Finite Group Databasebeta

← C2×#15853 #609581

Subgroups — C2×#15853 #609581

Order 512.

4002 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic
3C22×#391C211yesmaximal, characteristic
4C22×#387C211yesmaximal, characteristic
5#15853C2116yesmaximal, direct product factor
6C2×#1443C211yesmaximal, characteristic
7C2×#1442C211yesmaximal, characteristic
8C2×#1442C211yesmaximal, characteristic
9C2×#1442C211yesmaximal, characteristic
10C2×#1442C211yesmaximal, characteristic
11C2×#1441C211yesmaximal, characteristic
12C2×#1441C211yesmaximal, characteristic
13C2×#1441C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic
15C2×#1434C211yesmaximal, characteristic
16C2×#1434C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#395—28no—
27C2×#395C2218yes—
28C2×#391—28no—
29C2×#391—28no—
30C2×#391C2218yes—
31C2×#391C2218yes—
32C2×#387—28no—
33C2×#387C2218yes—
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
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1443C2218yes—
61#1442C2218yes—
62#1442C2218yes—
63#1442C2218yes—
64#1442C2218yes—
65#1441C2218yes—
66#1441C2218yes—
67#1441C2218yes—
68#1436C2218yes—
69#1434C2218yes—
70#1434C2218yes—
71C23×Q8—24no—
72C23×Q8—24no—
73C23×Q8—24no—
74C23×Q8—24no—
75C23×Q8—42no—
76C23×Q8—42no—
77C23×Q8D418yes—
78C23×Q8C2314yes—
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
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
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—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C42—24no—
119C22×C42—24no—
120C22×C42—24no—
121C22×C42—24no—
122C22×C42—24no—
123C22×C42—42no—
124C22×C42C2314yes—
125C22×C42C2314yes—
126#395—232no—
127#391—232no—
128#391—232no—
129#387—232no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
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—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—42no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95D418yes—
155C2×#95Q818yescomplemented
156C2×#95C2314yes—
157C2×#95C2314yes—
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—232no—
184C22×Q8—232no—
185C22×Q8—28no—
186C22×Q8—28no—
187C22×Q8—28no—
188C22×Q8—28no—
189C22×Q8—416no—
190C22×Q8—44no—
191C22×Q8—44no—
192C22×Q8—416no—
193C22×Q8—416no—
194C22×Q8—416no—
195C22×Q8—416no—
196C22×Q8C2×D4116yes—
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×C4—22no—
286C23×C4—22no—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×Q814yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q814yes—
296C23×C4#4114yes—
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—28no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—416no—
337C2×C4⋊C4—416no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4—416no—
341C2×C42—28no—
342C2×C42—28no—
343C2×C42—28no—
344C2×C42—28no—
345C2×C42—28no—
346C2×C42—44no—
347C2×C42—416no—
348C2×C42—416no—
349#95—28no—
350#95—28no—
351#95—28no—
352#95—28no—
353#95—28no—
354#95—28no—
355#95—28no—
356#95—28no—
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—28no—
367#95—28no—
368#95—28no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95C2×D4116yes—
374#95C2×Q8116yescomplemented
375C24C22×D412yes—
376C24C22×D412yes—
377C24C22×Q812yes—
378C24C2×#4112yes—
379C24C2×#4112yes—
380C24C2×#4112yes—
381C24C2×#4112yes—
382C24C2×#4112yes—
383C24C2×#4112yes—
384C24H(5,𝔽2)12yes—
385C24H(5,𝔽2)12yes—
386C242−1+412yes—
387C242−1+412yes—
388C242−1+412yes—
389C242−1+412yes—
390C24C2511yescharacteristic
391C2×Q8—232no—
392C2×Q8—232no—
393C2×Q8—416no—
394C2×Q8—4128no—
395C2×Q8—416no—
396C2×Q8—416no—
397C2×Q8—416no—
398C2×Q8—416no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—28no—
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—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
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—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
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#121116yes—
593C22×C4#123116yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D414yes—
598C22×C4C22×D414yes—
599C22×C4C22×D414yes—
600C22×C4C22×Q814yes—
601C22×C4C22×Q814yes—
602C22×C4C22×Q814yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C4⋊C4—232no—
610C4⋊C4—416no—
611C4⋊C4—416no—
612C4⋊C4—416no—
