Finite Group Databasebeta

← #11872760

Subgroups — #11872760

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic, complemented
2#10593989C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic, complemented
7#10590947C211yesmaximal, characteristic, complemented
8#10590768C211yesmaximal, characteristic, complemented
9#10590763C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12#10590705C211yesmaximal, characteristic, complemented
13#10590704C211yesmaximal, characteristic, complemented
14#10590349C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17#79386—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21#64083C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×#870C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63910—21no—
29#63910—21no—
30#63909C2211yescharacteristic
31#63909C2211yescharacteristic
32#63904—21no—
33#63897—21no—
34#63897—21no—
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic, complemented
37#63894C2211yescharacteristic, complemented
38Dic3×D12C2211yescharacteristic
39#63881—21no—
40#63841C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#5697—31no—
62#5545—31no—
63#5535—31no—
64#5521—31no—
65C3×#478—31no—
66C3×#433—31no—
67#5066—31no—
68#5015—31no—
69#4885—31no—
70#4872—31no—
71#4869—31no—
72#4866—31no—
73#4847—31no—
74#4847D311yescharacteristic, complemented
75#4843—31no—
76#4843—31no—
77#4843—31no—
78#4843—61no—
79#4840D311yescharacteristic, complemented
80#4785—31no—
81#4773—31no—
82#4773—31no—
83#4756—31no—
84#4737—31no—
85#4737—31no—
86#4732—31no—
87#4732—31no—
88#4711—31no—
89#4711—31no—
90C4×D24—31no—
91C4×D24—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3745—22no—
117#3745—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×#117—31no—
147D4×Dic3—31no—
148C2×#213—31no—
149C2×#213—31no—
150#930—31no—
151#930—31no—
152C4×#67—61no—
153C2×(C2×D3)⋊C4—61no—
154#926—31no—
155C2×D24—31no—
156C2×D24—31no—
157C2×D24—31no—
158C2×D24—31no—
159C2×D24—31no—
160C2×D24—31no—
161C2×D24—61no—
162C2×D24—61no—
163#895—31no—
164#895—31no—
165#895—61no—
166#895—61no—
167#894—61no—
168#894—61no—
169#894—61no—
170#894—61no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893—61no—
176#892—31no—
177#884—61no—
178#884—61no—
179#67⋊C4—61no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183#874—31no—
184#874—31no—
185#874—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#872C2×D311yescharacteristic
195#870C2×D311yescharacteristic, complemented
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic, complemented
201C3×C4⋊C8C2×D311yescharacteristic, complemented
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207C3×C4×C8—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818C2×D311yescharacteristic, complemented
224#817—31no—
225#817C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227C8×Dic3C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4⋊(C3⋊D3)—81no—
254C4⋊(C3⋊D3)#4112yes—
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—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267#626—24no—
268#626—81no—
269#626—81no—
270#624—81no—
271#624—81no—
272#624—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—31no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—31no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302D3×D4—62no—
303D3×D4—62no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—61no—
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—61no—
335C2×C4×D3—121no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—61no—
360#217—61no—
361#213—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
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—121no—
379(C2×D3)⋊C4D1211yescharacteristic
380(C2×D3)⋊C4D1211yescharacteristic
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4D1211yescharacteristic
390Dic3⋊C4D1211yescharacteristic
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396D24—62no—
397D24—62no—
398D24—62no—
399D24—62no—
400D24—62no—
401D24—62no—
402D24—122no—
403D24—122no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420D32—84no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×D4—91no—
433C2×D8—91no—
434C2×D8—91no—
435C2×D8—91no—
436C2×D8—91no—
437#127—91no—
438#125—31no—
439#123—181no—
440#123—181no—
441#121—91no—
442#121—91no—
443#121—181no—
444#121—181no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—31no—
454#117—91no—
455C2×C22⋊C4—181no—
456C2×C22⋊C4—181no—
457#107—31no—
458#107—91no—
459#106—31no—
460#106—91no—
461C4⋊C8—31no—
462C4⋊C8D3211yescharacteristic, complemented
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—31no—
472C22⋊C8—31no—
473#97—31no—
474C4×C8—31no—
475C23×C3—31no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—64no—
