Finite Group Databasebeta

← #154398

Subgroups — #154398

Order 512.

3766 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
1C22×#389C212yesmaximal
2C22×C4×C4⋊C4C211yesmaximal, characteristic
3C2×#1444C212yesmaximal
4C2×C4⋊#95C212yesmaximal
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7557C214yesmaximal
9C23×C4⋊C4C2211yescharacteristic
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2214yes—
14C23×C4⋊C4C2212yes—
15C23×C42C2212yes—
16C23×C42C2211yescharacteristic
17C2×#389—28no—
18C2×#389—28no—
19C2×#389—28no—
20C2×C4×C4⋊C4—28no—
21C2×C4×C4⋊C4—24no—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2214yes—
25C22×#95C2214yes—
26C22×#95C2214yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30#1444—28no—
31C4⋊#95—24no—
32C4⋊#95—28no—
33C4⋊#95C418yescomplemented
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2311yescharacteristic
37C24×C4C2314yes—
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2311yescharacteristic
42C22×C4⋊C4—24no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—28no—
58C22×C4⋊C4—28no—
59C22×C4⋊C4—28no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—28no—
66C22×C4⋊C4—28no—
67C22×C4⋊C4—44no—
68C22×C4⋊C4—44no—
69C22×C4⋊C4C2×C418yes—
70C22×C4⋊C4D414yes—
71C22×C4⋊C4D414yes—
72C22×C4⋊C4D418yes—
73C22×C4⋊C4Q814yes—
74C22×C4⋊C4Q814yes—
75C22×C4⋊C4Q818yes—
76C22×C42—24no—
77C22×C42—24no—
78C22×C42—24no—
79C22×C42—24no—
80C22×C42—24no—
81C22×C42—24no—
82C22×C42—24no—
83C22×C42—24no—
84C22×C42C2×C414yes—
85C22×C42D418yes—
86C22×C42D414yes—
87C22×C42Q814yes—
88#389—264no—
89C4×C4⋊C4—232no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—28no—
95C2×#95—28no—
96C2×#95—28no—
97C2×#95—24no—
98C2×#95—28no—
99C2×#95—28no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—28no—
103C2×#95—24no—
104C2×#95—28no—
105C2×#95—24no—
106C2×#95—42no—
107C2×#95—42no—
108C2×#95—44no—
109C2×#95—44no—
110C2×#95—44no—
111C2×#95C2×C418yes—
112C2×#95C2×C418yes—
113C25C2411yescharacteristic
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—24no—
119C23×C4—24no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—24no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—24no—
133C23×C4—24no—
134C23×C4—24no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—24no—
140C23×C4—24no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—24no—
147C23×C4—24no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—24no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—24no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—24no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—24no—
171C23×C4—22no—
172C23×C4—24no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—24no—
176C23×C4—22no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4C22×C418yes—
183C23×C4C22×C412yes—
184C23×C4C22×C412yes—
185C23×C4C22×C412yes—
186C23×C4C2×D414yes—
187C23×C4C2×D418yes—
188C23×C4C2×D412yes—
189C23×C4C2×D414yes—
190C23×C4C2×D414yes—
191C23×C4C2×D414yes—
192C23×C4C2×D412yes—
193C23×C4C2×D412yes—
194C23×C4C2×D414yes—
195C23×C4C2×D412yes—
196C23×C4C2×D412yes—
197C23×C4C2×D414yes—
198C23×C4C2×Q814yes—
199C23×C4C2×Q818yes—
200C23×C4C2×Q812yes—
201C23×C4C2×Q814yes—
202C23×C4C2×Q812yes—
203C23×C4C2×Q812yes—
204C23×C4C2×Q814yes—
205C23×C4C2×Q812yes—
206C23×C4C2×Q812yes—
207C23×C4#4114yes—
208C23×C4#4114yes—
209C23×C4#4112yes—
210C23×C4#4112yes—
211C23×C4#4112yes—
212C23×C4#4114yes—
213C23×C4#4112yes—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—216no—
