Finite Group Databasebeta

← #154397

Subgroups — #154397

Order 512.

2922 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1443C212yesmaximal
2C2×C4⋊#95C211yesmaximal, characteristic
3C2×C4⋊#95C211yesmaximal, characteristic
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C2×C4×#95C211yesmaximal, characteristic
9#7556C212yesmaximal
10#7556C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×#95C2212yes—
20C22×#95C2211yescharacteristic
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2212yes—
35#1443—28no—
36C4⋊#95—24no—
37C4⋊#95—24no—
38C4⋊#95—24no—
39C4⋊#95—24no—
40C4⋊#95—24no—
41C4⋊#95C418yescomplemented
42C4×#95—24no—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
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⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4C2×C414yes—
79C22×C4⋊C4C2×C414yes—
80C22×C4⋊C4D414yes—
81C22×C4⋊C4D414yes—
82C22×C42—22no—
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—22no—
94C22×C42—22no—
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42C2×C414yes—
101C22×C42D414yes—
102C22×C42Q814yes—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—24no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95C2×C418yes—
148C2×#95C2×C418yes—
149C2×#95D414yes—
150C2×#95Q814yes—
151C25C2411yescharacteristic
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
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—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4C22×C414yes—
281C23×C4C22×C414yes—
282C23×C4C22×C412yes—
283C23×C4C22×C412yes—
284C23×C4C22×C412yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×Q812yes—
296C23×C4C2×Q812yes—
297C23×C4C2×Q812yes—
298C23×C4C2×Q812yes—
299C23×C4C2×Q812yes—
300C23×C4C2×Q812yes—
301C23×C4#4112yes—
302C23×C4#4112yes—
303C23×C4#4112yes—
304C23×C4#4112yes—
305C23×C4#4112yes—
306C23×C4#4112yes—
307C23×C4#4112yes—
308C23×C4#4112yes—
309C23×C4#4112yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4112yes—
313C23×C4#4112yes—
314C23×C4#4112yes—
315C23×C4#4112yes—
316C23×C4#4112yes—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C42—28no—
346C2×C42—28no—
347C2×C42—28no—
348C2×C42—28no—
349C2×C42—28no—
350C2×C42—28no—
351C2×C42—28no—
352C2×C42—28no—
353C2×C42—28no—
354C2×C42—44no—
355C2×C42—44no—
356C2×C42—44no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42—44no—
361C2×C42—44no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42—44no—
365C2×C42—44no—
366#95—28no—
367#95—28no—
368#95—216no—
369#95—28no—
370#95—28no—
371#95—48no—
372#95—48no—
373#95—48no—
374#95—48no—
375#95—48no—
376#95—48no—
377#95—48no—
378#95—48no—
379#95—48no—
380#95—48no—
381#95—48no—
382C24C23×C411yescharacteristic
383C24C22×D411yescharacteristic
384C24C22×D411yescharacteristic
385C24C22×D411yescharacteristic
386C24C22×D411yescharacteristic
387C24C22×Q811yescharacteristic
388C24C22×Q811yescharacteristic
389C24C2×#4111yescharacteristic
390C24C2×#4111yescharacteristic
391C24C2×#4111yescharacteristic
392C24C2×#4111yescharacteristic
393C24C2×#4111yescharacteristic
394C24C2×#4111yescharacteristic
395C24C2×#4111yescharacteristic
396C24C2×#4111yescharacteristic
397C24C2×#4111yescharacteristic
398C24C2×#4111yescharacteristic
399C24C2×#4111yescharacteristic
400C24C2×#4111yescharacteristic
401C24C2×#4111yescharacteristic
402C24C2×#4111yescharacteristic
