Finite Group Databasebeta

← #11870460

Subgroups — #11870460

Order 1152.

1054 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595131C211yesmaximal, characteristic, complemented
2D3×#893C211yesmaximal, characteristic, complemented
3#10592485C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591433C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590778C211yesmaximal, characteristic, complemented
11#10590763C211yesmaximal, characteristic, complemented
12#10590655C211yesmaximal, characteristic, complemented
13#10590456C211yesmaximal, characteristic, complemented
14#10590430C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#81268—31nomaximal
17#79590—31nomaximal
18C2×#3804—21no—
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21#64149C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24#64102C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C3×#893C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30#63971—21no—
31#63953—21no—
32#63952—21no—
33D3×(C2×D3)⋊C4—21no—
34#63919C2211yescharacteristic, complemented
35#63909C2211yescharacteristic
36#63904—21no—
37#63898C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic, complemented
40#63881—21no—
41C4×D3×Dic3C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63641C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5596—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#480—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5150—31no—
69#5036—31no—
70C4×#213—31no—
71C4×#213—31no—
72#4967—31no—
73#4890—31no—
74#4890—31no—
75#4890—31no—
76#4882—31no—
77#4872—31no—
78#4872—31no—
79#4786—31no—
80#4786—31no—
81#4786—31no—
82#4786—61no—
83#4774D311yescharacteristic, complemented
84#4773—31no—
85#4759—31no—
86#4756—31no—
87#4756D311yescharacteristic, complemented
88#4732—31no—
89#4718—31no—
90C4×D24—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3804—44no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114D3×D12—22no—
115D3×D12—22no—
116C4×D32—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3753—22no—
120#3752—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3745—22no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3714—22no—
143#3100—91noSylow
144C2×#237—61no—
145C2×D3×D4—31no—
146C2×#235—61no—
147C22×D12—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C3×#121—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#940—31no—
156#940—31no—
157#940—61no—
158#939—61no—
159#938C2×D311yescharacteristic
160D4×Dic3—31no—
161D4×Dic3C2×D311yescharacteristic, complemented
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—61no—
166C2×#213C2×D311yescharacteristic
167#930—31no—
168C4×#67—61no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×C4×Dic3—31no—
172C2×D24—31no—
173C2×D24—31no—
174C2×D24—31no—
175C2×D24—61no—
176#895—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—61no—
183#893—61no—
184#893—61no—
185#893C2×D311yescharacteristic
186D3×C4⋊C4C2×D311yescharacteristic
187#888—31no—
188#888—31no—
189#885—61no—
190#885—61no—
191#884—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195C4×D12—31no—
196C4×D12—31no—
197C42×D3—31no—
198C3×#107—31no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic, complemented
205C3×#102C2×D311yescharacteristic, complemented
206C3×C22⋊C8—31no—
207C3×C4×C8—31no—
208#832—31no—
209#832C2×D311yescharacteristic, complemented
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818C2×D311yescharacteristic, complemented
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223C8×Dic3—31no—
224C8×Dic3C2×D311yescharacteristic, complemented
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235#807C2×D311yescharacteristic, complemented
236C4×C3⋊C8—31no—
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250#638—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)#4112yescomplemented
257C4×C3⋊D3—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12#4112yescomplemented
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272#627—42no—
273#626—24no—
274#626—42no—
275#624—42no—
276#624—42no—
277D3×Dic3—41no—
278D3×Dic3—42no—
279D3×Dic3D814yescomplemented
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#480—31no—
287#480—91no—
288#474—91no—
289#474—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—121no—
318C2×#67—121no—
319C22×Dic3—21no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—61no—
323#237—124no—
324D3×D4—62no—
325D3×D4—62no—
326#235—124no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3—124no—
351C2×C4×D3—124no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—61no—
354C2×Dic6—61no—
355C3×D8—62no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372#217—21no—
373#217—21no—
374#217—61no—
375#213—22no—
376#213—62no—
377#213—62no—
378#213—62no—
379#213—122no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24—62no—
411D24—62no—
412D24—62no—
413D24—122no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3C2×D812yes—
430D32—48no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3C2×D812yes—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3C2×D812yes—
442C2×#41—181no—
443C22×D4—91no—
444C23×C4—181no—
445C2×D8—31no—
446C2×D8—91no—
447C2×D8—91no—
448C2×D8—91no—
449C4⋊Q8—91no—
450#127—91no—
451#124—181no—
452#121—31no—
453#121—91no—
454#121—181no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C22⋊C4—181no—
466C2×C42—91no—
467#107—31no—
468#107—31no—
469#107—31no—
470#107—91no—
471C4⋊C8—91no—
472C4⋊C8—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102D3211yescharacteristic, complemented
481C22⋊C8—31no—
482C22⋊C8—91no—
