Finite Group Databasebeta

← #360356

Subgroups — #360356

Order 512.

1368 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1825C211yesmaximal, characteristic
2C2×#1753C211yesmaximal, characteristic
3C2×#1736C211yesmaximal, characteristic
4#13939C211yesmaximal, characteristic
5#13907C211yesmaximal, characteristic
6#11316C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11292C211yesmaximal, characteristic, complemented
10#10881C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10821C211yesmaximal, characteristic, complemented
13#10820C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic
15#10722C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×#97C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#380—21no—
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C2×C4×C22⋊C4C2211yescharacteristic
28#1825—24no—
29#1753—24no—
30#1736C418yescomplemented
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1441—21no—
50#1441—21no—
51#1440—21no—
52#1440—21no—
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60#1434—21no—
61C22⋊#95—21no—
62C24×C4—21no—
63C24×C4C2311yescharacteristic
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—41no—
69C22×M16—41no—
70C22×M16C2×C414yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117C2×C414yes—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—41no—
88C22×C4⋊C4—41no—
89C22×C4⋊C4C2×C414yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4D411yescharacteristic
102C22×C22⋊C4D411yescharacteristic
103C22×C42—21no—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8D414yes—
109C2×#97—22no—
110C2×#97—22no—
111C2×#97—41no—
112C2×C4×C8—22no—
113C2×C4×C8—22no—
114C2×C4×C8—41no—
115#389—22no—
116#389—22no—
117#389—41no—
118#389—41no—
119#380—22no—
120#380—22no—
121#380—22no—
122#380—22no—
123#380—44no—
124C4×C22⋊C4—22no—
125C4×C22⋊C4—22no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—22no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340C2×C414yes—
157#340C2×C414yes—
158#340C2×C414yes—
159#340C2×C414yes—
160#336—22no—
161#336—22no—
162C25C2×D411yescharacteristic
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—24no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4—81no—
185C23×C4—81no—
186C23×C4C22×C412yes—
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D412yes—
193C23×C4#4112yes—
194C23×C4#4112yes—
195C23×C4#4112yes—
196C23×C4#4112yes—
197C23×C4C2411yescharacteristic
198C2×M16—28no—
199C2×M16—28no—
200C2×M16—44no—
201C2×M16—44no—
202C2×M16—44no—
203C2×M16—44no—
204C2×M16—44no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
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×C8C22×C412yes—
228C22×C8C22×C412yes—
229C22×C8C2×D412yes—
230C22×C8C2×D412yes—
231C22×C8#4112yes—
232C22×C8#4112yes—
233#117—28no—
234#117—28no—
235#117—44no—
236#117—44no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—24no—
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—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C4⋊C4C22×C412yes—
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C412yes—
295C2×C4⋊C4C22×C412yes—
296C2×C4⋊C4#4112yes—
297C2×C4⋊C4#4112yes—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
313C2×C42—24no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—42no—
327C2×C42—42no—
328C22⋊C8—28no—
329#97—44no—
330C4×C8—44no—
331#95—22no—
332#95—22no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—81no—
344#95—81no—
345#95—81no—
346#95—81no—
347#95—81no—
348#95—81no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24C4×D412yes—
362C24#12112yes—
363C24#12412yes—
364C24C22×D411yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—48no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—48no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
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—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4#11714yes—
483C22×C4C4×D414yes—
484C22×C4C4×D412yes—
485C22×C4#12112yes—
486C22×C4#12314yes—
487C22×C4#12412yes—
488C22×C4#12614yes—
489C22×C4AGL(1,ℤ/8)12yes—
490C22×C4#13712yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C42−1+411yescharacteristic
504C22×C42−1+411yescharacteristic
505M16—416no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8#11714yes—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—48no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4#11714yes—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—48no—
