Finite Group Databasebeta

← #394890

Subgroups — #394890

Order 512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#479C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic
3C2×#2059C211yesmaximal, characteristic
4C2×#1865C211yesmaximal, characteristic
5C2×#1863C211yesmaximal, characteristic
6#15218C211yesmaximal, characteristic
7#11328C211yesmaximal, characteristic
8#11327C211yesmaximal, characteristic
9#11324C211yesmaximal, characteristic
10#11323C211yesmaximal, characteristic
11#11227C211yesmaximal, characteristic
12#11202C211yesmaximal, characteristic
13#10789C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C2×#479—24no—
21C2×#479—24no—
22C2×#479—24no—
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×C4⋊C8C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32Q8×C4⋊C4—24no—
33Q8×C4⋊C4—24no—
34C2×#389—21no—
35C2×#389—21no—
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#384—21no—
41C2×#384C2211yescharacteristic
42C2×C4×C4⋊C4—21no—
43C2×C4×C4⋊C4C2211yescharacteristic
44#2059—24no—
45#1865—24no—
46#1863—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1444—21no—
61#1444—21no—
62#1441—21no—
63#1441—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67C23×Q8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—22no—
75C2×#125—22no—
76C2×#125—41no—
77C2×#125—41no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8—22no—
84C2×C4×Q8—22no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—41no—
91C2×C4×Q8—41no—
92C2×C4×Q8—41no—
93C2×C4×Q8—41no—
94C2×C4×Q8D414yes—
95C2×C4×Q8Q814yes—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4D411yescharacteristic
108C22×C4⋊C4D411yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C42—21no—
117C22×C42—21no—
118C22×C42—21no—
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122#479—232no—
123C2×#107—22no—
124C2×#107—22no—
125C2×#107—22no—
126C2×#107—22no—
127C2×#107—22no—
128C2×#107—41no—
129C2×#106—22no—
130C2×#106—22no—
131C2×#106—22no—
132C2×#106—22no—
133C2×#106—22no—
134C2×#106—41no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×C4⋊C8—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103D414yes—
147C2×#103D414yes—
148C2×#103Q814yes—
149C2×#103Q814yes—
150#389—28no—
151#389—28no—
152#389—22no—
153#389—22no—
154#389—22no—
155#389—22no—
156#389—22no—
157#389—41no—
158#389—41no—
159#389D414yes—
160#384—28no—
161#384—22no—
162#384—22no—
163C4×C4⋊C4—28no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95D411yescharacteristic
177C2×#95D411yescharacteristic
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—41no—
185#340—41no—
186#336—22no—
187#336—22no—
188#336—22no—
189#336—22no—
190#336—22no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8C2×D412yes—
199C22×Q8C2×D412yes—
200C22×Q8C2×D412yes—
201C22×Q8C2×Q812yes—
202C22×Q8C2×Q812yes—
203C22×Q8C2×Q812yes—
204C22×Q8#4112yes—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2411yescharacteristic
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8C2×D412yes—
245C22×C8C2×D412yes—
246C22×C8C2×Q812yes—
247C22×C8C2×Q812yes—
248#125—28no—
249#125—44no—
250#125—44no—
251#125—44no—
252C4×Q8—28no—
253C4×Q8—28no—
254C4×Q8—28no—
255C4×Q8—28no—
256C4×Q8—28no—
257C4×Q8—44no—
258C4×Q8—44no—
259C4×Q8—44no—
260C4×Q8—44no—
261C4×Q8—44no—
262C4×Q8—44no—
263C4×Q8—44no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
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—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—81no—
329C2×C4⋊C4—81no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4—81no—
332C2×C4⋊C4—81no—
333C2×C4⋊C4—81no—
334C2×C4⋊C4—81no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4C2×D412yes—
337C2×C4⋊C4C2×D412yes—
338C2×C4⋊C4C2×D412yes—
339C2×C4⋊C4C2×D412yes—
340C2×C4⋊C4C2×D412yes—
341C2×C4⋊C4C2×Q812yes—
342C2×C4⋊C4C2×Q812yes—
343C2×C4⋊C4C2×Q812yes—
344C2×C4⋊C4#4112yes—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42C2×D412yes—
369C2×C42C2×D412yes—
370C2×C42C2×Q812yes—
371C2×C42#4112yes—
372#107—28no—
373#107—44no—
374#106—28no—
375#106—44no—
376C4⋊C8—28no—
377#103—28no—
378#103—28no—
379#103—28no—
380#103—28no—
381#95—24no—
382#95—24no—
383#95—22no—
384#95—22no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—81no—
390#95—81no—
391#95—81no—
392#95—81no—
393C24C22×D411yescharacteristic
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8#12014yes—
416C2×Q8C22⋊Q814yes—
417C2×Q8C22⋊Q814yes—
418C2×Q8C22⋊Q814yes—
419C2×Q8C4⋊Q814yes—
420C2×Q8C4⋊Q814yes—
421C2×Q8C4⋊Q814yes—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4#12012yes—
514C22×C4#12012yes—
515C22×C4C22⋊Q812yes—
516C22×C4C22⋊Q812yes—
