Finite Group Databasebeta

← #153754

Subgroups — #153754

Order 512.

3502 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#382C211yesmaximal, characteristic
2C22×C4×C4⋊C4C211yesmaximal, characteristic
3C2×C4⋊#95C211yesmaximal, characteristic
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4×#95C211yesmaximal, characteristic
8#7556C214yesmaximal
9#7554C214yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C23×C42C2212yes—
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#382—24no—
19C2×#382—24no—
20C2×#382C418yescomplemented
21C2×C4×C4⋊C4—24no—
22C2×C4×C4⋊C4—24no—
23C2×C4×C4⋊C4—24no—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2214yes—
27C22×#95C2214yes—
28C22×#95C2212yes—
29C22×#95C2214yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2214yes—
33C4⋊#95—24no—
34C4⋊#95—24no—
35C4⋊#95—24no—
36C4⋊#95C418yescomplemented
37C4×#95C418yescomplemented
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C22×C4⋊C4—22no—
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—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4C2×C414yes—
68C22×C4⋊C4C2×C414yes—
69C22×C4⋊C4C2×C414yes—
70C22×C4⋊C4C2×C414yes—
71C22×C4⋊C4D414yes—
72C22×C4⋊C4D414yes—
73C22×C4⋊C4D414yes—
74C22×C4⋊C4Q814yes—
75C22×C42—22no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42—24no—
86C22×C42—24no—
87C22×C42—24no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—28no—
93C22×C42—44no—
94C22×C42C2×C414yes—
95C22×C42C2×C414yes—
96C22×C42C2×C414yes—
97C22×C42C2×C414yes—
98C22×C42C2×C414yes—
99C22×C42D414yes—
100C22×C42Q814yes—
101#382—232no—
102C4×C4⋊C4—232no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—28no—
107C2×#95—28no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—28no—
113C2×#95—28no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—28no—
117C2×#95—28no—
118C2×#95—28no—
119C2×#95—44no—
120C2×#95—44no—
121C2×#95—44no—
122C2×#95—44no—
123C2×#95—44no—
124C2×#95C2×C418yes—
125C2×#95C2×C418yes—
126C2×#95C2×C4116yes—
127C2×#95C2×C4116yes—
128C25C2411yescharacteristic
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—21no—
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—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—24no—
158C23×C4—24no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—24no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—24no—
176C23×C4—24no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—24no—
181C23×C4—22no—
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—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—24no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4C22×C414yes—
204C23×C4C22×C414yes—
205C23×C4C22×C414yes—
206C23×C4C22×C414yes—
207C23×C4C22×C414yes—
208C23×C4C22×C414yes—
209C23×C4C22×C414yes—
210C23×C4C22×C412yes—
211C23×C4C22×C414yes—
212C23×C4C22×C412yes—
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C2×D414yes—
217C23×C4C2×D414yes—
218C23×C4C2×D414yes—
219C23×C4C2×D412yes—
220C23×C4C2×D412yes—
221C23×C4C2×D412yes—
222C23×C4C2×D412yes—
223C23×C4C2×D412yes—
224C23×C4C2×D412yes—
225C23×C4C2×Q814yes—
226C23×C4C2×Q812yes—
227C23×C4C2×Q812yes—
228C23×C4C2×Q812yes—
229C23×C4C2×Q812yes—
230C23×C4#4114yes—
231C23×C4#4114yes—
232C23×C4#4114yes—
233C23×C4#4114yes—
234C23×C4#4112yes—
