Finite Group Databasebeta

← #373257

Subgroups — #373257

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1923C211yesmaximal, characteristic
2#13876C211yesmaximal, characteristic
3C22⋊C4×C4⋊C4C211yesmaximal, characteristic
4#11267C211yesmaximal, characteristic, complemented
5#11231C211yesmaximal, characteristic, complemented
6#11095C211yesmaximal, characteristic
7#11095C211yesmaximal, characteristic
8#10908C211yesmaximal, characteristic, complemented
9#10908C211yesmaximal, characteristic, complemented
10#10908C211yesmaximal, characteristic, complemented
11#10849C211yesmaximal, characteristic, complemented
12#10820C211yesmaximal, characteristic, complemented
13#10730C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic, complemented
16C23×C4⋊C4C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C2×#388—21no—
24C2×#384C2211yescharacteristic
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4—21no—
32C2×C4×C22⋊C4C2211yescharacteristic
33#1923C418yescomplemented
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×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1442—21no—
51#1439—21no—
52#1436—21no—
53#1436—21no—
54#1436—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C22⋊#95—21no—
60C24×C4—21no—
61C24×C4C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C22×C4⋊C4—21no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—41no—
74C22×C4⋊C4—41no—
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4D411yescharacteristic
87C22×C22⋊C4D411yescharacteristic
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C2×#106—22no—
94C2×#106—22no—
95C2×#106—22no—
96C2×#106—41no—
97C2×#106—41no—
98C2×#106—41no—
99C2×C4⋊C8—41no—
100C2×C4⋊C8—41no—
101C2×C4⋊C8C2×C414yescomplemented
102C2×C22⋊C8—41no—
103C2×C22⋊C8—41no—
104C2×C22⋊C8—41no—
105C2×C22⋊C8—41no—
106C2×C22⋊C8C2×C414yes—
107C2×C22⋊C8C2×C414yes—
108C2×C4×C8—41no—
109C2×C4×C8—41no—
110C2×C4×C8C2×C414yescomplemented
111#388—44no—
112#384—22no—
113#384—41no—
114#380—22no—
115#380—22no—
116#380—22no—
117#380—22no—
118#380—41no—
119#380—41no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—41no—
124C4×C4⋊C4—41no—
125C4×C4⋊C4—41no—
126C4×C22⋊C4—44no—
127C4×C22⋊C4C2×C414yes—
128C4×C22⋊C4Q814yes—
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—22no—
152#340—22no—
153#340—22no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340—41no—
159#336C2×C414yescomplemented
160#336C2×C414yescomplemented
161C25C2×D411yescharacteristic
162C23×C4—21no—
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—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—24no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4—81no—
188C23×C4—81no—
189C23×C4C22×C412yes—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×Q812yes—
196C23×C4C2411yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
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×C8C22×C412yes—
222C22×C8C22×C412yes—
223C22×C8C22×C412yes—
224C22×C8C22×C412yes—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
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—24no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
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—44no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—81no—
277C2×C4⋊C4—81no—
278C2×C4⋊C4#4112yes—
279C2×C4⋊C4#4112yes—
280C2×C4⋊C4#4112yes—
281C2×C4⋊C4#4112yes—
282C2×C4⋊C4#4112yes—
283C2×C4⋊C4#4112yes—
284C2×C4⋊C4#4112yes—
285C2×C4⋊C4#4112yes—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—81no—
296C2×C22⋊C4—81no—
297C2×C22⋊C4C4⋊C414yes—
298C2×C22⋊C4C4⋊C414yes—
299C2×C22⋊C4SD1614yes—
300C2×C22⋊C4SD1614yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—81no—
316C2×C42—81no—
317C2×C42—81no—
318C2×C42C22×C412yes—
319C2×C42C22×C412yes—
320C2×C42C2×Q812yes—
321C2×C42C2×Q812yes—
322#106—44no—
323#106—44no—
324C4⋊C8—44no—
325C22⋊C8—44no—
326C22⋊C8—44no—
327C4×C8—44no—
328#95—24no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—81no—
340#95—81no—
341#95—81no—
342#95C4⋊C414yes—
343#95C4⋊C414yes—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24C2×C4⋊C412yes—
357C24C2×SD1612yes—
358C24C2×SD1612yes—
359C24C22×D411yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—48no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—48no—
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—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—84no—
473C22×C4—84no—
474C22×C4—84no—
475C22×C4—84no—
476C22×C4—84no—
477C22×C4C2×C4⋊C412yes—
478C22×C4C2×C4⋊C412yes—
479C22×C4C2×C4⋊C412yes—
480C22×C4C2×C4⋊C412yes—
481C22×C4C2×C4⋊C412yes—
482C22×C4C2×SD1612yes—
483C22×C4C2×SD1612yes—
484C22×C4C2×SD1612yes—
485C22×C4C2×SD1612yes—
486C22×C4C23×C411yescharacteristic
487C22×C4C22×Q811yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C4H(5,𝔽2)11yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