403C24C2×#4111yescharacteristic
404C24C2×#4111yescharacteristic
405C24H(5,𝔽2)11yescharacteristic
406C24H(5,𝔽2)11yescharacteristic
407C24H(5,𝔽2)11yescharacteristic
408C24H(5,𝔽2)11yescharacteristic
409C242−1+411yescharacteristic
410C242−1+411yescharacteristic
411C242−1+411yescharacteristic
412C242−1+411yescharacteristic
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4#11714yes—
758C22×C4#11714yes—
759C22×C4#11714yes—
760C22×C4C4×D414yes—
761C22×C4C4×D414yes—
762C22×C4C4×D414yes—
763C22×C4C4×D414yes—
764C22×C4C4×Q814yes—
765C22×C4C4×Q814yes—
766C22×C4#12114yes—
767C22×C4#12114yes—
768C22×C4#12114yes—
769C22×C4#12114yes—
770C22×C4C22⋊Q814yes—
771C22×C4C22⋊Q814yes—
772C22×C4C22⋊Q814yes—
773C22×C4C22⋊Q814yes—
774C22×C4#12314yes—
775C22×C4#12314yes—
776C22×C4#12314yes—
777C22×C4#12314yes—
778C22×C4#12314yes—
779C22×C4#12314yes—
780C22×C4#12414yes—
781C22×C4#12414yes—
782C22×C4#12414yes—
783C22×C4#12514yes—
784C22×C4#12514yes—
785C22×C4#12514yes—
786C22×C4#12514yes—
787C22×C4#12614yes—
788C22×C4#12614yes—
789C22×C4#12614yes—
790C22×C4#12614yes—
791C22×C4#12614yes—
792C22×C4#12614yes—
793C22×C4#12614yes—
794C22×C4#12614yes—
795C22×C4#12614yes—
796C22×C4#12614yes—
797C22×C4C4⋊Q814yes—
798C4⋊C4—416no—
799C4⋊C4—416no—
800C4⋊C4—416no—
801C4⋊C4—416no—
802C42—416no—
803C42—416no—
804C42—416no—
805C23C2×#11711yescharacteristic
806C23C2×#11711yescharacteristic
807C23C2×#11711yescharacteristic
808C23C2×C4×D411yescharacteristic
809C23C2×C4×D411yescharacteristic
810C23C2×C4×D411yescharacteristic
811C23C2×C4×D411yescharacteristic
812C23C2×C4×Q811yescharacteristic
813C23C2×C4×Q811yescharacteristic
814C23C4×#4111yescharacteristic
815C23C4×#4111yescharacteristic
816C23#51811yescharacteristic
817C23#51911yescharacteristic
818C23#52011yescharacteristic
819C23#52011yescharacteristic
820C23C2×#12111yescharacteristic
821C23C2×#12111yescharacteristic
822C23C2×#12111yescharacteristic
823C23C2×#12111yescharacteristic
824C23C2×C22⋊Q811yescharacteristic
825C23C2×C22⋊Q811yescharacteristic
826C23C2×C22⋊Q811yescharacteristic
827C23C2×C22⋊Q811yescharacteristic
828C23C2×#12311yescharacteristic
829C23C2×#12311yescharacteristic
830C23C2×#12311yescharacteristic
831C23C2×#12311yescharacteristic
832C23C2×#12311yescharacteristic
833C23C2×#12311yescharacteristic
834C23#52511yescharacteristic
835C23#52511yescharacteristic
836C23C2×#12411yescharacteristic
837C23C2×#12411yescharacteristic
838C23C2×#12411yescharacteristic
839C23C2×#12511yescharacteristic
840C23C2×#12511yescharacteristic
841C23C2×#12511yescharacteristic
842C23C2×#12511yescharacteristic
843C23C2×#12611yescharacteristic
844C23C2×#12611yescharacteristic
845C23C2×#12611yescharacteristic
846C23C2×#12611yescharacteristic
847C23C2×#12611yescharacteristic
848C23C2×#12611yescharacteristic
849C23C2×#12611yescharacteristic
850C23C2×#12611yescharacteristic
851C23C2×#12611yescharacteristic
852C23C2×#12611yescharacteristic
853C23#52911yescharacteristic
854C23#52911yescharacteristic
855C23#52911yescharacteristic
856C23#52911yescharacteristic
857C23#52911yescharacteristic
858C23#52911yescharacteristic
859C23#52911yescharacteristic
860C23#52911yescharacteristic
861C23C2×C4⋊Q811yescharacteristic
862C23#53211yescharacteristic
863C23#53211yescharacteristic
864C23#53211yescharacteristic
865C23#53211yescharacteristic
866C23#53311yescharacteristic
