Finite Group Databasebeta

← #366836

Subgroups — #366836

Order 512.

1415 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3091C211yesmaximal, characteristic
2C2×#1897C211yesmaximal, characteristic
3#20897C211yesmaximal, characteristic
4C2×#1855C211yesmaximal, characteristic, complemented
5#20685C211yesmaximal, characteristic, complemented
6C2×#1750C211yesmaximal, characteristic, complemented
7C2×#1733C211yesmaximal, characteristic, complemented
8#11376C211yesmaximal, characteristic, complemented
9#11376C211yesmaximal, characteristic, complemented
10#11125C211yesmaximal, characteristic, complemented
11#11125C211yesmaximal, characteristic, complemented
12#10930C211yesmaximal, characteristic, complemented
13#10929C211yesmaximal, characteristic, complemented
14#10860C211yesmaximal, characteristic, complemented
15#10859C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20#3091—24no—
21#3091—24no—
22C2×#484C411yescharacteristic, complemented
23C2×#481C411yescharacteristic, complemented
24C2×#485C411yescharacteristic, complemented
25C2×#485C411yescharacteristic, complemented
26C2×#482C411yescharacteristic, complemented
27C2×#482C411yescharacteristic, complemented
28C2×#483C411yescharacteristic, complemented
29C2×#480C411yescharacteristic, complemented
30C22×#108C2211yescharacteristic
31C22×#108C2211yescharacteristic
32C2×#427C2211yescharacteristic
33C2×#427C2211yescharacteristic
34C22×#104C2211yescharacteristic
35C22×#104C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C2×#416C2211yescharacteristic
38C2×#408C2211yescharacteristic
39C2×#408C2211yescharacteristic
40C2×#407C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×#97C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#1897—24no—
46#1870—22no—
47#1869—22no—
48#1855—24no—
49#1818—22no—
50#1817—22no—
51#1750—24no—
52C2×#341C2211yescharacteristic
53C2×#341C2211yescharacteristic
54#1733—24no—
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64#1729C2211yescharacteristic
65#1729C2211yescharacteristic
66#1729C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C22×#41C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C22×M16—21no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—41no—
77C22×M16—41no—
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C23×C8—21no—
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87#525—22no—
88#525—22no—
89#525—22no—
90#525—22no—
91C2×#123—21no—
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×#121C2×C411yescharacteristic
95C2×#121C2×C411yescharacteristic
96C2×#120—21no—
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×#117—21no—
100C2×#117—22no—
101C2×#117—21no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117—22no—
108C2×#117—41no—
109C2×#117—41no—
110C2×#117C2×C411yescharacteristic
111C2×#117C2×C411yescharacteristic
112C2×#117D414yes—
113C2×#117C2311yescharacteristic
114C2×#117C2311yescharacteristic
115C2×#117C2311yescharacteristic
116C22×C4⋊C4—21no—
117C22×C4⋊C4C2×C411yescharacteristic
118C22×C4⋊C4C2×C411yescharacteristic
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#485—24no—
125#485—24no—
126#484—24no—
127#483—24no—
128#482—24no—
129#482—24no—
130#481—24no—
131#480—24no—
132C2×#108—22no—
133C2×#108—22no—
134C2×#108—22no—
135C2×#108—22no—
136C2×#108—41no—
137C2×#108—41no—
138#427—22no—
139#427—22no—
140#427—22no—
141#427—22no—
142C2×#107C2×C411yescharacteristic
143C2×#107C2×C411yescharacteristic
144C2×#107C2×C411yescharacteristic
145C2×#107C2×C411yescharacteristic
146C2×#106C2×C411yescharacteristic
147C2×#106C2×C411yescharacteristic
148C2×#106C2×C411yescharacteristic
149C2×#106C2×C411yescharacteristic
150C2×#104—22no—
151C2×#104—22no—
152C2×#104—22no—
153C2×#104—22no—
154C2×#104—41no—
155C2×#104—41no—
156#416—22no—
157#416—22no—
158#416—22no—
159#416—22no—
160C2×#103C2×C411yescharacteristic
161C2×#103C2×C411yescharacteristic
162C2×#103C2×C411yescharacteristic
163C2×#103C2×C411yescharacteristic
164C2×#102C2×C411yescharacteristic
165C2×#102C2×C411yescharacteristic
166C2×#102C2×C411yescharacteristic