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—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—48no—
542C4⋊C4—41no—
543C4⋊C4—41no—
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—84no—
561C4⋊C4—84no—
562C4⋊C4#12614yes—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—84no—
566C22⋊C4—84no—
567C22⋊C4#106116yescomplemented
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—84no—
577C42—84no—
578C42—84no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
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—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23C2×#10614yes—
614C23C22×C4⋊C411yescharacteristic
615C23#52511yescharacteristic
616C23#52511yescharacteristic
617C23#54611yescharacteristic
618C23#54611yescharacteristic
619C23#54611yescharacteristic
620C23#54611yescharacteristic
621C23C22×SD1611yescharacteristic
622C23C22×SD1611yescharacteristic
623C23#57511yescharacteristic
624C23#57511yescharacteristic
625C23#57611yescharacteristic
626C23#57611yescharacteristic
627C23#57811yescharacteristic
628C23#57811yescharacteristic
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
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—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—816no—
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×C4C2×#10614yes—
728C2×C4C2×#10614yes—
729C2×C4C4×#4111yescharacteristic
730C2×C4C4×#4111yescharacteristic
731C2×C4C4×#4111yescharacteristic
732C2×C4C4×#4111yescharacteristic
733C2×C4#51811yescharacteristic
734C2×C4#51811yescharacteristic
735C2×C4C2×#12611yescharacteristic
736C2×C4#52911yescharacteristic
737C2×C4#52911yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#53311yescharacteristic
740C2×C4#53311yescharacteristic
741C2×C4#53811yescharacteristic
742C2×C4#53811yescharacteristic
743C2×C4#54011yescharacteristic
744C2×C4#54011yescharacteristic
745C2×C4#55111yescharacteristic
746C2×C4#55111yescharacteristic
747C2×C4#55111yescharacteristic
748C2×C4#55311yescharacteristic
749C2×C4#55311yescharacteristic
750C2×C4#55411yescharacteristic
751C2×C4#55411yescharacteristic
752C2×C4#55411yescharacteristic
753C2×C4#55411yescharacteristic
754C2×C4#55511yescharacteristic
755C2×C4#55511yescharacteristic
756C2×C4#55911yescharacteristic
757C8—42no—
758C8—42no—
759C8—42no—
760C8—42no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22#229611yescharacteristic
777C22#234911yescharacteristic
778C22#234911yescharacteristic
779C22#245711yescharacteristic
780C22#245911yescharacteristic
781C22#247611yescharacteristic
782C22#248011yescharacteristic
783C22C22×#10611yescharacteristic
784C22#291111yescharacteristic
785C22#291311yescharacteristic
786C22#291311yescharacteristic
787C22#310111yescharacteristic
788C22#310111yescharacteristic
789C22#310311yescharacteristic
790C22#310311yescharacteristic
791C22#312211yescharacteristic
792C22#312411yescharacteristic
793C22#312411yescharacteristic
794C22#312711yescharacteristic
795C22#329511yescharacteristic
796C22#329511yescharacteristic
797C22#329511yescharacteristic
798C22#329511yescharacteristic
799C22#329811yescharacteristic
800C22#329811yescharacteristic
801C22#329811yescharacteristic
802C22#329811yescharacteristic
803C22#330911yescharacteristic
804C22#331311yescharacteristic
805C22#331511yescharacteristic
806C22#331911yescharacteristic
807C22#332211yescharacteristic
808C22#332211yescharacteristic
809C22#332711yescharacteristic
810C22#332711yescharacteristic
811C4—24no—
812C4—24no—
813C4—42no—
814C4—44no—
815C4—42no—
816C4—42no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—161no—
823C4—161no—
824C4C4×#12611yescharacteristic
825C4#233311yescharacteristic
826C4#237211yescharacteristic
827C4#237411yescharacteristic
828C4#249711yescharacteristic
829C4#252211yescharacteristic
830C4#257411yescharacteristic
831C4#258911yescharacteristic
832C2—44no—
833C2#1411411yescharacteristic
834C2#2135911yescharacteristic
835C2#2136811yescharacteristic
836C2#2270311yescharacteristic
837C2#2270311yescharacteristic
838C2#2271211yescharacteristic
839C2#2271611yescharacteristic
840C2#2665811yescharacteristic
841C2#2666011yescharacteristic
842C2#2672211yescharacteristic
843C2#2672411yescharacteristic
844C2#2739211yescharacteristic
845C2#2739411yescharacteristic
846C2#2752011yescharacteristic
847C2#2752211yescharacteristic
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
4. #11267C2semidirect
5. #11231C2semidirect
8. #10908C2semidirect
9. #10908C2semidirect
10. #10908C2semidirect
11. #10849C2semidirect
12. #10820C2semidirect
15. C4×#340C2semidirect
33. #1923C4semidirect
101. C2×C4⋊C8C2×C4semidirect
110. C2×C4×C8C2×C4semidirect
159. #336C2×C4semidirect
160. #336C2×C4semidirect
567. C22⋊C4#106semidirect

Maximal subgroups

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

subgroupindex
C2×#19232
#138762
C22⋊C4×C4⋊C42
#112672
#112312
#110952
#109082
#108492
#108202
#107302
C4×#3402