Finite Group Databasebeta

← #420191

Subgroups — #420191

Order 512.

1354 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2439C211yesmaximal, characteristic
2C2×#2057C211yesmaximal, characteristic, complemented
3C2×#1993C211yesmaximal, characteristic, complemented
4C2×#1943C211yesmaximal, characteristic, complemented
5C2×#1854C211yesmaximal, characteristic
6#15220C211yesmaximal, characteristic
7#11328C211yesmaximal, characteristic, complemented
8#11325C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11208C211yesmaximal, characteristic, complemented
11#11208C211yesmaximal, characteristic, complemented
12#11096C211yesmaximal, characteristic
13#11096C211yesmaximal, characteristic
14#10922C211yesmaximal, characteristic
15#10731C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×#97C2211yescharacteristic
25#2439—24no—
26#2439—24no—
27C2×#396—21no—
28C2×#393—21no—
29C2×#391—21no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#387—21no—
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#2057—24no—
42#1993—24no—
43#1943—24no—
44#1854—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1443—21no—
61#1441—21no—
62#1439—21no—
63#1439—21no—
64C4⋊#95C2211yescharacteristic
65C23×Q8—21no—
66C24×C4C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—41no—
75C2×C4⋊Q8—41no—
76C2×C4⋊Q8D414yes—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—41no—
82C2×#117—41no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4D411yescharacteristic
101C22×C22⋊C4D411yescharacteristic
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×#107—22no—
106C2×#107—22no—
107C2×#107—22no—
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—41no—
113C2×#107—41no—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—41no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8Q814yescomplemented
122C2×C22⋊C8Q814yescomplemented
123C2×#97—22no—
124C2×#97—22no—
125C2×#97—41no—
126#396—28no—
127#393—28no—
128#391—28no—
129#389—22no—
130#389—22no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—22no—
135#389—41no—
136#389D414yes—
137#387—28no—
138#382—22no—
139#382—22no—
140#382—22no—
141#382—41no—
142#380—22no—
143#380—22no—
144#380—22no—
145#380—22no—
146#380—41no—
147#380—41no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—22no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95D411yescharacteristic
164C2×#95D411yescharacteristic
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340D414yes—
177#336—22no—
178#336—22no—
179#336—41no—
180C25C2×D411yescharacteristic
181C22×Q8—24no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—42no—
185C22×Q8—42no—
186C22×Q8—81no—
187C22×Q8—81no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×Q812yes—
214C23×C4C2×Q812yes—
215C23×C4C2411yescharacteristic
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
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×C8C2×D412yes—
239C22×C8C2×Q812yes—
240C22×C8C2×Q812yes—
241C22×C8C2×Q812yes—
242C22×C8C2×Q812yes—
243C22×C8#4112yes—
244C4⋊Q8—28no—
245C4⋊Q8—44no—
246C4⋊Q8—44no—
247C4⋊Q8—44no—
248#117—44no—
249#117—44no—
250#117—44no—
251#117—44no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
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—24no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C4⋊C4#4112yes—
314C2×C4⋊C4#4112yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—81no—
330C2×C22⋊C4—81no—
331C2×C22⋊C4—81no—
332C2×C22⋊C4—81no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—24no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42C2×D412yes—
347C2×C42C2×D412yes—
348#107—28no—
349#107—44no—
350#107—44no—
351#106—44no—
352C22⋊C8—28no—
353C22⋊C8—44no—
354#97—44no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—22no—
361#95—22no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—81no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24C4⋊Q812yes—
385C24C22×D411yescharacteristic
386C2×Q8—48no—
387C2×Q8—48no—
388C2×Q8—84no—
389C2×Q8—84no—
390C2×Q8—84no—
391C2×Q8—84no—
392C2×Q8—84no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
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#12012yes—
510C22×C4#12012yes—
511C22×C4C4⋊Q812yes—
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C22×Q811yescharacteristic
516C22×C4C22×Q811yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C42−1+411yescharacteristic
524C22×C42−1+411yescharacteristic
525C22×C42−1+411yescharacteristic
