Finite Group Databasebeta

← #619658

Subgroups — #619658

Order 512.

3670 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic
3C2×#2621C211yesmaximal, characteristic
4C2×#2625C211yesmaximal, characteristic
5#15911C214yesmaximal
6#15911C214yesmaximal
7#15848C214yesmaximal, complemented
8#15847C214yesmaximal, complemented
9#15238C211yesmaximal, characteristic, complemented
10#15228C211yesmaximal, characteristic, complemented
11#15190C211yesmaximal, characteristic, complemented
12#15188C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic
14#14258C211yesmaximal, characteristic
15#14024C211yesmaximal, characteristic, complemented
16#14024C211yesmaximal, characteristic, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19#13756C211yesmaximal, characteristic
20C2×#541—28no—
21C2×#541—28no—
22C2×#541—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126C2212yes—
27C22×#126C2212yes—
28C22×#125C2211yescharacteristic
29C22×#125C2212yes—
30C22×#125C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2857—28no—
40#2625—28no—
41#2621—28no—
42C2×#400C2212yes—
43C2×#398C2212yes—
44C2×#398C2214yes—
45C2×#397C2212yes—
46C2×#397C2212yes—
47C2×#397C2214yes—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#389C2214yes—
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#382C2211yescharacteristic
63C2×#380C2214yes—
64C2×#380C2211yescharacteristic
65#1444C2214yes—
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1440C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2212yes—
89C4⋊#95C2212yes—
90C22⋊#95C2214yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102#541—2128no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—42no—
112C2×#126—28no—
113C2×#126—28no—
114C2×#126—28no—
115C2×#126—28no—
116C2×#126—28no—
117C2×#126—28no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#125—28no—
121C2×#125—28no—
122C2×#125—28no—
123C2×#125—28no—
124C2×#125—28no—
125C2×#125—28no—
126C2×#125—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8D418yes—
135C2×C22⋊Q8D418yes—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117—24no—
145C2×#117—24no—
146C2×#117—42no—
147C2×#117D418yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2314yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2314yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C42—24no—
178C22×C42—24no—
179C22×C42—42no—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2312yes—
183C22×C42C2312yes—
184C22×C42C2312yes—
185C22×C42C2311yescharacteristic
186C22×C42C2311yescharacteristic
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189#400—28no—
190#398—216no—
191#398—28no—
192#397—216no—
193#397—28no—
194#397—28no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—24no—
199#391—24no—
200#391—24no—
201#391—24no—
202#391—24no—
203#391—42no—
204#391—42no—
205#389—216no—
206#389—24no—
207#389—24no—
208#384—24no—
209#382—24no—
210#380—24no—
211#380—216no—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C25C2411yescharacteristic
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8C2×D414yes—
261C22×Q8C2×D414yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C4⋊Q8—232no—
295C4⋊Q8—416no—
296C4⋊Q8—416no—
297#126—264no—
298#126—264no—
299#125—264no—
300#125—264no—
301#125—232no—
302C22⋊Q8—232no—
303C22⋊Q8—232no—
304C22⋊Q8—416no—
305C4×Q8—232no—
306C4×Q8—232no—
307#117—232no—
308#117—416no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D418yes—
372C2×C4⋊C4C2×D418yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4C2×D418yes—
392C2×C22⋊C4C2×D418yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—416no—
416C2×C42—42no—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42#4114yes—
420C2×C42#4114yes—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—28no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—28no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—24no—
441#95—28no—
442#95—24no—
443#95—44no—
444#95—42no—
445#95—44no—
446#95—42no—
447#95—44no—
448#95—44no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C2511yescharacteristic
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—216no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
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—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
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—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4#120116yes—
581C22×C4C22×D412yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C42−1+414yes—
601C22×C42−1+414yes—
602C22×C42−1+414yes—
603C22×C42−1+412yes—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—416no—
617C4⋊C4—48no—
618C4⋊C4—416no—
619C4⋊C4—416no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—84no—
633C42—216no—
634C42—216no—
635C42—28no—
636C42—28no—
637C42—28no—
638C42—28no—
639C42—48no—
640C42—44no—
641C42—44no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C2×#12014yes—
665C23C23×D411yescharacteristic
666C23C23×D411yescharacteristic
667C23C23×D411yescharacteristic
668C23C22×#4111yescharacteristic
669C23C22×#4111yescharacteristic
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×2−1+411yescharacteristic
672C23C2×2−1+412yes—
673C23C2×2−1+412yes—
674C23C2×2−1+412yes—
675C23#58512yes—
676Q8—416no—
677Q8—416no—
678Q8—88no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—232no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
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—28no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—432no—
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—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
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—44no—
779C2×C4—44no—
780C2×C4C2×#12014yes—
781C2×C4C2×#12014yes—
782C2×C4#53214yes—
783C2×C4#53714yes—
784C2×C4#54118yescomplemented
785C2×C4#54614yes—
786C2×C4#54614yes—
787C2×C4#54714yes—
788C2×C4#54714yes—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22C22×#12011yescharacteristic
801C22C2×#53211yescharacteristic
802C22C2×#53711yescharacteristic
803C22C2×#54112yes—
804C22#346112yes—
805C22C2×#54611yescharacteristic
806C22C2×#54611yescharacteristic
807C22C2×#54711yescharacteristic
808C22C2×#54711yescharacteristic
809C22#348612yes—
810C22#348912yes—
811C22#349512yes—
812C22#349712yes—
813C22#349911yescharacteristic
814C22#349911yescharacteristic
815C22#349912yes—
816C22#349911yescharacteristic
817C22#350011yescharacteristic
818C22#350912yes—
819C22#353812yes—
820C22#354112yes—
821C22#355512yes—
822C22#355612yes—
823C4—28no—
824C4—24no—
825C4—44no—
826C4—44no—
827C4—42no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—44no—
832C4—42no—
833C4—44no—
834C4—44no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4#243018yes—
841C2—44no—
842C2C2×#243011yescharacteristic
843C2#3531811yescharacteristic
844C2#3531911yescharacteristic
845C2#3566011yescharacteristic
846C2#3566611yescharacteristic
847C2#3738711yescharacteristic
848C2#3738911yescharacteristic
849C2#3766312yes—
850C2#3779312yes—
851C2#3935312yes—
852C2#3943512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #15848C2semidirect
8. #15847C2semidirect
9. #15238C2semidirect
10. #15228C2semidirect
11. #15190C2semidirect
12. #15188C2semidirect
15. #14024C2semidirect
16. #14024C2semidirect
17. #13978C2semidirect
18. #13976C2semidirect
784. C2×C4#541semidirect

Maximal subgroups

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

subgroupindex
C22×#5412
C2×#28572
C2×#26212
C2×#26252
#159112
#158482
#158472
#152382
#152282
#151902
#151882
#147022
#142582
#140242
#139782
#139762
#137562