235C23×C4#4112yes—
236C23×C4#4112yes—
237C23×C4#4112yes—
238C23×C4#4112yes—
239C23×C4#4112yes—
240C2×C4⋊C4—28no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—28no—
244C2×C4⋊C4—28no—
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—28no—
258C2×C4⋊C4—44no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4C22⋊C4116yes—
267C2×C4⋊C4C4⋊C4116yes—
268C2×C42—28no—
269C2×C42—28no—
270C2×C42—28no—
271C2×C42—28no—
272C2×C42—28no—
273C2×C42—28no—
274C2×C42—28no—
275C2×C42—28no—
276C2×C42—28no—
277C2×C42—28no—
278C2×C42—28no—
279C2×C42—28no—
280C2×C42—216no—
281C2×C42—28no—
282C2×C42—28no—
283C2×C42—28no—
284C2×C42—416no—
285C2×C42—416no—
286C2×C42—48no—
287C2×C42—44no—
288C2×C42—44no—
289C2×C42—48no—
290C2×C42—44no—
291C2×C42—44no—
292C2×C42C42116yescomplemented
293C2×C42C4⋊C4116yes—
294#95—216no—
295#95—232no—
296#95—216no—
297#95—216no—
298#95—416no—
299#95—416no—
300#95—416no—
301#95—48no—
302#95—48no—
303C24C23×C411yescharacteristic
304C24C23×C411yescharacteristic
305C24C23×C411yescharacteristic
306C24C22×D411yescharacteristic
307C24C22×D411yescharacteristic
308C24C22×D411yescharacteristic
309C24C22×D411yescharacteristic
310C24C22×Q811yescharacteristic
311C24C22×Q811yescharacteristic
312C24C2×#4111yescharacteristic
313C24C2×#4111yescharacteristic
314C24C2×#4111yescharacteristic
315C24C2×#4111yescharacteristic
316C24C2×#4111yescharacteristic
317C24C2×#4111yescharacteristic
318C24C2×#4112yes—
319C24C2×#4112yes—
320C24C2×#4112yes—
321C24C2×#4112yes—
322C24H(5,𝔽2)12yes—
323C24H(5,𝔽2)12yes—
324C242−1+412yes—
325C242−1+412yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
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—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—28no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—28no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—44no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—44no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—44no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
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×C4C2×C4218yes—
525C22×C4C2×C4214yes—
526C22×C4C2×C22⋊C418yes—
527C22×C4C2×C22⋊C414yes—
528C22×C4C2×C4⋊C414yes—
529C22×C4C2×C4⋊C418yes—
530C22×C4C2×C4⋊C414yes—
531C22×C4C2×C4⋊C414yes—
532C22×C4C2×C4⋊C414yes—
533C22×C4#11718yes—
534C22×C4#11718yes—
535C22×C4#11714yes—
536C22×C4#11714yes—
537C22×C4#11714yes—
538C22×C4C4×D414yes—
539C22×C4C4×D414yes—
540C22×C4C4×D414yes—
541C22×C4C4×D414yes—
542C22×C4C4×D414yes—
543C22×C4C4×D414yes—
544C22×C4C4×D414yes—
545C22×C4C4×D414yes—
546C22×C4C4×Q814yes—
547C22×C4C4×Q814yes—
548C22×C4C4×Q814yes—
549C22×C4C4×Q814yes—
550C22×C4#12014yes—
551C22×C4#12114yes—
552C22×C4#12114yes—
553C22×C4C22⋊Q814yes—
554C22×C4C22⋊Q814yes—
555C22×C4C22⋊Q814yes—
556C22×C4C22⋊Q814yes—
557C22×C4#12314yes—
558C22×C4#12314yes—
559C22×C4#12314yes—
560C22×C4#12414yes—
561C22×C4#12414yes—
562C22×C4#12414yes—
563C22×C4#12518yes—
564C22×C4#12514yes—
565C22×C4#12514yes—
566C22×C4#12614yes—
567C22×C4#12614yes—
568C22×C4C4⋊Q814yes—
569C4⋊C4—232no—
570C4⋊C4—232no—
571C4⋊C4—416no—
572C4⋊C4—416no—
573C42—232no—
574C42—232no—
575C42—432no—
576C42—416no—
577C23C22×C4211yescharacteristic
578C23C22×C22⋊C411yescharacteristic
