Finite Group Databasebeta

← #11872366

Subgroups — #11872366

Order 1152.

939 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#10596045C211yesmaximal, characteristic, complemented
2#10593950C211yesmaximal, characteristic, complemented
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591593C211yesmaximal, characteristic, complemented
6#10591593C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10590511C211yesmaximal, characteristic, complemented
10#10590510C211yesmaximal, characteristic, complemented
11#10590462C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13#10590355C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590257C211yesmaximal, characteristic, complemented
16#81208—31nomaximal
17#80364—31nomaximal
18C2×#3832C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64102—21no—
22#64102C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64081—21no—
28#64081C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#874C2211yescharacteristic
32C3×#870C2211yescharacteristic
33#63916C2211yescharacteristic
34#63916C2211yescharacteristic
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37#63886—21no—
38#63886—21no—
39#63884—21no—
40#63884—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5719—31no—
62#5697—31no—
63#5574—31no—
64#5574—31no—
65#5574—61no—
66C3×#479—31no—
67C3×#460—31no—
68#5172—31no—
69#5172—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5072—31no—
73#5066—31no—
74#5027D311yescharacteristic, complemented
75#5022D311yescharacteristic, complemented
76#4882—31no—
77#4872—31no—
78#4869—31no—
79#4863—31no—
80#4847—31no—
81#4843—31no—
82#4840—31no—
83#4840—31no—
84#4817—31no—
85#4810—31no—
86#4810—31no—
87#4788—31no—
88#4785—31no—
89#4777—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93#3832—22no—
94#3832—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116#3752D411yescharacteristic
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750D411yescharacteristic
122#3750D411yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#215—22no—
126C3×#215—22no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C3×#127—31no—
148C3×#125—31no—
149C3×C4×Q8—21no—
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×Q8C2×D311yescharacteristic
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155C2×#215C2×D311yescharacteristic
156C2×#215C2×D311yescharacteristic
157#939—61no—
158#939—61no—
159#938—31no—
160#938—31no—
161#935—61no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×D24—31no—
168C2×D24—31no—
169#895—31no—
170#895—31no—
171#895—61no—
172#895—61no—
173#894—61no—
174#894—61no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—61no—
180#893—61no—
181#893—61no—
182#893—62no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—62no—
189#874C2×D311yescharacteristic
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12—61no—
195C4×D12—62no—
196#872—31no—
197#872—31no—
198#872—61no—
199#872—61no—
200#872—61no—
201#872—62no—
202#870C2×D311yescharacteristic
203C3×#107—31no—
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
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—
225#815—31no—
226#815—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic
237C4⋊(C3⋊C8)C2×D311yescharacteristic
238C4⋊(C3⋊C8)C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C32×Q8—21no—
244C32×Q8#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—24no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)#4112yes—
257C4×C3⋊D3—24no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—81no—
261C4×C3⋊D3—81no—
262C4×C3⋊D3—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—81no—
270C3×D12—81no—
271#626—81no—
272#626—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#540—91no—
280#520—91no—
281#481—91no—
282#480—91no—
283#479—31no—
284#478—91no—
285#460—31no—
286#459—91no—
287#449—91no—
288#449—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C2×C3×Q8—21no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305#239—62no—
306#239—62no—
307#239—64no—
308#239—64no—
309#239—62no—
310#239—62no—
311C2×D12—21no—
312C2×D12—21no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—62no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C3×SD16—62no—
341C3×SD16—62no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C42—22no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#215—22no—
367#215—22no—
368#213—62no—
369#213—62no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
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—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—62no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—62no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—62no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D24—62no—
