Finite Group Databasebeta

← #370539

Subgroups — #370539

Order 512.

1291 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C211yesmaximal, characteristic
2#21304C211yesmaximal, characteristic, complemented
3C2×#1866C211yesmaximal, characteristic
4C2×#1765C211yesmaximal, characteristic
5#20336C211yesmaximal, characteristic
6#11386C211yesmaximal, characteristic, complemented
7#11376C211yesmaximal, characteristic, complemented
8#11233C211yesmaximal, characteristic, complemented
9#11221C211yesmaximal, characteristic, complemented
10#10909C211yesmaximal, characteristic, complemented
11#10877C211yesmaximal, characteristic, complemented
12#10860C211yesmaximal, characteristic, complemented
13#10791C211yesmaximal, characteristic
14#10791C211yesmaximal, characteristic
15#10790C211yesmaximal, characteristic
16C22×#131C2211yescharacteristic
17C22×#131C2211yescharacteristic
18C2×#533C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20#3076—24no—
21#3076—24no—
22C2×#479C411yescharacteristic, complemented
23C2×#479C411yescharacteristic, complemented
24C2×#477C411yescharacteristic, complemented
25C2×#475C411yescharacteristic, complemented
26C2×#478C411yescharacteristic, complemented
27C2×#478C411yescharacteristic, complemented
28C2×#476C411yescharacteristic, complemented
29C2×#474C411yescharacteristic, complemented
30C22×#108C2211yescharacteristic
31C2×#427C2211yescharacteristic
32C2×#427C2211yescharacteristic
33C2×#424C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#104C2211yescharacteristic
36C22×#104C2211yescharacteristic
37C2×#416C2211yescharacteristic
38C2×#416C2211yescharacteristic
39C2×#405C2211yescharacteristic
40C22×#97C2211yescharacteristic
41#1985—21no—
42#1985—21no—
43#1984—21no—
44#1984—21no—
45#1866—24no—
46#1765—24no—
47C2×#341C2211yescharacteristic
48C2×#341C2211yescharacteristic
49C2×#341C2211yescharacteristic
50C2×#339C2211yescharacteristic
51C2×#339C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56#1729—21no—
57#1729—21no—
58#1729C2211yescharacteristic
59#1729C2211yescharacteristic
60#1729C2211yescharacteristic
61#1729C2211yescharacteristic
62#1728—21no—
63#1728C2211yescharacteristic
64#1728C2211yescharacteristic
65C2×#336—21no—
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C2×#131—22no—
73C2×#131—22no—
74C2×#131—22no—
75C2×#131—22no—
76C2×#131—22no—
77C2×#131—22no—
78C2×#131—22no—
79C2×#131—41no—
80C2×#131—41no—
81C2×#131—41no—
82C2×#131—41no—
83C2×#131Q814yescomplemented
84C22×M16—21no—
85C22×M16—21no—
86C22×M16C2311yescharacteristic
87C22×M16C2311yescharacteristic
88C22×M16C2311yescharacteristic
89C22×M16C2311yescharacteristic
90C23×C8—21no—
91C23×C8—21no—
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96#533—22no—
97#533—22no—
98#533—41no—
99#533—41no—
100C2×C4⋊Q8C2×C411yescharacteristic
101C2×C4⋊Q8C2×C411yescharacteristic
102C2×#125C2×C411yescharacteristic
103C2×#125C2×C411yescharacteristic
104C2×C22⋊Q8—21no—
105C2×C22⋊Q8—21no—
106C4×#41—22no—
107C4×#41—22no—
108C4×#41—41no—
109C4×#41—41no—
110C2×C4×Q8—21no—
111C2×C4×Q8—21no—
112C2×C4×Q8C2×C411yescharacteristic
113C2×C4×Q8C2×C411yescharacteristic
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4C2×C411yescharacteristic
117C2×C4×D4C2×C411yescharacteristic
118C2×#117—21no—
119C2×#117C2311yescharacteristic
120C2×#117C2311yescharacteristic
121C2×#117C2311yescharacteristic
122C22×C42—21no—
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126#479—24no—
127#479—24no—
128#478—24no—
129#478—24no—
130#477—24no—
131#476—24no—
132#475—24no—
133#474—24no—
134C2×#108—22no—
135C2×#108—22no—
136C2×#108—41no—
137#427—22no—
138#427—22no—
139#427—22no—
140#427—22no—
141C2×#107C2×C411yescharacteristic
142C2×#107C2×C411yescharacteristic
143C2×#107C2×C411yescharacteristic
144C2×#107C2×C411yescharacteristic
145C2×#106C2×C411yescharacteristic
146C2×#106C2×C411yescharacteristic
147C2×#106C2×C411yescharacteristic
148C2×#106C2×C411yescharacteristic
149#424—22no—
150#424—41no—
151C2×C4⋊C8—22no—
152C2×C4⋊C8—22no—
153C2×C4⋊C8—21no—
154C2×C4⋊C8—21no—
155C2×C4⋊C8C2×C411yescharacteristic
156C2×C4⋊C8C2×C411yescharacteristic
157C2×C4⋊C8C2×C411yescharacteristic
158C2×C4⋊C8C2×C411yescharacteristic
159C2×#104—22no—
160C2×#104—22no—
161C2×#104—22no—
162C2×#104—22no—
163C2×#104—22no—
164C2×#104Q814yescomplemented
