Finite Group Databasebeta

← #11860751

Subgroups — #11860751

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic
3#10593994C211yesmaximal, characteristic
4C4×#3755C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic, complemented
6#10591566C211yesmaximal, characteristic, complemented
7#10591557C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic
10#10590571C211yesmaximal, characteristic, complemented
11#10590457C211yesmaximal, characteristic, complemented
12#10590453C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#82548—31nomaximal
17#79777—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×#892—21no—
26C3×#892C2211yescharacteristic
27C3×#887—21no—
28C3×#887C2211yescharacteristic, complemented
29C3×C4×D12C2211yescharacteristic
30C3×#872—21no—
31C3×#872C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic, complemented
34D3×#215C418yescomplemented
35#63921—21no—
36D3×(C2×D3)⋊C4—21no—
37#63904—21no—
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63881—21no—
41#63841C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic, complemented
49C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×#519—31no—
63C22×#215—31no—
64C2×D3×SD16—31no—
65#5572D311yescharacteristic, complemented
66#5545—31no—
67#5521—31no—
68C3×#440—31no—
69#5225—31no—
70#5164—31no—
71#5026—31no—
72#5026—31no—
73#5026—31no—
74#5026D311yescharacteristic, complemented
75C4×#215—31no—
76C4×#215—31no—
77C4×#215—31no—
78C4×#215—31no—
79C4×#215—31no—
80C4×#215—61no—
81C4×#214—31no—
82#5001—31no—
83#4998—31no—
84#4997—31no—
85#4889—31no—
86#4880—31no—
87#4802—31no—
88#4788—31no—
89#4770—31no—
90#4758—31no—
91#4710—31no—
92#4708—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12C2×C414yes—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3755C2×C414yescomplemented
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215C2×C414yescomplemented
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3715C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2949—91noSylow
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×D3×D4—31no—
150C22×D12—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×Q8—61no—
158C3×C4×Q8C2×D311yescharacteristic, complemented
159C3×C4×Q8C2×D311yescharacteristic, complemented
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—31no—
163C3×#117—61no—
164C3×#117—61no—
165Q8×Dic3C2×D311yescharacteristic, complemented
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—38no—
170C2×#215—31no—
171C2×#215—61no—
172C2×#215C2×D311yescharacteristic
173D4×Dic3—31no—
174C2×#214—31no—
175C4×#67—61no—
176C2×(C2×D3)⋊C4—61no—
177#926—31no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180D3×SD16—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8—31no—
184#893—31no—
185#893—61no—
186#893—61no—
187#892—21no—
188#892—31no—
189#892C2×D311yescharacteristic
190#887—21no—
191#887C2×D311yescharacteristic, complemented
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201C4×D12C2×D311yescharacteristic
202#872—21no—
203#872C2×D311yescharacteristic
204C4×Dic6—21no—
205C4×Dic6C2×D311yescharacteristic, complemented
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic, complemented
216#832—31no—
217#821—31no—
218#818—31no—
219#816—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#807—31no—
235#807C2×D311yescharacteristic, complemented
236#803—31no—
237#803C2×D311yescharacteristic, complemented
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
245C2×D32—24no—
246C2×D32—81no—
247C2×D32—81no—
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C22×C412yes—
258C4×C3⋊D3—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—24no—
268C3×C4×D3—81no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6—24no—
273C3×Dic6C22×C412yes—
274#626—24no—
275#624—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—31no—
283#518—91no—
284#440—31no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—34no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311D3×Q8—22no—
312D3×Q8C4×D314yescomplemented
313D3×D4—34no—
314D3×D4—62no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—34no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42—41no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364#217—61no—
365#217—61no—
366#215—34no—
367#215—34no—
368#215—34no—
369#215—34no—
370#215—64no—
371#215C4×D314yescomplemented
372#214—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—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382(C2×D3)⋊C4#6711yescharacteristic
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4#6711yescharacteristic
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—21no—
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
411#204—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—
424D32—84no—
425C32×C4—21no—
426C32×C4—22no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4C23×C411yescharacteristic
430C32×C4C2×#4111yescharacteristic
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—31no—
439C22×D4—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×SD16—98no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—91no—
446C22×C8—91no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×Q8—61no—
451C4×Q8—61no—
452C4×Q8D3211yescharacteristic, complemented
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458C4×D4—181no—
459#117—31no—
460#117—31no—
461#117—61no—
462#117—61no—