416D24—62no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—22no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C2×SD16—31no—
444C2×SD16—31no—
445C2×D8—91no—
446C2×D8—91no—
447#127—31no—
448#125—31no—
449#123—181no—
450#123—181no—
451#121—91no—
452#121—91no—
453#121—181no—
454#121—181no—
455C4×Q8—91no—
456C4×Q8D3211yescharacteristic
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463#117—91no—
464#117—181no—
465C2×C4⋊C4—91no—
466C2×C4⋊C4—181no—
467#107—31no—
468#107—91no—
469#106—31no—
470#106—91no—
471C4⋊C8—31no—
472C4⋊C8—31no—
473#103—31no—
474#103—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483#97—91no—
484C4×C8—91no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C3×Q8—22no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—22no—
499C3×Q8#23712yes—
500C3×Q8#23912yes—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—241no—
506C3×D4—241no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—241no—
525#67—241no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542D12—21no—
543D12—21no—
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—68no—
550D12—64no—
551D12—64no—
552D12—62no—
553D12—61no—
554D12—61no—
555D12—81no—
556D12—81no—
557D12—241no—
558D12—241no—
559C4×D3—68no—
560C4×D3—64no—
561C4×D3—64no—
562C4×D3—62no—
563C4×D3—62no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—242no—
577C4×D3—242no—
578C4×D3—242no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32#52511yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57711yescharacteristic
590C3⋊D3—41no—
591C3⋊D3—42no—
592C3×D3—81no—
593C3×D3—81no—
594#41—182no—
595#41—182no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—181no—
605C22×C4—91no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—62no—
613SD16—62no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—31no—
620C4⋊C4—21no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—21no—
640C42—91no—
641C42—181no—
642C42C2×D3211yescharacteristic
643C22×C3—21no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—64no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—62no—
667C2×D3—61no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C3×C4—24no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—42no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23711yescharacteristic
693C3×C4C2×#23911yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4D3×#4111yescharacteristic
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—121no—
706Dic3—121no—
707Dic3—122no—
708Dic3—121no—
709Dic3—121no—
710C32#311911yescharacteristic, complemented, Sylow
711C23—61no—
712C23—61no—
713C23—91no—
714C23—181no—
715Q8—21no—
716Q8#379612yes—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—61no—
721D4—92no—
722D4—184no—
723D4—181no—
724D4—241no—
725D4—241no—
726D4—721no—
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—184no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4#381111yescharacteristic
745C2×C4#381111yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—241no—
755C2×C3—241no—
756C2×C3#560611yescharacteristic
757C2×C3#562711yescharacteristic
758C2×C3#576211yescharacteristic
759C2×C3#576911yescharacteristic
760C2×C3#577411yescharacteristic
761C2×C3#577811yescharacteristic
762D3—81no—
763D3—81no—
764D3—122no—
765D3—124no—
766D3—121no—
767D3—122no—
768D3—121no—
769D3—122no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—182no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—361no—
781C22—361no—
782C22C2×#381111yescharacteristic
783C4—22no—
784C4—21no—
785C4—21no—
786C4—41no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—181no—
791C4—181no—
792C4—361no—
793C4C2×#379611yescharacteristic
794C4#6430611yescharacteristic
795C3—21no—
796C3#8036411yescharacteristic, complemented
797C3#8120811yescharacteristic, complemented
798C2—241no—
799C2—241no—
800C2—361no—
801C2—362no—
802C2#1059492211yescharacteristic
803C2#1059532411yescharacteristic
804C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3119
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. #10596045C2semidirect
2. #10593950C2semidirect
3. C3×#5027C2semidirect
4. C3×#5022C2semidirect
5. #10591593C2semidirect
6. #10591593C2semidirect
7. #10591572C2semidirect
8. #10591571C2semidirect
9. #10590511C2semidirect
10. #10590510C2semidirect
11. #10590462C2semidirect
12. #10590459C2semidirect
13. #10590355C2semidirect
14. #10590308C2semidirect
15. #10590257C2semidirect
74. #5027D3semidirect
75. #5022D3semidirect
710. C32#3119semidirect
796. C3#80364semidirect
797. C3#81208semidirect

Maximal subgroups

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

subgroupindex
#105960452
#105939502
C3×#50272
C3×#50222
#105915932
#105915722
#105915712
#105905112
#105905102
#105904622
#105904592
#105903552
#105903082
#105902572
#812083
#803643