Finite Group Databasebeta

← #11872302

Subgroups — #11872302

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5546C211yesmaximal, characteristic, complemented
2#10593989C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591452C211yesmaximal, characteristic, complemented
6#10591452C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590458C211yesmaximal, characteristic, complemented
10#10590457C211yesmaximal, characteristic, complemented
11#10590423C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590367C211yesmaximal, characteristic, complemented
14#10590286C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#81144—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64083C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×Dic3⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#877—21no—
30C3×#872C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63910—21no—
34#63910—21no—
35#63909C2211yescharacteristic
36#63909C2211yescharacteristic
37#63897—21no—
38#63897—21no—
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5697—31no—
63#5546D311yescharacteristic, complemented
64#5535—31no—
65C3×#478—31no—
66#5238—31no—
67#5238—31no—
68#5063—31no—
69#5027—31no—
70#5026—31no—
71C4×#215—31no—
72#5022—31no—
73#5015—31no—
74#5015—31no—
75#5015—61no—
76#5014—31no—
77C4×#213—31no—
78#5009D311yescharacteristic, complemented
79#5000—31no—
80#4968—31no—
81#4967—31no—
82#4889—31no—
83#4882—31no—
84#4863—31no—
85#4852—31no—
86#4848—31no—
87#4840—31no—
88#4785—31no—
89#4781—31no—
90#4781—31no—
91#4756—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237—22no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3753—22no—
114#3753—22no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
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#3717—22no—
140#3717—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C3×#125—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153C3×#117—31no—
154C3×#117—61no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—61no—
157C2×#215—31no—
158C2×#215—31no—
159D4×Dic3C2×D311yescharacteristic
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—61no—
165C2×#213—61no—
166#930—31no—
167#930—31no—
168C4×#67—21no—
169C2×Dic3⋊C4—21no—
170C2×#204—31no—
171C2×#204—31no—
172#895—31no—
173#895—31no—
174#895—61no—
175#895—61no—
176#894—61no—
177#894—61no—
178#894—61no—
179#894—61no—
180#893—31no—
181#893—31no—
182D3×C4⋊C4C2×D311yescharacteristic
183#887C2×D311yescharacteristic
184#884—61no—
185#884—61no—
186#67⋊C4—21no—
187#877—21no—
188#874—31no—
189#874—31no—
190#874—61no—
191C4×D12—31no—
192C4×D12—31no—
193#872C2×D311yescharacteristic
194#870C2×D311yescharacteristic
195C4×Dic6C2×D311yescharacteristic
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201#835—31no—
202#835—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
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#810—31no—
214#810—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—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—81no—
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—
252C3×#67—24no—
253C2×C3×Dic3—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
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—91no—
280#478—31no—
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—31no—
293C2×C3×D4—21no—
294C2×C3×D4—61no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309#237—22no—
310#237—22no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12—121no—
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×Dic6C22×D311yescharacteristic
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—31no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—21no—
360#215—62no—
361#215—62no—
362#213—62no—
363#213—62no—
364#213—62no—
365#213—62no—
366#213—122no—
367#213—122no—
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#6711yescharacteristic
377(C2×D3)⋊C4#6711yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
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
399#204—62no—
400#204—62no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3×Dic3—22no—
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×Q8—31no—
441C4×D4—31no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4D3211yescharacteristic
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—91no—
458#103—91no—
459#102—31no—
460#102—31no—
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—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—41no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3—121no—
479C22×D3C2×#6711yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—22no—
485C3×D4—41no—
486C3×D4—64no—
487C3×D4#23512yes—
488C3×D4#23912yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—64no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—81no—
506C2×C3×C4—81no—
507C2×C3×C4—82no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—24no—
517#67—241no—
518#67—241no—
519C2×Dic3—24no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—81no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—121no—
537D12—121no—
538D12—121no—
539D12—121no—
540D12—241no—
541D12—241no—
542D12—241no—
543D12—241no—
544D12—242no—
545D12—242no—
546D12—241no—
547D12—241no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—81no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555Dic6—21no—
556Dic6#23512yes—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8—121no—
567C2×C32—42no—
568C2×C32#52511yescharacteristic
569C2×C32#57611yescharacteristic
570C2×C32#57711yescharacteristic
571C3⋊D3—81no—
572C3⋊D3—81no—
573C3×D3—41no—
574#41—62no—
575#41—62no—
576C2×Q8—31no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—181no—
584C2×D4C2×D3211yescharacteristic
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—181no—
591C22×C4—181no—
592SD16—182no—
593SD16—182no—
594D8—182no—
595D8—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—91no—
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⋊C4—61no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42C2×D3211yescharacteristic
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—42no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
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—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—241no—
657C2×D3—241no—
658C2×D3—241no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C2×#23511yescharacteristic
678C3×C4C2×#23511yescharacteristic
679C3×C4C2×#23911yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—22no—
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688C32#311911yescharacteristic, complemented, Sylow
689C23—21no—
690C23—31no—
691C23—181no—
692C23—181no—
693Q8—32no—
694Q8—61no—
695D4—21no—
696D4—64no—
697D4—181no—
698D4—181no—
699D4—181no—
700D4—181no—
701D4—721no—
702D4—721no—
703D4—721no—
704D4—721no—
705D4#379912yes—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—64no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—81no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4D3×#6711yescharacteristic
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—181no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—82no—
735C2×C3—121no—
736C2×C3#562711yescharacteristic
737C2×C3#577011yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#579111yescharacteristic
740C2×C3#583511yescharacteristic
741C2×C3#583711yescharacteristic
742D3—41no—
743D3—241no—
744D3—241no—
745D3—241no—
746D3—241no—
747D3—481no—
748D3—481no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—361no—
756C22—361no—
757C22—361no—
758C22—361no—
759C22—361no—
760C22—361no—
761C22C2×D3×#6711yescharacteristic
762C4—21no—
763C4—21no—
764C4—41no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—62no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4C2×#379911yescharacteristic
773C4D3×#23511yescharacteristic
774C3—21no—
775C3#8114411yescharacteristic, complemented
776C3#8256811yescharacteristic, complemented
777C2—42no—
778C2—121no—
779C2—721no—
780C2—721no—
781C2#1059500511yescharacteristic
782C2#1059509711yescharacteristic
783C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5546C2semidirect
2. #10593989C2semidirect
3. #10592714C2semidirect
4. C3×#5009C2semidirect
5. #10591452C2semidirect
6. #10591452C2semidirect
7. #10591404C2semidirect
8. #10591400C2semidirect
9. #10590458C2semidirect
10. #10590457C2semidirect
11. #10590423C2semidirect
12. #10590422C2semidirect
13. #10590367C2semidirect
14. #10590286C2semidirect
15. #10590253C2semidirect
63. #5546D3semidirect
78. #5009D3semidirect
688. C32#3119semidirect
775. C3#81144semidirect
776. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55462
#105939892
#105927142
C3×#50092
#105914522
#105914042
#105914002
#105904582
#105904572
#105904232
#105904222
#105903672
#105902862
#105902532
#825683
#811443