Finite Group Databasebeta

← #11872310

Subgroups — #11872310

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5562C211yesmaximal, characteristic, complemented
2#10593887C211yesmaximal, characteristic, complemented
3#10592717C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591519C211yesmaximal, characteristic, complemented
6#10591439C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8#10591415C211yesmaximal, characteristic, complemented
9#10590613C211yesmaximal, characteristic, complemented
10#10590492C211yesmaximal, characteristic, complemented
11#10590467C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#79595—31nomaximal
18C2×#3795C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C3×#930—21no—
26C3×#929—21no—
27C3×#895C2211yescharacteristic
28C3×#890C2211yescharacteristic
29C3×#884—21no—
30C3×#883—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×#872C2211yescharacteristic
34#63902—21no—
35Dic3×D12C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63844C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63637C2211yescharacteristic
45#63634C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#540—31no—
62#5562D311yescharacteristic, complemented
63#5546—31no—
64#5523—31no—
65C3×C4×D8—31no—
66#5158—31no—
67#5150—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—
76#5018—31no—
77#5018—31no—
78#5018—61no—
79C4×#214—31no—
80#5014—31no—
81#5014—31no—
82C4×#213D311yescharacteristic, complemented
83#5000—31no—
84#4882—31no—
85#4877—31no—
86#4781—31no—
87#4777—31no—
88#4763—31no—
89#4762—31no—
90C4×#204—31no—
91#4690—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—22no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3716—22no—
140#3713—22no—
141#3119—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C2×C3×D8—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×D4—21no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4C2×D311yescharacteristic
157C3×C4×D4C2×D311yescharacteristic
158C3×#117—31no—
159#940C2×D311yescharacteristic
160#938C2×D311yescharacteristic
161D4×Dic3—31no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—31no—
165C2×#214—61no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213C2×D311yescharacteristic
169#930—21no—
170#929—21no—
171C4×#67—61no—
172C2×C4⋊Dic3—31no—
173C2×Dic3⋊C4—61no—
174C2×#204—31no—
175#895C2×D311yescharacteristic
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179#890C2×D311yescharacteristic
180#887—31no—
181#884—21no—
182#883—21no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186#877—61no—
187C4×D12—31no—
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×#107—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#832—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(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic
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#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic
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—
247C2×C3⋊Dic3—21no—
248#634—21no—
249#634#4112yes—
250C3×#67—81no—
251C3×#67—81no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#625—24no—
268D3×Dic3—24no—
269D3×Dic3—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—91no—
287C4×SD16—91no—
288C4×D8—31no—
289#433—91no—
290C2×C3×D4—21no—
291C2×C3×D4—31no—
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—
304C22×C3×C4—61no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#237—62no—
314#237—62no—
315#235—62no—
316#235—62no—
317C2×D12—21no—
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C3×D8—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—21no—
355#217—61no—
356#214—62no—
357#214—62no—
358#214—62no—
359#214—64no—
360#213—22no—
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—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368(C2×D3)⋊C4#6711yescharacteristic
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383Dic3⋊C4#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—121no—
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—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—22no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
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—22no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—91no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—31no—
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—91no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—31no—
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—91no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—41no—
472C23×C3—61no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3C2×#6711yescharacteristic
477C3×D4—22no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—32no—
483C3×D4—41no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—241no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—81no—
505C2×C3×C4—81no—
506C2×C3×C4—82no—
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—64no—
516#67—64no—
517#67—81no—
518#67—81no—
519#67—81no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—64no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534D12—21no—
535D12—21no—
536D12—21no—
537D12—81no—
538D12#23512yes—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—64no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—241no—
545C4×D3—241no—
546Dic6—32no—
547Dic6—32no—
548Dic6—62no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—62no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32—81no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3×D3—41no—
567C3×D3—42no—
568C3×D3—81no—
569#41—182no—
570#41—182no—
571C2×Q8—91no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587SD16—182no—
588SD16—182no—
589D8—62no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C42—31no—
615C42—181no—
616C42—181no—
617C42C2×D3211yescharacteristic
618C22×C3—21no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—62no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C22×#6711yescharacteristic
639C2×D3—22no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23511yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679C32#311911yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682C23—61no—
683C23—61no—
684Q8—92no—
685Q8—181no—
686D4—21no—
687D4—21no—
688D4—32no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—184no—
693D4—241no—
694D4—241no—
695D4—241no—
696D4—241no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—81no—
706C2×C4—184no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4D3×#6711yescharacteristic
714C2×C4D3×#6711yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—61no—
717C8—61no—
718C8—181no—
719C8—181no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—82no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—122no—
727C2×C3—121no—
728C2×C3—241no—
729C2×C3#554711yescharacteristic
730C2×C3#575711yescharacteristic
731C2×C3#577011yescharacteristic
732C2×C3#582811yescharacteristic
733C2×C3#583511yescharacteristic
734C2×C3#583611yescharacteristic
735D3—41no—
736D3—42no—
737D3—81no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—21no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—121no—
758C4—121no—
759C4—182no—
760C4—361no—
761C4D3×#23511yescharacteristic
762C4#6430611yescharacteristic
763C3—21no—
764C3#7959511yescharacteristic, complemented
765C3#8343411yescharacteristic, complemented
766C2—81no—
767C2—121no—
768C2—122no—
769C2—241no—
770C2#1059506011yescharacteristic
771C2#1059509611yescharacteristic
772C2#1059546611yescharacteristic
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. #10593887C2semidirect
3. #10592717C2semidirect
4. C3×C4×#213C2semidirect
5. #10591519C2semidirect
6. #10591439C2semidirect
7. #10591428C2semidirect
8. #10591415C2semidirect
9. #10590613C2semidirect
10. #10590492C2semidirect
11. #10590467C2semidirect
12. #10590438C2semidirect
13. C4×#3716C2semidirect
14. #10590344C2semidirect
15. #10590264C2semidirect
62. #5562D3semidirect
82. C4×#213D3semidirect
679. C32#3119semidirect
764. C3#79595semidirect
765. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#55622
#105938872
#105927172
C3×C4×#2132
#105915192
#105914392
#105914282
#105914152
#105906132
#105904922
#105904672
#105904382
C4×#37162
#105903442
#105902642
#834343
#795953