Finite Group Databasebeta

← C3×#80776 #11888003

Subgroups — C3×#80776 #11888003

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5641C211yesmaximal, characteristic, complemented
2C3×#5631C211yesmaximal, characteristic
3C32×#467C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C3×C8×#67C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4890C211yesmaximal, characteristic, complemented
11C3×#4888C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4792C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3302—31nomaximal
17#80776C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic
32C3×#898—21no—
33C3×#897C2211yescharacteristic
34C3×#894—21no—
35C3×#893C2211yescharacteristic
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4—21no—
38C3×#888C2211yescharacteristic
39C3×#887—21no—
40C3×#885—21no—
41C3×#884—21no—
42C3×#883—21no—
43C3×#879—21no—
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#556—31no—
62C3×#547—31no—
63#5641C2×C311yescharacteristic, complemented
64#5631C2×C311yescharacteristic
65C3×#487—31no—
66C3×#485—31no—
67C3×#485—31no—
68C3×#474—31no—
69C3×#467—21no—
70C3×#467—31no—
71C3×#467D311yescharacteristic, complemented
72C3×#467C2×C311yescharacteristic, complemented
73C3×#462—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C3×#416—31no—
80#5187C2×C311yescharacteristic, complemented
81#5182C2×C311yescharacteristic, complemented
82#5113C2×C311yescharacteristic, complemented
83C8×#67C2×C311yescharacteristic, complemented
84#5047C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4890C2×C311yescharacteristic, complemented
87#4888C2×C311yescharacteristic, complemented
88#4813C2×C311yescharacteristic, complemented
89#4804C2×C311yescharacteristic, complemented
90#4792C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
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×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C32×Q16—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#216—41no—
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
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#3302—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C22×C311yescharacteristic
153C2×C3×SD16—31no—
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×C4⋊Q8—31no—
159C3×C4⋊Q8—31no—
160C3×#126—61no—
161C3×#126—61no—
162C3×#124—61no—
163C3×#123—61no—
164C3×#123—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C22×C311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×#121—61no—
174C3×C4×Q8—31no—
175C3×C4×Q8—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C3×#117—31no—
179C3×#117—31no—
180C2×C3×C4⋊C4—61no—
181#946C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic
183#944C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185C2×#215C22×C311yescharacteristic
186C4×#67C22×C311yescharacteristic
187#926C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic
189#898—21no—
190#897C22×C311yescharacteristic
191#894—21no—
192#893C22×C311yescharacteristic
193#892C22×C311yescharacteristic
194D3×C4⋊C4—21no—
195#888C22×C311yescharacteristic
196#887—21no—
197#885—21no—
198#884—21no—
199#883—21no—
200#879—21no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic
204C3×#107C22×C311yescharacteristic
205C3×#106—31no—
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×#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×C4×C8—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232Dic3⋊C8C22×C311yescharacteristic
233C8×Dic3C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C3×#67—22no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—42no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#547—31no—
278#487—31no—
279#485—31no—
280#485—31no—
281#474—31no—
282#467—31no—
283#467C3×D311yescharacteristic, complemented
284#462—31no—
285#452—31no—
286#452—31no—
287C4×SD16—31no—
288C8×D4—31no—
289#416—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—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C2×#67—21no—
315C2×#67C3×D411yescharacteristic
316#239—22no—
317#239—41no—
318#235—22no—
319#235—41no—
320C2×D12—21no—
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3C23×C311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—41no—
329C3×Q16—41no—
330C3×Q16—42no—
331C3×Q16—121no—
332C3×SD16—62no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—41no—
338C2×C3×C8—41no—
339C2×C3×C8—42no—
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—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
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⋊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×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42—61no—
383#217—21no—
384#217C3×D411yescharacteristic
385#216—41no—
386#215—22no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4C3×D411yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
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
405C2×C3⋊C8C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407D3×C8—41no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—21no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3#13512yes—
