Finite Group Databasebeta

← #153753

Subgroups — #153753

Order 512.

3894 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#384C211yesmaximal, characteristic
2C22×C4×C4⋊C4C211yesmaximal, characteristic
3C2×#1436C214yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C2×C4×#95C211yesmaximal, characteristic
9#7557C214yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2214yes—
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2212yes—
17C23×C42C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×#384—24no—
20C2×#384—24no—
21C2×#384C418yescomplemented
22C2×C4×C4⋊C4—24no—
23C2×C4×C4⋊C4—24no—
24C2×C4×C4⋊C4—24no—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2214yes—
28C22×#95C2214yes—
29C22×#95C2212yes—
30C22×#95C2214yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33#1436—216no—
34C4⋊#95—24no—
35C4⋊#95—24no—
36C4⋊#95—24no—
37C4⋊#95C418yescomplemented
38C4×#95C418yescomplemented
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—28no—
61C22×C4⋊C4—28no—
62C22×C4⋊C4—28no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—28no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—44no—
73C22×C4⋊C4—44no—
74C22×C4⋊C4C2×C414yes—
75C22×C4⋊C4C2×C414yes—
76C22×C4⋊C4C2×C4116yes—
77C22×C4⋊C4C2×C414yes—
78C22×C4⋊C4C2×C414yes—
79C22×C4⋊C4D414yes—
80C22×C4⋊C4D414yes—
81C22×C4⋊C4D414yes—
82C22×C4⋊C4Q814yes—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42—22no—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—24no—
94C22×C42—24no—
95C22×C42—24no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—28no—
101C22×C42—44no—
102C22×C42C2×C414yes—
103C22×C42C2×C414yes—
104C22×C42C2×C414yes—
105C22×C42C2×C414yes—
106C22×C42C2×C414yes—
107C22×C42D414yes—
108C22×C42Q814yes—
109#384—232no—
110C4×C4⋊C4—232no—
111C2×#95—28no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—28no—
118C2×#95—28no—
119C2×#95—28no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—28no—
123C2×#95—28no—
124C2×#95—28no—
125C2×#95—44no—
126C2×#95—44no—
127C2×#95—44no—
128C2×#95C2×C418yes—
129C2×#95C2×C4116yes—
130C2×#95C2×C418yes—
131C2×#95D418yes—
132C2×#95Q818yes—
133C25C2411yescharacteristic
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—24no—
153C23×C4—24no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—24no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—24no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—24no—
180C23×C4—22no—
181C23×C4—24no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4C22×C414yes—
205C23×C4C22×C414yes—
206C23×C4C22×C414yes—
207C23×C4C22×C414yes—
208C23×C4C22×C412yes—
209C23×C4C22×C414yes—
210C23×C4C22×C414yes—
211C23×C4C22×C414yes—
212C23×C4C22×C414yes—
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C412yes—
217C23×C4C2×D414yes—
218C23×C4C2×D414yes—
219C23×C4C2×D414yes—
220C23×C4C2×D414yes—
221C23×C4C2×D412yes—
222C23×C4C2×D414yes—
223C23×C4C2×D414yes—
224C23×C4C2×D412yes—
225C23×C4C2×D412yes—
226C23×C4C2×D412yes—
227C23×C4C2×D412yes—
228C23×C4C2×D412yes—
229C23×C4C2×Q814yes—
230C23×C4C2×Q814yes—
231C23×C4C2×Q812yes—
232C23×C4C2×Q814yes—
233C23×C4C2×Q814yes—
234C23×C4C2×Q812yes—
235C23×C4C2×Q812yes—
236C23×C4C2×Q812yes—
237C23×C4#4114yes—
238C23×C4#4114yes—
239C23×C4#4112yes—
240C23×C4#4112yes—
241C23×C4#4112yes—
242C23×C4#4112yes—
243C23×C4#4112yes—
244C23×C4#4112yes—
245C2×C4⋊C4—28no—
246C2×C4⋊C4—28no—
247C2×C4⋊C4—28no—
248C2×C4⋊C4—28no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4—28no—