165#416—22no—
166#416—22no—
167#416D414yes—
168#416D414yes—
169C2×#103C2×C411yescharacteristic
170C2×#103C2×C411yescharacteristic
171C2×#103C2×C411yescharacteristic
172C2×#103C2×C411yescharacteristic
173C2×#102C2×C411yescharacteristic
174C2×#102C2×C411yescharacteristic
175C2×#102C2×C411yescharacteristic
176C2×#102C2×C411yescharacteristic
177#405—22no—
178#405—41no—
179C2×#97—22no—
180C2×#97—21no—
181C2×#97—22no—
182C2×#97—41no—
183C2×C4×C8—21no—
184C2×#95—21no—
185C2×#95—21no—
186#341—22no—
187#341—22no—
188#341—41no—
189#339—22no—
190#339—22no—
191#339—41no—
192#339—41no—
193#339—41no—
194#339—41no—
195#336—22no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—22no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—41no—
210#336D411yescharacteristic
211#336D411yescharacteristic
212#336D411yescharacteristic
213#336D411yescharacteristic
214C2×#41—21no—
215C2×#41—21no—
216C2×#41—21no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41C2×D412yes—
221C2×#41C2×D412yes—
222C2×#41C2×Q812yes—
223C2×#41C2×Q812yes—
224C2×#41#4112yes—
225C2×#41#4112yes—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×Q8C22×C411yescharacteristic
229C22×D4—21no—
230C22×D4C22×C411yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4#4111yescharacteristic
237C23×C4#4111yescharacteristic
238C23×C4C2411yescharacteristic
239#131—28no—
240#131—44no—
241#131—44no—
242#131—44no—
243#131—44no—
244#131—44no—
245#131—44no—
246#131—44no—
247C2×M16—24no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—24no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—42no—
271C2×M16—42no—
272C2×M16—42no—
273C2×M16—42no—
274C2×M16C2×Q812yes—
275C2×M16C2×Q812yes—
276C2×M16#4112yes—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—24no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—24no—
302C22×C8—21no—
303C22×C8—42no—
304C22×C8—42no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8C22×C411yescharacteristic
308C22×C8C22×C411yescharacteristic
309C22×C8C22×C411yescharacteristic
310C22×C8C22×C411yescharacteristic
311C22×C8C2×D411yescharacteristic
312C22×C8C2×D411yescharacteristic
313C22×C8C2×D412yes—
314C22×C8C2×D412yes—
315C22×C8C2×D411yescharacteristic
316C22×C8C2×D411yescharacteristic
317C22×C8C2×Q812yes—
318C22×C8#4112yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—41no—
322C4⋊Q8—41no—
323#125—22no—
324#125—22no—
325#125—41no—
326#125—41no—
327C22⋊Q8—42no—
328C22⋊Q8—42no—
329C22⋊Q8—42no—
330C22⋊Q8—42no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—42no—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8—42no—
337C4×Q8—41no—
338C4×Q8—41no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—41no—
342C4×D4—41no—
343C4×D4—42no—
344C4×D4—42no—
345C4×D4—42no—
346C4×D4—42no—
347#117—21no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—42no—
358#117—42no—
359#117C2×D412yes—
360#117C2×D412yes—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C22×C411yescharacteristic
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×Q812yes—
407#108—44no—
408#107—22no—
409#107—22no—
410#107—22no—
411#107—22no—
412#106—22no—
413#106—22no—
414#106—22no—
415#106—22no—
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8—42no—
421C4⋊C8—42no—
422#104—28no—
423#104—44no—
424#103—22no—
425#103—22no—
426#103C22⋊C414yes—
427#103C22⋊C414yes—
428#102—22no—
429#102—22no—
430#102C22⋊C414yes—
431#102C22⋊C414yes—
432#97—42no—
433#97—44no—
434C4×C8—42no—
435#95—42no—
436#95—42no—
437C24—21no—
438C24C2×#4111yescharacteristic
439#41—22no—
440#41—22no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41—22no—
449#41—22no—
450#41—22no—
451#41C22⋊Q814yes—
452#41C22⋊Q814yes—
453#41#12414yes—
454#41C4⋊Q814yes—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8—81no—
464C2×Q8C2×C22⋊C412yes—
465C2×Q8C4×Q812yes—
466C2×Q8C4×Q812yes—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4C2×C22⋊C412yes—
477C2×D4C4×Q812yes—
478C2×D4C4×Q812yes—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4C4×D411yescharacteristic
521C22×C4C4×D411yescharacteristic
522C22×C4C4×D411yescharacteristic
523C22×C4C4×D411yescharacteristic
524C22×C4C23×C411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×Q811yescharacteristic
529C22×C4C22×Q811yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4H(5,𝔽2)11yescharacteristic
