Finite Group Databasebeta

← #457663

Subgroups — #457663

Order 512.

1260 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2058C211yesmaximal, characteristic, complemented
2C2×#1824C211yesmaximal, characteristic
3#15125C211yesmaximal, characteristic
4#13907C211yesmaximal, characteristic
5#11384C211yesmaximal, characteristic, complemented
6#11378C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11292C211yesmaximal, characteristic, complemented
9#11292C211yesmaximal, characteristic, complemented
10#11231C211yesmaximal, characteristic, complemented
11#11228C211yesmaximal, characteristic, complemented
12#11095C211yesmaximal, characteristic
13#11095C211yesmaximal, characteristic
14#11042C211yesmaximal, characteristic
15#10730C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C2×#393—21no—
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#380—21no—
27C2×#380C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31#2058—24no—
32#1824—24no—
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
49C2×#336C2211yescharacteristic
50#1446—21no—
51#1442—21no—
52#1441—21no—
53#1441—21no—
54#1439—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C23×Q8—21no—
62C24×C4—21no—
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4⋊Q8—22no—
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—41no—
71C2×C4⋊Q8—41no—
72C2×C4⋊Q8—41no—
73C2×C4⋊Q8—41no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—41no—
82C22×C4⋊C4—41no—
83C22×C4⋊C4Q814yescomplemented
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4D411yescharacteristic
96C22×C22⋊C4D411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×#106—22no—
100C2×#106—22no—
101C2×#106—22no—
102C2×#106—41no—
103C2×#106—41no—
104C2×#106—41no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—41no—
107C2×C4⋊C8—41no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114#393—44no—
115#389—22no—
116#389—22no—
117#389—41no—
118#389—41no—
119#380—22no—
120#380—22no—
121#380—44no—
122#380—41no—
123#380—41no—
124#380—41no—
125#380—41no—
126C4×C22⋊C4—41no—
127C4×C22⋊C4—41no—
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×#95—21no—
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340D414yes—
159#336—22no—
160#336—41no—
161#336—41no—
162C25C2×D411yescharacteristic
163C22×Q8—42no—
164C22×Q8—42no—
165C22×Q8—42no—
166C22×Q8—42no—
167C22×Q8—42no—
168C22×Q8—81no—
169C22×Q8—81no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—24no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—81no—
196C23×C4—81no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×Q812yes—
203C23×C4#4112yes—
204C23×C4C2411yescharacteristic
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×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8C2×D412yes—
232C22×C8#4112yes—
233C4⋊Q8—44no—
234C4⋊Q8—44no—
235C4⋊Q8—44no—
236C4⋊Q8—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—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—81no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4C2×D412yes—
297C2×C4⋊C4C2×Q812yes—
298C2×C4⋊C4C2×Q812yes—
299C2×C4⋊C4#4112yes—
300C2×C4⋊C4#4112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—81no—
314C2×C22⋊C4—81no—
315C2×C22⋊C4SD1614yes—
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—21no—
327C2×C42—21no—
328#106—44no—
329#106—44no—
330C4⋊C8—44no—
331C22⋊C8—44no—
332C22⋊C8—44no—
333#95—41no—
334#95—41no—
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—42no—
344#95—42no—
345#95—42no—
346#95—81no—
347#95—81no—
348#95—81no—
349#95—81no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24C22⋊Q812yes—
363C24C2×SD1612yes—
364C24#13712yes—
365C24C22×D411yescharacteristic
366C2×Q8—48no—
367C2×Q8—84no—
368C2×Q8—84no—
369C2×Q8—84no—
370C2×Q8—84no—
371C2×Q8—84no—
372C2×Q8—84no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—48no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
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—48no—
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—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—84no—
491C22×C4—84no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4C22⋊Q812yes—
496C22×C4C2×SD1612yes—
497C22×C4C2×SD1612yes—
498C22×C4AGL(1,ℤ/8)12yes—
499C22×C4C22×D411yescharacteristic
500C22×C4C22×Q811yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C42−1+411yescharacteristic
511C22×C42−1+411yescharacteristic
512C22×C42−1+411yescharacteristic