463#117—91no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—91no—
469#106—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—31no—
479#97—91no—
480C4×C8—91no—
481C4×C8—91no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—64no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—64no—
489C22×D3—121no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3C2×#6711yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—22no—
498C3×Q8—32no—
499C3×Q8—41no—
500C3×Q8—64no—
501C3×Q8—61no—
502C3×Q8C2×C4×D312yes—
503C3×Q8C2×C4×D312yes—
504C3×D4—32no—
505C3×D4—61no—
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—31no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—64no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—64no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—241no—
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—21no—
543D12—32no—
544D12—32no—
545D12—62no—
546D12—64no—
547D12—61no—
548D12—61no—
549D12—121no—
550D12C2×C4×D312yes—
551C4×D3—24no—
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—
562Dic6—24no—
563Dic6C2×C4×D312yes—
564C3×C8—32no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—32no—
568C3⋊C8—32no—
569C3⋊C8—62no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8C2×C4×D312yes—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—42no—
578C3×D3—22no—
579C3×D3—42no—
580C24—181no—
581C2×Q8—34no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×Q8—62no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C2×D4—94no—
588C2×D4—91no—
589C2×D4—182no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—34no—
598SD16—94no—
599SD16—94no—
600SD16—94no—
601M16—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8—91no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—21no—
626C42—31no—
627C42—61no—
628C42—61no—
629C42—61no—
630C42—61no—
631C42—181no—
632C42C2×D3211yescharacteristic
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—244no—
657C2×D3—244no—
658C2×D3C4×#6712yes—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—62no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C22×C4×D311yescharacteristic
680C3×C4C22×C4×D311yescharacteristic
681C3×C4C2×#23511yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—22no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3C4×#6712yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—31no—
694C23—61no—
695C23—184no—
696C23—181no—
697C23—721no—
698C23—721no—
699Q8—21no—
700Q8—32no—
701Q8—64no—
702Q8—61no—
703Q8C4×D3212yes—
704D4—32no—
705D4—61no—
706D4—92no—
707D4—184no—
708D4—181no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—31no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—64no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—181no—
721C2×C4—241no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4D3×#6711yescharacteristic
726C2×C4D3×#6711yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—32no—
729C8—61no—
730C8—92no—
731C8—181no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—62no—
736C2×C3—122no—
737C2×C3C4×D3×D411yescharacteristic
738C2×C3#577511yescharacteristic
739C2×C3#577811yescharacteristic
740C2×C3C2×C4×#6711yescharacteristic
741C2×C3#583711yescharacteristic
742C2×C3#583711yescharacteristic
743D3—22no—
744D3—42no—
745D3—122no—
746D3—122no—
747D3—242no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—361no—
756C22—361no—
757C22—724no—
758C22C2×D3×#6711yescharacteristic
759C4—21no—
760C4—22no—
761C4—21no—
762C4—32no—
763C4—41no—
764C4—61no—
765C4—62no—
766C4—61no—
767C4—121no—
768C4—121no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23511yescharacteristic
772C3—21no—
773C3#7977711yescharacteristic, complemented
774C3#8254811yescharacteristic, complemented
775C2—62no—
776C2—122no—
777C2—362no—
778C2C4×D3×#6711yescharacteristic
779C2#1059531911yescharacteristic
780C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2949
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×#5572C2semidirect
4. C4×#3755C2semidirect
5. C3×#5026C2semidirect
6. #10591566C2semidirect
7. #10591557C2semidirect
8. #10591536C2semidirect
10. #10590571C2semidirect
11. #10590457C2semidirect
12. #10590453C2semidirect
13. #10590362C2semidirect
14. C4×#3715C2semidirect
15. #10590319C2semidirect
20. C32×C4×Q8C22semidirect
23. C3×Q8×Dic3C22semidirect
28. C3×#887C22semidirect
33. C3×C4×Dic6C22semidirect
34. D3×#215C4semidirect
46. #63662C22semidirect
48. #63635C22semidirect
49. C4×C3⋊(C3⋊C8)C22semidirect
50. C3×#835C22semidirect
52. C3×#807C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
65. #5572D3semidirect
74. #5026D3semidirect
98. C3×D3×Q8C2×C4semidirect
114. #3755C2×C4semidirect
119. C3×#215C2×C4semidirect
142. #3717C2×C4semidirect
143. #3715C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
158. C3×C4×Q8C2×D3semidirect
159. C3×C4×Q8C2×D3semidirect
165. Q8×Dic3C2×D3semidirect
191. #887C2×D3semidirect
205. C4×Dic6C2×D3semidirect
215. #835C2×D3semidirect
235. #807C2×D3semidirect
237. #803C2×D3semidirect
312. D3×Q8C4×D3semidirect
371. #215C4×D3semidirect
452. C4×Q8D32semidirect
692. C32#2949semidirect
773. C3#79777semidirect
774. C3#82548semidirect

Maximal subgroups

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

subgroupindex
C3×#55722
C2×D3×#2152
#105939942
C4×#37552
C3×#50262
#105915662
#105915572
#105915362
#105905922
#105905712
#105904572
#105904532
#105903622
C4×#37152
#105903192
#825483
#797773