Finite Group Databasebeta

← #398084

Subgroups — #398084

Order 512.

1638 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2439C211yesmaximal, characteristic
2C2×#2024C211yesmaximal, characteristic, complemented
3C2×#1894C211yesmaximal, characteristic
4C2×#1873C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6#14139C211yesmaximal, characteristic
7#11384C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11292C211yesmaximal, characteristic, complemented
10#11268C211yesmaximal, characteristic, complemented
11#11067C211yesmaximal, characteristic, complemented
12#11067C211yesmaximal, characteristic, complemented
13#11052C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic
15#10715C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26#2439—24no—
27#2439—24no—
28C2×#396—21no—
29C2×#393—21no—
30C2×#391—21no—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#387—21no—
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#2024—24no—
40#1894—24no—
41#1873—24no—
42#1736—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1441—21no—
60#1441—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C22⋊#95—21no—
64C22⋊#95—21no—
65C23×Q8—21no—
66C23×Q8C2311yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8—41no—
85C2×C4⋊Q8—41no—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8—22no—
91C2×C22⋊Q8Q814yescomplemented
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117D414yes—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4D411yescharacteristic
120C22×C22⋊C4D411yescharacteristic
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—41no—
133C2×#103—41no—
134C2×#103—41no—
135C2×#103—41no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139#396—28no—
140#393—28no—
141#391—28no—
142#391—22no—
143#391—22no—
144#391—41no—
145#391—41no—
146#389—22no—
147#389—22no—
148#389—22no—
149#389—22no—
150#387—28no—
151#382—22no—
152#382—22no—
153#380—22no—
154#380D414yes—
155C4×C22⋊C4—22no—
156C4×C22⋊C4—22no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95D411yescharacteristic
171C2×#95D411yescharacteristic
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—41no—
182#340—41no—
183#340D414yes—
184#336—22no—
185#336—22no—
186#336—41no—
187#336—41no—
188C25C2×D411yescharacteristic
189C22×Q8—24no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—42no—
204C22×Q8—42no—
205C22×Q8—42no—
206C22×Q8—42no—
207C22×Q8—81no—
208C22×Q8—81no—
209C22×Q8C2×Q812yes—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D412yes—
239C23×C4C2×D412yes—
240C23×C4C2×Q812yes—
241C23×C4#4112yes—
242C23×C4#4112yes—
243C23×C4#4112yes—
244C23×C4C2411yescharacteristic
245C2×M16—28no—
246C2×M16—44no—
247C2×M16—44no—
248C2×M16—44no—
249C2×M16—44no—
250C2×M16—44no—
251C2×M16—44no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8C2×D412yes—
279C22×C8#4112yes—
280C4⋊Q8—44no—
281C4⋊Q8—44no—
282C4⋊Q8—44no—
283C4⋊Q8—44no—
284C22⋊Q8—28no—
285C22⋊Q8—28no—
286C22⋊Q8—44no—
287C22⋊Q8—44no—
288#117—28no—
289#117—44no—
290#117—44no—
291#117—44no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—81no—
343C2×C4⋊C4—81no—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4C2×D412yes—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D412yes—
350C2×C4⋊C4C2×Q812yes—
351C2×C4⋊C4#4112yes—
352C2×C4⋊C4#4112yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—81no—
367C2×C22⋊C4—81no—
368C2×C42—24no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—42no—
382C2×C42—42no—
383#103—44no—
384#103—44no—
385#103—44no—
386#103—44no—
387C22⋊C8—44no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—22no—
394#95—22no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—81no—
400#95—81no—
401#95—81no—
402#95—81no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24#12012yes—
416C24C22⋊Q812yes—
417C24#12412yes—
418C24C22×D411yescharacteristic
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—48no—
426C2×Q8—48no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—84no—
450C2×Q8—84no—
451C2×Q8—84no—
452C2×Q8—84no—
453C2×Q8—84no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
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—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
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—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—48no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4#12012yes—
572C22×C4C22⋊Q814yes—
573C22×C4C22⋊Q814yes—
574C22×C4C22⋊Q812yes—
575C22×C4#12414yes—
576C22×C4#12414yes—
577C22×C4#12412yes—
578C22×C4#13712yes—
579C22×C4#13712yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×Q811yescharacteristic
