Finite Group Databasebeta

← #11866334

Subgroups — #11866334

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63811C211yesmaximal, characteristic, complemented
2C2×#63796C211yesmaximal, characteristic, complemented
3#10594010C211yesmaximal, characteristic
4#10593848C211yesmaximal, characteristic, complemented
5#10592538C211yesmaximal, characteristic, complemented
6C3×#4848C211yesmaximal, characteristic, complemented
7C3×#4845C211yesmaximal, characteristic, complemented
8#10590956C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10#10590876C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590797C211yesmaximal, characteristic, complemented
13#10590796C211yesmaximal, characteristic, complemented
14#10590364C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#80600—31nomaximal
17#80385—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64081C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C3×#875C2211yescharacteristic
29C3×#874C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic, complemented
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63922—21no—
33#63922—21no—
34#63914C2211yescharacteristic
35#63885—21no—
36#63885—21no—
37#63863C2211yescharacteristic
38#63849C2211yescharacteristic
39#63843C2211yescharacteristic, complemented
40#63843C2211yescharacteristic, complemented
41#63837—21no—
42#63837—21no—
43#63836—21no—
44#63836—21no—
45C2×#3718C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49#63811—24no—
50#63796—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C2×#918—31no—
64C2×#915—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67#5715—31no—
68#5674—31no—
69#5572—31no—
70#5572—31no—
71C3×#464—31no—
72C3×#460—31no—
73#5185—31no—
74#5166—31no—
75#5163—31no—
76#5163—31no—
77#5075—31no—
78#5054—31no—
79#5028—31no—
80#5027—31no—
81#4848D311yescharacteristic, complemented
82#4845D311yescharacteristic, complemented
83#4839—31no—
84#4839—31no—
85#4839—61no—
86#4804—31no—
87#4798—31no—
88#4772—31no—
89#4770—31no—
90#4770—31no—
91#4767—31no—
92#4762—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#625—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802—22no—
113#3797—22no—
114#3797D414yescomplemented
115#3796—22no—
116#3796—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752D411yescharacteristic
121#3752D411yescharacteristic
122#3750D411yescharacteristic
123#3750D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3743—22no—
128C8×C3⋊D3—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×Dic12—22no—
138C3×#204—22no—
139C3×#204—22no—
140C3×#204—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32—21no—
149#3718—22no—
150#3715—22no—
151#3715—22no—
152#3715—22no—
153#3043—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×#237—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C3×#127—31no—
165C3×#124—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—31no—
168#947—31no—
169Q8×Dic3—31no—
170Q8×Dic3—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—31no—
176#940—31no—
177#940—31no—
178#939—61no—
179#939—61no—
180#937—61no—
181#937—61no—
182#936—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186#918—64no—
187#915—64no—
188D3×SD16—64no—
189D3×SD16—64no—
190C2×Dic12C2×D311yescharacteristic, complemented
191C2×#204C2×D311yescharacteristic
192C2×#204C2×D311yescharacteristic
193C2×#204C2×D311yescharacteristic, complemented
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—61no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—61no—
200#892—31no—
201#892—31no—
202#892—61no—
203#892—61no—
204#887—31no—
205#887—31no—
206#887—61no—
207#887—61no—
208#884—61no—
209#884—61no—
210#882—61no—
211#882—61no—
212#875C2×D311yescharacteristic
213#874C2×D311yescharacteristic
214#872—31no—
215#872—31no—
216#872—61no—
217#872—61no—
218#872—61no—
219C4×Dic6—61no—
220C4×Dic6—61no—
221C4×Dic6C2×D311yescharacteristic, complemented
222C4×Dic6C2×D311yescharacteristic, complemented
223C3×C4⋊C8—21no—
224C3×C4⋊C8C2×D311yescharacteristic, complemented
225C3×C4⋊C8C2×D311yescharacteristic, complemented
226C3×#103—31no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#821C2×D311yescharacteristic