217C2×C4⋊C4—216no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—216no—
221C2×C4⋊C4—216no—
222C2×C4⋊C4—216no—
223C2×C4⋊C4—216no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—216no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—216no—
228C2×C4⋊C4—216no—
229C2×C4⋊C4—216no—
230C2×C4⋊C4—232no—
231C2×C4⋊C4—216no—
232C2×C4⋊C4—28no—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—216no—
235C2×C4⋊C4—416no—
236C2×C4⋊C4—416no—
237C2×C4⋊C4—416no—
238C2×C4⋊C4—416no—
239C2×C4⋊C4—416no—
240C2×C4⋊C4—44no—
241C2×C4⋊C4—416no—
242C2×C4⋊C4—48no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—48no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4C4⋊C4132yescomplemented
248C2×C42—216no—
249C2×C42—28no—
250C2×C42—216no—
251C2×C42—28no—
252C2×C42—216no—
253C2×C42—216no—
254C2×C42—216no—
255C2×C42—48no—
256C2×C42—48no—
257C2×C42—48no—
258C2×C42—48no—
259C2×C42C4⋊C4116yescomplemented
260#95—216no—
261#95—232no—
262#95—216no—
263#95—48no—
264#95—416no—
265#95—416no—
266#95—48no—
267#95—48no—
268C24C23×C411yescharacteristic
269C24C22×D411yescharacteristic
270C24C22×D412yes—
271C24C22×D412yes—
272C24C22×D411yescharacteristic
273C24C22×D411yescharacteristic
274C24C22×Q811yescharacteristic
275C24C22×Q812yes—
276C24C22×Q811yescharacteristic
277C24C22×Q811yescharacteristic
278C24C2×#4112yes—
279C24C2×#4111yescharacteristic
280C24C2×#4111yescharacteristic
281C24C2×#4111yescharacteristic
282C24C2×#4111yescharacteristic
283C24C2×#4112yes—
284C24C2×#4112yes—
285C24H(5,𝔽2)11yescharacteristic
286C24H(5,𝔽2)11yescharacteristic
287C24H(5,𝔽2)12yes—
288C242−1+411yescharacteristic
289C242−1+411yescharacteristic
290C242−1+412yes—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—28no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—28no—
312C22×C4—22no—
313C22×C4—28no—
314C22×C4—22no—
315C22×C4—24no—
316C22×C4—28no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—28no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—28no—
331C22×C4—28no—
332C22×C4—22no—
333C22×C4—28no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—28no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—28no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—28no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—28no—
372C22×C4—28no—
373C22×C4—28no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—28no—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—28no—
384C22×C4—24no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—44no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—44no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—42no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—44no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—44no—
477C22×C4C2×C4⋊C414yes—
478C22×C4C2×C4⋊C4116yes—
479C22×C4C2×C4⋊C414yes—
480C22×C4C2×C4⋊C414yes—
481C22×C4C2×C4⋊C418yes—
482C22×C4C4×D414yes—
483C22×C4C4×D418yes—
484C22×C4C4×D414yes—
485C22×C4C4×Q814yes—
486C22×C4C4×Q814yes—
487C22×C4#12014yes—
488C22×C4#12018yes—
489C22×C4#12118yes—
490C22×C4#12114yes—
491C22×C4#12118yes—
492C22×C4#12114yes—
493C22×C4C22⋊Q818yes—
494C22×C4C22⋊Q814yes—
495C22×C4C22⋊Q818yes—
496C22×C4C22⋊Q818yes—
497C22×C4C22⋊Q818yes—
498C22×C4C22⋊Q814yes—
499C22×C4C22⋊Q818yes—
500C22×C4#12314yes—
501C22×C4#12318yes—
502C22×C4#12514yes—
503C22×C4#12514yes—
504C22×C4#12518yes—
505C22×C4#12714yes—
506C22×C4C4⋊Q814yes—
507C22×C4C4⋊Q814yes—
508C22×C4C4⋊Q818yes—
509C22×C4C4⋊Q818yes—
510C22×C4C4⋊Q814yes—
511C4⋊C4—232no—
512C4⋊C4—232no—
513C4⋊C4—264no—
514C4⋊C4—464no—