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8C22⋊Q814yes—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C4⋊C4—84no—
590C4⋊C4#12114yes—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—48no—
594C22⋊C4—84no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—48no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23C2×#12011yescharacteristic
642C23C2×C4⋊Q811yescharacteristic
643C23#53611yescharacteristic
644C23D4211yescharacteristic
645C23#54611yescharacteristic
646C23#54611yescharacteristic
647C23#54711yescharacteristic
648C23#57511yescharacteristic
649C23#57511yescharacteristic
650C23#57511yescharacteristic
651C23#57511yescharacteristic
652C23#57611yescharacteristic
653C23#57611yescharacteristic
654C23#57811yescharacteristic
655C23#57811yescharacteristic
656Q8—816no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
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—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4C2×#12111yescharacteristic
757C2×C4C2×C22⋊Q811yescharacteristic
758C2×C4#52511yescharacteristic
759C2×C4#53311yescharacteristic
760C2×C4#53411yescharacteristic
761C2×C4#53711yescharacteristic
762C2×C4#53711yescharacteristic
763C2×C4#53911yescharacteristic
764C2×C4#54111yescharacteristic
765C2×C4#54211yescharacteristic
766C2×C4#54311yescharacteristic
767C2×C4#54411yescharacteristic
768C2×C4D4211yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54711yescharacteristic
771C2×C4#54811yescharacteristic
772C2×C4D4×Q811yescharacteristic
773C2×C4D4×Q811yescharacteristic
774C2×C4D4×Q811yescharacteristic
775C2×C4D4×Q811yescharacteristic
776C2×C4D4×Q811yescharacteristic
777C2×C4#55011yescharacteristic
778C2×C4#55411yescharacteristic
779C2×C4#55411yescharacteristic
780C2×C4#55411yescharacteristic
781C2×C4#55611yescharacteristic
782C2×C4#56211yescharacteristic
783C2×C4#56311yescharacteristic
784C8—24no—
785C8—42no—
786C8—42no—
787C8—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22#240711yescharacteristic
804C22#241011yescharacteristic
805C22#243411yescharacteristic
806C22#244011yescharacteristic
807C22#254911yescharacteristic
808C22#267211yescharacteristic
809C22#268911yescharacteristic
810C22#300511yescharacteristic
811C22#300511yescharacteristic
812C22#300811yescharacteristic
813C22#301111yescharacteristic
814C22#316211yescharacteristic
815C22#316411yescharacteristic
816C22#316411yescharacteristic
817C22#316611yescharacteristic
818C22#324011yescharacteristic
819C22#324011yescharacteristic
820C22#324311yescharacteristic
821C22#324311yescharacteristic
822C22#326811yescharacteristic
823C22#326911yescharacteristic
824C22#327311yescharacteristic
825C22#327711yescharacteristic
826C22#331311yescharacteristic
827C22#331311yescharacteristic
828C22#331311yescharacteristic
829C22#331911yescharacteristic
830C22#331911yescharacteristic
831C22#331911yescharacteristic
832C22#332211yescharacteristic
833C22#332711yescharacteristic
834C22#334711yescharacteristic
835C22#334711yescharacteristic
836C22#334911yescharacteristic
837C22#334911yescharacteristic
838C4—42no—
839C4—42no—
840C4—44no—
841C4—42no—
842C4—81no—
843C4—82no—
844C4—82no—
845C4—81no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—161no—
850C4—161no—
851C4#242911yescharacteristic
852C4#244911yescharacteristic
853C4#246511yescharacteristic
854C4#253811yescharacteristic
855C4#268311yescharacteristic
856C4#270411yescharacteristic
857C4#272911yescharacteristic
858C4#273211yescharacteristic
859C2—82no—
860C2#1527611yescharacteristic
861C2#2412911yescharacteristic
862C2#2413511yescharacteristic
863C2#2444711yescharacteristic
864C2#2445011yescharacteristic
865C2#2581711yescharacteristic
866C2#2582111yescharacteristic
867C2#2606911yescharacteristic
868C2#2607911yescharacteristic
869C2#2877711yescharacteristic
870C2#2878711yescharacteristic
871C2#3065411yescharacteristic
872C2#3066011yescharacteristic
873C2#3144711yescharacteristic
874C2#3145311yescharacteristic
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×#2057C2semidirect
3. C2×#1993C2semidirect
4. C2×#1943C2semidirect
7. #11328C2semidirect
8. #11325C2semidirect
9. #11219C2semidirect
10. #11208C2semidirect
11. #11208C2semidirect
121. C2×C22⋊C8Q8semidirect
122. C2×C22⋊C8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24392
C2×#20572
C2×#19932
C2×#19432
C2×#18542
#152202
#113282
#113252
#112192
#112082
#110962
#109222
#107312