483C4×C8—31no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3D3×D411yescharacteristic
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—61no—
512C3×D4—122no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—42no—
531#67—64no—
532#67—122no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—122no—
537#67—242no—
538#67—242no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—34no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—42no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—32no—
557D12—32no—
558D12—62no—
559D12—64no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12—121no—
568D12—121no—
569D12—122no—
570D12#23512yescomplemented
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—34no—
574C4×D3—42no—
575C4×D3—42no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3—121no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—242no—
585Dic6—122no—
586Dic6—122no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—41no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—121no—
597C2×C32—81no—
598C2×C32#52511yescharacteristic
599C2×C32C22×D811yescharacteristic
600C2×C32#57511yescharacteristic
601C3⋊D3—42no—
602C3⋊D3—81no—
603C3×D3—22no—
604C3×D3—42no—
605C24—181no—
606#41—364no—
607C2×Q8—181no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—181no—
613C2×D4—182no—
614C2×D4—182no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4C2×D3211yescharacteristic
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—181no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4—364no—
630D8—62no—
631D8—182no—
632D8—182no—
633D8—182no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—61no—
642C4⋊C4—181no—
643C4⋊C4C2×D3211yescharacteristic
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—91no—
654C42—91no—
655C42—91no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—122no—
682C2×D3—128no—
683C2×D3—128no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3D3×D812yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—32no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—81no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4C2×#23511yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4D3×#4111yescharacteristic
714C3×C4D3×#4111yescharacteristic
715Dic3—21no—
716Dic3—21no—
717Dic3—32no—
718Dic3—32no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—62no—
723Dic3—61no—
724Dic3—61no—
725Dic3—121no—
726Dic3D3×D812yes—
727C32#310011yescharacteristic, complemented, Sylow
728C23—21no—
729C23—31no—
730C23—61no—
731C23—184no—
732C23—181no—
733C23—181no—
734C23—362no—
735C23—362no—
736Q8—362no—
737D4—21no—
738D4—21no—
739D4—32no—
740D4—61no—
741D4—92no—
742D4—122no—
743D4—184no—
744D4—181no—
745D4—181no—
746D4—181no—
747D4—362no—
748D4—362no—
749D4—362no—
750C2×C4—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—94no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—362no—
766C2×C4—362no—
767C2×C4—362no—
768C2×C4—361no—
769C2×C4—362no—
770C2×C4C22×D3211yescharacteristic
771C8—21no—
772C8—61no—
773C8—61no—
774C8—181no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—62no—
779C2×C3—81no—
780C2×C3—81no—
781C2×C3—122no—
782C2×C3—161no—
783C2×C3#554711yescharacteristic
784C2×C3#565611yescharacteristic
785C2×C3C2×D3×D811yescharacteristic
786C2×C3C2×D3×D811yescharacteristic
787C2×C3#576811yescharacteristic
788C2×C3#577711yescharacteristic
789D3—22no—
790D3—42no—
791D3—122no—
792D3—122no—
793D3—242no—
794D3—241no—
795D3—241no—
796D3—481no—
797C22—32no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—61no—
802C22—61no—
803C22—62no—
804C22—121no—
805C22—121no—
806C22—182no—
807C22—368no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22D32×D411yescharacteristic
814C4—32no—
815C4—41no—
816C4—61no—
817C4—61no—
818C4—92no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—181no—
823C4D3×#23511yescharacteristic
824C4#6431211yescharacteristic
825C3—21no—
826C3#7959011yescharacteristic, complemented
827C3#8126811yescharacteristic, complemented
828C2—62no—
829C2—81no—
830C2—122no—
831C2—362no—
832C2—721no—
833C2#1059426611yescharacteristic
834C2D32×D811yescharacteristic
835C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595131C2semidirect
2. D3×#893C2semidirect
3. #10592485C2semidirect
4. C3×#4774C2semidirect
5. C3×#4756C2semidirect
6. #10591515C2semidirect
7. #10591433C2semidirect
8. #10591400C2semidirect
9. #10590947C2semidirect
10. #10590778C2semidirect
11. #10590763C2semidirect
12. #10590655C2semidirect
13. #10590456C2semidirect
14. #10590430C2semidirect
15. #10590422C2semidirect
21. #64149C22semidirect
26. C3×D4×Dic3C22semidirect
34. #63919C22semidirect
39. #63894C22semidirect
43. C32×#102C22semidirect
44. #63641C22semidirect
45. #63636C22semidirect
46. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63572C22semidirect
57. #63564C22semidirect
60. Dic3×C3⋊C8C22semidirect
83. #4774D3semidirect
87. #4756D3semidirect
161. D4×Dic3C2×D3semidirect
204. C3×#102C2×D3semidirect
205. C3×#102C2×D3semidirect
209. #832C2×D3semidirect
217. #818C2×D3semidirect
224. C8×Dic3C2×D3semidirect
234. #807C2×D3semidirect
235. #807C2×D3semidirect
256. C4⋊(C3⋊D3)#41semidirect
267. C3×D12#41semidirect
279. D3×Dic3D8semidirect
480. #102D32semidirect
570. D12#235semidirect
727. C32#3100semidirect
826. C3#79590semidirect
827. C3#81268semidirect

Maximal subgroups

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

subgroupindex
#105951312
D3×#8932
#105924852
C3×#47742
C3×#47562
#105915152
#105914332
#105914002
#105909472
#105907782
#105907632
#105906552
#105904562
#105904302
#105904222
#812683
#795903