Finite Group Databasebeta

← #11872179

Subgroups — #11872179

Order 1152.

873 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#10595215C211yesmaximal, characteristic, complemented
2#10594494C211yesmaximal, characteristic, complemented
3#10592457C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591468C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591436C211yesmaximal, characteristic, complemented
9#10590777C211yesmaximal, characteristic, complemented
10#10590755C211yesmaximal, characteristic, complemented
11#10590708C211yesmaximal, characteristic, complemented
12#10590698C211yesmaximal, characteristic, complemented
13#10590465C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590446C211yesmaximal, characteristic, complemented
16#80952—31nomaximal
17#79992—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21#64096C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic, complemented
33Dic3×D12C2211yescharacteristic
34#63887—21no—
35#63884—21no—
36#63863—21no—
37#63862—21no—
38#63860C2211yescharacteristic, complemented
39#63857C2211yescharacteristic
40#63855C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63643C2211yescharacteristic, complemented
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5798—31no—
62#5733—31no—
63#5603—31no—
64#5545—31no—
65C3×#474—31no—
66C3×#447—31no—
67#5218—31no—
68#5153—31no—
69#5153—31no—
70#5152—31no—
71Dic3×D8—31no—
72#5084—31no—
73#5035—31no—
74#5016—31no—
75#4889—31no—
76#4888—31no—
77#4885—31no—
78#4872—31no—
79#4844—31no—
80#4840—31no—
81#4785—31no—
82#4776—31no—
83#4773D311yescharacteristic
84#4761—31no—
85#4759D311yescharacteristic, complemented
86#4758—31no—
87#4758—31no—
88#4758—61no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757—21no—
111#3754—22no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×D24—22no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—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)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3716—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×C4⋊Q8—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C2×#217—61no—
150C2×#217—61no—
151#947—61no—
152#946—61no—
153#936—31no—
154#936—61no—
155#935—61no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—61no—
162D4×Dic3—61no—
163D4×Dic3—61no—
164D4×Dic3C2×D311yescharacteristic
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169C2×#213C2×D311yescharacteristic
170C4×#67—61no—
171C2×(C2×D3)⋊C4—61no—
172#926—31no—
173#926—31no—
174#924—31no—
175C2×D24C2×D311yescharacteristic
176C2×#204—31no—
177#898—61no—
178#897—31no—
179#895C2×D311yescharacteristic
180#894—61no—
181#893—31no—
182#893—31no—
183#892—31no—
184#888C2×D311yescharacteristic, complemented
185#887—31no—
186#887—31no—
187#887—61no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191#878—61no—
192#875—31no—
193C4×D12—31no—
194#872—31no—
195C3×#107—31no—
196C3×#107—31no—
197C3×C4⋊C8—31no—
198C3×#102—21no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102C2×D311yescharacteristic
202C3×#102C2×D311yescharacteristic
203C3×C22⋊C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832C2×D311yescharacteristic
208#830—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#818C2×D311yescharacteristic, complemented
213#817—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—61no—
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#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—81no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—21no—
252#634—21no—
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—81no—
268D3×Dic3—81no—
269D3×Dic3—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—91no—
279#476—91no—
280#474—31no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—31no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—61no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—121no—
312D3×D4—22no—
313D3×D4—22no—
314C2×D12—21no—
315C2×D12C22×D311yescharacteristic
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—21no—
322C2×Dic6—31no—
323C2×Dic6—31no—
324C2×Dic6—61no—
325C3×D8—62no—
326C3×D8—62no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—31no—
341#217—21no—
342#217—31no—
343#217—31no—
344#217—61no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—121no—
354#214—62no—
355#214—64no—
356#214—62no—
357#214—62no—
358#213—22no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
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—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—22no—
399#204—62no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—22no—
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—
413C2×C3×D3—84no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—31no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—31no—
430C2×D8—31no—
431C4⋊Q8—31no—
432#126—181no—
433#124—91no—
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—91no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—31no—
452#107—31no—
453#106—91no—
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#102D3211yescharacteristic
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—64no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—241no—
477C23×C3—241no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3D3×D411yescharacteristic
484C3×Q8—241no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—32no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—241no—
495C3×D4#23712yes—
496C3×D4#23912yes—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
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—24no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—81no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3—242no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—21no—
537D12—21no—
538D12—21no—
539D12—81no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546Dic6—62no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—81no—
552Dic6—121no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—62no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C2×C32—42no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—61no—
571C2×Q8—61no—
572C2×Q8—91no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—62no—
578C2×D4—62no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586SD16—182no—
587SD16—182no—
588D8—62no—
589D8—62no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8C2×D3211yescharacteristic
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—91no—
606C22⋊C4—91no—
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—91no—
617C42—181no—
618C42—181no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—244no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—84no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23711yescharacteristic
662C3×C4C2×#23711yescharacteristic
663C3×C4C2×#23911yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—121no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—61no—
688C23—241no—
689C23—241no—
690Q8—181no—
691Q8—181no—
692Q8—241no—
693D4—21no—
694D4—32no—
695D4—64no—
696D4—61no—
697D4—61no—
698D4—61no—
699D4—241no—
700D4#379612yes—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—61no—
721C8—61no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—121no—
730C2×C3—122no—
731C2×C3—241no—
732C2×C3#558611yescharacteristic
733C2×C3#562711yescharacteristic
734C2×C3#575711yescharacteristic
735C2×C3#575711yescharacteristic
736C2×C3#577511yescharacteristic
737C2×C3#577811yescharacteristic
738D3—41no—
739D3—42no—
740D3—81no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—62no—
746C22—61no—
747C22—61no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—244no—
754C22D32×D411yescharacteristic
755C4—41no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—181no—
762C4—181no—
763C4—361no—
764C4—361no—
765C4C2×#379611yescharacteristic
766C4D3×#23711yescharacteristic
767C3—21no—
768C3#7999211yescharacteristic, complemented
769C3#8095211yescharacteristic, complemented
770C2—42no—
771C2—121no—
772C2—122no—
773C2—241no—
774C2#1059405511yescharacteristic
775C2#1059473111yescharacteristic
776C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC3×#4773C2
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. #10595215C2semidirect
2. #10594494C2semidirect
3. #10592457C2semidirect
5. C3×#4759C2semidirect
6. #10591468C2semidirect
7. #10591459C2semidirect
8. #10591436C2semidirect
9. #10590777C2semidirect
10. #10590755C2semidirect
11. #10590708C2semidirect
12. #10590698C2semidirect
13. #10590465C2semidirect
14. #10590461C2semidirect
15. #10590446C2semidirect
21. #64096C22semidirect
26. C3×#888C22semidirect
32. #63898C22semidirect
38. #63860C22semidirect
44. #63643C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63635C22semidirect
49. C3×#818C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
60. #63555C22semidirect
85. #4759D3semidirect
184. #888C2×D3semidirect
212. #818C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
233. #807C2×D3semidirect
682. C32#3118semidirect
768. C3#79992semidirect
769. C3#80952semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105944942
#105924572
C3×#47732
C3×#47592
#105914682
#105914592
#105914362
#105907772
#105907552
#105907082
#105906982
#105904652
#105904612
#105904462
#809523
#799923