515C4⋊C4—416no—
516C4⋊C4—416no—
517C42—232no—
518C42—432no—
519C23C22×C4⋊C411yescharacteristic
520C23C22×C4⋊C412yes—
521C23C2×C4×D412yes—
522C23C2×C4×D411yescharacteristic
523C23C2×C4×D411yescharacteristic
524C23C2×C4×Q811yescharacteristic
525C23C2×C4×Q811yescharacteristic
526C23C4×#4112yes—
527C23#51811yescharacteristic
528C23#51911yescharacteristic
529C23#52012yes—
530C23C2×#12011yescharacteristic
531C23C2×#12012yes—
532C23C2×#12111yescharacteristic
533C23C2×#12112yes—
534C23C2×#12112yes—
535C23C2×#12111yescharacteristic
536C23C2×C22⋊Q811yescharacteristic
537C23C2×C22⋊Q812yes—
538C23C2×C22⋊Q812yes—
539C23C2×C22⋊Q811yescharacteristic
540C23C2×C22⋊Q812yes—
541C23C2×C22⋊Q812yes—
542C23C2×C22⋊Q812yes—
543C23C2×#12311yescharacteristic
544C23C2×#12312yes—
545C23#52512yes—
546C23#52511yescharacteristic
547C23#52512yes—
548C23#52511yescharacteristic
549C23C2×#12511yescharacteristic
550C23C2×#12511yescharacteristic
551C23C2×#12512yes—
552C23#52912yes—
553C23#52912yes—
554C23C2×#12711yescharacteristic
555C23C2×C4⋊Q812yes—
556C23C2×C4⋊Q811yescharacteristic
557C23C2×C4⋊Q811yescharacteristic
558C23C2×C4⋊Q811yescharacteristic
559C23C2×C4⋊Q812yes—
560C23#53212yes—
561C23#53312yes—
562C23#53312yes—
563C23#53511yescharacteristic
564C23#53512yes—
565C23#53611yescharacteristic
566C23#53612yes—
567C23#53711yescharacteristic
568C23#53711yescharacteristic
569C23#53712yes—
570C23#53712yes—
571C23#54012yes—
572C23#54112yes—
573C23#54212yes—
574C23#54212yes—
575C23#54412yes—
576C23#54411yescharacteristic
577C23#54411yescharacteristic
578C23D4212yes—
579C23D4211yescharacteristic
580C23#54612yes—
581C23#54612yes—
582C23#54612yes—
583C23#54712yes—
584C23#54711yescharacteristic
585C23#54711yescharacteristic
586C23#54812yes—
587C23#54812yes—
588C23#54812yes—
589C23D4×Q812yes—
590C23D4×Q812yes—
591C23D4×Q811yescharacteristic
592C23D4×Q811yescharacteristic
593C23#55012yes—
594C23#55011yescharacteristic
595C23#55011yescharacteristic
596C23#55212yes—
597C23#55312yes—
598C23#55412yes—
599C23#55412yes—
600C23#55412yes—
601C23#55412yes—
602C23#55411yescharacteristic
603C23#55411yescharacteristic
604C23#55511yescharacteristic
605C23#55612yes—
606C23#55611yescharacteristic
607C23#55611yescharacteristic
608C23#55712yes—
609C23#55712yes—
610C23#55712yes—
611C23#55711yescharacteristic
612C23#55712yes—
613C23#55711yescharacteristic
614C23Q8212yes—
615C23Q8211yescharacteristic
616C23#55912yes—
617C23#55911yescharacteristic
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—28no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—28no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—28no—
632C2×C4—216no—
633C2×C4—216no—
634C2×C4—28no—
635C2×C4—28no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—24no—
639C2×C4—216no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—48no—
643C2×C4—48no—
644C2×C4—44no—
645C2×C4—42no—
646C2×C4—44no—
647C2×C4—42no—
648C2×C4—48no—
649C2×C4—48no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—48no—
661C2×C4—48no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—48no—
671C2×C4—48no—
672C2×C4—48no—
673C2×C4—48no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—48no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—48no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—48no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#38418yes—
707C2×C4#38518yes—
708C2×C4#385116yes—
709C2×C4#38918yes—
710C2×C4#389116yes—
711C2×C4#38918yescomplemented
712C2×C4#39218yes—
713C2×C4#395116yes—
