Finite Group Databasebeta

← #11889715

Subgroups — #11889715

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596106C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic
3C3×#5051C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591656C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591590C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591157C211yesmaximal, characteristic, complemented
10#10591103C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590612C211yesmaximal, characteristic, complemented
13#10590541C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590471C211yesmaximal, characteristic, complemented
16#80777—31nomaximal
17#80163—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64155C2211yescharacteristic, complemented
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C4×#638C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25#64106—21no—
26C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
27#64098—21no—
28#64097C2211yescharacteristic, complemented
29#64090—21no—
30#64087—21no—
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36#63977—21no—
37D3×#217—21no—
38#63916C2211yescharacteristic
39#63898C2211yescharacteristic
40#63886—21no—
41#63884—21no—
42#63863C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5635—31no—
63#5635—31no—
64#5635—61no—
65#5630—31no—
66C3×#467—31no—
67C3×#450—31no—
68C2×#832—31no—
69#5187—31no—
70#5185—31no—
71#5174—31no—
72#5173—31no—
73#5166—31no—
74#5164—31no—
75C2×#821—31no—
76#5111—31no—
77#5051D311yescharacteristic, complemented
78#5046D311yescharacteristic, complemented
79#5044—31no—
80#4890—31no—
81#4882—31no—
82#4817—31no—
83#4812—31no—
84#4803—31no—
85#4794—31no—
86#4774—31no—
87#4771—31no—
88#4765—31no—
89#4759—31no—
90#4730—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757D411yescharacteristic
116#3752—21no—
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124#3750—21no—
125#3750D411yescharacteristic
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#217—21no—
129C3×#216—41no—
130C3×#215—22no—
131C3×#215—41no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3712—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157#953—61no—
158C2×#217—61no—
159#947—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166C2×#216C2×D311yescharacteristic, complemented
167C2×#215C2×D311yescharacteristic
168C2×#215C2×D311yescharacteristic
169#939—61no—
170#938—31no—
171#936—31no—
172#935—61no—
173D4×Dic3—31no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—61no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180#924C2×D311yescharacteristic
181C22×C3⋊C8C2×D311yescharacteristic
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184#897—61no—
185#897—61no—
186#897—62no—
187#895—31no—
188#895—61no—
189#894—61no—
190#893—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—61no—
194#889—61no—
195#889—61no—
196#889—62no—
197#888—31no—
198#888—31no—
199#888—61no—
200#882—61no—
201#67⋊C4—61no—
202#67⋊C4—61no—
203#67⋊C4—62no—
204D3×C22⋊C4—61no—
205#878—61no—
206#878—61no—
207#878—62no—
208C3×#107—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×C22⋊C8—31no—
214#835—31no—
215#835—31no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228#818—31no—
229#818—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236#810C2×D311yescharacteristic, complemented
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic
239#807—31no—
240#807—31no—
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C32×Q8—21no—
250C32×Q8—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—22no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—81no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—81no—
267#634—81no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×D12#4112yes—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—81no—
279D3×Dic3—42no—
280D3×Dic3—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—91no—
287#489—91no—
288#484—91no—
289#480—91no—
290#474—91no—
291#468—91no—
292#467—31no—
293#464—91no—
294#452—91no—
295#450—31no—
296#440—91no—
297#435—91no—
298#417—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C22×C3×C4—21no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—62no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324#239—62no—
325#239—121no—
326#237—62no—
327#237—121no—
328C2×D12—22no—
329C2×D12—21no—
330C2×D12—41no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—62no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—62no—
346C2×Dic6C22×D311yescharacteristic
347C3×Q16—121no—
348C3×SD16—62no—
349C3×SD16—121no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—22no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—61no—
367#217—21no—
368#217—31no—
369#217—31no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#216—41no—
376#215—22no—
377#215—41no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—62no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—62no—
397C4⋊Dic3—62no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—62no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425ΓL(1,𝔽25)—121no—
426ΓL(1,𝔽25)—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32#13712yes—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—84no—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4C2×#4111yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—91no—
454C22×D4—31no—
455C2×Q16—31no—
456C2×SD16—31no—
457C2×SD16—31no—
458C2×M16—91no—
459C22×C8—31no—
460C4⋊Q8—91no—
461#125—181no—
462#124—91no—
463#123—181no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8—181no—
