23×C311yescharacteristic
405#208—41no—
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13712yes—
416C32×C4—22no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C22×Q8C2×C3×D311yescharacteristic
432C2×Q16—31no—
433C2×Q16C2×C3×D311yescharacteristic
434C2×Q16C2×C3×D311yescharacteristic
435C2×M16—31no—
436C22×C8—31no—
437C4⋊Q8—31no—
438C4⋊Q8—61no—
439#126—61no—
440#125—31no—
441#125—61no—
442#123—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448C22⋊Q8C2×C3×D311yescharacteristic
449C4×Q8—31no—
450C4×Q8—31no—
451C4×D4—31no—
452C4×D4—61no—
453#117—31no—
454#117—61no—
455C2×C4⋊C4—31no—
456#107—31no—
457#106—31no—
458#106—31no—
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470C22⋊C8—31no—
471C22⋊C8C2×C3×D311yescharacteristic
472#97—31no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×C3×D411yescharacteristic
477C22×D3C2×C3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
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—22no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—42no—
495C3×Q8—42no—
496C3×Q8—44no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—122no—
500C3×Q8#23712yes—
501C3×Q8C3×#4112yes—
502C3×D4—62no—
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—42no—
527C2×C3×C4—42no—
528C2×C3×C4—44no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—122no—
536C2×C3×C4—122no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C24×C311yescharacteristic
541#67—22no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—42no—
553Dic6—21no—
554Dic6—21no—
555Dic6—42no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—41no—
567C2×C32#54611yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57811yescharacteristic
570C3×D3—22no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—31no—
574C2×Q8—41no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—121no—
578C2×Q8C22×C3×D311yescharacteristic
579C2×Q8C22×C3×D311yescharacteristic
580C2×Q8C22×C3×D311yescharacteristic
581C2×D4—31no—
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4C22×C3×D311yescharacteristic
587Q16—22no—
588Q16—41no—
589Q16—121no—
590M16—121no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—121no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C4⋊C4—21no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
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—21no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42—61no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—32no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×C3×D411yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3C3×#13712yes—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—41no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23711yescharacteristic
666C3×C4#100411yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668C3×C4C3×H(5,𝔽2)11yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676C32#331211yescharacteristic, complemented, Sylow
677C23—31no—
678C23C3×D3×D411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—42no—
685Q8—61no—
686Q8—61no—
687Q8—122no—
688Q8C3×#23712yes—
689D4—62no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—42no—
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×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—21no—
711C8—21no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—62no—
721C2×C3#559111yescharacteristic
722C2×C3#576611yescharacteristic
723C2×C3D3×#13711yescharacteristic
724C2×C3C3×#54611yescharacteristic
725C2×C3C2×C3×#13711yescharacteristic
726C2×C3C3×#57811yescharacteristic
727D3—22no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—32no—
732C22—61no—
733C22—61no—
734C22C2×C3×D3×D411yescharacteristic
735C4—21no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—61no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4C2×C3×#23711yescharacteristic
748C4C3×#100411yescharacteristic
749C3—21no—
750C3#8019611yescharacteristic, direct product factor
751C3C3×#331211yescharacteristic, complemented
752C2—41no—
753C2—62no—
754C2C3×#559111yescharacteristic
755C2C3×#576611yescharacteristic
756C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#451D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
3. C32×#451C2semidirect
4. C3×#5225C2semidirect
5. C3×#5188C2semidirect
6. C3×#5186C2semidirect
7. C3×#5184C2semidirect
8. C3×#5182C2semidirect
9. C3×#5052C2semidirect
10. C3×#4805C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4797C2semidirect
13. C3×#4796C2semidirect
15. C3×#4723C2semidirect
17. #80196C3direct (N × H)
74. C3×#451D3semidirect
75. C3×#451C2×C3semidirect
80. #5225C2×C3semidirect
81. #5188C2×C3semidirect
82. #5186C2×C3semidirect
83. #5184C2×C3semidirect
84. #5182C2×C3semidirect
85. #5052C2×C3semidirect
86. #4805C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4797C2×C3semidirect
89. #4796C2×C3semidirect
91. #4723C2×C3semidirect
285. #451C3×D3semidirect
676. C32#3312semidirect
750. C3#80196direct (N × H)
751. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C3×#56392
C32×#4512
C3×#52252
C3×#51882
C3×#51862
C3×#51842
C3×#51822
C3×#50522
C3×#48052
C3×D3×#1032
C3×#47972
C3×#47962
C3×#47282
C3×#47232
C3×#33123
#801963