Finite Group Databasebeta

← #11872347

Subgroups — #11872347

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5697C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5#10590615C211yesmaximal, characteristic, complemented
6#10590615C211yesmaximal, characteristic, complemented
7#10590589C211yesmaximal, characteristic, complemented
8#10590478C211yesmaximal, characteristic, complemented
9#10590475C211yesmaximal, characteristic, complemented
10#10590456C211yesmaximal, characteristic, complemented
11#10590441C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13#10590364C211yesmaximal, characteristic, complemented
14#10590355C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#81208—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#895—21no—
22C3×#895—21no—
23C3×#895C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#894—21no—
26C3×#894—21no—
27C3×#893C2211yescharacteristic
28C3×#893C2211yescharacteristic
29C3×#874C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63894C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63883—21no—
35#63881—21no—
36#63880—21no—
37Dic3×Dic6C2211yescharacteristic
38#63836—21no—
39C2×#3715C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62#5697D311yescharacteristic, complemented
63#5574—31no—
64#5523—31no—
65C3×#479—31no—
66#5075—31no—
67#5072—31no—
68#5066—31no—
69#5066—31no—
70#5066—61no—
71#5063D311yescharacteristic, complemented
72#5037—31no—
73#5037—31no—
74#5034—31no—
75#5033—31no—
76#5027—31no—
77#5018—31no—
78C4×#214—31no—
79#5014—31no—
80C4×#213—31no—
81#5000—31no—
82#4882—31no—
83#4872—31no—
84#4869—31no—
85#4863—31no—
86#4843—31no—
87#4840—31no—
88#4817—31no—
89#4810—31no—
90#4810—31no—
91#4788—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3799—22no—
109#3799—22no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136Dic32—21no—
137#3715—22no—
138#3715—22no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C3×#127—31no—
145C3×#125—21no—
146C3×#125C2×D311yescharacteristic
147C3×#125C2×D311yescharacteristic
148C3×#123—61no—
149C3×#123—61no—
150C3×#121—31no—
151C3×#121—31no—
152C3×#121—61no—
153C3×#121—61no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158Q8×Dic3—31no—
159C2×#215—31no—
160C2×#215—31no—
161C2×#214—31no—
162C2×#214—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×C4⋊Dic3—31no—
166C2×D24—31no—
167C2×D24—31no—
168#895—21no—
169#895—21no—
170#895C2×D311yescharacteristic
171#895C2×D311yescharacteristic
172#894—21no—
173#894—21no—
174#893—31no—
175#893—61no—
176#893C2×D311yescharacteristic
177#893C2×D311yescharacteristic
178#892—61no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—61no—
181D3×C4⋊C4—61no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#874C2×D311yescharacteristic
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190#872—61no—
191#872C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6C2×D311yescharacteristic
194C3×#107—31no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#821—31no—
206#821—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209#815—31no—
210C8×Dic3—31no—
211#810C2×D311yescharacteristic
212#810C2×D311yescharacteristic
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)#4112yes—
247C4×C3⋊D3—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—81no—
258C3×D12—81no—
259C3×D12—81no—
260C3×D12—81no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#626—24no—
268#624—24no—
269#624—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—31no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—31no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C2×C3×Q8—31no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302#239—62no—
303#239—62no—
304#235—62no—
305#235—62no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12—21no—
309C2×D12—21no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12C22×D311yescharacteristic
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—121no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#215—62no—
358#215—62no—
359#214—62no—
360#214—62no—
361#213—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4#6711yescharacteristic
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3C22×D311yescharacteristic
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397D24—62no—
398D24—62no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—22no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—91no—
425C2×SD16—91no—
426C2×SD16—91no—
427C2×D8—91no—
428C2×D8—91no—
429#127—31no—
430#125D3211yescharacteristic
431#123—61no—
432#123—61no—
433#121—31no—