613C4⋊C4—416no—
614C4⋊C4—416no—
615C42—416no—
616C42—416no—
617C23C2×#12114yes—
618C23C2×#12314yes—
619C23#52514yes—
620C23#52914yes—
621C23#53314yes—
622C23#53314yes—
623C23#53414yes—
624C23#53614yes—
625C23#54114yes—
626C23#54114yes—
627C23#54114yes—
628C23#54214yes—
629C23#54214yes—
630C23#54214yes—
631C23#54414yes—
632C23#54614yes—
633C23#54614yes—
634C23#54714yes—
635C23#54814yes—
636C23#54814yes—
637C23#54814yes—
638C23D4×Q814yes—
639C23D4×Q814yes—
640C23#55114yes—
641C23#55114yes—
642C23#55214yes—
643C23#55214yes—
644C23#55214yes—
645C23#55414yes—
646C23#55514yes—
647C23#55614yes—
648C23#55614yes—
649C23#55714yes—
650C23#56314yes—
651C23#56314yes—
652C23C23×D411yescharacteristic
653C23C23×D411yescharacteristic
654C23C23×Q811yescharacteristic
655C23C22×#4111yescharacteristic
656C23C22×#4111yescharacteristic
657C23C22×#4111yescharacteristic
658C23C22×#4111yescharacteristic
659C23C22×#4111yescharacteristic
660C23C22×#4111yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×2−1+411yescharacteristic
664C23C2×2−1+411yescharacteristic
665C23C2×2−1+411yescharacteristic
666C23C2×2−1+411yescharacteristic
667Q8—464no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—232no—
671C2×C4—232no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
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—24no—
689C2×C4—24no—
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—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
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—416no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—42no—
755C2×C4—42no—
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—42no—
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—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—88no—
783C2×C4—88no—
784C2×C4—88no—
785C2×C4—88no—
786C2×C4C2×#12118yes—
787C2×C4C2×#12318yes—
788C22#241218yes—
789C22#242118yes—
790C22#242918yes—
791C22#244618yes—
792C22#246518yes—
793C22#247418yes—
794C22#252018yes—
795C22#253618yes—
796C22#261218yes—
797C22#269818yes—
798C22#271318yes—
799C22#272918yes—
800C22#273118yes—
801C22#275818yes—
802C22#276218yes—
803C22C22×#12111yescharacteristic
804C22C22×#12311yescharacteristic
805C22C2×#52511yescharacteristic
806C22C2×#52911yescharacteristic
807C22C2×#53311yescharacteristic
808C22C2×#53311yescharacteristic
809C22C2×#53411yescharacteristic
810C22C2×#53611yescharacteristic
811C22C2×#54111yescharacteristic
812C22C2×#54111yescharacteristic
813C22C2×#54111yescharacteristic
814C22C2×#54211yescharacteristic
815C22C2×#54211yescharacteristic
816C22C2×#54211yescharacteristic
817C22C2×#54411yescharacteristic
818C22C2×#54611yescharacteristic
819C22C2×#54611yescharacteristic
820C22C2×#54711yescharacteristic
821C22C2×#54811yescharacteristic
822C22C2×#54811yescharacteristic
823C22C2×#54811yescharacteristic
824C22C2×D4×Q811yescharacteristic
825C22C2×D4×Q811yescharacteristic
826C22C2×#55111yescharacteristic
827C22C2×#55111yescharacteristic
828C22C2×#55211yescharacteristic
829C22C2×#55211yescharacteristic
830C22C2×#55211yescharacteristic
831C22C2×#55411yescharacteristic
832C22C2×#55511yescharacteristic
833C22C2×#55611yescharacteristic
834C22C2×#55611yescharacteristic
835C22C2×#55711yescharacteristic
836C22C2×#56311yescharacteristic
837C22C2×#56311yescharacteristic
838C4—28no—
839C4—28no—
840C4—44no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—82no—
853C2#15853116yesdirect product factor
854C2C2×#241211yescharacteristic
855C2C2×#246511yescharacteristic
856C2C2×#242911yescharacteristic
857C2C2×#244611yescharacteristic
858C2C2×#242111yescharacteristic
859C2C2×#247411yescharacteristic
860C2C2×#252011yescharacteristic
861C2C2×#261211yescharacteristic
862C2C2×#253611yescharacteristic
863C2C2×#269811yescharacteristic
864C2C2×#271311yescharacteristic
865C2C2×#272911yescharacteristic
866C2C2×#273111yescharacteristic
867C2C2×#275811yescharacteristic
868C2C2×#276211yescharacteristic
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
5. #15853C2direct (N × H)
155. C2×#95Q8semidirect
374. #95C2×Q8semidirect
853. C2#15853direct (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×#3912
C22×#3872
#158532
C2×#14432
C2×#14422
C2×#14412
C2×#14362
C2×#14342