167C2×#102C2×C411yescharacteristic
168#408—22no—
169#408—22no—
170#408—41no—
171#408—41no—
172#407—22no—
173#407—22no—
174C2×C22⋊C8—22no—
175C2×C22⋊C8—22no—
176C2×C22⋊C8—21no—
177C2×C22⋊C8—21no—
178C2×C22⋊C8—22no—
179C2×C22⋊C8—22no—
180C2×C22⋊C8C2×C411yescharacteristic
181C2×C22⋊C8C2×C411yescharacteristic
182C2×C22⋊C8C2×C411yescharacteristic
183C2×C22⋊C8C2×C411yescharacteristic
184C2×C22⋊C8D412yes—
185C2×C22⋊C8D412yes—
186C2×C22⋊C8D414yes—
187C2×C22⋊C8D414yes—
188C2×#97—22no—
189C2×#97—22no—
190C2×#97—41no—
191C2×C4×C8—22no—
192C2×C4×C8—22no—
193C2×C4×C8—41no—
194#341—22no—
195#341—22no—
196#339—22no—
197#339—22no—
198#339—22no—
199#339—22no—
200#339—22no—
201#339—22no—
202#336—22no—
203#336—22no—
204#336—22no—
205#336—22no—
206#336—22no—
207#336—22no—
208#336—22no—
209#336—22no—
210C25#4111yescharacteristic
211C2×#41—21no—
212C2×#41—21no—
213C2×#41—21no—
214C2×#41—21no—
215C2×#41—21no—
216C2×#41—21no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—21no—
222C2×#41—21no—
223C22×Q8C22×C411yescharacteristic
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4C22×C411yescharacteristic
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D412yes—
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4#4111yescharacteristic
249C23×C4#4112yes—
250C23×C4C2411yescharacteristic
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—28no—
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—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—42no—
275C2×M16—42no—
276C2×M16—44no—
277C2×M16—44no—
278C2×M16—44no—
279C2×M16—42no—
280C2×M16#4112yes—
281C2×M16#4112yes—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
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—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8C22×C411yescharacteristic
310C22×C8C22×C411yescharacteristic
311C22×C8C22×C411yescharacteristic
312C22×C8C22×C411yescharacteristic
313C22×C8C2×D412yes—
314C22×C8C2×D412yes—
315C22×C8C2×D412yes—
316C22×C8C2×D412yes—
317C22×C8C2×D412yes—
318C22×C8C2×D412yes—
319#123—42no—
320#123—42no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325#121—22no—
326#121—22no—
327#121—22no—
328#121—22no—
329#120—42no—
330#120—42no—
331C4×D4—42no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—42no—
335#117—28no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—21no—
344#117—21no—
345#117—21no—
346#117—21no—
347#117—21no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—44no—
353#117—44no—
354#117—44no—
355#117—42no—
356#117—42no—
357#117—42no—
358#117—42no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
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—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42#4112yes—
408C2×C42#4112yes—
409#108—44no—
410#108—44no—
411#107—22no—
412#107—22no—
413#107—22no—
414#107—22no—
415#106—22no—
416#106—22no—
417#106—22no—
418#106—22no—
419#104—44no—
420#104—44no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—22no—
425#102—22no—
426#102—22no—
427#102—22no—
428#102—22no—
429C22⋊C8—24no—
430C22⋊C8—24no—
431C22⋊C8—44no—
432C22⋊C8—44no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8C22⋊C414yes—
436C22⋊C8C22⋊C414yes—
437C22⋊C8C22⋊C414yes—
438C22⋊C8C22⋊C414yes—
439#97—44no—
440C4×C8—44no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—42no—
447C24—42no—
448C24C4×D411yescharacteristic
449C24C4×D411yescharacteristic
450C24#12112yes—
451C24#12412yes—
452C24C2×#4111yescharacteristic
453#41—41no—
454#41—41no—
455#41—41no—
456#41—41no—
457#41—41no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467#41—41no—
468#41—41no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—44no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—82no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—44no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—82no—
554C22×C4C2×C22⋊C412yes—
555C22×C4C2×C22⋊C412yes—
556C22×C4C4×D412yes—
557C22×C4C4×D412yes—
558C22×C4C4×D411yescharacteristic
559C22×C4C4×D411yescharacteristic
560C22×C4#12112yes—
561C22×C4#12112yes—