468C22⋊Q8D3211yescharacteristic
469#121—91no—
470#121—181no—
471#120—181no—
472C4×Q8—91no—
473C4×D4—91no—
474C4×D4—91no—
475C4×D4—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—181no—
479#107—31no—
480#107—91no—
481#107—91no—
482C4⋊C8—91no—
483#103—31no—
484#103—31no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—31no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493C22⋊C8—31no—
494C22⋊C8—91no—
495#97—91no—
496C23×C3—21no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—61no—
511C22×D3—81no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—41no—
517C3×Q8—41no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×D4—32no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—64no—
546#67—62no—
547#67—62no—
548#67—122no—
549#67—241no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—122no—
568C2×Dic3—241no—
569C2×Dic3—241no—
570C2×Dic3—241no—
571C2×Dic3—242no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—42no—
576D12—122no—
577D12—241no—
578D12#23712yes—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—121no—
584C4×D3—121no—
585C4×D3—122no—
586C4×D3—241no—
587C4×D3—241no—
588C4×D3—241no—
589C4×D3—242no—
590Dic6—21no—
591Dic6—21no—
592Dic6—241no—
593Dic6—241no—
594Dic6—242no—
595C3×C8—61no—
596C3×C8—61no—
597C3×C8—61no—
598C3×C8—61no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32—22no—
604C2×C32#54611yescharacteristic
605C2×C32C2×#13711yescharacteristic
606C2×C32#57611yescharacteristic
607C3⋊D3—41no—
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611#41—182no—
612#41—361no—
613C2×Q8—31no—
614C2×Q8—181no—
615C2×Q8C2×D3211yescharacteristic
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—62no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—121no—
622C2×D4—181no—
623C2×D4—181no—
624C22×C4—91no—
625C22×C4—181no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630Q16—121no—
631SD16—62no—
632SD16—121no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—121no—
639C4⋊C4—21no—
640C4⋊C4—31no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4C2×D3211yescharacteristic
651C22⋊C4—21no—
652C22⋊C4—61no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C42—91no—
661C42—181no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—62no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—244no—
677C22×C3#91512yes—
678C22×C3#91812yes—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—22no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—62no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—84no—
695C2×D3—121no—
696C2×D3—121no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23711yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4D3×#4111yescharacteristic
714Dic3—41no—
715Dic3—41no—
716Dic3—62no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—122no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#331411yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—91no—
735C23—122no—
736C23—122no—
737C23—241no—
738C23#381111yescharacteristic
739Q8—21no—
740Q8—21no—
741Q8—61no—
742Q8—61no—
743Q8—721no—
744D4—32no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—122no—
749D4—182no—
750D4—362no—
751D4—721no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—362no—
766C2×C4—721no—
767C2×C4—721no—
768C2×C4—721no—
769C2×C4#381111yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—61no—
774C8—61no—
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—42no—
781C2×C3—122no—
782C2×C3—241no—
783C2×C3#559111yescharacteristic
784C2×C3#561011yescharacteristic
785C2×C3C2×#91511yescharacteristic
786C2×C3C2×#91811yescharacteristic
787C2×C3#576911yescharacteristic
788C2×C3#577411yescharacteristic
789D3—42no—
790D3—81no—
791D3—122no—
792D3—121no—
793D3—121no—
794C22—21no—
795C22—21no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—244no—
806C22#6395112yes—
807C22C2×#381111yescharacteristic
808C4—21no—
809C4—41no—
810C4—41no—
811C4—121no—
812C4—121no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—361no—
817C4—361no—
818C4D3×#23711yescharacteristic
819C4#6431311yescharacteristic
820C3—21no—
821C3#8016311yescharacteristic, complemented
822C3#8077711yescharacteristic, complemented
823C2—22no—
824C2—122no—
825C2—241no—
826C2—361no—
827C2#1059530711yescharacteristic
828C2C2×#6395111yescharacteristic
829C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC22⋊Q8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596106C2semidirect
3. C3×#5051C2semidirect
4. C3×#5046C2semidirect
5. #10591656C2semidirect
6. #10591612C2semidirect
7. #10591590C2semidirect
8. #10591572C2semidirect
9. #10591157C2semidirect
10. #10591103C2semidirect
11. C2×#63563C2semidirect
12. #10590612C2semidirect
13. #10590541C2semidirect
14. #10590510C2semidirect
15. #10590471C2semidirect
21. #64155C22semidirect
22. Q8×C3⋊Dic3C22semidirect
26. C4⋊C4×C3⋊D3C22semidirect
28. #64097C22semidirect
31. C2×C3×#216C22semidirect
43. C2×#3712C22semidirect
44. C3×#835C22semidirect
46. C3×#810C22semidirect
49. C3×#807C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. #63572C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
77. #5051D3semidirect
78. #5046D3semidirect
166. C2×#216C2×D3semidirect
216. #835C2×D3semidirect
236. #810C2×D3semidirect
241. #807C2×D3semidirect
731. C32#3314semidirect
821. C3#80163semidirect
822. C3#80777semidirect

Maximal subgroups

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

subgroupindex
#105961062
#105948892
C3×#50512
C3×#50462
#105916562
#105916122
#105915902
#105915722
#105911572
#105911032
C2×#635632
#105906122
#105905412
#105905102
#105904712
#807773
#801633