251C2×C4⋊C4—28no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—232no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—232no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—416no—
266C2×C4⋊C4—416no—
267C2×C4⋊C4—416no—
268C2×C4⋊C4—416no—
269C2×C4⋊C4—416no—
270C2×C4⋊C4—44no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4C22⋊C4116yes—
279C2×C4⋊C4C4⋊C4116yescomplemented
280C2×C42—28no—
281C2×C42—28no—
282C2×C42—28no—
283C2×C42—28no—
284C2×C42—28no—
285C2×C42—28no—
286C2×C42—28no—
287C2×C42—28no—
288C2×C42—28no—
289C2×C42—28no—
290C2×C42—28no—
291C2×C42—28no—
292C2×C42—216no—
293C2×C42—28no—
294C2×C42—28no—
295C2×C42—28no—
296C2×C42—416no—
297C2×C42—416no—
298C2×C42—48no—
299C2×C42—44no—
300C2×C42—44no—
301C2×C42—44no—
302C2×C42—44no—
303C2×C42—48no—
304C2×C42C42116yescomplemented
305C2×C42C4⋊C4116yescomplemented
306#95—216no—
307#95—216no—
308#95—232no—
309#95—416no—
310#95—416no—
311#95—48no—
312#95—48no—
313#95C4⋊C4132yescomplemented
314C24C23×C411yescharacteristic
315C24C23×C411yescharacteristic
316C24C23×C411yescharacteristic
317C24C22×D411yescharacteristic
318C24C22×D411yescharacteristic
319C24C22×D411yescharacteristic
320C24C22×D411yescharacteristic
321C24C22×D412yes—
322C24C22×Q811yescharacteristic
323C24C22×Q811yescharacteristic
324C24C22×Q812yes—
325C24C2×#4111yescharacteristic
326C24C2×#4111yescharacteristic
327C24C2×#4111yescharacteristic
328C24C2×#4111yescharacteristic
329C24C2×#4111yescharacteristic
330C24C2×#4111yescharacteristic
331C24C2×#4112yes—
332C24C2×#4112yes—
333C24H(5,𝔽2)12yes—
334C24H(5,𝔽2)12yes—
335C242−1+412yes—
336C242−1+412yes—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—28no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—28no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—28no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—28no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—28no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—44no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—44no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—44no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—44no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4C2×C4218yes—
530C22×C4C2×C4214yes—
531C22×C4C2×C22⋊C418yes—
532C22×C4C2×C22⋊C414yes—
533C22×C4C2×C4⋊C418yes—
534C22×C4C2×C4⋊C414yes—
535C22×C4C2×C4⋊C418yes—
536C22×C4C2×C4⋊C418yes—
537C22×C4C2×C4⋊C418yes—
538C22×C4C2×C4⋊C414yes—
539C22×C4C2×C4⋊C414yes—
540C22×C4C2×C4⋊C414yes—
541C22×C4#11718yes—
542C22×C4#11714yes—
543C22×C4#11714yes—
544C22×C4#11714yes—
545C22×C4C4×D418yes—
546C22×C4C4×D418yes—
547C22×C4C4×D414yes—
548C22×C4C4×D414yes—
549C22×C4C4×D414yes—
550C22×C4C4×D414yes—
551C22×C4C4×D414yes—
552C22×C4C4×D414yes—
553C22×C4C4×D414yes—
554C22×C4C4×D414yes—
555C22×C4C4×Q818yes—
556C22×C4C4×Q818yes—
557C22×C4C4×Q814yes—
558C22×C4C4×Q814yes—
559C22×C4C4×Q814yes—
560C22×C4C4×Q814yes—
561C22×C4#12014yes—
562C22×C4#12114yes—
563C22×C4#12114yes—
564C22×C4C22⋊Q814yes—
565C22×C4C22⋊Q814yes—
566C22×C4C22⋊Q814yes—
567C22×C4C22⋊Q814yes—
568C22×C4#12314yes—
569C22×C4#12314yes—
570C22×C4#12314yes—
571C22×C4#12414yes—
572C22×C4#12514yes—
573C22×C4#12514yes—
574C22×C4#12614yes—
575C22×C4#12614yes—
576C22×C4#12714yes—
577C22×C4C4⋊Q814yes—
578C22×C4C4⋊Q818yes—
579C22×C4C4⋊Q814yes—
580C4⋊C4—232no—
581C4⋊C4—232no—
582C4⋊C4—464no—
583C4⋊C4—416no—
584C4⋊C4—416no—
585C42—232no—
586C42—232no—