579C23C22×C4⋊C411yescharacteristic
580C23C22×C4⋊C411yescharacteristic
581C23C2×#11711yescharacteristic
582C23C2×#11711yescharacteristic
583C23C2×#11712yes—
584C23C2×#11712yes—
585C23C2×#11711yescharacteristic
586C23C2×C4×D411yescharacteristic
587C23C2×C4×D411yescharacteristic
588C23C2×C4×D411yescharacteristic
589C23C2×C4×D411yescharacteristic
590C23C2×C4×D411yescharacteristic
591C23C2×C4×D411yescharacteristic
592C23C2×C4×D411yescharacteristic
593C23C2×C4×D411yescharacteristic
594C23C2×C4×Q811yescharacteristic
595C23C2×C4×Q811yescharacteristic
596C23C2×C4×Q811yescharacteristic
597C23C2×C4×Q811yescharacteristic
598C23C4×#4112yes—
599C23C4×#4112yes—
600C23C4×#4112yes—
601C23C4×#4112yes—
602C23#51812yes—
603C23#51912yes—
604C23#52012yes—
605C23#52012yes—
606C23#52012yes—
607C23#52012yes—
608C23C2×#12011yescharacteristic
609C23C2×#12111yescharacteristic
610C23C2×#12111yescharacteristic
611C23C2×C22⋊Q811yescharacteristic
612C23C2×C22⋊Q811yescharacteristic
613C23C2×C22⋊Q811yescharacteristic
614C23C2×C22⋊Q811yescharacteristic
615C23C2×#12311yescharacteristic
616C23C2×#12311yescharacteristic
617C23C2×#12311yescharacteristic
618C23C2×#12411yescharacteristic
619C23C2×#12411yescharacteristic
620C23C2×#12411yescharacteristic
621C23C2×#12512yes—
622C23C2×#12511yescharacteristic
623C23C2×#12511yescharacteristic
624C23C2×#12611yescharacteristic
625C23C2×#12611yescharacteristic
626C23#52912yes—
627C23#52912yes—
628C23#52912yes—
629C23#52912yes—
630C23C2×C4⋊Q811yescharacteristic
631C23#53211yescharacteristic
632C23#53211yescharacteristic
633C23#53312yes—
634C23#53511yescharacteristic
635C23#53511yescharacteristic
636C23#53611yescharacteristic
637C23#53611yescharacteristic
638C23#54012yes—
639C23#54112yes—
640C23#54212yes—
641C23#54212yes—
642C23#54412yes—
643C23#54412yes—
644C23#54612yes—
645C23#54612yes—
646C23#54612yes—
647C23#54612yes—
648C23#54712yes—
649C23#54712yes—
650C23#54812yes—
651C23#54812yes—
652C23#54812yes—
653C23#54812yes—
654C23#55012yes—
655C23#55012yes—
656C23#55212yes—
657C23#55212yes—
658C23#55212yes—
659C23#55212yes—
660C23#55312yes—
661C23#55312yes—
662C23#55312yes—
663C23#55312yes—
664C23#55412yes—
665C23#55412yes—
666C23#55512yes—
667C23#55512yes—
668C23#55612yes—
669C23#55612yes—
670C23#55612yes—
671C23#55612yes—
672C23#55712yes—
673C23#55712yes—
674C23#55912yes—
675C23#55912yes—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—216no—
688C2×C4—216no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—48no—
722C2×C4—44no—
723C2×C4—48no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—84no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—84no—
767C2×C4—82no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4C4×C22⋊C418yes—
772C2×C4C4×C4⋊C418yes—
773C2×C4C4×C4⋊C418yes—
774C2×C4#38218yescomplemented
775C2×C4#38518yes—
776C2×C4#38518yes—
777C2×C4#38618yes—
778C2×C4#38718yes—
779C2×C4#38718yes—
780C2×C4#38718yes—
781C2×C4#38718yes—
782C2×C4#38818yes—
783C2×C4#38818yes—
784C2×C4#38918yes—
785C2×C4#38918yes—
786C2×C4#39118yes—
787C22C2×C4×C22⋊C411yescharacteristic
788C22C2×C4×C4⋊C411yescharacteristic
789C22C2×C4×C4⋊C411yescharacteristic
790C22C4×#11712yes—
791C22#227412yes—
792C22C2×#38211yescharacteristic
793C22#228312yes—
794C22#228511yescharacteristic