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—41no—
520C2×C8—41no—
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—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—48no—
551C4⋊C4—48no—
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—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C4⋊C4C22⋊Q814yes—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23#47514yes—
625C23C2×C22⋊Q811yescharacteristic
626C23#53411yescharacteristic
627C23#53611yescharacteristic
628C23D4211yescharacteristic
629C23#54611yescharacteristic
630C23#54611yescharacteristic
631C23#54711yescharacteristic
632C23C22×SD1611yescharacteristic
633C23C2×AGL(1,ℤ/8)11yescharacteristic
634C23C2×#13711yescharacteristic
635C23#57511yescharacteristic
636C23#57611yescharacteristic
637C23#57711yescharacteristic
638C23#57711yescharacteristic
639C23#57811yescharacteristic
640Q8—816no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—816no—
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—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×C4C2×C22⋊Q811yescharacteristic
742C2×C4#53311yescharacteristic
743C2×C4#53511yescharacteristic
744C2×C4#53611yescharacteristic
745C2×C4#53811yescharacteristic
746C2×C4#53811yescharacteristic
747C2×C4#53911yescharacteristic
748C2×C4#53911yescharacteristic
749C2×C4#54211yescharacteristic
750C2×C4#54211yescharacteristic
751C2×C4#54211yescharacteristic
752C2×C4#54211yescharacteristic
753C2×C4#54311yescharacteristic
754C2×C4#54411yescharacteristic
755C2×C4#54411yescharacteristic
756C2×C4#54411yescharacteristic
757C2×C4#54611yescharacteristic
758C2×C4#54611yescharacteristic
759C2×C4#54811yescharacteristic
760C2×C4#55111yescharacteristic
761C2×C4#55111yescharacteristic
762C2×C4#55211yescharacteristic
763C2×C4#55511yescharacteristic
764C2×C4#55611yescharacteristic
765C2×C4#56011yescharacteristic
766C2×C4#56211yescharacteristic
767C2×C4#56211yescharacteristic
768C2×C4#56311yescharacteristic
769C8—42no—
770C8—42no—
771C8—81no—
772C8—81no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22#243711yescharacteristic
789C22#243811yescharacteristic
790C22#262711yescharacteristic
791C22#267411yescharacteristic
792C22#267811yescharacteristic
793C22#268611yescharacteristic
794C22#270011yescharacteristic
795C22C2×#47511yescharacteristic
796C22#307711yescharacteristic
797C22#308111yescharacteristic
798C22#308211yescharacteristic
799C22#318711yescharacteristic
800C22#319311yescharacteristic
801C22#319811yescharacteristic
802C22#320111yescharacteristic
803C22#322711yescharacteristic
804C22#323611yescharacteristic
805C22#324311yescharacteristic
806C22#324411yescharacteristic
807C22#326511yescharacteristic
808C22#327011yescharacteristic
809C22#327311yescharacteristic
810C22D4×SD1611yescharacteristic
811C22#329511yescharacteristic
812C22#329811yescharacteristic
813C22#330811yescharacteristic
814C22#331111yescharacteristic
815C22#331611yescharacteristic
816C22#332011yescharacteristic
817C22#332311yescharacteristic
818C22#332511yescharacteristic
819C22#333511yescharacteristic
820C22#334611yescharacteristic
821C22#334911yescharacteristic
822C22#335411yescharacteristic
823C4—42no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—42no—
828C4—82no—
829C4—82no—
830C4—81no—
831C4—82no—
832C4—161no—
833C4—161no—
834C4—161no—
835C4—161no—
836C4#243911yescharacteristic
837C4#262811yescharacteristic
838C4#266511yescharacteristic
839C4#268711yescharacteristic
840C4#269611yescharacteristic
841C4#273711yescharacteristic
842C4#274511yescharacteristic
843C4#284111yescharacteristic
844C2—44no—
845C2#1629911yescharacteristic
846C2#2595511yescharacteristic
847C2#2597411yescharacteristic
848C2#2599211yescharacteristic
849C2#2600611yescharacteristic
850C2#2996711yescharacteristic
851C2#2997511yescharacteristic
852C2#3077511yescharacteristic
853C2#3079511yescharacteristic
854C2#3102411yescharacteristic
855C2#3104311yescharacteristic
856C2#3132011yescharacteristic
857C2#3133611yescharacteristic
858C2#3174011yescharacteristic
859C2#3176411yescharacteristic
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
1. C2×#2058C2semidirect
5. #11384C2semidirect
6. #11378C2semidirect
7. #11315C2semidirect
8. #11292C2semidirect
9. #11292C2semidirect
10. #11231C2semidirect
11. #11228C2semidirect
83. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#20582
C2×#18242
#151252
#139072
#113842
#113782
#113152
#112922
#112312
#112282
#110952
#110422
#107302