Finite Group Databasebeta

← #11889150

Subgroups — #11889150

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic
2#10594457C211yesmaximal, characteristic, complemented
3#10592483C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4764C211yesmaximal, characteristic, complemented
6#10591464C211yesmaximal, characteristic, complemented
7#10591438C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590728C211yesmaximal, characteristic, complemented
12#10590680C211yesmaximal, characteristic, complemented
13#10590594C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#81725—31nomaximal
17#80160—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21#64147C2211yescharacteristic
22#64101C2211yescharacteristic, complemented
23C3×#940C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic
26C3×#897C2211yescharacteristic, complemented
27C3×#890C2211yescharacteristic, complemented
28#63983—21no—
29#63976—21no—
30#63970—21no—
31#63908C2211yescharacteristic
32C4×#626C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63890—21no—
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63878—21no—
37#63872—21no—
38#63871C2211yescharacteristic, complemented
39#63848—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic, complemented
42C2×#3712C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61D4×#67—31no—
62#5717—31no—
63#5694—31no—
64#5642—31no—
65C3×#490—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5169—31no—
70#5164—31no—
71#5163—31no—
72#5075—31no—
73#5066—31no—
74#5048—31no—
75#4784—31no—
76#4784—31no—
77#4784—61no—
78#4780—31no—
79#4778—31no—
80#4776—31no—
81#4776D311yescharacteristic, complemented
82#4774—31no—
83#4770—31no—
84#4770—31no—
85D3×#102—31no—
86#4766—31no—
87#4764D311yescharacteristic, complemented
88#4736—31no—
89#4730—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#214—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—22no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3715—41no—
143#3712—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×#127—31no—
155C3×#125—31no—
156C3×C22⋊Q8—31no—
157#953—61no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161#940C2×D311yescharacteristic
162#939—61no—
163#938—31no—
164#938—31no—
165#938—31no—
166#938—61no—
167#938—61no—
168#937—61no—
169#937—61no—
170#937—61no—
171D4×Dic3—31no—
172C2×#214—31no—
173C2×#214C2×D311yescharacteristic, complemented
174#930—31no—
175C4×#67—31no—
176C2×C4⋊Dic3—31no—
177C22×C3⋊C8—31no—
178C2×#204C2×D311yescharacteristic
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#898—61no—
183#898—61no—
184#897—31no—
185#897C2×D311yescharacteristic, complemented
186#894—61no—
187#892—31no—
188#892—31no—
189#892—61no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890—61no—
193#890—61no—
194#890C2×D311yescharacteristic, complemented
195#886—61no—
196#877—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic, complemented
206C3×#102C2×D311yescharacteristic, complemented
207C3×C22⋊C8—31no—
208C3×#97—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224#818—31no—
225#818—31no—
226#818—31no—
227#818—61no—
228#816—31no—
229#815C2×D311yescharacteristic, complemented
230Dic3⋊C8—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238C4⋊(C3⋊C8)—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C3×#67—42no—
261C3×#67—42no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—22no—
277#625—42no—
278#625—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—31no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—62no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—31no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—121no—
327C2×#67—124no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—121no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—31no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—62no—
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—31no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#215—121no—
370#214—41no—
371#214—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—121no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—22no—
414ΓL(1,𝔽25)—121no—
415ΓL(1,𝔽25)—121no—
416D3×C8—121no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—84no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—31no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—91no—
454#127—31no—
455#126—181no—
456#125—31no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—91no—
468C4×D4—91no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—91no—
473#107—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102D3211yescharacteristic, complemented
486C22⋊C8—31no—
487C22⋊C8—91no—
488#97—31no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—81no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3D3×D411yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—42no—