867C23#53311yescharacteristic
868C23#53311yescharacteristic
869C23#53311yescharacteristic
870C23#53311yescharacteristic
871C23#53311yescharacteristic
872C23#53511yescharacteristic
873C23#53611yescharacteristic
874C23#53711yescharacteristic
875C23#53711yescharacteristic
876C23#54011yescharacteristic
877C23#54011yescharacteristic
878C23#54011yescharacteristic
879C23#54011yescharacteristic
880C23#54111yescharacteristic
881C23#54111yescharacteristic
882C23#54111yescharacteristic
883C23#54111yescharacteristic
884C23#54211yescharacteristic
885C23#54211yescharacteristic
886C23#54211yescharacteristic
887C23#54211yescharacteristic
888C23#54211yescharacteristic
889C23#54211yescharacteristic
890C23#54211yescharacteristic
891C23#54211yescharacteristic
892C23#54411yescharacteristic
893C23#54411yescharacteristic
894C23#54411yescharacteristic
895C23#54411yescharacteristic
896C23D4211yescharacteristic
897C23D4211yescharacteristic
898C23#54611yescharacteristic
899C23#54611yescharacteristic
900C23#54611yescharacteristic
901C23#54611yescharacteristic
902C23#54711yescharacteristic
903C23#54711yescharacteristic
904C23#54711yescharacteristic
905C23#54711yescharacteristic
906C23#54711yescharacteristic
907C23#54711yescharacteristic
908C23#54811yescharacteristic
909C23#54811yescharacteristic
910C23#54811yescharacteristic
911C23#54811yescharacteristic
912C23D4×Q811yescharacteristic
913C23D4×Q811yescharacteristic
914C23#55011yescharacteristic
915C23#55011yescharacteristic
916C23#55011yescharacteristic
917C23#55011yescharacteristic
918C23#55211yescharacteristic
919C23#55211yescharacteristic
920C23#55211yescharacteristic
921C23#55211yescharacteristic
922C23#55211yescharacteristic
923C23#55211yescharacteristic
924C23#55211yescharacteristic
925C23#55211yescharacteristic
926C23#55311yescharacteristic
927C23#55311yescharacteristic
928C23#55311yescharacteristic
929C23#55311yescharacteristic
930C23#55311yescharacteristic
931C23#55311yescharacteristic
932C23#55311yescharacteristic
933C23#55311yescharacteristic
934C23#55411yescharacteristic
935C23#55411yescharacteristic
936C23#55411yescharacteristic
937C23#55411yescharacteristic
938C23#55511yescharacteristic
939C23#55511yescharacteristic
940C23#55511yescharacteristic
941C23#55511yescharacteristic
942C23#55611yescharacteristic
943C23#55611yescharacteristic
944C23#55611yescharacteristic
945C23#55611yescharacteristic
946C23#55611yescharacteristic
947C23#55611yescharacteristic
948C23#55611yescharacteristic
949C23#55611yescharacteristic
950C23#55611yescharacteristic
951C23#55611yescharacteristic
952C23#55711yescharacteristic
953C23#55711yescharacteristic
954C23#55911yescharacteristic
955C23#55911yescharacteristic
956C23#55911yescharacteristic
957C23#55911yescharacteristic
958C23#55911yescharacteristic
959C23#55911yescharacteristic
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—82no—
1079C2×C4—82no—
1080C2×C4—82no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—82no—
1092C2×C4—82no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—82no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—82no—
1103C2×C4—82no—
1104C2×C4—82no—
1105C2×C4—82no—
1106C2×C4—82no—
1107C2×C4—82no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4#38318yes—
1111C2×C4#38718yes—
1112C2×C4#38718yes—
1113C2×C4#38718yes—