517C22×C4#13512yes—
518C22×C4#13712yes—
519C22×C4#13712yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×Q811yescharacteristic
525C22×C4C22×Q811yescharacteristic
526C22×C4C22×Q811yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C42−1+411yescharacteristic
533C22×C42−1+411yescharacteristic
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—28no—
563C4⋊C4—216no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—44no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—84no—
598C4⋊C4—84no—
599C4⋊C4—84no—
600C4⋊C4—84no—
601C4⋊C4—84no—
602C4⋊C4C22⋊Q814yes—
603C42—216no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—48no—
613C42—48no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C23C2×#12011yescharacteristic
619C23C2×C22⋊Q811yescharacteristic
620C23#52511yescharacteristic
621C23D4211yescharacteristic
622C23D4211yescharacteristic
623C23D4×Q811yescharacteristic
624C23D4×Q811yescharacteristic
625C23C2×#13511yescharacteristic
626C23C2×#13711yescharacteristic
627C23C2×#13711yescharacteristic
628C23#57511yescharacteristic
629C23#57611yescharacteristic
630C23#57711yescharacteristic
631C23#57711yescharacteristic
632C23#57811yescharacteristic
633Q8—24no—
634Q8—24no—
635Q8—24no—
636Q8—24no—
637Q8—24no—
638Q8—24no—
639Q8—24no—
640Q8#39518yes—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4#47914yescomplemented
739C2×C4C2×#12011yescharacteristic
740C2×C4C2×C22⋊Q811yescharacteristic
741C2×C4C2×C22⋊Q811yescharacteristic
742C2×C4C2×C22⋊Q811yescharacteristic
743C2×C4C2×C22⋊Q811yescharacteristic
744C2×C4#52511yescharacteristic
745C2×C4#52511yescharacteristic
746C2×C4C2×C4⋊Q811yescharacteristic
747C2×C4C2×C4⋊Q811yescharacteristic
748C2×C4C2×C4⋊Q811yescharacteristic
749C2×C4#53411yescharacteristic
750C2×C4#53611yescharacteristic
751C2×C4#53911yescharacteristic
752C2×C4#53911yescharacteristic
753C2×C4#54411yescharacteristic
754C2×C4#54411yescharacteristic
755C2×C4D4211yescharacteristic
756C2×C4D4211yescharacteristic
757C2×C4#54711yescharacteristic
758C2×C4#54711yescharacteristic
759C2×C4#54711yescharacteristic
760C2×C4#54711yescharacteristic
761C2×C4D4×Q811yescharacteristic
762C2×C4D4×Q811yescharacteristic
763C2×C4#55411yescharacteristic
764C2×C4#55411yescharacteristic
765C2×C4#55411yescharacteristic
766C2×C4#55411yescharacteristic
767C8—42no—
768C8—42no—
769C8—42no—
770C8—42no—
771C22#240311yescharacteristic
772C22#243411yescharacteristic
773C22#244011yescharacteristic
774C22#244011yescharacteristic
775C22#244911yescharacteristic
776C22#244911yescharacteristic
777C22#284811yescharacteristic
778C22#300211yescharacteristic
779C22#300411yescharacteristic
780C22#301211yescharacteristic
781C22#301311yescharacteristic
782C22C2×#47911yescharacteristic
783C22#307811yescharacteristic
784C22#308311yescharacteristic
785C22#308411yescharacteristic
786C22#310811yescharacteristic
787C22#311711yescharacteristic
788C22#311911yescharacteristic
789C22#312011yescharacteristic
790C22#326611yescharacteristic
791C22#326811yescharacteristic
792C22#327011yescharacteristic
793C22#327111yescharacteristic
794C22#327611yescharacteristic
795C22#327811yescharacteristic
796C22#328411yescharacteristic
797C22#328711yescharacteristic
798C22#338111yescharacteristic
799C22#338311yescharacteristic
800C22#338511yescharacteristic
801C22#338511yescharacteristic
802C22#338711yescharacteristic
803C22#338711yescharacteristic
804C22#338811yescharacteristic
805C22#339011yescharacteristic
806C4—28no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—44no—
813C4—82no—
814C4—82no—
815C4—81no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4C2×#39511yescharacteristic
821C4#240611yescharacteristic
822C4#244011yescharacteristic
823C4#244011yescharacteristic
824C4#244911yescharacteristic
825C4#244911yescharacteristic
826C4#258311yescharacteristic
827C4#262711yescharacteristic
828C2#1472011yescharacteristic
829C2#2385711yescharacteristic
830C2#2386811yescharacteristic
831C2#2584211yescharacteristic
832C2#2584711yescharacteristic
833C2#2604311yescharacteristic
834C2#2604711yescharacteristic
835C2#2605411yescharacteristic
836C2#2605511yescharacteristic
837C2#2637111yescharacteristic
838C2#2637911yescharacteristic
839C2#2638711yescharacteristic
840C2#2639511yescharacteristic
841C2#3296011yescharacteristic
842C2#3296811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
738. C2×C4#479semidirect

Maximal subgroups

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

subgroupindex
C22×#4792
C2×Q8×C4⋊C42
C2×#20592
C2×#18652
C2×#18632
#152182
#113282
#113272
#113242
#113232
#112272
#112022
#107892