543#67—62no—
544#67—81no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—242no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568D12—21no—
569D12—21no—
570D12—21no—
571D12—62no—
572D12#23712yes—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—122no—
582C4×D3—122no—
583Dic6—21no—
584Dic6—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32—81no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—41no—
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—81no—
603C24—61no—
604C24—181no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—62no—
612C2×D4—91no—
613C2×D4—121no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—361no—
619C2×D4—364no—
620C2×D4C2×D3211yescharacteristic
621C22×C4—31no—
622C22×C4—91no—
623C22×C4—181no—
624C22×C4—181no—
625SD16—62no—
626SD16—121no—
627SD16—361no—
628M16—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—361no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—61no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—181no—
655C42—181no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—84no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3#91412yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23711yescharacteristic
710C3×C4#100411yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4#100911yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—21no—
716Dic3—41no—
717Dic3—41no—
718Dic3—61no—
719Dic3—61no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726Dic3—241no—
727C32#331011yescharacteristic, complemented, Sylow
728C23—21no—
729C23—31no—
730C23—61no—
731C23—61no—
732C23—91no—
733C23—122no—
734C23—122no—
735C23—241no—
736C23—362no—
737C23—362no—
738C23—721no—
739Q8—61no—
740Q8—61no—
741D4—21no—
742D4—21no—
743D4—32no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
748D4—122no—
749D4—182no—
750D4—241no—
751D4—362no—
752D4—362no—
753D4—362no—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—91no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—362no—
768C2×C4—362no—
769C2×C4C22×D3211yescharacteristic
770C8—21no—
771C8—61no—
772C8—61no—
773C8—181no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—62no—
778C2×C3—81no—
779C2×C3—81no—
780C2×C3—122no—
781C2×C3—161no—
782C2×C3—241no—
783C2×C3#559111yescharacteristic
784C2×C3#567611yescharacteristic
785C2×C3C2×#91411yescharacteristic
786C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
787C2×C3#577511yescharacteristic
788C2×C3#577511yescharacteristic
789D3—22no—
790D3—42no—
791D3—81no—
792D3—121no—
793D3—121no—
794D3—241no—
795C22—32no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—61no—
800C22—61no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—244no—
811C22—724no—
812C22D32×D411yescharacteristic
813C4—41no—
814C4—61no—
815C4—61no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—181no—
820C4—361no—
821C4—361no—
822C4#6430711yescharacteristic
823C4D3×#23711yescharacteristic
824C3—21no—
825C3#8016011yescharacteristic, complemented
826C3#8172511yescharacteristic, complemented
827C2—62no—
828C2—81no—
829C2—122no—
830C2—241no—
831C2—361no—
832C2#1059428111yescharacteristic
833C2#1059473311yescharacteristic
834C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595293C2
hypercenter#102D32
hypocenterC32#3310
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
2. #10594457C2semidirect
3. #10592483C2semidirect
4. C3×#4776C2semidirect
5. C3×#4764C2semidirect
6. #10591464C2semidirect
7. #10591438C2semidirect
8. D3×#832C2semidirect
9. #10590943C2semidirect
10. #10590766C2semidirect
11. #10590728C2semidirect
12. #10590680C2semidirect
13. #10590594C2semidirect
14. #10590501C2semidirect
15. #10590469C2semidirect
22. #64101C22semidirect
24. C2×C3×#214C22semidirect
26. C3×#897C22semidirect
27. C3×#890C22semidirect
35. D3×C4⋊Dic3C22semidirect
38. #63871C22semidirect
40. Dic3×Dic6C22semidirect
41. C2×#3715C22semidirect
42. C2×#3712C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
49. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#815C22semidirect
54. C3×#809C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
59. #63563C22semidirect
81. #4776D3semidirect
87. #4764D3semidirect
173. C2×#214C2×D3semidirect
185. #897C2×D3semidirect
194. #890C2×D3semidirect
205. C3×#102C2×D3semidirect
206. C3×#102C2×D3semidirect
216. #832C2×D3semidirect
219. #821C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
229. #815C2×D3semidirect
233. #809C2×D3semidirect
485. #102D32semidirect
727. C32#3310semidirect
825. C3#80160semidirect
826. C3#81725semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105944572
#105924832
C3×#47762
C3×#47642
#105914642
#105914382
D3×#8322
#105909432
#105907662
#105907282
#105906802
#105905942
#105905012
#105904692
#817253
#801603