Finite Group Databasebeta

← #11889108

Subgroups — #11889108

Order 1152.

962 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595069C211yesmaximal, characteristic
2#10594825C211yesmaximal, characteristic, complemented
3#10592429C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#4731C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590943C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10#10590888C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590845C211yesmaximal, characteristic, complemented
13#10590780C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590651C211yesmaximal, characteristic, complemented
16#81303—31nomaximal
17#80160—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×#3743C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
26C3×#924C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29#63976—21no—
30#63966—21no—
31#63955—21no—
32#63922—21no—
33#63916C2211yescharacteristic
34#63914C2211yescharacteristic
35#63898C2211yescharacteristic
36#63885—21no—
37#63872C2211yescharacteristic, complemented
38#63871C2211yescharacteristic, complemented
39#63849C2211yescharacteristic, complemented
40#63848—21no—
41#63846—21no—
42#63843C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63642C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61D4×#67—31no—
62#5642—31no—
63#5609—31no—
64#5513—31no—
65C3×#480—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5169—31no—
70#5164—31no—
71#5163—31no—
72#5048—31no—
73#5041—31no—
74C2×#809—31no—
75#4891—31no—
76#4889—31no—
77#4886—31no—
78#4885—31no—
79#4784—31no—
80#4776—31no—
81#4770—31no—
82#4770—31no—
83#4766—31no—
84#4764—31no—
85#4764—31no—
86#4762—31no—
87#4736D311yescharacteristic, complemented
88#4731D311yescharacteristic, complemented
89#4730—31no—
90#4730—31no—
91#4730—61no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3757D411yescharacteristic
117#3752D411yescharacteristic
118#3750D411yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743—41no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×#204—22no—
133C3×#204—41no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144#3715—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C2×C3×C4⋊C4—31no—
157#953—61no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161#940—31no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166#937—61no—
167D4×Dic3—31no—
168C2×#214—31no—
169#930C2×D311yescharacteristic
170#929—61no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—61no—
174#926—61no—
175C2×C4⋊Dic3C2×D311yescharacteristic, complemented
176#924C2×D311yescharacteristic, complemented
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×#204C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic, complemented
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—61no—
185#898—61no—
186#898—61no—
187#897—31no—
188#895—31no—
189#893—31no—
190#892—31no—
191#892—31no—
192#890—31no—
193#890—31no—
194#890—61no—
195#889—61no—
196#887—31no—
197#886—61no—
198#884—61no—
199#882—61no—
200#877—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic, complemented
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223#818C2×D311yescharacteristic, complemented
224#818C2×D311yescharacteristic, complemented
225#815—31no—
226#815—31no—
227#815—61no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—61no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—22no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—42no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yes—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#625—42no—
278#625—42no—
279#625—81no—
280D3×Dic3—42no—
281C32×C8—21no—
282C32×C8—21no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—31no—
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—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—21no—
317C2×#67—31no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—124no—
328C22×Dic3—21no—
329C22×Dic3—61no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—121no—
333D3×D4—121no—
334D3×D4—124no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12—41no—
338C2×D12—61no—
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—62no—
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363#217—21no—
364#217—31no—
365#217—31no—
366#217—61no—
367#217—61no—
368#217—61no—
369#215—121no—
370#214—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
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—
381C4⋊Dic3—21no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8—122no—
414#204—22no—
415#204—41no—
416ΓL(1,𝔽25)—121no—
417ΓL(1,𝔽25)—121no—
418ΓL(1,𝔽25)—122no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32AGL(1,ℤ/8)12yes—
422C22×C32C22×D411yescharacteristic
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—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436D32—84no—
437C32×C4—21no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127—91no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463#121—31no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—31no—
474#107—31no—
475#107—31no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8D3211yescharacteristic, complemented
490#97—91no—
491C23×C3—21no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C23×C3D3×D411yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—61no—