535C22×C4H(5,𝔽2)11yescharacteristic
536C22×C4H(5,𝔽2)11yescharacteristic
537C22×C42−1+411yescharacteristic
538M16—22no—
539M16—22no—
540M16—22no—
541M16—22no—
542M16—22no—
543M16—22no—
544M16—48no—
545M16—48no—
546M16—41no—
547M16—41no—
548M16—41no—
549M16—41no—
550M16—41no—
551M16—41no—
552M16—41no—
553M16—41no—
554M16—41no—
555M16—41no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—22no—
579C2×C8—21no—
580C2×C8—22no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—22no—
587C2×C8—48no—
588C2×C8—48no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8C2×C22⋊C412yes—
607C2×C8C2×C22⋊C412yes—
608C2×C8C22⋊Q812yes—
609C2×C8C22⋊Q812yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C2×C22⋊C412yes—
629C4⋊C4C2×C22⋊C412yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—22no—
649C42—22no—
650C42—42no—
651C42—42no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C42—41no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23C2×C4×D411yescharacteristic
674C23#52911yescharacteristic
675C23#53311yescharacteristic
676C23#54611yescharacteristic
677C23#54611yescharacteristic
678C23#55211yescharacteristic
679C23#55411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—84no—
684Q8—84no—
685Q8#39114yes—
686D4—24no—
687D4—24no—
688D4—24no—
689D4—24no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4#39114yes—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—84no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—84no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4#44412yes—
751C2×C4C22×C22⋊C411yescharacteristic
752C2×C4C2×C4×Q811yescharacteristic
753C2×C4C2×C4×Q811yescharacteristic
754C2×C4C4×#4111yescharacteristic
755C2×C4#51811yescharacteristic
756C2×C4#52011yescharacteristic
757C2×C4C2×C22⋊Q811yescharacteristic
758C2×C4C2×C22⋊Q811yescharacteristic
759C2×C4C2×C22⋊Q811yescharacteristic
760C2×C4#52511yescharacteristic
761C2×C4C2×#12411yescharacteristic
762C2×C4C2×C4⋊Q811yescharacteristic
763C2×C4#53811yescharacteristic
764C2×C4#53911yescharacteristic
765C2×C4#54311yescharacteristic
766C2×C4#54411yescharacteristic
767C2×C4D4211yescharacteristic
768C2×C4D4211yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54611yescharacteristic
772C2×C4#54711yescharacteristic
773C2×C4#54711yescharacteristic
774C2×C4D4×Q811yescharacteristic
775C2×C4#55111yescharacteristic
776C2×C4#55111yescharacteristic
777C2×C4#55411yescharacteristic
778C2×C4#55411yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—42no—
786C8—42no—
787C8—41no—
788C8—41no—
789C8—42no—
790C8—81no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22C4×C22⋊Q811yescharacteristic
811C22D4×C22⋊C411yescharacteristic
812C22#236011yescharacteristic
813C22#243811yescharacteristic
814C22#245011yescharacteristic
815C22#248811yescharacteristic
816C22#254911yescharacteristic
817C22C2×#44411yescharacteristic
818C22#295511yescharacteristic
819C22#295611yescharacteristic
820C22#295711yescharacteristic
821C4—22no—
822C4—24no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—42no—
828C4—82no—
829C4—82no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#39111yescharacteristic
835C4#232911yescharacteristic
836C4#233911yescharacteristic
837C4#236811yescharacteristic
838C4#243711yescharacteristic
839C4#244011yescharacteristic
840C4#244911yescharacteristic
841C4#247211yescharacteristic
842C2—21no—
843C2—21no—
844C2—21no—
845C2—21no—
846C2—44no—
847C2#1405211yescharacteristic
848C2#2162811yescharacteristic
849C2#2162911yescharacteristic
850C2#2245211yescharacteristic
851C2#2245311yescharacteristic
852C2#2298311yescharacteristic
853C2#2298411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×#336 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21304C2semidirect
6. #11386C2semidirect
7. #11376C2semidirect
8. #11233C2semidirect
9. #11221C2semidirect
10. #10909C2semidirect
11. #10877C2semidirect
12. #10860C2semidirect
22. C2×#479C4semidirect
23. C2×#479C4semidirect
24. C2×#477C4semidirect
25. C2×#475C4semidirect
26. C2×#478C4semidirect
27. C2×#478C4semidirect
28. C2×#476C4semidirect
29. C2×#474C4semidirect
83. C2×#131Q8semidirect
164. C2×#104Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
#213042
C2×#18662
C2×#17652
#203362
#113862
#113762
#112332
#112212
#109092
#108772
#108602
#107912
#107902