562C22×C4#12112yes—
563C22×C4#12412yes—
564C22×C4#12712yes—
565C22×C4#12712yes—
566C22×C4C23×C411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4H(5,𝔽2)11yescharacteristic
577C22×C4H(5,𝔽2)11yescharacteristic
578C22×C42−1+411yescharacteristic
579C22×C42−1+411yescharacteristic
580M16—22no—
581M16—22no—
582M16—22no—
583M16—22no—
584M16—48no—
585M16—41no—
586M16—41no—
587M16—41no—
588M16—41no—
589M16—41no—
590M16—41no—
591M16—41no—
592M16—41no—
593M16—41no—
594M16—41no—
595M16—41no—
596M16—41no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—48no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8C2×C22⋊C412yes—
641C2×C8C2×C22⋊C412yes—
642C2×C8C2×C22⋊C412yes—
643C2×C8C2×C22⋊C412yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—48no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C22⋊C4—48no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—42no—
688C42—42no—
689C42#12314yes—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—82no—
714C23—82no—
715C23—82no—
716C23—82no—
717C23#39012yes—
718C23#39012yes—
719C23C2×C4×D411yescharacteristic
720C23C2×#12111yescharacteristic
721C23C2×#12411yescharacteristic
722C23#55111yescharacteristic
723C23#55111yescharacteristic
724C23#55211yescharacteristic
725C23#55211yescharacteristic
726Q8—41no—
727Q8—41no—
728Q8—41no—
729Q8—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—84no—
735D4—84no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4#39012yes—
796C2×C4#39012yes—
797C2×C4C22×C22⋊C411yescharacteristic
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C4×#4111yescharacteristic
800C2×C4C4×#4111yescharacteristic
801C2×C4#52011yescharacteristic
802C2×C4#52011yescharacteristic
803C2×C4C2×#12111yescharacteristic
804C2×C4C2×#12311yescharacteristic
805C2×C4#52511yescharacteristic
806C2×C4#52911yescharacteristic
807C2×C4#52911yescharacteristic
808C2×C4C2×#12711yescharacteristic
809C2×C4#53411yescharacteristic
810C2×C4#53611yescharacteristic
811C2×C4#53911yescharacteristic
812C2×C4#53911yescharacteristic
813C2×C4#54611yescharacteristic
814C2×C4#54611yescharacteristic
815C2×C4#54611yescharacteristic
816C2×C4#54611yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54611yescharacteristic
819C2×C4#54711yescharacteristic
820C2×C4#54711yescharacteristic
821C2×C4#54711yescharacteristic
822C2×C4#54711yescharacteristic
823C2×C4#54711yescharacteristic
824C2×C4#54711yescharacteristic
825C8—22no—
826C8—22no—
827C8—22no—
828C8—22no—
829C8—42no—
830C8—42no—
831C8—42no—
832C8—42no—
833C8—81no—
834C8—81no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22C2×#39011yescharacteristic
863C22#235911yescharacteristic
864C22#235911yescharacteristic
865C22#241211yescharacteristic
866C22#241311yescharacteristic
867C22#248811yescharacteristic
868C22#248811yescharacteristic
869C22#295512yes—
870C22#295712yes—
871C4—22no—
872C4—22no—
873C4—44no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C4×#12311yescharacteristic
883C4#232211yescharacteristic
884C4#233911yescharacteristic
885C4#233911yescharacteristic
886C4#242511yescharacteristic
887C4#242511yescharacteristic
888C4#250111yescharacteristic
889C4#253911yescharacteristic
890C2—21no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—42no—
895C2—42no—
896C2—161no—
897C2#1399611yescharacteristic
898C2#2124011yescharacteristic
899C2#2124211yescharacteristic
900C2#2294912yes—
901C2#2295112yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1855C2semidirect
5. #20685C2semidirect
6. C2×#1750C2semidirect
7. C2×#1733C2semidirect
8. #11376C2semidirect
9. #11376C2semidirect
10. #11125C2semidirect
11. #11125C2semidirect
12. #10930C2semidirect
13. #10929C2semidirect
14. #10860C2semidirect
15. #10859C2semidirect
22. C2×#484C4semidirect
23. C2×#481C4semidirect
24. C2×#485C4semidirect
25. C2×#485C4semidirect
26. C2×#482C4semidirect
27. C2×#482C4semidirect
28. C2×#483C4semidirect
29. C2×#480C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30912
C2×#18972
#208972
C2×#18552
#206852
C2×#17502
C2×#17332
#113762
#111252
#109302
#109292
#108602
#108592