1114C2×C4#38818yes—
1115C2×C4#38818yes—
1116C2×C4#38818yes—
1117C2×C4#39618yes—
1118C2×C4#39718yes—
1119C2×C4#39718yes—
1120C2×C4#39718yes—
1121C2×C4#40018yes—
1122C2×C4#40018yes—
1123C2×C4#40018yes—
1124C2×C4#40118yes—
1125C22C2×#38311yescharacteristic
1126C22C2×#38711yescharacteristic
1127C22C2×#38711yescharacteristic
1128C22C2×#38711yescharacteristic
1129C22C2×#38811yescharacteristic
1130C22C2×#38811yescharacteristic
1131C22C2×#38811yescharacteristic
1132C22#229311yescharacteristic
1133C22#229511yescharacteristic
1134C22C4×#12111yescharacteristic
1135C22C4×C22⋊Q811yescharacteristic
1136C22C4×#12511yescharacteristic
1137C22C4×C4⋊Q811yescharacteristic
1138C22#231911yescharacteristic
1139C22#232011yescharacteristic
1140C22#232311yescharacteristic
1141C22#232411yescharacteristic
1142C22#233011yescharacteristic
1143C22#233111yescharacteristic
1144C22#234411yescharacteristic
1145C22#234511yescharacteristic
1146C22#234611yescharacteristic
1147C22#234711yescharacteristic
1148C22#235411yescharacteristic
1149C22#235511yescharacteristic
1150C22#235611yescharacteristic
1151C22#235711yescharacteristic
1152C22#236011yescharacteristic
1153C22#236111yescharacteristic
1154C22#236211yescharacteristic
1155C22#236311yescharacteristic
1156C22#236511yescharacteristic
1157C22#236611yescharacteristic
1158C22#236711yescharacteristic
1159C22#236711yescharacteristic
1160C22C2×#39611yescharacteristic
1161C22C2×#39711yescharacteristic
1162C22C2×#39711yescharacteristic
1163C22C2×#39711yescharacteristic
1164C22C2×#40011yescharacteristic
1165C22C2×#40011yescharacteristic
1166C22C2×#40011yescharacteristic
1167C22C2×#40111yescharacteristic
1168C22#241411yescharacteristic
1169C22#241511yescharacteristic
1170C22#241611yescharacteristic
1171C22#241711yescharacteristic
1172C22#242011yescharacteristic
1173C22#242111yescharacteristic
1174C22#242211yescharacteristic
1175C22#242311yescharacteristic
1176C22#242611yescharacteristic
1177C22#242711yescharacteristic
1178C22#242811yescharacteristic
1179C22#242911yescharacteristic
1180C22#243911yescharacteristic
1181C22#243911yescharacteristic
1182C22#244011yescharacteristic
1183C22#244011yescharacteristic
1184C22#244111yescharacteristic
1185C22#244111yescharacteristic
1186C22#244211yescharacteristic
1187C22#244211yescharacteristic
1188C22#244511yescharacteristic
1189C22#244511yescharacteristic
1190C22#244511yescharacteristic
1191C22#244611yescharacteristic
1192C22#244611yescharacteristic
1193C22#244611yescharacteristic
1194C22#244711yescharacteristic
1195C22#244711yescharacteristic
1196C22#244711yescharacteristic
1197C22#244811yescharacteristic
1198C22#244811yescharacteristic
1199C22#244811yescharacteristic
1200C22#248511yescharacteristic
1201C22#248511yescharacteristic
1202C22#248611yescharacteristic
1203C22#248711yescharacteristic
1204C22#248911yescharacteristic
1205C22#248911yescharacteristic
1206C22#249011yescharacteristic
1207C22#249011yescharacteristic
1208C22#249111yescharacteristic
1209C22#249111yescharacteristic
1210C22#249211yescharacteristic
1211C22#249211yescharacteristic
1212C22#249411yescharacteristic
1213C22#249411yescharacteristic
1214C22#249411yescharacteristic
1215C22#249411yescharacteristic
1216C22#249511yescharacteristic
1217C22#249511yescharacteristic
1218C22#249511yescharacteristic
1219C22#249511yescharacteristic