572C22⋊C4—84no—
573C22⋊C4—84no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—48no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23#38814yes—
618C23C2×C4×D411yescharacteristic
619C23C2×#12111yescharacteristic
620C23C2×#12411yescharacteristic
621C23#54611yescharacteristic
622C23#54611yescharacteristic
623C23#54711yescharacteristic
624C23#54711yescharacteristic
625C23C2×AGL(1,ℤ/8)11yescharacteristic
626C23C2×#13711yescharacteristic
627C23#57511yescharacteristic
628C23#57511yescharacteristic
629C23#57611yescharacteristic
630C23#57711yescharacteristic
631C23#57711yescharacteristic
632C23#57811yescharacteristic
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—816no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
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#38814yes—
733C2×C4C2×#11711yescharacteristic
734C2×C4C2×#11711yescharacteristic
735C2×C4C2×#11711yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4#51811yescharacteristic
738C2×C4#51911yescharacteristic
739C2×C4C2×#12311yescharacteristic
740C2×C4C2×#12611yescharacteristic
741C2×C4#52911yescharacteristic
742C2×C4#52911yescharacteristic
743C2×C4#52911yescharacteristic
744C2×C4#52911yescharacteristic
745C2×C4#53911yescharacteristic
746C2×C4#53911yescharacteristic
747C2×C4#53911yescharacteristic
748C2×C4#53911yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54711yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#55111yescharacteristic
754C2×C4#55111yescharacteristic
755C2×C4#55111yescharacteristic
756C2×C4#55111yescharacteristic
757C2×C4#55211yescharacteristic
758C2×C4#55211yescharacteristic
759C2×C4#55211yescharacteristic
760C2×C4#55211yescharacteristic
761C8—24no—
762C8—42no—
763C8—42no—
764C8—42no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22C2×#38811yescharacteristic
781C22#234211yescharacteristic
782C22#234411yescharacteristic
783C22#242511yescharacteristic
784C22#242511yescharacteristic
785C22#248811yescharacteristic
786C22#248811yescharacteristic
787C22C4×AGL(1,ℤ/8)11yescharacteristic
788C22C4×#13711yescharacteristic
789C22#294611yescharacteristic
790C22#294711yescharacteristic
791C22#305511yescharacteristic
792C22#305611yescharacteristic
793C22#306011yescharacteristic
794C22#306111yescharacteristic
795C22#313611yescharacteristic
796C22#313711yescharacteristic
797C22#314111yescharacteristic
798C22#314211yescharacteristic
799C22#331011yescharacteristic
800C22#331211yescharacteristic
801C22#331911yescharacteristic
802C22#332111yescharacteristic
803C22#332311yescharacteristic
804C22#332511yescharacteristic
805C22#332711yescharacteristic
806C22#332911yescharacteristic
807C22#334511yescharacteristic
808C22#334611yescharacteristic
809C22#334911yescharacteristic
810C22#335011yescharacteristic
811C22#335111yescharacteristic
812C22#335311yescharacteristic
813C22#335511yescharacteristic
814C22#335611yescharacteristic
815C4—24no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—81no—
823C4—81no—
824C4—161no—
825C4—161no—
826C4—161no—
827C4—161no—
828C4#228311yescharacteristic
829C4#231311yescharacteristic
830C4#234211yescharacteristic
831C4#234411yescharacteristic
832C4#241911yescharacteristic
833C4#241911yescharacteristic
834C4#249311yescharacteristic
835C4#249311yescharacteristic
836C2—44no—
837C2#1387411yescharacteristic
838C2#2109211yescharacteristic
839C2#2109311yescharacteristic
840C2#2258411yescharacteristic
841C2#2258511yescharacteristic
842C2#2262211yescharacteristic
843C2#2262311yescharacteristic
844C2#2524111yescharacteristic
845C2#2524511yescharacteristic
846C2#2525911yescharacteristic
847C2#2526311yescharacteristic
848C2#2770411yescharacteristic
849C2#2770811yescharacteristic
850C2#2772211yescharacteristic
851C2#2772611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×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
6. #11316C2semidirect
7. #11315C2semidirect
8. #11293C2semidirect
9. #11292C2semidirect
10. #10881C2semidirect
11. #10880C2semidirect
12. #10821C2semidirect
13. #10820C2semidirect
30. #1736C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18252
C2×#17532
C2×#17362
#139392
#139072
#113162
#113152
#112932
#112922
#108812
#108802
#108212
#108202
#107302
#107222