714C2×C4#39518yes—
715C2×C4#398116yes—
716C2×C4#39818yes—
717C2×C4#39918yes—
718C22C2×#38411yescharacteristic
719C22C2×#38511yescharacteristic
720C22C2×#38512yes—
721C22C2×#38911yescharacteristic
722C22C2×#38912yes—
723C22C2×#38911yescharacteristic
724C22#229611yescharacteristic
725C22C4×#12112yes—
726C22C4×C22⋊Q812yes—
727C22#231611yescharacteristic
728C22#231711yescharacteristic
729C22#232312yes—
730C22#232412yes—
731C22D4×C4⋊C412yes—
732C22#234912yes—
733C22Q8×C4⋊C412yes—
734C22#235112yes—
735C22#236511yescharacteristic
736C22#236511yescharacteristic
737C22#236611yescharacteristic
738C22#236712yes—
739C22#236911yescharacteristic
740C22#237012yes—
741C22C2×#39211yescharacteristic
742C22C2×#39512yes—
743C22C2×#39511yescharacteristic
744C22C2×#39812yes—
745C22C2×#39811yescharacteristic
746C22C2×#39911yescharacteristic
747C22#240712yes—
748C22#240712yes—
749C22#240812yes—
750C22#240912yes—
751C22#241412yes—
752C22#241512yes—
753C22#241612yes—
754C22#241712yes—
755C22#244512yes—
756C22#244612yes—
757C22#244712yes—
758C22#244812yes—
759C22#245112yes—
760C22#245112yes—
761C22#245212yes—
762C22#245212yes—
763C22#245312yes—
764C22#245312yes—
765C22#245412yes—
766C22#245412yes—
767C22#250612yes—
768C22#250712yes—
769C22#250812yes—
770C22#250912yes—
771C22#253511yescharacteristic
772C22#253611yescharacteristic
773C22#253711yescharacteristic
774C22#253812yes—
775C22#253811yescharacteristic
776C22#253811yescharacteristic
777C22#254011yescharacteristic
778C22#254011yescharacteristic
779C22#254111yescharacteristic
780C22#254211yescharacteristic
781C22#254612yes—
782C22#254611yescharacteristic
783C22#255012yes—
784C22#255012yes—
785C22#255012yes—
786C22#255111yescharacteristic
787C22#255112yes—
788C22#255211yescharacteristic
789C22#255211yescharacteristic
790C22#255212yes—
791C22#256712yes—
792C22#256711yescharacteristic
793C22#257012yes—
794C22#257111yescharacteristic
795C22#258011yescharacteristic
796C22#258012yes—
797C22#258111yescharacteristic
798C22#258112yes—
799C22#258212yes—
800C22#258211yescharacteristic
801C22#258411yescharacteristic
802C22#258411yescharacteristic
803C22#258412yes—
804C22#258412yes—
805C22#261511yescharacteristic
806C22#261611yescharacteristic
807C22#262411yescharacteristic
808C22#262511yescharacteristic
809C22#262812yes—
810C22#262912yes—
811C22#284711yescharacteristic
812C22#284811yescharacteristic
813C22#285112yes—
814C22#285411yescharacteristic
815C22#285511yescharacteristic
816C22#285712yes—
817C4—28no—
818C4—48no—
819C4—48no—
820C4—44no—
821C4—416no—
822C4—84no—
823C4—84no—
824C4#1444116yescomplemented
825C2C2×#144411yescharacteristic
826C2#1391011yescharacteristic
827C2#1395411yescharacteristic
828C2#1401712yes—
829C2#1401812yes—
830C2#1404512yes—
831C2#1404612yes—
832C2#1415011yescharacteristic
833C2#1415111yescharacteristic
834C2#1426411yescharacteristic
835C2#1469711yescharacteristic
836C2#1512311yescharacteristic
837C2#1512812yes—
838C2#1513312yes—
839C2#1514811yescharacteristic
840C2#1514911yescharacteristic
841C2#1515811yescharacteristic
842C2#1517711yescharacteristic
843C2#1519311yescharacteristic
844C2#1519411yescharacteristic
845C2#1520211yescharacteristic
846C2#1521812yes—
847C2#1522112yes—
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
33. C4⋊#95C4semidirect
247. C2×C4⋊C4C4⋊C4semidirect
259. C2×C42C4⋊C4semidirect
711. C2×C4#389semidirect
824. C4#1444semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C22×C4×C4⋊C42
C2×#14442
C2×C4⋊#952
#75572