1220C22#249611yescharacteristic
1221C22#249611yescharacteristic
1222C22#249611yescharacteristic
1223C22#249611yescharacteristic
1224C22#249711yescharacteristic
1225C22#249711yescharacteristic
1226C22#249711yescharacteristic
1227C22#249711yescharacteristic
1228C22#251111yescharacteristic
1229C22#251111yescharacteristic
1230C22#251111yescharacteristic
1231C22#251111yescharacteristic
1232C22#251111yescharacteristic
1233C22#251211yescharacteristic
1234C22#251211yescharacteristic
1235C22#251211yescharacteristic
1236C22#251211yescharacteristic
1237C22#251211yescharacteristic
1238C22#251311yescharacteristic
1239C22#251311yescharacteristic
1240C22#251311yescharacteristic
1241C22#251311yescharacteristic
1242C22#251311yescharacteristic
1243C22#251411yescharacteristic
1244C22#251411yescharacteristic
1245C22#251411yescharacteristic
1246C22#251411yescharacteristic
1247C22#251411yescharacteristic
1248C22#253511yescharacteristic
1249C22#253611yescharacteristic
1250C22#253711yescharacteristic
1251C22#253811yescharacteristic
1252C22#254811yescharacteristic
1253C22#255211yescharacteristic
1254C22#255211yescharacteristic
1255C22#256811yescharacteristic
1256C22#257011yescharacteristic
1257C22#257011yescharacteristic
1258C22#257011yescharacteristic
1259C22#257011yescharacteristic
1260C22#257111yescharacteristic
1261C22#257111yescharacteristic
1262C22#259211yescharacteristic
1263C22#259211yescharacteristic
1264C22#262411yescharacteristic
1265C22#262511yescharacteristic
1266C22#262811yescharacteristic
1267C22#262911yescharacteristic
1268C22#264411yescharacteristic
1269C22#264511yescharacteristic
1270C22#264711yescharacteristic
1271C22#264711yescharacteristic
1272C22#285111yescharacteristic
1273C22#285411yescharacteristic
1274C22#285511yescharacteristic
1275C22#285711yescharacteristic
1276C22#285911yescharacteristic
1277C22#286011yescharacteristic
1278C22#286311yescharacteristic
1279C22#286411yescharacteristic
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—44no—
1285C4—44no—
1286C4—84no—
1287C4—84no—
1288C4—84no—
1289C4—84no—
1290C4#1443116yescomplemented
1291C2C2×#144311yescharacteristic
1292C2#1392111yescharacteristic
1293C2#1393611yescharacteristic
1294C2#1398111yescharacteristic
1295C2#1398211yescharacteristic
1296C2#1399311yescharacteristic
1297C2#1399411yescharacteristic
1298C2#1402111yescharacteristic
1299C2#1402211yescharacteristic
1300C2#1402911yescharacteristic
1301C2#1403011yescharacteristic
1302C2#1414111yescharacteristic
1303C2#1414211yescharacteristic
1304C2#1426611yescharacteristic
1305C2#1469911yescharacteristic
1306C2#1513111yescharacteristic
1307C2#1513211yescharacteristic
1308C2#1513811yescharacteristic
1309C2#1514611yescharacteristic
1310C2#1514611yescharacteristic
1311C2#1514711yescharacteristic
1312C2#1515211yescharacteristic
1313C2C4⋊#40111yescharacteristic
1314C2#1518311yescharacteristic
1315C2#1518611yescharacteristic
1316C2#1519211yescharacteristic
1317C2#1519811yescharacteristic
1318C2#1522011yescharacteristic
1319C2#1523211yescharacteristic
1320C2#1523211yescharacteristic
1321C2#1523511yescharacteristic
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
41. C4⋊#95C4semidirect
1290. C4#1443semidirect

Maximal subgroups

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

subgroupindex
C2×#14432
C2×C4⋊#952
C2×C4×#952
#75562