235#821C2×D311yescharacteristic
236#821C2×D311yescharacteristic, complemented
237#816C2×D311yescharacteristic, complemented
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8—61no—
244#810—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C2×D32—42no—
256C2×D32—81no—
257C2×D32—81no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3C2×D412yes—
265C4×C3⋊D3#4112yes—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—81no—
278C3×D12—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6C2×D412yes—
284C3×Dic6C2×D412yes—
285#627—24no—
286#626—42no—
287#625—42no—
288#625—81no—
289#625—81no—
290#624—24no—
291D3×Dic3—42no—
292C32×C8—21no—
293C32×C8—21no—
294C3⋊(C3⋊C8)—21no—
295C3⋊(C3⋊C8)—21no—
296C2×#137—91no—
297C22×SD16—91no—
298#535—91no—
299#519—91no—
300#464—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—31no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C22×Dic3—61no—
329#239—62no—
330#239—62no—
331D3×Q8—34no—
332D3×Q8—34no—
333D3×Q8—62no—
334D3×Q8—62no—
335#237—62no—
336#237—62no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—62no—
340D3×D4—62no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—61no—
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C2×Dic6C22×D311yescharacteristic
358C3×Q16—62no—
359C3×SD16—62no—
360C3×SD16—62no—
361C3×SD16—62no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—21no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42C22×D311yescharacteristic
378C3×C42C22×D311yescharacteristic
379#217—61no—
380#217—61no—
381#216—62no—
382#216—62no—
383#215—62no—
384#215—62no—
385#215—62no—
386#214—62no—
387#214—62no—
388#214—62no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—31no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3—21no—
416C4×Dic3—21no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8—61no—
432Dic12—22no—
433#204—22no—
434#204—22no—
435#204—22no—
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—122no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—122no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3#12112yes—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455D32—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3#12112yes—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471#137—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—91no—
482C22×C8—91no—
483#127—31no—
484#127—91no—
485#124—31no—
486#124—91no—
487#121—181no—
488#121—181no—
489#120—181no—
490#120—181no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—91no—
494C4×Q8—91no—
495C4×Q8—181no—
496C4×Q8—181no—
497#117—91no—
498#117—91no—
499#117—181no—
500#117—181no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8D3211yescharacteristic, complemented
505#103—31no—
506#103—91no—
507#102—31no—
508#102—31no—
509#102—31no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—61no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C3×Q8—32no—
529C3×Q8—32no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—241no—
541C3×D4—241no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—122no—
557#67—122no—
558#67—122no—
559#67—241no—
560#67—241no—
561#67—241no—
562#67—241no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—122no—
578D12—21no—
579D12—21no—
580D12—21no—
581D12—21no—
582D12—21no—
583D12—21no—
584D12—81no—
585D12—81no—
586D12—122no—
587C4×D3—32no—
588C4×D3—32no—
589C4×D3—32no—
590C4×D3—32no—
591C4×D3—62no—
592C4×D3—62no—
593C4×D3—64no—
594C4×D3—64no—
595C4×D3—122no—
596Dic6—21no—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6—64no—
601Dic6—64no—
602Dic6D3×D412yes—
603Dic6D3×D412yes—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—41no—
609C3×C8—41no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—121no—
615C3⋊C8—121no—
616C2×C32C2×#12111yescharacteristic
617C2×C32#57711yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3×D3—81no—
621C3×D3—81no—
622C3×D3—81no—
623C24—181no—
624#41—182no—
625#41—182no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—31no—
629C2×Q8—94no—
630C2×Q8—181no—
631C2×Q8—182no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—181no—
