Finite Group Databasebeta

← #11860947

Subgroups — #11860947

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic
3#10593890C211yesmaximal, characteristic, complemented
4C4×#3755C211yesmaximal, characteristic, complemented
5C3×#5030C211yesmaximal, characteristic, complemented
6#10591576C211yesmaximal, characteristic, complemented
7#10591550C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic, complemented
10#10590589C211yesmaximal, characteristic, complemented
11D3×#808C211yesmaximal, characteristic, complemented
12#10590475C211yesmaximal, characteristic, complemented
13C4×#3715C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#82558—31nomaximal
17#79832—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4—21no—
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63949C418yescomplemented
35#63894C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63883—21no—
38#63881—21no—
39#63880—21no—
40Dic3×Dic6C2211yescharacteristic
41#63836—21no—
42C2×#3715C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×#520—31no—
63C2×#950—31no—
64C2×#919—31no—
65#5574—31no—
66#5574D311yescharacteristic, complemented
67#5523—31no—
68C3×#441—31no—
69#5232—31no—
70#5184—31no—
71#5030—31no—
72#5030D311yescharacteristic, complemented
73C4×#215—31no—
74C4×#215—31no—
75C4×#215—31no—
76C4×#215—31no—
77C4×#215—61no—
78C4×#214—31no—
79C4×#214—31no—
80#5014—31no—
81#5014—31no—
82#4997—31no—
83#4966—31no—
84C2×#808—31no—
85#4869—31no—
86D3×#106—31no—
87#4803—31no—
88#4803—31no—
89#4788—31no—
90#4788—31no—
91#4711—31no—
92#4708—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×#239—22no—
97C3×#239C2×C414yescomplemented
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3755C2×C414yescomplemented
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3715C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#239—31no—
149C2×#239C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—61no—
165#950—38no—
166Q8×Dic3—31no—
167Q8×Dic3C2×D311yescharacteristic
168C2×#216C2×D311yescharacteristic
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#214—31no—
174C2×#213—31no—
175C2×C4⋊Dic3—31no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178#919—38no—
179C2×D24—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#893—21no—
183#893—31no—
184#893—61no—
185#893C2×D311yescharacteristic
186#892—61no—
187D3×C4⋊C4—21no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4C2×D311yescharacteristic
192#67⋊C4—61no—
193#67⋊C4—61no—
194C4×D12—21no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199C4×D12—61no—
200C4×D12C2×D311yescharacteristic
201#872—21no—
202#872—61no—
203#872C2×D311yescharacteristic
204C4×Dic6—31no—
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#832—31no—
217#821—31no—
218#821—31no—
219#817—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic
236#803—31no—
237#803C2×D311yescharacteristic
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—24no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×C4×D3—24no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#626—24no—
274#624—24no—
275#624—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—31no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—31no—
287#441—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311#239—22no—
312#239—34no—
313#239—62no—
314#239C4×D314yescomplemented
315#235—34no—
316#235—62no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—34no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—31no—
361C3×C42—41no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42C22×D311yescharacteristic
365C3×C42C22×D311yescharacteristic
366#216C4×D314yescomplemented
367#215—34no—
368#215—34no—
369#215—34no—
370#215—64no—
371#214—34no—
372#213—34no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380(C2×D3)⋊C4#6711yescharacteristic
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4#6711yescharacteristic
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401#208—62no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—34no—
412ΓL(1,𝔽25)—62no—
413D3×C8—34no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—21no—
425C32×C4—22no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8D3211yescharacteristic
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458#117—31no—
459#117—61no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—61no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#97—31no—
478#97—91no—
479C4×C8—91no—
480C4×C8—91no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3C2×#6711yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C2×C4×D312yes—
496C3×D4—32no—
497C3×D4—64no—
498C3×D4—61no—
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—31no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—64no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—64no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—241no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537D12—24no—
538D12—21no—
539D12—32no—
540D12—32no—
541D12—62no—
542D12—64no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12C2×C4×D312yes—
547C4×D3—24no—
548C4×D3—64no—
549C4×D3—64no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3—81no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—242no—
559C4×D3C2×C4×D312yes—
560C4×D3#23512yes—
561Dic6—21no—
562Dic6C2×C4×D312yes—
563C3×C8—32no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—32no—
567C3⋊C8—32no—
568C3⋊C8—62no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8C2×C4×D312yes—
573C2×C32C2×C4×D411yescharacteristic
574C2×C32#57711yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—42no—
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—34no—
599SD16—94no—
600SD16—94no—
601D8—94no—
602M16—182no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—94no—
606C2×C8—91no—
607C2×C8—91no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—21no—
627C42—31no—
628C42—61no—
629C42—61no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3C4×#6712yes—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—32no—
666C3×C4—41no—
667C3×C4—42no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C22×C4×D311yescharacteristic
677C3×C4C22×C4×D311yescharacteristic
678C3×C4C2×#23511yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—22no—
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3C4×#6712yes—
689C32#295211yescharacteristic, complemented, Sylow
690C23—31no—
691C23—61no—
692C23—181no—
693Q8—21no—
694Q8—32no—
695Q8—61no—
696Q8C4×D3212yes—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—92no—
701D4—184no—
702D4—181no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—64no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—184no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4D3×#6711yescharacteristic
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—32no—
726C8—61no—
727C8—92no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—62no—
733C2×C3—122no—
734C2×C3C4×D3×D411yescharacteristic
735C2×C3#577811yescharacteristic
736C2×C3#577811yescharacteristic
737C2×C3C2×C4×#6711yescharacteristic
738C2×C3#583611yescharacteristic
739C2×C3#583711yescharacteristic
740D3—22no—
741D3—42no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—22no—
757C4—21no—
758C4—32no—
759C4—41no—
760C4—61no—
761C4—62no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—361no—
766C4C2×C4×D3211yescharacteristic
767C4D3×#23511yescharacteristic
768C3—21no—
769C3#7983211yescharacteristic, complemented
770C3#8255811yescharacteristic, complemented
771C2—62no—
772C2—122no—
773C2—362no—
774C2C4×D3×#6711yescharacteristic
775C2#1059531911yescharacteristic
776C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63949C2
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5574C2semidirect
3. #10593890C2semidirect
4. C4×#3755C2semidirect
5. C3×#5030C2semidirect
6. #10591576C2semidirect
7. #10591550C2semidirect
8. #10591536C2semidirect
9. #10590609C2semidirect
10. #10590589C2semidirect
11. D3×#808C2semidirect
12. #10590475C2semidirect
13. C4×#3715C2semidirect
14. #10590346C2semidirect
15. #10590319C2semidirect
34. #63949C4semidirect
66. #5574D3semidirect
72. #5030D3semidirect
97. C3×#239C2×C4semidirect
111. #3799C2×C4semidirect
116. #3755C2×C4semidirect
121. C3×#216C2×C4semidirect
142. #3715C2×C4semidirect
143. #3714C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
314. #239C4×D3semidirect
366. #216C4×D3semidirect
689. C32#2952semidirect
769. C3#79832semidirect
770. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
C2×#639492
#105938902
C4×#37552
C3×#50302
#105915762
#105915502
#105915362
#105906092
#105905892
D3×#8082
#105904752
C4×#37152
#105903462
#105903192
#825583
#798323