Finite Group Databasebeta

← #11872182

Subgroups — #11872182

Order 1152.

878 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#10595215C211yesmaximal, characteristic, complemented
2#10594343C211yesmaximal, characteristic, complemented
3#10592484C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591471C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic
8#10591445C211yesmaximal, characteristic, complemented
9#10590779C211yesmaximal, characteristic, complemented
10#10590754C211yesmaximal, characteristic, complemented
11#10590705C211yesmaximal, characteristic, complemented
12#10590699C211yesmaximal, characteristic, complemented
13#10590465C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590448C211yesmaximal, characteristic, complemented
16#80952—31nomaximal
17#80136—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64102C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63909C2211yescharacteristic
32#63907—21no—
33#63898C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63871—21no—
36#63864C2211yescharacteristic, complemented
37#63855C2211yescharacteristic
38#63853—21no—
39#63848—21no—
40#63843C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45#63642C2211yescharacteristic, 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#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5733—31no—
63#5643—31no—
64#5545—31no—
65C3×#474—31no—
66C3×#450—31no—
67#5217—31no—
68#5165—31no—
69#5165—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5084—31no—
73#5045—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#4785—31no—
83#4785—61no—
84#4776D311yescharacteristic, complemented
85#4773—31no—
86#4761—31no—
87#4759D311yescharacteristic, complemented
88#4758—31no—
89#4756—31no—
90#4737—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
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×#214—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—22no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3714—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—31no—
147C3×C22⋊Q8—31no—
148C3×C4×D4—31no—
149C2×#217—61no—
150C2×#217—61no—
151#947—31no—
152#947—61no—
153#946—61no—
154Q8×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—61no—
160D4×Dic3—61no—
161D4×Dic3—61no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214C2×D311yescharacteristic
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#926—31no—
172#926—31no—
173C2×D24—31no—
174C2×#204C2×D311yescharacteristic
175#898—61no—
176#898—61no—
177#897—61no—
178#897C2×D311yescharacteristic
179#895—31no—
180#894—61no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#892—31no—
186#888C2×D311yescharacteristic, complemented
187#887—31no—
188#885—61no—
189#883—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—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#835—31no—
205#835—31no—
206#832—31no—
207#832C2×D311yescharacteristic
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—61no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818C2×D311yescharacteristic, complemented
216#817—31no—
217#816—31no—
218#815—31no—
219#815—31no—
220#815—61no—
221Dic3⋊C8—31no—
222Dic3⋊C8C2×D311yescharacteristic, complemented
223C8×Dic3—31no—
224C8×Dic3—31no—
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—21no—
238C22×C3×D3—24no—
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—81no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—81no—
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—81no—
268#626—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—31no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—61no—
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—121no—
311D3×D4—22no—
312D3×D4—22no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—121no—
323C2×C4×D3C22×D311yescharacteristic
324C2×Dic6—21no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—62no—
327C3×SD16—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⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343#217—21no—
344#217—31no—
345#217—31no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—121no—
352#214—22no—
353#213—62no—
354#213—64no—
355#213—62no—
356#213—62no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
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—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
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
398D24—62no—
399#204—22no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
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—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—31no—
427C2×SD16—31no—
428C2×SD16—31no—
429C2×D8—91no—
430C2×D8—91no—
431C4⋊Q8—31no—
432#126—181no—
433#124—91no—
434#124—181no—
435#123—181no—
436C22⋊Q8—31no—
437C22⋊Q8—181no—
438#121—91no—
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—241no—
476C23×C3—241no—
477C22×D3—21no—
478C22×D3—24no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3—121no—
484C22×D3D3×D411yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—241no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—22no—
491C3×D4—32no—
492C3×D4—41no—
493C3×D4—64no—
494C3×D4—61no—
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—61no—
509C2×C3×C4—241no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—24no—
513#67—241no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—81no—
526C2×Dic3—121no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—242no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—21no—
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—241no—
543D12#23712yes—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551Dic6—21no—
552Dic6—21no—
553Dic6—81no—
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—42no—
565C2×C32#52511yescharacteristic
566C2×C32#57611yescharacteristic
567C2×C32#57711yescharacteristic
568C3⋊D3—81no—
569C3×D3—41no—
570C3×D3—42no—
571C24—61no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587SD16—62no—
588SD16—62no—
589D8—182no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—91no—
618C42—181no—
619C42—181no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—84no—
646C2×D3—122no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
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×C4C2×#23711yescharacteristic
668C3×C4C2×#23911yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—64no—
689C23—61no—
690C23—181no—
691C23—241no—
692C23—241no—
693Q8—61no—
694Q8—61no—
695Q8—241no—
696D4—21no—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—181no—
701D4—181no—
702D4—721no—
703D4#379612yes—
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—42no—
730C2×C3—42no—
731C2×C3—82no—
732C2×C3—121no—
733C2×C3—122no—
734C2×C3#558611yescharacteristic
735C2×C3#562711yescharacteristic
736C2×C3#575711yescharacteristic
737C2×C3#576211yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#577811yescharacteristic
740D3—41no—
741D3—42no—
742D3—242no—
743D3—241no—
744D3—241no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—62no—
750C22—61no—
751C22—61no—
752C22—121no—
753C22—121no—
754C22—244no—
755C22—361no—
756C22—361no—
757C22—361no—
758C22D32×D411yescharacteristic
759C4—41no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—361no—
769C4C2×#379611yescharacteristic
770C4D3×#23711yescharacteristic
771C3—21no—
772C3#8013611yescharacteristic, complemented
773C3#8095211yescharacteristic, complemented
774C2—42no—
775C2—121no—
776C2—122no—
777C2—721no—
778C2#1059405511yescharacteristic
779C2#1059473211yescharacteristic
780C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591448C2
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. #10594343C2semidirect
3. #10592484C2semidirect
4. C3×#4776C2semidirect
5. C3×#4759C2semidirect
6. #10591471C2semidirect
8. #10591445C2semidirect
9. #10590779C2semidirect
10. #10590754C2semidirect
11. #10590705C2semidirect
12. #10590699C2semidirect
13. #10590465C2semidirect
14. #10590459C2semidirect
15. #10590448C2semidirect
21. #64102C22semidirect
26. C3×#888C22semidirect
36. #63864C22semidirect
40. #63843C22semidirect
44. #63648C22semidirect
45. #63642C22semidirect
46. #63635C22semidirect
49. C3×#818C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
57. #63564C22semidirect
60. #63553C22semidirect
84. #4776D3semidirect
87. #4759D3semidirect
186. #888C2×D3semidirect
215. #818C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
233. #807C2×D3semidirect
685. C32#3118semidirect
772. C3#80136semidirect
773. C3#80952semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105943432
#105924842
C3×#47762
C3×#47592
#105914712
#105914482
#105914452
#105907792
#105907542
#105907052
#105906992
#105904652
#105904592
#105904482
#809523
#801363