Finite Group Databasebeta

← #11872173

Subgroups — #11872173

Order 1152.

872 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
1#10593994C211yesmaximal, characteristic, complemented
2#10593983C211yesmaximal, characteristic, complemented
3#10592409C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5C3×#4709C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic, complemented
7#10590944C211yesmaximal, characteristic
8#10590860C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10#10590762C211yesmaximal, characteristic, complemented
11#10590759C211yesmaximal, characteristic, complemented
12#10590755C211yesmaximal, characteristic, complemented
13#10590709C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15C4×#3714C211yesmaximal, characteristic, complemented
16#79886—31nomaximal
17#79383—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic, complemented
22C2×C3×D24C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic, complemented
25C3×#872C2211yescharacteristic
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63918C2211yescharacteristic, complemented
29#63915—21no—
30#63908C2211yescharacteristic
31#63905—21no—
32#63904—21no—
33#63894C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63881—21no—
36#63862—21no—
37#63860C2211yescharacteristic, complemented
38#63857C2211yescharacteristic
39#63851—21no—
40#63841C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#97C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C4×C3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#5561—31no—
62#5545—31no—
63#5534—31no—
64#5521—31no—
65C3×#442—31no—
66C3×#433—31no—
67#5156—31no—
68#5153—31no—
69C4×#214—31no—
70C4×#213—31no—
71#4870—31no—
72#4868—31no—
73#4846—31no—
74#4844—31no—
75#4844—31no—
76#4842—31no—
77#4787—31no—
78#4784—31no—
79#4776—31no—
80#4759—31no—
81#4737—31no—
82#4732—31no—
83#4731—31no—
84#4723—31no—
85#4711D311yescharacteristic, complemented
86#4710—31no—
87#4710—31no—
88#4710—61no—
89#4709D311yescharacteristic, complemented
90C4×D24—31no—
91C4×#204—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#625—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116#3744—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D24—22no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3716—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148#938—31no—
149#936—31no—
150D4×Dic3—31no—
151C2×#214—31no—
152C2×#213—31no—
153#930—31no—
154#929—61no—
155C4×#67—61no—
156C2×(C2×D3)⋊C4—61no—
157#926—31no—
158#924—31no—
159#924—61no—
160C2×D24—31no—
161C2×D24C2×D311yescharacteristic
162C2×#204—31no—
163C2×#204—31no—
164C2×#204—31no—
165C2×#204—61no—
166#898—61no—
167#897—31no—
168#896—61no—
169#893—31no—
170#893—61no—
171#893—61no—
172#892—31no—
173#888—31no—
174#885—61no—
175#885—61no—
176#883—61no—
177#67⋊C4—61no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180D3×C22⋊C4—61no—
181#879—61no—
182#875—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—61no—
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic, complemented
190#872C2×D311yescharacteristic
191#869—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—21no—
203C3×#97C2×D311yescharacteristic, complemented
204C3×#97C2×D311yescharacteristic, complemented
205C3×C4×C8—31no—
206#832—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic, complemented
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818—31no—
220#818—31no—
221#818—61no—
222#817—31no—
223#817C2×D311yescharacteristic, complemented
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228Dic3⋊C8C2×D311yescharacteristic, complemented
229Dic3⋊C8C2×D311yescharacteristic, complemented
230#810—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234C4×C3⋊C8C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—81no—
251#634—21no—
252#634—21no—
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#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266#627—81no—
267#626—24no—
268#625—81no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—31no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3—61no—
301D3×D4—62no—
302D3×D4—62no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×D12—62no—
307C2×D12—61no—
308C2×D12—62no—
309C2×D12C22×D311yescharacteristic
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—121no—
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C3×D8—62no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—21no—
343C3×C42—31no—
344C3×C42C22×D311yescharacteristic
345C3×C42C22×D311yescharacteristic
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#214—62no—
353#213—62no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4D1211yescharacteristic
368(C2×D3)⋊C4D1211yescharacteristic
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384Dic3⋊C4D1211yescharacteristic
385Dic3⋊C4D1211yescharacteristic
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394D24—22no—
395D24—62no—
396#204—62no—
397#204—62no—
398#204—64no—
