Finite Group Databasebeta

← #11872309

Subgroups — #11872309

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5562C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591438C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591415C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590493C211yesmaximal, characteristic, complemented
11#10590468C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13C4×#3715C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#79812—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×#930—21no—
26C3×#929—21no—
27C3×#895C2211yescharacteristic
28C3×#890C2211yescharacteristic
29C3×#884—21no—
30C3×#883—21no—
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63894C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63883—21no—
37#63881—21no—
38#63880—21no—
39Dic3×Dic6C2211yescharacteristic
40#63836—21no—
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic
46C4×C3⋊(C3⋊C8)C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#803C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#540—31no—
62#5574—31no—
63#5562D311yescharacteristic, complemented
64#5523—31no—
65C3×#440—31no—
66#5172—31no—
67#5163—31no—
68#5075—31no—
69#5072—31no—
70#5066—31no—
71#5063—31no—
72#5037—31no—
73#5037—31no—
74#5034—31no—
75#5033—31no—
76C4×#215—31no—
77#5018D311yescharacteristic, complemented
78C4×#214—31no—
79#5014—31no—
80C4×#213—31no—
81C4×#213—31no—
82C4×#213—61no—
83#5000—31no—
84#4891—31no—
85#4882—31no—
86#4810—31no—
87#4799—31no—
88#4786—31no—
89#4777—31no—
90#4711—31no—
91#4709—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
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⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3753—22no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#214—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
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
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138Dic32—21no—
139#3715—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#123—61no—
148C3×#123—61no—
149C3×#121—31no—
150C3×#121—31no—
151C3×#121—61no—
152C3×#121—61no—
153C3×C4×Q8—31no—
154C3×C4×D4—21no—
155C3×C4×D4—31no—
156C3×C4×D4C2×D311yescharacteristic
157C3×C4×D4C2×D311yescharacteristic
158C3×#117—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161#940C2×D311yescharacteristic
162#938C2×D311yescharacteristic
163C2×#214—31no—
164C2×#214C2×D311yescharacteristic
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—61no—
169#930—21no—
170#929—21no—
171C2×C4⋊Dic3—31no—
172C2×D24—31no—
173#895C2×D311yescharacteristic
174#893—31no—
175#893—61no—
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—61no—
180#890C2×D311yescharacteristic
181#884—21no—
182#883—21no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190C4×D12C2×D311yescharacteristic
191#872—61no—
192#872C2×D311yescharacteristic
193C4×Dic6—31no—
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810C2×D311yescharacteristic
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#808—31no—
223#808—31no—
224#808—31no—
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803C2×D311yescharacteristic
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)#4112yes—
249C4×C3⋊D3—81no—
250C3×#67—81no—
251C3×#67—81no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
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—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—41no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—62no—
311#235—62no—
312#235—62no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—62no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—21no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—21no—
357#215—62no—
358#214—22no—
359#214—62no—
360#213—62no—
361#213—62no—
362#213—62no—
363#213—64no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4#6711yescharacteristic
372(C2×D3)⋊C4#6711yescharacteristic
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4#6711yescharacteristic
386Dic3⋊C4#6711yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
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—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—21no—
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—
424C3×Dic3—41no—
425C2×#41—91no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—91no—
429C2×D8—91no—
430#127—31no—
431#125—31no—
432#123—61no—
433#123—61no—
434#121—31no—
435#121—31no—
436#121—61no—
437#121—61no—
438C4×Q8—31no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445C4×D4D3211yescharacteristic
446#117—31no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450#107—31no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—31no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—41no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C22×D3C2×#6711yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×D4—22no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—41no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C3×D4—241no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—81no—
507C2×C3×C4—81no—
508C2×C3×C4—82no—
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—64no—
517#67—81no—
518#67—81no—
519#67—81no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530D12—21no—
531D12—21no—
532D12—32no—
533D12—32no—
534D12—62no—
535D12—64no—
536D12—61no—
537D12—61no—
538D12—81no—
539D12—121no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—64no—
543C4×D3—64no—
544C4×D3—81no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551Dic6—21no—
552Dic6#23512yes—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—81no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3⋊D3—42no—
568C3×D3—41no—
569C3×D3—81no—
570#41—182no—
571#41—182no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588SD16—62no—
589SD16—182no—
590D8—182no—
591D8—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—91no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—122no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—241no—
651C2×D3—241no—
652C3×C4—22no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—62no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—22no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311911yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—61no—
686C23—181no—
687Q8—32no—
688Q8—61no—
689D4—21no—
690D4—21no—
691D4—61no—
692D4—61no—
693D4—92no—
694D4—184no—
695D4—181no—
696D4—241no—
697D4—241no—
698D4—241no—
699D4—241no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—81no—
710C2×C4—184no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4D3×#6711yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—61no—
720C8—61no—
721C8—181no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—82no—
727C2×C3—81no—
728C2×C3—81no—
729C2×C3—121no—
730C2×C3—241no—
731C2×C3#554711yescharacteristic
732C2×C3#577411yescharacteristic
733C2×C3#577811yescharacteristic
734C2×C3#582811yescharacteristic
735C2×C3#583511yescharacteristic
736C2×C3#583611yescharacteristic
737D3—41no—
738D3—81no—
739D3—122no—
740D3—122no—
741D3—242no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—62no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4D3×#23511yescharacteristic
766C4#6430611yescharacteristic
767C3—21no—
768C3#7981211yescharacteristic, complemented
769C3#8343411yescharacteristic, complemented
770C2—81no—
771C2—121no—
772C2—241no—
773C2—362no—
774C2#1059506011yescharacteristic
775C2#1059509711yescharacteristic
776C2#1059546411yescharacteristic
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×#5562C2semidirect
2. #10593890C2semidirect
3. C4×#3753C2semidirect
4. C3×#5018C2semidirect
5. #10591521C2semidirect
6. #10591438C2semidirect
7. #10591429C2semidirect
8. #10591415C2semidirect
9. #10590615C2semidirect
10. #10590493C2semidirect
11. #10590468C2semidirect
12. #10590438C2semidirect
13. C4×#3715C2semidirect
14. #10590346C2semidirect
15. #10590265C2semidirect
63. #5562D3semidirect
77. #5018D3semidirect
682. C32#3119semidirect
768. C3#79812semidirect
769. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#55622
#105938902
C4×#37532
C3×#50182
#105915212
#105914382
#105914292
#105914152
#105906152
#105904932
#105904682
#105904382
C4×#37152
#105903462
#105902652
#834343
#798123