Finite Group Databasebeta

← #11872200

Subgroups — #11872200

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595126C211yesmaximal, characteristic, complemented
2#10594604C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic, complemented
4C3×#4787C211yesmaximal, characteristic, complemented
5C3×#4779C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic
7#10591436C211yesmaximal, characteristic, complemented
8#10591432C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590775C211yesmaximal, characteristic, complemented
11#10590759C211yesmaximal, characteristic, complemented
12#10590698C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#81352—31nomaximal
17#80509—31nomaximal
18C2×D3×D12C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#3753C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#936C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63982—21no—
29#63962—21no—
30#63959—21no—
31#63956—21no—
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63918C2211yescharacteristic, complemented
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic
38#63880—21no—
39#63856C2211yescharacteristic
40#63855C2211yescharacteristic
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5682—31no—
62#5603—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#463—31no—
67#5169—31no—
68Dic3×SD16—31no—
69#5156—31no—
70#5152—31no—
71#5057—31no—
72#5036—31no—
73#5007—31no—
74#4996—31no—
75#4890—31no—
76#4889—31no—
77#4870—31no—
78#4852—31no—
79#4842—31no—
80#4840—31no—
81#4817—31no—
82#4815—31no—
83#4787—31no—
84#4787D311yescharacteristic, complemented
85#4785—31no—
86#4779D311yescharacteristic, complemented
87#4756—31no—
88#4756—31no—
89#4756—61no—
90#4731—31no—
91#4720—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757—21no—
111#3753—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3717—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#124—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C3×#117—31no—
150#946—31no—
151Q8×Dic3—31no—
152C2×#215—31no—
153#938C2×D311yescharacteristic
154#936—61no—
155#936C2×D311yescharacteristic, complemented
156#935—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—61no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—61no—
164C2×#213C2×D311yescharacteristic
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167#926—31no—
168#924—31no—
169C2×#204—31no—
170C2×#204C2×D311yescharacteristic
171#893—31no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—61no—
176#893C2×D311yescharacteristic
177#892C2×D311yescharacteristic
178#888—31no—
179#887—31no—
180#886—61no—
181#885—61no—
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#879—61no—
187#879—61no—
188#878—61no—
189#878—61no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193#872—31no—
194#869—31no—
195C3×#107—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#102—21no—
200C3×#102—31no—
201C3×#102C2×D311yescharacteristic, complemented
202C3×#102C2×D311yescharacteristic, complemented
203C3×C22⋊C8—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832C2×D311yescharacteristic, complemented
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#817—31no—
217#817C2×D311yescharacteristic, complemented
218#815—31no—
219#815—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225#810—31no—
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—81no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—81no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—81no—
268#626—24no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—31no—
279#476—91no—
280#474—91no—
281#463—31no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—21no—
301C2×#67—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—121no—
306D3×D4—62no—
307D3×D4—62no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—62no—
327C3×D8—62no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—31no—
344C3×C42—61no—
345#217—21no—
346#217—21no—
347#217—21no—
348#217—31no—
349#217—31no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355#215—62no—
356#213—22no—
357#213—62no—
358#213—62no—
359#213—64no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
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—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398#204—22no—
399#204—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—22no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413D32—84no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—31no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—31no—
434#124—181no—
435#123—181no—
436C22⋊Q8—91no—
437C22⋊Q8—181no—
438#121—31no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
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—31no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—91no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102D3211yescharacteristic, complemented
465C22⋊C8—31no—
466C22⋊C8—91no—
467#97—91no—
468C4×C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—41no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C22×D3D3×D411yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—22no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—32no—
493C3×D4—41no—
494C3×D4—61no—
495C3×D4—241no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—64no—
512#67—81no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—242no—
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—242no—
549C4×D3—241no—
550Dic6—21no—
551Dic6—21no—
552Dic6—241no—
553Dic6—241no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—62no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C2×C32—81no—
565C2×C32#52511yescharacteristic
566C2×C32#57611yescharacteristic
567C2×C32#57711yescharacteristic
568C3⋊D3—42no—
569C3×D3—41no—
570C3×D3—42no—
571C24—181no—
572C2×Q8—31no—
573C2×Q8—181no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—182no—
579C2×D4—182no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587SD16—62no—
588SD16—182no—
589D8—62no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—61no—
618C42—91no—
619C42—181no—
620C22×C3—21no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—62no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—22no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—122no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—244no—
654C2×D3—244no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23711yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—62no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—61no—
689C23—184no—
690C23—181no—
691C23—721no—
692C23—721no—
693Q8—61no—
694Q8—61no—
695Q8—721no—
696D4—21no—
697D4—21no—
698D4—32no—
699D4—61no—
700D4—92no—
701D4—184no—
702D4—181no—
703D4—241no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—61no—
724C8—61no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—82no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—121no—
733C2×C3—122no—
734C2×C3#560611yescharacteristic
735C2×C3#565611yescharacteristic
736C2×C3#577011yescharacteristic
737C2×C3#577011yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#577411yescharacteristic
740D3—42no—
741D3—41no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—361no—
756C22—361no—
757C22—724no—
758C22D32×D411yescharacteristic
759C4—41no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—361no—
769C4#6430611yescharacteristic
770C4D3×#23711yescharacteristic
771C3—21no—
772C3#8050911yescharacteristic, complemented
773C3#8135211yescharacteristic, complemented
774C2—81no—
775C2—121no—
776C2—122no—
777C2—362no—
778C2#1059426711yescharacteristic
779C2#1059473511yescharacteristic
780C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591515C2
hypercenter#102D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595126C2semidirect
2. #10594604C2semidirect
3. #10592455C2semidirect
4. C3×#4787C2semidirect
5. C3×#4779C2semidirect
7. #10591436C2semidirect
8. #10591432C2semidirect
9. #10590942C2semidirect
10. #10590775C2semidirect
11. #10590759C2semidirect
12. #10590698C2semidirect
13. #10590555C2semidirect
14. #10590521C2semidirect
15. #10590484C2semidirect
19. D4×C3⋊Dic3C22semidirect
23. C3×#936C22semidirect
34. #63918C22semidirect
41. #63843C22semidirect
43. C32×#102C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63634C22semidirect
47. C3×#832C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
60. #63555C22semidirect
84. #4787D3semidirect
86. #4779D3semidirect
155. #936C2×D3semidirect
201. C3×#102C2×D3semidirect
202. C3×#102C2×D3semidirect
207. #832C2×D3semidirect
217. #817C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
226. #810C2×D3semidirect
233. #807C2×D3semidirect
464. #102D32semidirect
685. C32#3118semidirect
772. C3#80509semidirect
773. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105951262
#105946042
#105924552
C3×#47872
C3×#47792
#105915152
#105914362
#105914322
#105909422
#105907752
#105907592
#105906982
#105905552
#105905212
#105904842
#813523
#805093