431C2×#41—31no—
432C2×#41—31no—
433C2×Q16—31no—
434C2×Q16C2×C3×D311yescharacteristic
435C2×SD16—31no—
436C22×C8—31no—
437C22×C8C2×C3×D311yescharacteristic
438C4⋊Q8—31no—
439C4⋊Q8—31no—
440#126—61no—
441#126—61no—
442#124—61no—
443#123—61no—
444#123—61no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8C2×C3×D311yescharacteristic
448C22⋊Q8C2×C3×D311yescharacteristic
449#121—61no—
450C4×Q8—31no—
451C4×Q8—61no—
452C4×D4—31no—
453C4×D4—31no—
454#117—31no—
455#117—31no—
456C2×C4⋊C4—61no—
457#107—31no—
458#107C2×C3×D311yescharacteristic
459#106—31no—
460C4⋊C8—31no—
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—
473C4×C8—31no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—61no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3—21no—
480C22×D3C2×C3×D411yescharacteristic
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—41no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—122no—
496C3×D4—32no—
497C3×D4—62no—
498C3×D4—61no—
499C3×D4—122no—
500C3×D4—122no—
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—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C24×C311yescharacteristic
536#67—22no—
537#67—42no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544D12—21no—
545D12—42no—
546D12C3×#4112yes—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3—42no—
552Dic6—21no—
553Dic6—21no—
554Dic6—42no—
555C3×C8—22no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32—41no—
566C2×C32#54611yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57811yescharacteristic
569C3×D3—41no—
570C3×D3—42no—
571#41—62no—
572#41—62no—
573#41—121no—
574#41—121no—
575C2×Q8—31no—
576C2×Q8—61no—
577C2×Q8C22×C3×D311yescharacteristic
578C2×Q8C22×C3×D311yescharacteristic
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4C22×C3×D311yescharacteristic
588Q16—41no—
589Q16—121no—
590SD16—62no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—41no—
594C2×C8—121no—
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C22×C3×D311yescharacteristic
609C4⋊C4C22×C3×D311yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
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—41no—
632C22×C3—41no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×C3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
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—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4#100411yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673C3×C4C3×H(5,𝔽2)11yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3C3×#13512yes—
680C32#330211yescharacteristic, complemented, Sylow
681C23—31no—
682C23—61no—
683C23C3×D3×D411yescharacteristic
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—61no—
689Q8—61no—
690Q8—122no—
691D4—32no—
692D4—62no—
693D4—61no—
694D4—122no—
695D4—122no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4C3×D3×D411yescharacteristic
714C2×C4C23×C3×D311yescharacteristic
715C8—21no—
716C8—21no—
717C8—61no—
718C8—61no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—121no—
726C2×C3—122no—
727C2×C3#561011yescharacteristic
728C2×C3#576611yescharacteristic
729C2×C3D3×#13511yescharacteristic
730C2×C3C3×#54611yescharacteristic
731C2×C3C2×C3×#13511yescharacteristic
732C2×C3C3×#57811yescharacteristic
733D3—41no—
734D3—42no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—62no—
742C22—121no—
743C22—121no—
744C22C2×C3×D3×D411yescharacteristic
745C4—21no—
746C4—32no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4C3×#100411yescharacteristic
757C4C3×D3×#4111yescharacteristic
758C3—21no—
759C3#8077611yescharacteristic, direct product factor
760C3C3×#330211yescharacteristic, complemented
761C2—41no—
762C2—121no—
763C2—122no—
764C2C3×#561011yescharacteristic
765C2C3×#576611yescharacteristic
766C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC3×#5631C2
hypercenterC3×#467D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
1. C3×#5641C2semidirect
3. C32×#467C2semidirect
4. C3×#5187C2semidirect
5. C3×#5182C2semidirect
6. C3×#5113C2semidirect
7. C3×C8×#67C2semidirect
8. C3×#5047C2semidirect
9. C3×#5045C2semidirect
10. C3×#4890C2semidirect
11. C3×#4888C2semidirect
12. C3×#4813C2semidirect
13. C3×#4804C2semidirect
14. C3×#4792C2semidirect
15. C3×#4788C2semidirect
17. #80776C3direct (N × H)
63. #5641C2×C3semidirect
71. C3×#467D3semidirect
72. C3×#467C2×C3semidirect
80. #5187C2×C3semidirect
81. #5182C2×C3semidirect
82. #5113C2×C3semidirect
83. C8×#67C2×C3semidirect
84. #5047C2×C3semidirect
85. #5045C2×C3semidirect
86. #4890C2×C3semidirect
87. #4888C2×C3semidirect
88. #4813C2×C3semidirect
89. #4804C2×C3semidirect
90. #4792C2×C3semidirect
91. #4788C2×C3semidirect
283. #467C3×D3semidirect
680. C32#3302semidirect
759. C3#80776direct (N × H)
760. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#56412
C3×#56312
C32×#4672
C3×#51872
C3×#51822
C3×#51132
C3×C8×#672
C3×#50472
C3×#50452
C3×#48902
C3×#48882
C3×#48132
C3×#48042
C3×#47922
C3×#47882
C3×#33023
#807763