508C22×D3—81no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—241no—
514C22×D3—241no—
515C3×Q8—61no—
516C3×Q8—61no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—122no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—42no—
544#67—62no—
545#67—62no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—241no—
553#67—241no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—42no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—122no—
570D12—21no—
571D12—21no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—42no—
576D12—122no—
577D12#23712yes—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—121no—
583C4×D3—121no—
584C4×D3—122no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—41no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C2×C32—22no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—41no—
604C3×D3—42no—
605C3×D3—81no—
606C3×D3—81no—
607C24—61no—
608C24—181no—
609C2×Q8—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—91no—
617C2×D4—121no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—182no—
623C2×D4—361no—
624C2×D4—364no—
625C22×C4—61no—
626C22×C4—91no—
627C22×C4—181no—
628C22×C4C2×D3211yescharacteristic
629SD16—62no—
630SD16—121no—
631SD16—361no—
632M16—361no—
633C2×C8—91no—
634C2×C8—91no—
635C2×C8—361no—
636C2×C8C2×D3211yescharacteristic
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—91no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—91no—
658C42—181no—
659C42—181no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—22no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—244no—
678C22×C3#91112yes—
679C22×C3#91412yes—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C2×D3×D411yescharacteristic
682C2×D3—22no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—84no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—244no—
702C2×D3—244no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—41no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23711yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4D3×#4111yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—61no—
723Dic3—61no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—61no—
735C23—91no—
736C23—122no—
737C23—122no—
738C23—241no—
739C23—362no—
740C23—362no—
741C23—721no—
742C23#380211yescharacteristic
743Q8—61no—
744Q8—61no—
745D4—32no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—182no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—721no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—122no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4#380211yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—21no—
776C8—181no—
777C8—181no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3—122no—
785C2×C3—241no—
786C2×C3—241no—
787C2×C3#559111yescharacteristic
788C2×C3#565411yescharacteristic
789C2×C3C2×#91111yescharacteristic
790C2×C3C2×#91411yescharacteristic
791C2×C3#577511yescharacteristic
792C2×C3#577811yescharacteristic
793D3—42no—
794D3—81no—
795D3—81no—
796D3—121no—
797D3—121no—
798D3—241no—
799C22—21no—
800C22—21no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—244no—
814C22—724no—
815C22#6379812yes—
816C22C2×#380211yescharacteristic
817C4—21no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4D3×#23711yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#8016011yescharacteristic, complemented
830C3#8130311yescharacteristic, complemented
831C2—22no—
832C2—122no—
833C2—241no—
834C2—241no—
835C2—361no—
836C2#1059429411yescharacteristic
837C2C2×#6379811yescharacteristic
838C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595069C2
hypercenterC22⋊C8D32
hypocenterC32#3310
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
2. #10594825C2semidirect
3. #10592429C2semidirect
4. C3×#4736C2semidirect
5. C3×#4731C2semidirect
6. #10591179C2semidirect
7. C2×#63562C2semidirect
8. #10590943C2semidirect
9. #10590941C2semidirect
10. #10590888C2semidirect
11. #10590876C2semidirect
12. #10590845C2semidirect
13. #10590780C2semidirect
14. #10590779C2semidirect
15. #10590651C2semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
23. C2×#3743C22semidirect
25. C2×C3×C4⋊Dic3C22semidirect
26. C3×#924C22semidirect
28. C2×C3×#204C22semidirect
37. #63872C22semidirect
38. #63871C22semidirect
39. #63849C22semidirect
42. #63843C22semidirect
43. C2×#3715C22semidirect
44. C32×C22⋊C8C22semidirect
45. #63647C22semidirect
46. #63642C22semidirect
47. #63641C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×#818C22semidirect
53. C3×#818C22semidirect
54. #63574C22semidirect
55. #63565C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
87. #4736D3semidirect
88. #4731D3semidirect
175. C2×C4⋊Dic3C2×D3semidirect
176. #924C2×D3semidirect
181. C2×#204C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
217. #821C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
223. #818C2×D3semidirect
224. #818C2×D3semidirect
489. C22⋊C8D32semidirect
731. C32#3310semidirect
829. C3#80160semidirect
830. C3#81303semidirect

Maximal subgroups

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

subgroupindex
#105950692
#105948252
#105924292
C3×#47362
C3×#47312
#105911792
C2×#635622
#105909432
#105909412
#105908882
#105908762
#105908452
#105907802
#105907792
#105906512
#813033
#801603