Finite Group Databasebeta

← #11872163

Subgroups — #11872163

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596053C211yesmaximal, characteristic, complemented
2#10593996C211yesmaximal, characteristic, complemented
3C3×#5026C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591652C211yesmaximal, characteristic, complemented
6#10591570C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591561C211yesmaximal, characteristic, complemented
9#10590598C211yesmaximal, characteristic
10#10590472C211yesmaximal, characteristic, complemented
11#10590471C211yesmaximal, characteristic, complemented
12#10590451C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590298C211yesmaximal, characteristic, complemented
16#79785—31nomaximal
17#79696—31nomaximal
18C2×#3802C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic, complemented
20#64156C2211yescharacteristic, complemented
21#64155C2211yescharacteristic
22#64105—21no—
23#64104C2211yescharacteristic
24#64103—21no—
25#64097C2211yescharacteristic, complemented
26#64085—21no—
27#64084—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29#64081C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63879—21no—
39#63879—21no—
40#63849C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#835C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×#803C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5582—31no—
62#5582—31no—
63#5582—61no—
64#5545—31no—
65#5545—31no—
66C3×#440—31no—
67C3×C4×SD16—31no—
68#5169—31no—
69#5169—31no—
70#5165—31no—
71#5165—31no—
72#5026D311yescharacteristic, complemented
73C4×#215D311yescharacteristic, complemented
74#5014—31no—
75C4×#213—31no—
76#4890—31no—
77#4885—31no—
78#4870—31no—
79#4866—31no—
80#4819—31no—
81#4819—31no—
82#4815—31no—
83#4814—31no—
84#4773—31no—
85#4773—31no—
86#4761—31no—
87#4759—31no—
88#4711—31no—
89#4709—31no—
90C4×D24—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×#625—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—22no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122#3750D411yescharacteristic
123#3750D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#215—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4×Q8—21no—
147C3×C4×Q8C2×D311yescharacteristic, complemented
148C3×C4×Q8C2×D311yescharacteristic, complemented
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151#947—31no—
152#947—31no—
153#947—61no—
154#946—31no—
155#946—31no—
156#946—61no—
157C2×#215C2×D311yescharacteristic
158C2×#215C2×D311yescharacteristic
159D4×Dic3—31no—
160D4×Dic3—31no—
161C2×#213—31no—
162C2×#213—31no—
163C4×#67—61no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×D24—31no—
168C2×D24—31no—
169#896—61no—
170#896—61no—
171#896—62no—
172#895—31no—
173#895—31no—
174#895—61no—
175#894—61no—
176#894—61no—
177#894—62no—
178#893—31no—
179#893—31no—
180#892—31no—
181#892—31no—
182#888—31no—
183#888—31no—
184#888—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#876—61no—
190#876—61no—
191#876—62no—
192#875—61no—
193#875—61no—
194#875—62no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#872—31no—
201#872—31no—
202#872—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×C4×C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#817—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C2×D32—24no—
244C2×D32—81no—
245C2×D32—81no—
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—81no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—81no—
263#634—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12#4112yes—
269C3×D12#4112yes—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272#625—24no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—91no—
280#518—91no—
281#485—91no—
282#482—91no—
283#476—91no—
284#474—91no—
285#463—91no—
286#463—91no—
287#450—91no—
288#447—91no—
289#442—91no—
290#440—31no—
291C4×SD16—31no—
292C4×D8—91no—
293#433—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307D3×D4—62no—
308D3×D4—62no—
309D3×D4—62no—
310D3×D4—62no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—62no—
317C2×D12C22×D311yescharacteristic
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—62no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—62no—
332C3×SD16—62no—
333C3×SD16—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—22no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—61no—
355#217—61no—
356#215—22no—
357#215—22no—
358#213—62no—
359#213—62no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
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—62no—
381(C2×D3)⋊C4—62no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414D24—62no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428D32—84no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C22×D4—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×D8—91no—
445C2×D8—91no—
446C4⋊Q8—91no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—181no—