479C22×D3—64no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—121no—
488C22×D3—121no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×D1211yescharacteristic
494C3×D4—32no—
495C3×D4—61no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4C2×D1211yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—241no—
516#67—241no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—241no—
524C2×Dic3C2×D1211yescharacteristic
525C2×Dic3C2×D1211yescharacteristic
526C2×Dic3C2×D1211yescharacteristic
527D12—21no—
528D12—32no—
529D12—32no—
530D12—62no—
531D12—64no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—121no—
543D12—121no—
544D12—121no—
545D12—121no—
546D12—121no—
547D12—241no—
548D12—241no—
549D12—241no—
550D12—241no—
551D12—242no—
552D12—242no—
553D12—241no—
554D12—241no—
555D12#23912yes—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—81no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—242no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C2×C32#52511yescharacteristic
580C2×C32#57611yescharacteristic
581C2×C32#57611yescharacteristic
582C3⋊D3—42no—
583C3⋊D3—81no—
584C3⋊D3—81no—
585C3×D3—41no—
586C3×D3—42no—
587C24—181no—
588C2×D4—31no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4—91no—
592C2×D4—181no—
593C2×D4—182no—
594C2×D4—182no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4—181no—
598C2×D4—181no—
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606D8—182no—
607D8—182no—
608D8—182no—
609D8—182no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8C2×D3211yescharacteristic
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—181no—
635C42C2×D3211yescharacteristic
636C22×C3—21no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C22×D1211yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4C2×#23911yescharacteristic
695C3×C4D3×#4111yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4D3×#4111yescharacteristic
698Dic3—21no—
699Dic3—21no—
700Dic3—21no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—184no—
711C23—181no—
712C23—181no—
713C23—181no—
714C23—721no—
715C23—721no—
716D4—32no—
717D4—61no—
718D4—92no—
719D4—184no—
720D4—181no—
721D4—181no—
722D4—181no—
723D4—181no—
724D4—181no—
725D4—721no—
726D4—721no—
727D4—721no—
728D4—721no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4D3×D1211yescharacteristic
745C2×C4D3×D1211yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—21no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—122no—
755C2×C3—121no—
756C2×C3#552411yescharacteristic
757C2×C3#562711yescharacteristic
758C2×C3#575211yescharacteristic
759C2×C3#575211yescharacteristic
760C2×C3#576911yescharacteristic
761C2×C3#577411yescharacteristic
762D3—41no—
763D3—42no—
764D3—122no—
765D3—122no—
766D3—242no—
767D3—241no—
768D3—241no—
769D3—241no—
770D3—241no—
771D3—481no—
772D3—481no—
773C22—61no—
774C22—62no—
775C22—61no—
776C22—61no—
777C22—121no—
778C22—121no—
779C22—182no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—361no—
784C22—361no—
785C22—361no—
786C22—361no—
787C22—361no—
788C22—724no—
789C22C2×D3×D1211yescharacteristic
790C4—21no—
791C4—21no—
792C4—61no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—361no—
799C4#6431211yescharacteristic
800C4D3×#23911yescharacteristic
801C3—21no—
802C3#7938611yescharacteristic, complemented
803C3#8114611yescharacteristic, complemented
804C2—121no—
805C2—122no—
806C2—362no—
807C2—721no—
808C2—721no—
809C2#1059462711yescharacteristic
810C2#1059468011yescharacteristic
811C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593989C2semidirect
3. #10592542C2semidirect
4. C3×#4847C2semidirect
5. C3×#4840C2semidirect
6. #10590947C2semidirect
7. #10590947C2semidirect
8. #10590768C2semidirect
9. #10590763C2semidirect
10. #10590746C2semidirect
11. #10590745C2semidirect
12. #10590705C2semidirect
13. #10590704C2semidirect
14. #10590349C2semidirect
15. #10590308C2semidirect
21. #64083C22semidirect
25. C3×#870C22semidirect
36. #63894C22semidirect
37. #63894C22semidirect
43. C32×C4⋊C8C22semidirect
44. #63648C22semidirect
45. #63648C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
74. #4847D3semidirect
79. #4840D3semidirect
195. #870C2×D3semidirect
200. C3×C4⋊C8C2×D3semidirect
201. C3×C4⋊C8C2×D3semidirect
223. #818C2×D3semidirect
225. #817C2×D3semidirect
226. #815C2×D3semidirect
227. C8×Dic3C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
462. C4⋊C8D32semidirect
707. C32#3122semidirect
802. C3#79386semidirect
803. C3#81146semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105939892
#105925422
C3×#48472
C3×#48402
#105909472
#105907682
#105907632
#105907462
#105907452
#105907052
#105907042
#105903492
#105903082
#811463
#793863