Finite Group Databasebeta

← #11889772

Subgroups — #11889772

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594633C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4887C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590966C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590797C211yesmaximal, characteristic, complemented
9#10590723C211yesmaximal, characteristic, complemented
10#10590609C211yesmaximal, characteristic, complemented
11#10590596C211yesmaximal, characteristic, complemented
12#10590541C211yesmaximal, characteristic, complemented
13#10590515C211yesmaximal, characteristic, complemented
14#10590484C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#81289—31nomaximal
17#80777—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64102C2211yescharacteristic
21#64097C2211yescharacteristic, complemented
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28#63922—21no—
29#63921—21no—
30#63916—21no—
31C4×#625C2211yescharacteristic
32#63896—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34#63879—21no—
35#63863C2211yescharacteristic
36#63857—21no—
37#63856C2211yescharacteristic, complemented
38#63854—21no—
39#63847—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5635—31no—
62#5630—31no—
63#5612—31no—
64#5511—31no—
65C3×#480—31no—
66C3×#467—31no—
67#5187—31no—
68#5185—31no—
69C2×#821—31no—
70#5111—31no—
71#5046—31no—
72#5044—31no—
73#5042—31no—
74#4966—31no—
75#4890—31no—
76#4890—31no—
77#4890—61no—
78#4889—31no—
79#4887D311yescharacteristic, complemented
80#4884—31no—
81#4882D311yescharacteristic, complemented
82#4817—31no—
83#4812—31no—
84#4803—31no—
85#4794—31no—
86#4776—31no—
87D3×#102—31no—
88#4767—31no—
89#4765—31no—
90#4733—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#625D411yescharacteristic
106C2×#624—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×D3×C8—41no—
131#3724—21no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3717—22no—
142#3715—41no—
143#3711—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—31no—
155#947—31no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159C2×#215—31no—
160#938—61no—
161#937—61no—
162#936—31no—
163C2×#214—31no—
164C4×#67—31no—
165C4×#67—31no—
166C4×#67—61no—
167C2×C4⋊Dic3—31no—
168#924—31no—
169#924—61no—
170C2×#208—31no—
171C2×Dic12C2×D311yescharacteristic, complemented
172C2×#204—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×D3×C8C2×D311yescharacteristic
175#897—61no—
176#897C2×D311yescharacteristic
177#897C2×D311yescharacteristic
178#896—61no—
179#895—61no—
180#895C2×D311yescharacteristic
181#894—61no—
182#893—31no—
183#893—31no—
184#893—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4C2×D311yescharacteristic, complemented
187#889—61no—
188#889—61no—
189#888—31no—
190#888—31no—
191#888—61no—
192#887—31no—
193#883—61no—
194#882—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#878—61no—
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic, complemented
202C3×#107C2×D311yescharacteristic, complemented
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic, complemented
220#816—31no—
221#815—31no—
222#815—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226#810—31no—
227#810C2×D311yescharacteristic, complemented
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254#634—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—81no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#626—42no—
274#625—22no—
275#624—42no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—31no—
286#474—91no—
287#468—91no—
288#467—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310#239—62no—
311#239—121no—
312D3×D4—62no—
313D3×D4—121no—
314#235—62no—
315#235—121no—
316C2×D12—21no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—62no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—121no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359#217—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#215—62no—
365#215—121no—
366#214—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401#208—121no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—41no—
408#204—62no—
409ΓL(1,𝔽25)—121no—
410D3×C8—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13712yes—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#107—91no—
465#107D3211yescharacteristic, complemented
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3D3×D411yescharacteristic
494C22×D3D3×D411yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—62no—
522#67—62no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—241no—
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540D12—21no—
541D12—21no—
542D12—32no—
543D12—32no—
544D12—62no—
545D12—61no—
546D12—61no—
547D12—81no—
548D12—121no—
549D12—122no—
550D12—122no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—81no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—241no—
567Dic6—241no—
568Dic6—242no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13711yescharacteristic
581C2×C32#57611yescharacteristic
582C3⋊D3—42no—
583C3×D3—22no—
584C3×D3—41no—
585C3×D3—81no—
586C24—181no—
587#41—182no—
588#41—361no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—182no—
598C2×D4—181no—
599C2×D4—361no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606Q16—121no—
607SD16—182no—
608SD16—361no—
609M16—361no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—121no—
614C2×C8C2×D3211yescharacteristic
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—91no—
637C42—181no—
638C22×C3—21no—
639C22×C3—32no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—122no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—241no—
666C2×D3—241no—
667C2×D3—244no—
668C2×D3—244no—
669C2×D3#91812yes—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4#100411yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#331411yescharacteristic, complemented, Sylow
702C23—31no—
703C23—31no—
704C23—61no—
705C23—181no—
706C23—362no—
707C23—362no—
708C23—721no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—721no—
714D4—61no—
715D4—61no—
716D4—92no—
717D4—182no—
718D4—181no—
719D4—241no—
720D4—362no—
721D4—362no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—181no—
736C2×C4—241no—
737C2×C4—362no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4C22×D3211yescharacteristic
741C8—21no—
742C8—61no—
743C8—61no—
744C8—181no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—62no—
749C2×C3—121no—
750C2×C3—241no—
751C2×C3#561011yescharacteristic
752C2×C3#565411yescharacteristic
753C2×C3#575711yescharacteristic
754C2×C3C2×#91811yescharacteristic
755C2×C3#576911yescharacteristic
756C2×C3D3×#13711yescharacteristic
757D3—22no—
758D3—41no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—182no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22D32×D411yescharacteristic
777C4—41no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—181no—
786C4—361no—
787C4#6430711yescharacteristic
788C4#6431911yescharacteristic
789C3—21no—
790C3#8077711yescharacteristic, complemented
791C3#8128911yescharacteristic, complemented
792C2—62no—
793C2—121no—
794C2—241no—
795C2—362no—
796C2#1059461711yescharacteristic
797C2#1059473411yescharacteristic
798C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594633C2
hypercenter#107D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594532C2semidirect
3. #10592589C2semidirect
4. C3×#4887C2semidirect
5. C3×#4882C2semidirect
6. #10590966C2semidirect
7. D3×#821C2semidirect
8. #10590797C2semidirect
9. #10590723C2semidirect
10. #10590609C2semidirect
11. #10590596C2semidirect
12. #10590541C2semidirect
13. #10590515C2semidirect
14. #10590484C2semidirect
15. #10590440C2semidirect
21. #64097C22semidirect
22. C2×C3×Dic12C22semidirect
27. C3×D3×C4⋊C4C22semidirect
37. #63856C22semidirect
40. #63843C22semidirect
43. C2×#3711C22semidirect
44. C32×#107C22semidirect
46. #63641C22semidirect
48. #63634C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#810C22semidirect
54. C3×#807C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. #63555C22semidirect
79. #4887D3semidirect
81. #4882D3semidirect
171. C2×Dic12C2×D3semidirect
186. D3×C4⋊C4C2×D3semidirect
201. C3×#107C2×D3semidirect
202. C3×#107C2×D3semidirect
219. (C2×D3)⋊C8C2×D3semidirect
227. #810C2×D3semidirect
228. #810C2×D3semidirect
237. #807C2×D3semidirect
465. #107D32semidirect
701. C32#3314semidirect
790. C3#80777semidirect
791. C3#81289semidirect

Maximal subgroups

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

subgroupindex
#105946332
#105945322
#105925892
C3×#48872
C3×#48822
#105909662
D3×#8212
#105907972
#105907232
#105906092
#105905962
#105905412
#105905152
#105904842
#105904402
#812893
#807773