584C22×C4C2×#4111yescharacteristic
585C22×C4C2×#4111yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C4H(5,𝔽2)11yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C42−1+411yescharacteristic
594M16—416no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—48no—
654C4⋊C4—84no—
655C4⋊C4#12114yes—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—84no—
661C42—48no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23#39314yes—
705C23C2×#12011yescharacteristic
706C23C2×C22⋊Q811yescharacteristic
707C23C2×#12411yescharacteristic
708C23D4211yescharacteristic
709C23#54611yescharacteristic
710C23#54611yescharacteristic
711C23#54711yescharacteristic
712C23C2×#13711yescharacteristic
713C23C2×#13711yescharacteristic
714C23#57511yescharacteristic
715C23#57511yescharacteristic
716C23#57611yescharacteristic
717C23#57711yescharacteristic
718C23#57711yescharacteristic
719C23#57811yescharacteristic
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—816no—
725Q8—81no—
726Q8—81no—
727Q8—81no—
728Q8—81no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—816no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4#39314yes—
829C2×C4C2×#12111yescharacteristic
830C2×C4C2×C22⋊Q811yescharacteristic
831C2×C4C2×C22⋊Q811yescharacteristic
832C2×C4#52511yescharacteristic
833C2×C4#52511yescharacteristic
834C2×C4C2×#12411yescharacteristic
835C2×C4C2×#12411yescharacteristic
836C2×C4#52911yescharacteristic
837C2×C4#52911yescharacteristic
838C2×C4#53211yescharacteristic
839C2×C4#53411yescharacteristic
840C2×C4#53711yescharacteristic
841C2×C4#53811yescharacteristic
842C2×C4#53811yescharacteristic
843C2×C4#53911yescharacteristic
844C2×C4#53911yescharacteristic
845C2×C4D4211yescharacteristic
846C2×C4#54611yescharacteristic
847C2×C4#54611yescharacteristic
848C2×C4#54611yescharacteristic
849C2×C4#54711yescharacteristic
850C2×C4D4×Q811yescharacteristic
851C2×C4#55111yescharacteristic
852C2×C4#55111yescharacteristic
853C2×C4#55211yescharacteristic
854C2×C4#55411yescharacteristic
855C2×C4#55411yescharacteristic
856C2×C4#55411yescharacteristic
857C8—42no—
858C8—42no—
859C8—81no—
860C8—81no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22C2×#39311yescharacteristic
877C22#241011yescharacteristic
878C22#243011yescharacteristic
879C22#244911yescharacteristic
880C22#245011yescharacteristic
881C22#247211yescharacteristic
882C22#248811yescharacteristic
883C22#300711yescharacteristic
884C22#300711yescharacteristic
885C22#301211yescharacteristic
886C22#301311yescharacteristic
887C22#307811yescharacteristic
888C22#307811yescharacteristic
889C22#308311yescharacteristic
890C22#308411yescharacteristic
891C22#313611yescharacteristic
892C22#313711yescharacteristic
893C22#313911yescharacteristic
894C22#314011yescharacteristic
895C22#326611yescharacteristic
896C22#327011yescharacteristic
897C22#327311yescharacteristic
898C22#327511yescharacteristic
899C22#331111yescharacteristic
900C22#331411yescharacteristic
901C22#331611yescharacteristic
902C22#331911yescharacteristic
903C22#332311yescharacteristic
904C22#332711yescharacteristic
905C22#332811yescharacteristic
906C22#332911yescharacteristic
907C22#334811yescharacteristic
908C22#334911yescharacteristic
909C22#335611yescharacteristic
910C22#335711yescharacteristic
911C4—24no—
912C4—42no—
913C4—42no—
914C4—44no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4—81no—
922C4—82no—
923C4—81no—
924C4#241711yescharacteristic
925C4#244911yescharacteristic
926C4#245011yescharacteristic
927C4#247211yescharacteristic
928C4#248811yescharacteristic
929C4#256411yescharacteristic
930C4#263911yescharacteristic
931C4#285011yescharacteristic
932C2—44no—
933C2#1475911yescharacteristic
934C2#2345511yescharacteristic
935C2#2345811yescharacteristic
936C2#2444911yescharacteristic
937C2#2445211yescharacteristic
938C2#2555211yescharacteristic
939C2#2555811yescharacteristic
940C2#2635611yescharacteristic
941C2#2635811yescharacteristic
942C2#2642811yescharacteristic
943C2#2643011yescharacteristic
944C2#2727711yescharacteristic
945C2#2728111yescharacteristic
946C2#2770511yescharacteristic
947C2#2772111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2024C2semidirect
7. #11384C2semidirect
8. #11293C2semidirect
9. #11292C2semidirect
10. #11268C2semidirect
11. #11067C2semidirect
12. #11067C2semidirect
13. #11052C2semidirect
91. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24392
C2×#20242
C2×#18942
C2×#18732
C2×#17362
#141392
#113842
#112932
#112922
#112682
#110672
#110522
#107302
#107152