587C42—432no—
588C42—416no—
589C23C22×C4211yescharacteristic
590C23C22×C22⋊C411yescharacteristic
591C23C22×C4⋊C411yescharacteristic
592C23C22×C4⋊C412yes—
593C23C22×C4⋊C411yescharacteristic
594C23C2×#11711yescharacteristic
595C23C2×#11711yescharacteristic
596C23C2×#11712yes—
597C23C2×#11711yescharacteristic
598C23C2×C4×D411yescharacteristic
599C23C2×C4×D411yescharacteristic
600C23C2×C4×D412yes—
601C23C2×C4×D412yes—
602C23C2×C4×D411yescharacteristic
603C23C2×C4×D411yescharacteristic
604C23C2×C4×D411yescharacteristic
605C23C2×C4×D411yescharacteristic
606C23C2×C4×D411yescharacteristic
607C23C2×C4×D411yescharacteristic
608C23C2×C4×Q811yescharacteristic
609C23C2×C4×Q811yescharacteristic
610C23C2×C4×Q812yes—
611C23C2×C4×Q812yes—
612C23C2×C4×Q811yescharacteristic
613C23C2×C4×Q811yescharacteristic
614C23#51812yes—
615C23#51912yes—
616C23#52012yes—
617C23#52012yes—
618C23#52012yes—
619C23#52012yes—
620C23C2×#12011yescharacteristic
621C23C2×#12111yescharacteristic
622C23C2×#12111yescharacteristic
623C23C2×C22⋊Q811yescharacteristic
624C23C2×C22⋊Q811yescharacteristic
625C23C2×C22⋊Q811yescharacteristic
626C23C2×C22⋊Q811yescharacteristic
627C23C2×#12311yescharacteristic
628C23C2×#12311yescharacteristic
629C23C2×#12311yescharacteristic
630C23C2×#12411yescharacteristic
631C23C2×#12511yescharacteristic
632C23C2×#12511yescharacteristic
633C23C2×#12611yescharacteristic
634C23C2×#12611yescharacteristic
635C23C2×#12711yescharacteristic
636C23C2×C4⋊Q811yescharacteristic
637C23C2×C4⋊Q812yes—
638C23C2×C4⋊Q811yescharacteristic
639C23#53211yescharacteristic
640C23#53211yescharacteristic
641C23#53212yes—
642C23#53212yes—
643C23#53312yes—
644C23#53312yes—
645C23#53312yes—
646C23#53511yescharacteristic
647C23#53511yescharacteristic
648C23#53611yescharacteristic
649C23#53611yescharacteristic
650C23#54012yes—
651C23#54112yes—
652C23#54212yes—
653C23#54212yes—
654C23#54412yes—
655C23#54412yes—
656C23D4212yes—
657C23D4212yes—
658C23D4212yes—
659C23#54612yes—
660C23#54612yes—
661C23#54712yes—
662C23#54712yes—
663C23#54712yes—
664C23#54712yes—
665C23#54812yes—
666C23#54812yes—
667C23D4×Q812yes—
668C23D4×Q812yes—
669C23D4×Q812yes—
670C23D4×Q812yes—
671C23#55012yes—
672C23#55012yes—
673C23#55212yes—
674C23#55212yes—
675C23#55312yes—
676C23#55312yes—
677C23#55412yes—
678C23#55412yes—
679C23#55412yes—
680C23#55412yes—
681C23#55512yes—
682C23#55612yes—
683C23#55612yes—
684C23#55712yes—
685C23#55712yes—
686C23Q8212yes—
687C23#55912yes—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—216no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—216no—
717C2×C4—28no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—48no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—84no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—84no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4C4×C22⋊C418yes—
783C2×C4C4×C4⋊C418yes—
784C2×C4C4×C4⋊C418yes—
785C2×C4C4×C4⋊C4116yescomplemented
786C2×C4#38418yescomplemented
787C2×C4#38518yes—
788C2×C4#38518yes—
789C2×C4#38618yes—
790C2×C4#38718yes—
791C2×C4#38718yes—
792C2×C4#38718yes—
793C2×C4#38718yes—
794C2×C4#38818yes—
795C2×C4#38818yes—
796C2×C4#38918yes—
797C2×C4#38918yes—
798C2×C4#39118yes—
799C22C2×C4×C22⋊C411yescharacteristic
800C22C2×C4×C4⋊C411yescharacteristic
801C22C2×C4×C4⋊C411yescharacteristic
802C22C2×C4×C4⋊C412yes—
803C22#227412yes—
804C22C2×#38411yescharacteristic
805C22#228512yes—
806C22#228511yescharacteristic
