Finite Group Databasebeta

← C2×#15672 #609308

Subgroups — C2×#15672 #609308

Order 512.

6098 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#400C211yesmaximal, characteristic, complemented
3C22×#398C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic
5#15672C2116yesmaximal, direct product factor
6C2×#1446C211yesmaximal, characteristic, complemented
7C2×#1446C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic
11C2×#1439C211yesmaximal, characteristic
12C2×#1439C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×C4⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8—28no—
20C22×C22⋊Q8—28no—
21C22×C22⋊Q8—28no—
22C22×C22⋊Q8C2218yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#400—28no—
37C2×#400C2218yescomplemented
38C2×#398—28no—
39C2×#398C2218yescomplemented
40C2×#388—28no—
41C2×#388C2218yes—
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
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1446C2218yescomplemented
63#1446C2218yescomplemented
64#1442C2218yescomplemented
65#1441C2218yescomplemented
66#1440C2218yes—
67#1439C2218yes—
68#1439C2218yes—
69#1436C2218yescomplemented
70C4⋊#95C2218yescomplemented
71C22⋊#95C2218yes—
72C22⋊#95C2218yes—
73C26C2311yescharacteristic
74C23×Q8—24no—
75C23×Q8—24no—
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—24no—
79C23×Q8—42no—
80C23×Q8—42no—
81C23×Q8C2314yes—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2314yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C2×C22⋊Q8—2128no—
105C2×C22⋊Q8—232no—
106C2×C22⋊Q8—232no—
107C2×C22⋊Q8—232no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4D418yes—
125C22×C4⋊C4D418yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4D418yes—
149C22×C22⋊C4Q818yescomplemented
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C42—24no—
157C22×C42—24no—
158C22×C42—42no—
159C22×C42C2314yes—
160#400—232no—
161#398—232no—
162#388—232no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—42no—
177C2×#95—42no—
178C2×#95—42no—
179C2×#95—42no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95—42no—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25C2×D414yes—
216C25C2×Q814yes—
217C25#4114yes—
218C25C2412yes—
219C25C2411yescharacteristic
220C22×Q8—232no—
221C22×Q8—28no—
222C22×Q8—28no—
223C22×Q8—28no—
224C22×Q8—28no—
225C22×Q8—28no—
226C22×Q8—44no—
227C22×Q8—44no—
228C22×Q8—416no—
229C22×Q8—416no—
230C22×Q8—416no—
231C22×Q8—416no—
232C22×Q8—416no—
233C22×Q8—416no—
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—232no—
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—28no—
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×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—28no—
293C23×C4—28no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—28no—
323C23×C4—28no—
324C23×C4—44no—
325C23×C4—44no—
326C23×C4—416no—
327C23×C4—416no—
328C23×C4—416no—
329C23×C4—416no—
330C23×C4—416no—
331C23×C4—416no—
332C23×C4C2×D414yes—
333C23×C4C2×D414yes—
334C23×C4C2×D414yes—
335C23×C4C2×D414yes—
336C23×C4C2×D414yes—
337C23×C4C2×D414yes—
338C23×C4C2×D414yes—
339C23×C4C2×D414yes—
340C23×C4C2×Q814yes—
341C23×C4C2×Q814yes—
342C23×C4#4114yes—
343C23×C4#4114yes—
344C23×C4#4114yes—
345C23×C4#4114yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C22⋊Q8—2256no—
361C2×C4⋊C4—232no—
362C2×C4⋊C4—232no—
363C2×C4⋊C4—232no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—416no—
381C2×C4⋊C4—416no—
382C2×C4⋊C4—416no—
383C2×C4⋊C4C2×D4116yes—
384C2×C4⋊C4C2×D4116yes—
