Finite Group Databasebeta

← C2×#15592 #609176

Subgroups — C2×#15592 #609176

Order 512.

3938 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3#15592C2116yesmaximal, direct product factor
4C2×#1446C211yesmaximal, characteristic
5C2×#1446C211yesmaximal, characteristic
6C2×#1444C211yesmaximal, characteristic
7C2×#1442C211yesmaximal, characteristic
8C2×#1441C211yesmaximal, characteristic
9C2×#1441C211yesmaximal, characteristic
10C2×#1441C211yesmaximal, characteristic
11C2×#1441C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic
15C2×C4⋊#95C211yesmaximal, characteristic
16C2×C4⋊#95C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C2×#395—28no—
29C2×#395C2218yes—
30C2×#387—28no—
31C2×#387C2218yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1446C2218yes—
57#1446C2218yes—
58#1444C2218yes—
59#1442C2218yes—
60#1441C2218yes—
61#1441C2218yes—
62#1441C2218yes—
63#1441C2218yes—
64#1436C2218yes—
65#1436C2218yes—
66#1436C2218yes—
67C4⋊#95C2218yes—
68C4⋊#95C2218yes—
69C23×Q8—24no—
70C23×Q8—24no—
71C23×Q8—24no—
72C23×Q8—42no—
73C23×Q8—42no—
74C23×Q8—42no—
75C23×Q8—42no—
76C23×Q8C2314yes—
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4Q818yescomplemented
115C22×C4⋊C4Q818yescomplemented
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42—24no—
127C22×C42—42no—
128C22×C42—42no—
129C22×C42—42no—
130C22×C42C2314yes—
131C22×C42C2314yes—
132#395—232no—
133#387—232no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95—42no—
150C2×#95—42no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95D418yes—
157C2×#95Q818yescomplemented
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C25C2411yescharacteristic
183C22×Q8—28no—
184C22×Q8—28no—
185C22×Q8—28no—
186C22×Q8—44no—
187C22×Q8—44no—
188C22×Q8—44no—
189C22×Q8—44no—
190C22×Q8—416no—
191C22×Q8—416no—
192C22×Q8—416no—
193C22×Q8—416no—
194C22×Q8—416no—
195C22×Q8—416no—
196C22×Q8—416no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×Q814yes—
289C23×C4C2×Q814yes—
290C23×C4C2×Q814yes—
291C23×C4C2×Q814yes—
292C23×C4C2×Q814yes—
293C23×C4C2×Q814yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q814yes—
296C23×C4C2×Q814yes—
297C23×C4#4114yes—
298C23×C4#4114yes—
299C23×C4#4114yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C2×C4⋊C4—232no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—416no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—416no—
345C2×C4⋊C4—416no—
346C2×C4⋊C4—416no—
347C2×C4⋊C4C2×Q8116yescomplemented
348C2×C4⋊C4C2×Q8116yescomplemented
349C2×C42—28no—
350C2×C42—28no—
351C2×C42—28no—
352C2×C42—44no—
353C2×C42—44no—
354C2×C42—44no—
355C2×C42—416no—
356C2×C42—416no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95C2×D4116yes—
380#95C2×Q8116yescomplemented
381C24C22×D412yes—
382C24C22×Q812yes—
383C24C22×Q812yes—
384C24C22×Q812yes—
385C24C2×#4112yes—
386C24C2×#4112yes—
387C24C2×#4112yes—
388C24C2×#4112yes—
389C24C2×#4112yes—
390C24H(5,𝔽2)12yes—
391C24H(5,𝔽2)12yes—
392C24H(5,𝔽2)12yes—
393C24H(5,𝔽2)12yes—
394C24H(5,𝔽2)12yes—
395C242−1+412yes—
396C24C2511yescharacteristic
397C2×Q8—416no—
398C2×Q8—416no—
399C2×Q8—416no—
400C2×Q8—416no—
401C2×Q8—416no—
402C2×Q8—416no—
403C2×Q8—4128no—
404C2×Q8—416no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
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—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C22⋊Q8116yes—
597C22×C4C4⋊Q8116yes—
598C22×C4C22×D414yes—
599C22×C4C22×D414yes—
600C22×C4C22×D414yes—
601C22×C4C22×Q814yes—
602C22×C4C22×Q814yes—
603C22×C4C22×Q814yes—
604C22×C4C22×Q814yes—
605C22×C4C22×Q814yes—
606C22×C4C22×Q814yes—
607C22×C4C22×Q814yes—
608C22×C4C22×Q814yes—
609C22×C4C22×Q814yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4114yes—
615C4⋊C4—232no—
616C4⋊C4—416no—
617C4⋊C4—416no—
618C4⋊C4—416no—
619C4⋊C4—416no—
620C4⋊C4—416no—
621C4⋊C4—416no—
622C4⋊C4—416no—
623C42—416no—
624C42—416no—
625C23C2×C22⋊Q814yes—
626C23#52914yes—