638C2×D4—182no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C22×C4—91no—
644C22×C4—181no—
645C22×C4—181no—
646Q16—62no—
647Q16—182no—
648SD16—62no—
649SD16—62no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654M16—182no—
655C2×C8—91no—
656C2×C8—91no—
657C2×C8—182no—
658C2×C8C2×D3211yescharacteristic
659C2×C8C2×D3211yescharacteristic
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C42—61no—
676C42—61no—
677C42—91no—
678C42—181no—
679C42—181no—
680C42—181no—
681C42C2×D3211yescharacteristic
682C22×C3—21no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C2×D3—32no—
695C2×D3—32no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—244no—
713C2×D3—244no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C2×D3×D411yescharacteristic
729C3×C4D3×#4111yescharacteristic
730C3×C4D3×#4111yescharacteristic
731Dic3—22no—
732Dic3—22no—
733Dic3—32no—
734Dic3—32no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745C32#304311yescharacteristic, complemented, Sylow
746C23—61no—
747C23—61no—
748C23—61no—
749C23—91no—
750C23—362no—
751C23—721no—
752C23—721no—
753Q8—32no—
754Q8—32no—
755Q8—61no—
756Q8—61no—
757Q8—61no—
758Q8—61no—
759Q8—184no—
760D4—61no—
761D4—61no—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—241no—
767D4—241no—
768D4—362no—
769D4—362no—
770D4—721no—
771D4—721no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—91no—
778C2×C4—92no—
779C2×C4—92no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—184no—
783C2×C4—362no—
784C2×C4#380211yescharacteristic
785C2×C4#380211yescharacteristic
786C2×C4C22×D3211yescharacteristic
787C8—21no—
788C8—21no—
789C8—181no—
790C8—181no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—241no—
795C2×C3—241no—
796C2×C3—241no—
797C2×C3D3×#12111yescharacteristic
798C2×C3D3×#12111yescharacteristic
799C2×C3#576211yescharacteristic
800C2×C3#577011yescharacteristic
801C2×C3#577511yescharacteristic
802C2×C3#577811yescharacteristic
803D3—62no—
804D3—62no—
805D3—81no—
806D3—81no—
807D3—81no—
808D3—122no—
809C22—92no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—181no—
820C22—181no—
821C22—724no—
822C22C2×#380211yescharacteristic
823C4—21no—
824C4—21no—
825C4—62no—
826C4—62no—
827C4—92no—
828C4—121no—
829C4—121no—
830C4—121no—
831C4—181no—
832C4—181no—
833C4D32×D411yescharacteristic
834C4#6431911yescharacteristic
835C3—21no—
836C3#8038511yescharacteristic, complemented
837C3#8060011yescharacteristic, complemented
838C2—182no—
839C2—241no—
840C2—241no—
841C2—241no—
842C2#1059461211yescharacteristic
843C2#1059468611yescharacteristic
844C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594010C2
hypercenterC4⋊C8D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63811C2semidirect
2. C2×#63796C2semidirect
4. #10593848C2semidirect
5. #10592538C2semidirect
6. C3×#4848C2semidirect
7. C3×#4845C2semidirect
8. #10590956C2semidirect
9. #10590941C2semidirect
10. #10590876C2semidirect
11. #10590876C2semidirect
12. #10590797C2semidirect
13. #10590796C2semidirect
14. #10590364C2semidirect
15. #10590267C2semidirect
24. C2×C3×Dic12C22semidirect
27. C2×C3×#204C22semidirect
30. C3×C4×Dic6C22semidirect
31. C3×C4×Dic6C22semidirect
39. #63843C22semidirect
40. #63843C22semidirect
45. C2×#3718C22semidirect
48. C2×#3715C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63641C22semidirect
53. #63641C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
57. C3×#821C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
62. #63562C22semidirect
81. #4848D3semidirect
82. #4845D3semidirect
114. #3797D4semidirect
190. C2×Dic12C2×D3semidirect
193. C2×#204C2×D3semidirect
221. C4×Dic6C2×D3semidirect
222. C4×Dic6C2×D3semidirect
224. C3×C4⋊C8C2×D3semidirect
225. C3×C4⋊C8C2×D3semidirect
236. #821C2×D3semidirect
237. #816C2×D3semidirect
504. C4⋊C8D32semidirect
745. C32#3043semidirect
836. C3#80385semidirect
837. C3#80600semidirect

Maximal subgroups

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

subgroupindex
C2×#638112
C2×#637962
#105940102
#105938482
#105925382
C3×#48482
C3×#48452
#105909562
#105909412
#105908762
#105907972
#105907962
#105903642
#105902672
#806003
#803853