Finite Group Databasebeta

← #11872365

Subgroups — #11872365

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2#10593989C211yesmaximal, characteristic, complemented
3#10592726C211yesmaximal, characteristic, complemented
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591588C211yesmaximal, characteristic, complemented
6#10591588C211yesmaximal, characteristic, complemented
7#10591540C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590589C211yesmaximal, characteristic, complemented
10#10590456C211yesmaximal, characteristic, complemented
11#10590423C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590349C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#81208—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64083C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#893—21no—
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×C4×D12—21no—
29C3×C4×D12C2211yescharacteristic
30C3×#872—21no—
31C3×#872C2211yescharacteristic
32C3×#870C2211yescharacteristic
33#63910—21no—
34#63910—21no—
35#63909C2211yescharacteristic
36#63909C2211yescharacteristic
37#63897—21no—
38#63897—21no—
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5697—31no—
63#5574D311yescharacteristic, complemented
64#5535—31no—
65C3×#479—31no—
66#5238—31no—
67#5238—31no—
68#5066—31no—
69#5027—31no—
70#5027—31no—
71#5027—61no—
72#5026—31no—
73C4×#215—31no—
74#5022D311yescharacteristic, complemented
75#5015—31no—
76#5014—31no—
77C4×#213—31no—
78#5009—31no—
79#5000—31no—
80#4968—31no—
81#4967—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×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3755—22no—
115#3755—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C3×#125—31no—
145C3×C4×Q8—21no—
146C3×C4×Q8—31no—
147C3×C4×Q8C2×D311yescharacteristic
148C3×C4×Q8C2×D311yescharacteristic
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—61no—
152C3×C4×D4—61no—
153C3×#117—31no—
154C3×#117—61no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—61no—
157Q8×Dic3C2×D311yescharacteristic
158C2×#215—31no—
159C2×#215—31no—
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—61no—
163C2×#215—61no—
164C2×#213—31no—
165C2×#213—31no—
166#930—31no—
167#930—31no—
168C2×D24—31no—
169C2×D24—31no—
170#895—31no—
171#895—31no—
172#895—61no—
173#895—61no—
174#894—61no—
175#894—61no—
176#894—61no—
177#894—61no—
178#893—21no—
179#893—31no—
180#893—31no—
181#893C2×D311yescharacteristic
182D3×C4⋊C4—21no—
183D3×C4⋊C4C2×D311yescharacteristic
184#884—61no—
185#884—61no—
186#874—31no—
187#874—31no—
188#874—61no—
189C4×D12—21no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12C2×D311yescharacteristic
193#872—21no—
194#872C2×D311yescharacteristic
195#870C2×D311yescharacteristic
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#103—31no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#830—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#815—31no—
212C8×Dic3—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#809—61no—
223#808—31no—
224#808—31no—
225#808C2×D311yescharacteristic
226#807—31no—
227#807—31no—
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
239C32×Q8—21no—
240C32×Q8#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—81no—
251C4⋊(C3⋊D3)—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—24no—
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—24no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#626—81no—
268#626—81no—
269#624—81no—
270#624—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—31no—
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—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C2×#67—61no—
304#239—22no—
305#239—22no—
306C2×D12—21no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—121no—
320C2×D12—121no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
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—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—31no—
356C3×C42—41no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#215—62no—
361#215—62no—
362#215—62no—
363#215—62no—
364#215—122no—
365#215—122no—
366#213—62no—
367#213—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
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#6711yescharacteristic
379(C2×D3)⋊C4#6711yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D24—62no—
400D24—62no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—21no—
415C32×C4—22no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—31no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8—91no—
431#127—91no—
432#125—31no—
433#123—181no—
434#123—181no—
435#121—91no—
436#121—91no—
437#121—181no—
438#121—181no—
439C4×Q8—31no—
440C4×Q8D3211yescharacteristic
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—91no—
446C4×D4—91no—
447#117—31no—
448#117—61no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—61no—
451#107—31no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—91no—
457#103—31no—
458#103—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467#97—91no—
468C4×C8—91no—
469C23×C3—31no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C22×D3—121no—
478C22×D3C2×#6711yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—41no—
483C3×Q8#23512yes—
484C3×Q8#23912yes—
485C3×D4—32no—
486C3×D4—64no—
487C3×D4—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—241no—
516#67—241no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3C2×#6711yescharacteristic
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523D12—24no—
524D12—21no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—121no—
535D12—121no—
536D12—121no—
537D12—241no—
538D12—241no—
539D12—241no—
540D12—241no—
541D12—242no—
542D12—242no—
543D12—241no—
544D12—241no—
545D12#23512yes—
546C4×D3—24no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—81no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32#52511yescharacteristic
567C2×C32#57611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—81no—
570C3⋊D3—81no—
571C3×D3—41no—
572C3×D3—42no—
573#41—62no—
574#41—62no—
575C2×Q8C2×D3211yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—181no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—181no—
590C22×C4—181no—
591SD16—182no—
592SD16—182no—
593D8—182no—
594D8—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8—91no—
599C4⋊C4—21no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—21no—
619C42—31no—
620C42—61no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—62no—
626C22×C3—61no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C22×#6711yescharacteristic
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3—241no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—22no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23511yescharacteristic
676C3×C4C2×#23511yescharacteristic
677C3×C4C2×#23911yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685C32#311911yescharacteristic, complemented, Sylow
686C23—31no—
687C23—61no—
688C23—181no—
689C23—181no—
690Q8—21no—
691Q8#379912yes—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—181no—
696D4—181no—
697D4—181no—
698D4—181no—
699D4—721no—
700D4—721no—
701D4—721no—
702D4—721no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—64no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4D3×#6711yescharacteristic
720C2×C4D3×#6711yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—61no—
723C8—61no—
724C8—181no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—121no—
730C2×C3—122no—
731C2×C3#562711yescharacteristic
732C2×C3#576911yescharacteristic
733C2×C3#577811yescharacteristic
734C2×C3#579111yescharacteristic
735C2×C3#583511yescharacteristic
736C2×C3#583711yescharacteristic
737D3—41no—
738D3—42no—
739D3—241no—
740D3—241no—
741D3—241no—
742D3—241no—
743D3—481no—
744D3—481no—
745C22—61no—
746C22—62no—
747C22—61no—
748C22—61no—
749C22—121no—
750C22—121no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22C2×D3×#6711yescharacteristic
758C4—21no—
759C4—22no—
760C4—21no—
761C4—41no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4C2×#379911yescharacteristic
769C4D3×#23511yescharacteristic
770C3—21no—
771C3#8120811yescharacteristic, complemented
772C3#8256811yescharacteristic, complemented
773C2—121no—
774C2—122no—
775C2—721no—
776C2—721no—
777C2#1059500511yescharacteristic
778C2#1059531911yescharacteristic
779C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C3×#5574C2semidirect
2. #10593989C2semidirect
3. #10592726C2semidirect
4. C3×#5022C2semidirect
5. #10591588C2semidirect
6. #10591588C2semidirect
7. #10591540C2semidirect
8. #10591536C2semidirect
9. #10590589C2semidirect
10. #10590456C2semidirect
11. #10590423C2semidirect
12. #10590422C2semidirect
13. #10590349C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
63. #5574D3semidirect
74. #5022D3semidirect
685. C32#3119semidirect
771. C3#81208semidirect
772. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
#105939892
#105927262
C3×#50222
#105915882
#105915402
#105915362
#105905892
#105904562
#105904232
#105904222
#105903492
#105902702
#105902532
#825683
#812083