627C23C2×C4⋊Q814yes—
628C23#53314yes—
629C23#53314yes—
630C23#53314yes—
631C23#53514yes—
632C23#53814yes—
633C23#53814yes—
634C23#53814yes—
635C23#53814yes—
636C23#53914yes—
637C23#54314yes—
638C23#54414yes—
639C23#54414yes—
640C23#54614yes—
641C23#54614yes—
642C23#54614yes—
643C23#54814yes—
644C23#55114yes—
645C23#55114yes—
646C23#55414yes—
647C23#55414yes—
648C23#55414yes—
649C23#55414yes—
650C23#55414yes—
651C23#55414yes—
652C23#55414yes—
653C23#55514yes—
654C23#55614yes—
655C23#55714yes—
656C23Q8214yes—
657C23Q8214yes—
658C23#56014yes—
659C23#56214yes—
660C23C23×D411yescharacteristic
661C23C23×Q811yescharacteristic
662C23C23×Q811yescharacteristic
663C23C23×Q811yescharacteristic
664C23C22×#4111yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C22×#4111yescharacteristic
669C23C2×H(5,𝔽2)11yescharacteristic
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×2−1+411yescharacteristic
675Q8—464no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—232no—
689C2×C4—232no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—416no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—416no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—416no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—416no—
776C2×C4—416no—
777C2×C4—416no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—88no—
793C2×C4—88no—
794C2×C4C2×C22⋊Q818yes—
795C2×C4C2×C4⋊Q818yes—
796C22#243918yes—
797C22#245018yes—
798C22#254918yes—
799C22#255018yes—
800C22#256718yes—
801C22#257418yes—
802C22#258618yes—
803C22#258618yes—
804C22#258818yes—
805C22#268518yes—
806C22#269618yes—
807C22#278418yes—
808C22#278818yes—
809C22#279218yes—
810C22#280618yes—
811C22C22×C22⋊Q811yescharacteristic
812C22C2×#52911yescharacteristic
813C22C22×C4⋊Q811yescharacteristic
814C22C2×#53311yescharacteristic
815C22C2×#53311yescharacteristic
816C22C2×#53311yescharacteristic
817C22C2×#53511yescharacteristic
818C22C2×#53811yescharacteristic
819C22C2×#53811yescharacteristic
820C22C2×#53811yescharacteristic
821C22C2×#53811yescharacteristic
822C22C2×#53911yescharacteristic
823C22C2×#54311yescharacteristic
824C22C2×#54411yescharacteristic
825C22C2×#54411yescharacteristic
826C22C2×#54611yescharacteristic
827C22C2×#54611yescharacteristic
828C22C2×#54611yescharacteristic
829C22C2×#54811yescharacteristic
830C22C2×#55111yescharacteristic
831C22C2×#55111yescharacteristic
832C22C2×#55411yescharacteristic
833C22C2×#55411yescharacteristic
834C22C2×#55411yescharacteristic
835C22C2×#55411yescharacteristic
836C22C2×#55411yescharacteristic
837C22C2×#55411yescharacteristic
838C22C2×#55411yescharacteristic
839C22C2×#55511yescharacteristic
840C22C2×#55611yescharacteristic
841C22C2×#55711yescharacteristic
842C22C2×Q8211yescharacteristic
843C22C2×Q8211yescharacteristic
844C22C2×#56011yescharacteristic
845C22C2×#56211yescharacteristic
846C4—28no—
847C4—28no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—44no—
859C4—82no—
860C4—82no—
861C2#15592116yesdirect product factor
862C2C2×#245011yescharacteristic
863C2C2×#243911yescharacteristic
864C2C2×#254911yescharacteristic
865C2C2×#257411yescharacteristic
866C2C2×#258611yescharacteristic
867C2C2×#258611yescharacteristic
868C2C2×#258811yescharacteristic
869C2C2×#255011yescharacteristic
870C2C2×#256711yescharacteristic
871C2C2×#268511yescharacteristic
872C2C2×#269611yescharacteristic
873C2C2×#278411yescharacteristic
874C2C2×#278811yescharacteristic
875C2C2×#279211yescharacteristic
876C2C2×#280611yescharacteristic
subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #15592C2direct (N × H)
114. C22×C4⋊C4Q8semidirect
115. C22×C4⋊C4Q8semidirect
157. C2×#95Q8semidirect
347. C2×C4⋊C4C2×Q8semidirect
348. C2×C4⋊C4C2×Q8semidirect
380. #95C2×Q8semidirect
861. C2#15592direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3952
C22×#3872
#155922
C2×#14462
C2×#14442
C2×#14422
C2×#14412
C2×#14362
C2×C4⋊#952