385C2×C22⋊C4—232no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—232no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—416no—
405C2×C22⋊C4—416no—
406C2×C22⋊C4—416no—
407C2×C22⋊C4C2×D4116yes—
408C2×C22⋊C4C2×Q8116yescomplemented
409C2×C42—28no—
410C2×C42—28no—
411C2×C42—44no—
412C2×C42—416no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—28no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—44no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—44no—
479C24C22⋊Q8116yes—
480C24C22×D414yes—
481C24C22×D412yes—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C22×Q814yes—
485C24C22×Q812yes—
486C24C2×#4114yes—
487C24C2×#4112yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24H(5,𝔽2)12yes—
493C24H(5,𝔽2)12yes—
494C24H(5,𝔽2)12yes—
495C242−1+412yes—
496C242−1+412yes—
497C242−1+412yes—
498C24C2511yescharacteristic
499C2×Q8—232no—
500C2×Q8—416no—
501C2×Q8—416no—
502C2×Q8—416no—
503C2×Q8—416no—
504C2×Q8—416no—
505C2×Q8—4128no—
506C2×Q8—416no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
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—232no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—416no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4—416no—
632C22×C4—416no—
633C22×C4—4128no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—416no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4#120116yes—
696C22×C4#124116yes—
697C22×C4C22×D414yes—
698C22×C4C22×D414yes—
699C22×C4C22×D414yes—
700C22×C4C22×D414yes—
701C22×C4C22×D414yes—
702C22×C4C22×D414yes—
703C22×C4C22×D414yes—
704C22×C4C22×D414yes—
705C22×C4C22×Q814yes—
706C22×C4C22×Q814yes—
707C22×C4C2×#4114yes—
708C22×C4C2×#4114yes—
709C22×C4C2×#4114yes—
710C22×C4C2×#4114yes—
711C4⋊C4—232no—
712C4⋊C4—232no—
713C4⋊C4—232no—
714C4⋊C4—416no—
715C4⋊C4—416no—
716C4⋊C4—416no—
717C22⋊C4—232no—
718C22⋊C4—232no—
719C22⋊C4—232no—
720C22⋊C4—416no—
721C22⋊C4—416no—
722C22⋊C4—416no—
723C42—416no—
724C23—24no—
725C23—232no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—232no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—232no—
745C23—416no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—416no—
754C23—42no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—416no—
762C23—42no—
763C23—416no—
764C23—42no—
765C23—416no—
766C23—42no—
767C23—416no—
768C23—416no—
769C23—416no—
770C23—42no—
771C23—42no—
772C23—416no—
773C23C2×#12014yes—
774C23C2×C22⋊Q818yes—
775C23C2×C22⋊Q814yes—
776C23C2×#12414yes—
777C23#52914yes—
778C23#53214yes—
779C23#53314yes—
780C23#53514yes—
781C23#53614yes—
782C23#53714yes—
783C23#53814yes—
784C23#53914yes—
785C23#53914yes—
786C23#54114yes—
787C23#54214yes—
788C23#54414yes—
789C23#54614yes—
790C23#54614yes—
791C23#54614yes—
792C23#54614yes—
793C23#54614yes—
794C23#54614yes—
795C23#54714yes—
796C23#54714yes—
797C23#54814yes—
798C23#54814yes—
799C23D4×Q814yes—
800C23D4×Q814yes—
801C23#55114yes—
802C23#55214yes—
803C23#55214yes—
804C23#55414yes—
805C23#55414yes—
806C23#55614yes—
807C23#56214yes—
808C23#56314yes—
809C23C23×D411yescharacteristic
810C23C23×D411yescharacteristic
811C23C23×D411yescharacteristic
812C23C23×Q811yescharacteristic
813C23C22×#4111yescharacteristic
814C23C22×#4111yescharacteristic
815C23C22×#4111yescharacteristic
816C23C22×#4111yescharacteristic
817C23C22×#4111yescharacteristic
818C23C2×H(5,𝔽2)11yescharacteristic
819C23C2×H(5,𝔽2)11yescharacteristic
820C23C2×H(5,𝔽2)11yescharacteristic
821C23C2×2−1+411yescharacteristic
822C23C2×2−1+411yescharacteristic
823C23C2×2−1+411yescharacteristic