795C22C2×#38511yescharacteristic
796C22C2×#38511yescharacteristic
797C22C2×#38611yescharacteristic
798C22C2×#38711yescharacteristic
799C22C2×#38711yescharacteristic
800C22C2×#38711yescharacteristic
801C22C2×#38711yescharacteristic
802C22C2×#38811yescharacteristic
803C22C2×#38811yescharacteristic
804C22C2×#38911yescharacteristic
805C22C2×#38911yescharacteristic
806C22C2×#39111yescharacteristic
807C22C4×#12411yescharacteristic
808C22C4×#12411yescharacteristic
809C22C4×#12411yescharacteristic
810C22C4×#12411yescharacteristic
811C22C4×#12512yes—
812C22C4×#12512yes—
813C22#231412yes—
814C22#231711yescharacteristic
815C22#231711yescharacteristic
816C22#232611yescharacteristic
817C22#232611yescharacteristic
818C22#232711yescharacteristic
819C22#232811yescharacteristic
820C22#233012yes—
821C22#233112yes—
822C22#233912yes—
823C22#234112yes—
824C22#234612yes—
825C22#234712yes—
826C22#234912yes—
827C22#235112yes—
828C22#235212yes—
829C22#235212yes—
830C22#235212yes—
831C22#235212yes—
832C22#235412yes—
833C22#235412yes—
834C22#235512yes—
835C22#235512yes—
836C22#235612yes—
837C22#235712yes—
838C22#236212yes—
839C22#236212yes—
840C22#236312yes—
841C22#236312yes—
842C22#236712yes—
843C22#236712yes—
844C22#237012yes—
845C22#237012yes—
846C22#242012yes—
847C22#242112yes—
848C22#242612yes—
849C22#242712yes—
850C22#243111yescharacteristic
851C22#243211yescharacteristic
852C22#243511yescharacteristic
853C22#243611yescharacteristic
854C22#243912yes—
855C22#244112yes—
856C22#244212yes—
857C22#244212yes—
858C22#244712yes—
859C22#244812yes—
860C22#245312yes—
861C22#245412yes—
862C22#248912yes—
863C22#249012yes—
864C22#249412yes—
865C22#249512yes—
866C22#249911yescharacteristic
867C22#250011yescharacteristic
868C22#250311yescharacteristic
869C22#250411yescharacteristic
870C22#250812yes—
871C22#250912yes—
872C22#251312yes—
873C22#251412yes—
874C22#254411yescharacteristic
875C22#254511yescharacteristic
876C22#254711yescharacteristic
877C22#254811yescharacteristic
878C22#255012yes—
879C22#255212yes—
880C22#256311yescharacteristic
881C22#256511yescharacteristic
882C22#256611yescharacteristic
883C22#256811yescharacteristic
884C22#257012yes—
885C22#257112yes—
886C4—28no—
887C4—48no—
888C4—44no—
889C4—48no—
890C4—48no—
891C4—48no—
892C4—84no—
893C4—84no—
894C4#1436116yes—
895C2C2×#143611yescharacteristic
896C2C4×#38211yescharacteristic
897C2#1377911yescharacteristic
898C2#1380112yes—
899C2#1380412yes—
900C2#1387512yes—
901C2#1387911yescharacteristic
902C2#1388111yescharacteristic
903C2#1388512yes—
904C2#1390911yescharacteristic
905C2#1391111yescharacteristic
906C2#1397811yescharacteristic
907C2#1397911yescharacteristic
908C2#1398212yes—
909C2#1400211yescharacteristic
910C2#1400311yescharacteristic
911C2#1400612yes—
912C2#1402611yescharacteristic
913C2#1402711yescharacteristic
914C2#1403012yes—
915C2#1405011yescharacteristic
916C2#1405111yescharacteristic
917C2#1405412yes—
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
20. C2×#382C4semidirect
36. C4⋊#95C4semidirect
37. C4×#95C4semidirect
292. C2×C42C42semidirect
774. C2×C4#382semidirect

Maximal subgroups

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

subgroupindex
C22×#3822
C22×C4×C4⋊C42
C2×C4⋊#952
C2×C4×#952
#75562
#75542