Finite Group Databasebeta

← #11889724

Subgroups — #11889724

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594991C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic
3#10592429C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591188C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590961C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10#10590866C211yesmaximal, characteristic, complemented
11#10590845C211yesmaximal, characteristic, complemented
12#10590796C211yesmaximal, characteristic, complemented
13#10590779C211yesmaximal, characteristic, complemented
14#10590778C211yesmaximal, characteristic, complemented
15#10590650C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#80163—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×#3743C2211yescharacteristic, complemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28#63977—21no—
29D3×#217—21no—
30#63964—21no—
31#63952—21no—
32#63919C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63900C2211yescharacteristic, complemented
35#63898C2211yescharacteristic
36#63895—21no—
37#63886—21no—
38#63884—21no—
39#63871C2211yescharacteristic, complemented
40#63863C2211yescharacteristic
41#63847—21no—
42#63843C2211yescharacteristic, complemented
43C2×#3718C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63642C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5635—31no—
63#5630—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5173—31no—
70#5166—31no—
71#5164—31no—
72#5051—31no—
73#5051—31no—
74C2×#809—31no—
75#4890—31no—
76#4889—31no—
77#4886—31no—
78#4882—31no—
79#4808—31no—
80#4803—31no—
81#4798—31no—
82#4794—31no—
83#4774—31no—
84#4771—31no—
85#4765—31no—
86#4759—31no—
87#4731D311yescharacteristic, complemented
88#4730—31no—
89#4730—31no—
90#4730—61no—
91#4722D311yescharacteristic, complemented
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757D411yescharacteristic
115#3752D411yescharacteristic
116#3750D411yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3743—41no—
122C3×#217—21no—
123C3×#217—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×#204—22no—
132C3×#204—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3718—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157#946—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#216—31no—
161#939—61no—
162#938—31no—
163#936—31no—
164#935—61no—
165D4×Dic3—31no—
166C4×#67—31no—
167C4×#67—31no—
168C4×#67—61no—
169C4×#67—61no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171#924—61no—
172#924C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—61no—
177C2×#204C2×D311yescharacteristic
178C2×#204C2×D311yescharacteristic
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—61no—
182#897—31no—
183#897—61no—
184#896—61no—
185#895—31no—
186#895—61no—
187#894—61no—
188#893—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#889—61no—
192#889—61no—
193#888—31no—
194#888—31no—
195#887—31no—
196#882—61no—
197#67⋊C4—61no—
198D3×C22⋊C4—61no—
199#878—61no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8C2×D311yescharacteristic
208C3×C22⋊C8C2×D311yescharacteristic
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818C2×D311yescharacteristic, complemented
221#818C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224#815—31no—
225#815—31no—
226#815—61no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230#810—31no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—22no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—81no—
272#626—42no—
273#626—81no—
274#624—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3⋊(C3⋊C8)—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—31no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#239—62no—
318#239—121no—
319#237—62no—
320#237—121no—
321C2×D12—22no—
322C2×D12—21no—
323C2×D12—41no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C3×SD16—121no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356#217—21no—
357#217—21no—
358#217—31no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#216—121no—
366#216—121no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—21no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—122no—
408#204—22no—
409#204—41no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—121no—
412ΓL(1,𝔽25)—122no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#13712yes—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8D3211yescharacteristic
481#97—91no—
482C23×C3—21no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—61no—
497C22×D3—81no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×D4—32no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—62no—
527#67—62no—
528#67—122no—
529#67—122no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547C2×Dic3—122no—
548C2×Dic3—241no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12—42no—
553D12—122no—
554D12—241no—
555D12#23712yes—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—121no—
561C4×D3—121no—
562C4×D3—122no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—241no—
571Dic6—241no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—41no—
578C3⋊C8—62no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32—22no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13711yescharacteristic
587C2×C32#57611yescharacteristic
588C3⋊D3—41no—
589C3×D3—42no—
590C3×D3—81no—
591C24—61no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—31no—
596C2×Q8—181no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—121no—
603C2×D4—181no—
604C2×D4—181no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4C2×D3211yescharacteristic
611Q16—361no—
612SD16—62no—
613SD16—121no—
614M16—361no—
615C2×C8—91no—
616C2×C8—91no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—91no—
642C42—181no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—62no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—244no—
658C22×C3#91512yes—
659C22×C3#91812yes—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—84no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—61no—
710C23—61no—
711C23—91no—
712C23—122no—
713C23—122no—
714C23—241no—
715C23#380211yescharacteristic
716Q8—61no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—721no—
721D4—32no—
722D4—61no—
723D4—61no—
724D4—61no—
725D4—122no—
726D4—182no—
727D4—362no—
728D4—721no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—241no—
743C2×C4—362no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4#380211yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—21no—
750C8—181no—
751C8—181no—
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—122no—
759C2×C3—241no—
760C2×C3#559111yescharacteristic
761C2×C3#565411yescharacteristic
762C2×C3C2×#91511yescharacteristic
763C2×C3C2×#91811yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3#577411yescharacteristic
766D3—42no—
767D3—81no—
768D3—121no—
769D3—121no—
770D3—241no—
771C22—21no—
772C22—21no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—244no—
783C22#6381112yes—
784C22C2×#380211yescharacteristic
785C4—21no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—181no—
793C4—181no—
794C4—181no—
795C4D3×#23711yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#8016311yescharacteristic, complemented
799C3#8148611yescharacteristic, complemented
800C2—22no—
801C2—122no—
802C2—241no—
803C2—361no—
804C2#1059429411yescharacteristic
805C2C2×#6381111yescharacteristic
806C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC22⋊C8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594991C2semidirect
3. #10592429C2semidirect
4. C3×#4731C2semidirect
5. C3×#4722C2semidirect
6. #10591188C2semidirect
7. C2×#63562C2semidirect
8. #10590961C2semidirect
9. #10590957C2semidirect
10. #10590866C2semidirect
11. #10590845C2semidirect
12. #10590796C2semidirect
13. #10590779C2semidirect
14. #10590778C2semidirect
15. #10590650C2semidirect
22. C2×#3743C22semidirect
32. #63919C22semidirect
34. #63900C22semidirect
39. #63871C22semidirect
42. #63843C22semidirect
43. C2×#3718C22semidirect
45. #63647C22semidirect
46. #63642C22semidirect
47. #63641C22semidirect
50. C3×#818C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
87. #4731D3semidirect
91. #4722D3semidirect
220. #818C2×D3semidirect
221. #818C2×D3semidirect
222. #816C2×D3semidirect
223. #816C2×D3semidirect
708. C32#3314semidirect
798. C3#80163semidirect
799. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105949912
#105948892
#105924292
C3×#47312
C3×#47222
#105911882
C2×#635622
#105909612
#105909572
#105908662
#105908452
#105907962
#105907792
#105907782
#105906502
#814863
#801633