824Q8—464no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—232no—
830C2×C4—232no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—464no—
864C2×C4—42no—
865C2×C4—416no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—416no—
881C2×C4—42no—
882C2×C4—416no—
883C2×C4—416no—
884C2×C4—416no—
885C2×C4—416no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—416no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—416no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—88no—
933C2×C4—88no—
934C2×C4—88no—
935C2×C4—88no—
936C2×C4C2×#12018yes—
937C2×C4C2×#12418yes—
938C22—28no—
939C22—28no—
940C22—28no—
941C22—44no—
942C22—44no—
943C22—464no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22#240918yes—
955C22#243018yes—
956C22#243518yes—
957C22#243818yes—
958C22#245018yes—
959C22#248918yes—
960C22#249218yes—
961C22#255618yes—
962C22#256018yes—
963C22#268718yes—
964C22#268918yes—
965C22#269618yes—
966C22#270218yes—
967C22#270418yes—
968C22#272018yes—
969C22C22×#12011yescharacteristic
970C22C22×C22⋊Q811yescharacteristic
971C22C22×#12411yescharacteristic
972C22C2×#52911yescharacteristic
973C22C2×#53211yescharacteristic
974C22C2×#53311yescharacteristic
975C22C2×#53511yescharacteristic
976C22C2×#53611yescharacteristic
977C22C2×#53711yescharacteristic
978C22C2×#53811yescharacteristic
979C22C2×#53911yescharacteristic
980C22C2×#53911yescharacteristic
981C22C2×#54111yescharacteristic
982C22C2×#54211yescharacteristic
983C22C2×#54411yescharacteristic
984C22C2×#54611yescharacteristic
985C22C2×#54611yescharacteristic
986C22C2×#54611yescharacteristic
987C22C2×#54611yescharacteristic
988C22C2×#54611yescharacteristic
989C22C2×#54611yescharacteristic
990C22C2×#54711yescharacteristic
991C22C2×#54711yescharacteristic
992C22C2×#54811yescharacteristic
993C22C2×#54811yescharacteristic
994C22C2×D4×Q811yescharacteristic
995C22C2×D4×Q811yescharacteristic
996C22C2×#55111yescharacteristic
997C22C2×#55211yescharacteristic
998C22C2×#55211yescharacteristic
999C22C2×#55411yescharacteristic
1000C22C2×#55411yescharacteristic
1001C22C2×#55611yescharacteristic
1002C22C2×#56211yescharacteristic
1003C22C2×#56311yescharacteristic
1004C4—28no—
1005C4—28no—
1006C4—44no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—82no—
1015C4—82no—
1016C4—82no—
1017C4—82no—
1018C2—48no—
1019C2#15672116yesdirect product factor
1020C2C2×#245011yescharacteristic
1021C2C2×#240911yescharacteristic
1022C2C2×#243511yescharacteristic
1023C2C2×#243011yescharacteristic
1024C2C2×#243811yescharacteristic
1025C2C2×#249211yescharacteristic
1026C2C2×#248911yescharacteristic
1027C2C2×#255611yescharacteristic
1028C2C2×#256011yescharacteristic
1029C2C2×#268711yescharacteristic
1030C2C2×#268911yescharacteristic
1031C2C2×#269611yescharacteristic
1032C2C2×#270211yescharacteristic
1033C2C2×#270411yescharacteristic
1034C2C2×#272011yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#400C2semidirect
3. C22×#398C2semidirect
5. #15672C2direct (N × H)
6. C2×#1446C2semidirect
7. C2×#1446C2semidirect
8. C2×#1442C2semidirect
9. C2×#1441C2semidirect
13. C2×#1436C2semidirect
14. C2×C4⋊#95C2semidirect
37. C2×#400C22semidirect
39. C2×#398C22semidirect
62. #1446C22semidirect
63. #1446C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
149. C22×C22⋊C4Q8semidirect
408. C2×C22⋊C4C2×Q8semidirect
1019. C2#15672direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C22×#4002
C22×#3982
C22×#3882
#156722
C2×#14462
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14362
C2×C4⋊#952
C2×C22⋊#952