399#204—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
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—
413D32—84no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—31no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—91no—
434#124—181no—
435#123—181no—
436C22⋊Q8—91no—
437C22⋊Q8—181no—
438#121—91no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—31no—
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—31no—
466C22⋊C8—31no—
467#97D3211yescharacteristic, complemented
468C4×C8—31no—
469C23×C3—31no—
470C23×C3—61no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3C2×D1211yescharacteristic
484C3×D4—32no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—241no—
499C2×C3×C4—241no—
500C2×C3×C4C2×D1211yescharacteristic
501C2×C3×C4C2×D1211yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—64no—
507#67—241no—
508#67—241no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—121no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—241no—
521C2×Dic3C2×D1211yescharacteristic
522C2×Dic3C2×D1211yescharacteristic
523C2×Dic3C2×D1211yescharacteristic
524D12—21no—
525D12—21no—
526D12—21no—
527D12—32no—
528D12—32no—
529D12—62no—
530D12—64no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12#23512yes—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—81no—
538C4×D3—81no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—242no—
545Dic6—62no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—241no—
552Dic6—241no—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—181no—
571C2×Q8—91no—
572C2×Q8—181no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—182no—
578C2×D4—182no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586SD16—182no—
587SD16—182no—
588D8—62no—
589D8—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8C2×D3211yescharacteristic
593C2×C8C2×D3211yescharacteristic
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—181no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—62no—
623C22×C3—61no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C22×D1211yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—241no—
648C2×D3—241no—
649C2×D3—244no—
650C2×D3—244no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
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—122no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—61no—
686C23—184no—
687C23—181no—
688C23—721no—
689C23—721no—
690Q8—181no—
691Q8—181no—
692Q8—721no—
693D4—32no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—92no—
698D4—184no—
699D4—181no—
700D4—721no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×D1211yescharacteristic
717C2×C4D3×D1211yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—21no—
721C8—61no—
722C8—61no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—121no—
727C2×C3—122no—
728C2×C3—241no—
729C2×C3#552411yescharacteristic
730C2×C3#554711yescharacteristic
731C2×C3#575111yescharacteristic
732C2×C3#575211yescharacteristic
733C2×C3#577411yescharacteristic
734C2×C3#577511yescharacteristic
735D3—42no—
736D3—41no—
737D3—81no—
738D3—122no—
739D3—122no—
740D3—242no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—182no—
751C22—361no—
752C22—361no—
753C22—724no—
754C22C2×D3×D1211yescharacteristic
755C4—21no—
756C4—21no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4—361no—
763C4—361no—
764C4—361no—
765C4D3×#23511yescharacteristic
766C4#6430611yescharacteristic
767C3—21no—
768C3#7938311yescharacteristic, complemented
769C3#7988611yescharacteristic, complemented
770C2—121no—
771C2—122no—
772C2—241no—
773C2—362no—
774C2#1059399711yescharacteristic
775C2#1059471311yescharacteristic
776C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10590944C2
hypercenter#97D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593983C2semidirect
3. #10592409C2semidirect
4. C3×#4711C2semidirect
5. C3×#4709C2semidirect
6. #10590946C2semidirect
8. #10590860C2semidirect
9. #10590834C2semidirect
10. #10590762C2semidirect
11. #10590759C2semidirect
12. #10590755C2semidirect
13. #10590709C2semidirect
14. C4×#3716C2semidirect
15. C4×#3714C2semidirect
21. C4×#634C22semidirect
24. C3×C4×D12C22semidirect
28. #63918C22semidirect
37. #63860C22semidirect
43. C32×#97C22semidirect
45. #63645C22semidirect
46. #63643C22semidirect
48. C3×#821C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C4×C3⋊C8C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
60. #63563C22semidirect
85. #4711D3semidirect
89. #4709D3semidirect
189. C4×D12C2×D3semidirect
203. C3×#97C2×D3semidirect
204. C3×#97C2×D3semidirect
215. #821C2×D3semidirect
223. #817C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
234. C4×C3⋊C8C2×D3semidirect
467. #97D32semidirect
682. C32#3118semidirect
768. C3#79383semidirect
769. C3#79886semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105939832
#105924092
C3×#47112
C3×#47092
#105909462
#105909442
#105908602
#105908342
#105907622
#105907592
#105907552
#105907092
C4×#37162
C4×#37142
#798863
#793833