807C22C2×#38511yescharacteristic
808C22C2×#38511yescharacteristic
809C22C2×#38611yescharacteristic
810C22C2×#38711yescharacteristic
811C22C2×#38711yescharacteristic
812C22C2×#38711yescharacteristic
813C22C2×#38711yescharacteristic
814C22C2×#38811yescharacteristic
815C22C2×#38811yescharacteristic
816C22C2×#38911yescharacteristic
817C22C2×#38911yescharacteristic
818C22C2×#39111yescharacteristic
819C22C4×#12711yescharacteristic
820C22C4×#12711yescharacteristic
821C22C4×C4⋊Q811yescharacteristic
822C22C4×C4⋊Q812yes—
823C22C4×C4⋊Q811yescharacteristic
824C22C4×C4⋊Q812yes—
825C22#231412yes—
826C22#231711yescharacteristic
827C22#231711yescharacteristic
828C22#232611yescharacteristic
829C22#232611yescharacteristic
830C22#232711yescharacteristic
831C22#232811yescharacteristic
832C22#233012yes—
833C22#233112yes—
834C22D4×C22⋊C412yes—
835C22Q8×C22⋊C412yes—
836C22#234412yes—
837C22#234512yes—
838C22D4×C4⋊C412yes—
839C22D4×C4⋊C412yes—
840C22D4×C4⋊C412yes—
841C22D4×C4⋊C412yes—
842C22Q8×C4⋊C412yes—
843C22Q8×C4⋊C412yes—
844C22#235212yes—
845C22#235212yes—
846C22#235412yes—
847C22#235412yes—
848C22#235512yes—
849C22#235512yes—
850C22#236012yes—
851C22#236012yes—
852C22#236112yes—
853C22#236112yes—
854C22#236512yes—
855C22#236512yes—
856C22#236612yes—
857C22#236912yes—
858C22#242212yes—
859C22#242312yes—
860C22#242812yes—
861C22#242912yes—
862C22#243111yescharacteristic
863C22#243211yescharacteristic
864C22#243311yescharacteristic
865C22#243411yescharacteristic
866C22#243912yes—
867C22#244012yes—
868C22#244012yes—
869C22#244112yes—
870C22#244512yes—
871C22#244612yes—
872C22#245112yes—
873C22#245212yes—
874C22#249112yes—
875C22#249212yes—
876C22#249612yes—
877C22#249712yes—
878C22#249911yescharacteristic
879C22#250011yescharacteristic
880C22#250111yescharacteristic
881C22#250211yescharacteristic
882C22#250612yes—
883C22#250712yes—
884C22#251112yes—
885C22#251212yes—
886C22#254111yescharacteristic
887C22#254211yescharacteristic
888C22#254411yescharacteristic
889C22#254511yescharacteristic
890C22#254611yescharacteristic
891C22#255012yes—
892C22#255112yes—
893C22#255212yes—
894C22#256511yescharacteristic
895C22#256611yescharacteristic
896C22#256711yescharacteristic
897C22#257012yes—
898C4—28no—
899C4—216no—
900C4—48no—
901C4—44no—
902C4—48no—
903C4—48no—
904C4—84no—
905C4—84no—
906C4#1436116yescomplemented
907C2C2×#143611yescharacteristic
908C2C4×#38411yescharacteristic
909C2#1377911yescharacteristic
910C2C22⋊C4×C4⋊C412yes—
911C2C4⋊C4212yes—
912C2#1387612yes—
913C2#1387911yescharacteristic
914C2#1388011yescharacteristic
915C2#1388412yes—
916C2#1390911yescharacteristic
917C2#1391011yescharacteristic
918C2#1397611yescharacteristic
919C2#1397711yescharacteristic
920C2#1398112yes—
921C2#1400011yescharacteristic
922C2#1400111yescharacteristic
923C2#1400512yes—
924C2#1402411yescharacteristic
925C2#1402511yescharacteristic
926C2#1402912yes—
927C2#1404811yescharacteristic
928C2#1404911yescharacteristic
929C2#1405312yes—
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
21. C2×#384C4semidirect
37. C4⋊#95C4semidirect
38. C4×#95C4semidirect
279. C2×C4⋊C4C4⋊C4semidirect
304. C2×C42C42semidirect
305. C2×C42C4⋊C4semidirect
313. #95C4⋊C4semidirect
785. C2×C4C4×C4⋊C4semidirect
786. C2×C4#384semidirect
906. C4#1436semidirect

Maximal subgroups

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

subgroupindex
C22×#3842
C22×C4×C4⋊C42
C2×#14362
C2×C4⋊#952
C2×C4×#952
#75572