453#121—91no—
454C4×Q8D3211yescharacteristic, complemented
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462#117—91no—
463#117—91no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—31no—
469#106—91no—
470C4⋊C8—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482#97—31no—
483C4×C8—31no—
484C23×C3—61no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—62no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—241no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—32no—
507C3×D4—32no—
508C3×D4—61no—
509C3×D4—61no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—64no—
530#67—64no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547D12—21no—
548D12—21no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12—121no—
555D12—241no—
556D12—241no—
557D12—242no—
558D12#23512yes—
559D12#23512yes—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—121no—
567C4×D3—121no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—242no—
573Dic6—241no—
574Dic6—241no—
575Dic6—242no—
576C3×C8—61no—
577C3×C8—61no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C2×C32#52511yescharacteristic
585C2×C32#57611yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—41no—
588C3⋊D3—81no—
589C3×D3—42no—
590C3×D3—42no—
591C24—181no—
592C2×Q8—181no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—181no—
599C2×D4—182no—
600C2×D4—182no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—91no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607SD16—62no—
608SD16—62no—
609D8—182no—
610D8—182no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—31no—
615C4⋊C4—21no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—21no—
637C42—91no—
638C42—181no—
639C42C2×D3211yescharacteristic
640C22×C3—21no—
641C22×C3—62no—
642C22×C3—62no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—122no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—244no—
674C2×D3—244no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4C2×#23511yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4D3×#4111yescharacteristic
695Dic3—41no—
696Dic3—41no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—122no—
707Dic3—121no—
708Dic3—121no—
709C32#311811yescharacteristic, complemented, Sylow
710C23—61no—
711C23—61no—
712C23—91no—
713C23—184no—
714C23—181no—
715C23—721no—
716C23—721no—
717Q8—21no—
718Q8—21no—
719Q8—721no—
720D4—32no—
721D4—32no—
722D4—61no—
723D4—61no—
724D4—184no—
725D4—181no—
726D4—181no—
727D4—721no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4#381111yescharacteristic
744C2×C4#381111yescharacteristic
745C2×C4C22×D3211yescharacteristic
746C8—61no—
747C8—61no—
748C8—61no—
749C8—61no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—122no—
754C2×C3—122no—
755C2×C3#554711yescharacteristic
756C2×C3#554711yescharacteristic
757C2×C3#576211yescharacteristic
758C2×C3#576911yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3#577811yescharacteristic
761D3—42no—
762D3—42no—
763D3—121no—
764D3—121no—
765D3—241no—
766D3—242no—
767D3—241no—
768D3—241no—
769C22—62no—
770C22—62no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22C2×#381111yescharacteristic
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—181no—
791C4—181no—
792C4—361no—
793C4D3×#23511yescharacteristic
794C4D3×#23511yescharacteristic
795C3—21no—
796C3#7969611yescharacteristic, complemented
797C3#7978511yescharacteristic, complemented
798C2—122no—
799C2—122no—
800C2—361no—
801C2—721no—
802C2#1059507611yescharacteristic
803C2#1059532411yescharacteristic
804C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590598C2
hypercenterC4×Q8D32
hypocenterC32#3118
LCSG ▷ C2×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. #10596053C2semidirect
2. #10593996C2semidirect
3. C3×#5026C2semidirect
4. C3×C4×#215C2semidirect
5. #10591652C2semidirect
6. #10591570C2semidirect
7. #10591570C2semidirect
8. #10591561C2semidirect
10. #10590472C2semidirect
11. #10590471C2semidirect
12. #10590451C2semidirect
13. #10590346C2semidirect
14. C4×#3714C2semidirect
15. #10590298C2semidirect
19. C32×C4×Q8C22semidirect
20. #64156C22semidirect
25. #64097C22semidirect
28. C4×C4⋊(C3⋊D3)C22semidirect
43. C3×#835C22semidirect
44. C3×#835C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×#803C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
72. #5026D3semidirect
73. C4×#215D3semidirect
147. C3×C4×Q8C2×D3semidirect
148. C3×C4×Q8C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
234. #808C2×D3semidirect
236. #807C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
454. C4×Q8D32semidirect
709. C32#3118semidirect
796. C3#79696semidirect
797. C3#79785semidirect

Maximal subgroups

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

subgroupindex
#105960532
#105939962
C3×#50262
C3×C4×#2152
#105916522
#105915702
#105915612
#105905982
#105904722
#105904712
#105904512
#105903462
C4×#37142
#105902982
#797853
#796963