434#121—31no—
435#121—61no—
436#121—61no—
437C4×Q8—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—31no—
446#117—181no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449#107—31no—
450#107—91no—
451#106—31no—
452#106—91no—
453C4⋊C8—31no—
454C4⋊C8—91no—
455#103—31no—
456#103—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—31no—
468C23×C3—61no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—121no—
475C22×D3C2×#6711yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—241no—
483C3×D4—241no—
484C3×D4—241no—
485C3×D4—241no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—241no—
503C2×C3×C4—241no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—64no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—241no—
517C2×Dic3C2×#6711yescharacteristic
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520D12—21no—
521D12—21no—
522D12—21no—
523D12—21no—
524D12—32no—
525D12—32no—
526D12—62no—
527D12—64no—
528D12—61no—
529D12—61no—
530D12—81no—
531D12—81no—
532D12—81no—
533D12—81no—
534D12—121no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—64no—
538C4×D3—64no—
539C4×D3—81no—
540C4×D3—81no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—242no—
547Dic6—21no—
548Dic6#23912yes—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C2×C32#52511yescharacteristic
560C2×C32#57611yescharacteristic
561C2×C32#57711yescharacteristic
562C3⋊D3—42no—
563C3×D3—41no—
564C3×D3—81no—
565C3×D3—81no—
566#41—182no—
567#41—182no—
568C2×Q8—31no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—91no—
576C2×D4—181no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584SD16—182no—
585SD16—182no—
586D8—182no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—61no—
613C42—181no—
614C42C2×D3211yescharacteristic
615C22×C3—21no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3C2×D3×D411yescharacteristic
626C22×C3C22×#6711yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—122no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—241no—
644C2×D3—241no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—62no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4C2×#23911yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—22no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676C32#311911yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679C23—61no—
680C23—181no—
681Q8—32no—
682Q8—61no—
683D4—61no—
684D4—61no—
685D4—61no—
686D4—61no—
687D4—92no—
688D4—184no—
689D4—181no—
690D4—241no—
691D4—241no—
692D4—241no—
693D4—241no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—184no—
704C2×C4—181no—
705C2×C4—241no—
706C2×C4—241no—
707C2×C4—721no—
708C2×C4—721no—
709C2×C4—721no—
710C2×C4D3×#6711yescharacteristic
711C2×C4D3×#6711yescharacteristic
712C2×C4C22×D3211yescharacteristic
713C8—61no—
714C8—61no—
715C8—181no—
716C8—181no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—121no—
721C2×C3—241no—
722C2×C3—241no—
723C2×C3#562711yescharacteristic
724C2×C3#576911yescharacteristic
725C2×C3#577811yescharacteristic
726C2×C3#582811yescharacteristic
727C2×C3#583511yescharacteristic
728C2×C3#583611yescharacteristic
729D3—41no—
730D3—81no—
731D3—81no—
732D3—122no—
733D3—122no—
734D3—242no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—182no—
745C22—361no—
746C22—361no—
747C22C2×D3×#6711yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—41no—
752C4—61no—
753C4—62no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—361no—
758C4D3×#23911yescharacteristic
759C4#6431911yescharacteristic
760C3—21no—
761C3#8120811yescharacteristic, complemented
762C3#8343411yescharacteristic, complemented
763C2—121no—
764C2—241no—
765C2—241no—
766C2—362no—
767C2#1059542411yescharacteristic
768C2#1059545611yescharacteristic
769C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
hypercenter#125D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5697C2semidirect
2. #10593890C2semidirect
3. #10592765C2semidirect
4. C3×#5063C2semidirect
5. #10590615C2semidirect
6. #10590615C2semidirect
7. #10590589C2semidirect
8. #10590478C2semidirect
9. #10590475C2semidirect
10. #10590456C2semidirect
11. #10590441C2semidirect
12. #10590438C2semidirect
13. #10590364C2semidirect
14. #10590355C2semidirect
15. #10590253C2semidirect
62. #5697D3semidirect
71. #5063D3semidirect
676. C32#3119semidirect
761. C3#81208semidirect
762. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#56972
#105938902
#105927652
C3×#50632
#105906152
#105905892
#105904782
#105904752
#105904562
#105904412
#105904382
#105903642
#105903552
#105902532
#834343
#812083