Finite Group Databasebeta

← #154389

Subgroups — #154389

Order 512.

3182 conjugacy classes of subgroups.

The subgroup lattice has 1337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C2×#1442C212yesmaximal
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#7557C212yesmaximal
10#7556C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#389—24no—
21C2×#389—24no—
22C2×#389—24no—
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38#1442—28no—
39C4⋊#95—24no—
40C4⋊#95—24no—
41C4⋊#95—24no—
42C4⋊#95—24no—
43C4⋊#95C418yescomplemented
44C4×#95—24no—
45C24×C4C2312yes—
46C24×C4C2312yes—
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
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—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—24no—
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⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—42no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4C2×C414yes—
86C22×C4⋊C4C2×C414yes—
87C22×C4⋊C4D414yes—
88C22×C4⋊C4D414yes—
89C22×C4⋊C4D414yes—
90C22×C4⋊C4Q814yes—
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×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42C2×C414yes—
110C22×C42D414yes—
111C22×C42Q814yes—
112#389—232no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95—42no—
150C2×#95—42no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95C2×C418yes—
155C2×#95C2×C418yes—
156C2×#95D414yes—
157C2×#95Q814yes—
158C25C2411yescharacteristic
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—22no—
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—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
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—22no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
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×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4C22×C414yes—
286C23×C4C22×C414yes—
287C23×C4C22×C412yes—
288C23×C4C22×C412yes—
289C23×C4C22×C412yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4C2×D412yes—
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D412yes—
302C23×C4C2×Q814yes—
303C23×C4C2×Q812yes—
304C23×C4C2×Q812yes—
305C23×C4C2×Q812yes—
306C23×C4C2×Q812yes—
307C23×C4C2×Q812yes—
308C23×C4C2×Q812yes—
309C23×C4C2×Q812yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4112yes—
313C23×C4#4112yes—
314C23×C4#4112yes—
315C23×C4#4112yes—
316C23×C4#4112yes—
317C23×C4#4112yes—
318C23×C4#4112yes—
319C23×C4#4112yes—
320C23×C4#4112yes—
321C23×C4#4112yes—
322C23×C4#4112yes—
323C23×C4#4112yes—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—216no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—48no—
341C2×C4⋊C4—48no—
342C2×C4⋊C4—48no—
343C2×C4⋊C4—48no—
344C2×C4⋊C4—48no—
345C2×C4⋊C4—48no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C4⋊C4116yes—
359C2×C42—28no—
360C2×C42—28no—
361C2×C42—28no—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—28no—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—44no—
369C2×C42—44no—
370C2×C42—44no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42—44no—
374C2×C42—44no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—44no—
380#95—28no—
381#95—28no—
382#95—216no—
383#95—216no—
384#95—28no—
385#95—28no—
386#95—48no—
387#95—48no—
388#95—48no—
389#95—48no—
390#95—48no—
391#95—48no—
392#95—48no—
393#95—48no—
394#95—48no—
395C24C23×C411yescharacteristic
396C24C22×D411yescharacteristic
397C24C22×D411yescharacteristic
398C24C22×D411yescharacteristic
399C24C22×D411yescharacteristic
400C24C22×D411yescharacteristic
401C24C22×Q811yescharacteristic
402C24C22×Q811yescharacteristic
403C24C22×Q811yescharacteristic
404C24C2×#4111yescharacteristic
405C24C2×#4111yescharacteristic
406C24C2×#4111yescharacteristic
407C24C2×#4111yescharacteristic
408C24C2×#4111yescharacteristic
409C24C2×#4111yescharacteristic
410C24C2×#4111yescharacteristic
411C24C2×#4111yescharacteristic
412C24C2×#4111yescharacteristic
413C24C2×#4111yescharacteristic
414C24C2×#4111yescharacteristic
415C24C2×#4111yescharacteristic
416C24C2×#4111yescharacteristic
417C24C2×#4111yescharacteristic
418C24H(5,𝔽2)11yescharacteristic
419C24H(5,𝔽2)11yescharacteristic
420C24H(5,𝔽2)11yescharacteristic
421C24H(5,𝔽2)11yescharacteristic
422C242−1+411yescharacteristic
423C242−1+411yescharacteristic
424C242−1+411yescharacteristic
425C242−1+411yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
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—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
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—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
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—42no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
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—42no—
600C22×C4—42no—
601C22×C4—42no—
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—42no—
611C22×C4—41no—
612C22×C4—42no—
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—42no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—42no—
630C22×C4—42no—
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—42no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—42no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
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—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4C2×C4⋊C418yes—
770C22×C4C2×C4⋊C414yes—
771C22×C4#11714yes—
772C22×C4#11714yes—
773C22×C4C4×D414yes—
774C22×C4C4×D414yes—
775C22×C4C4×D414yes—
776C22×C4C4×D414yes—
777C22×C4C4×Q814yes—
778C22×C4C4×Q814yes—
779C22×C4#12014yes—
780C22×C4#12114yes—
781C22×C4#12114yes—
782C22×C4#12114yes—
783C22×C4#12114yes—
784C22×C4C22⋊Q814yes—
785C22×C4C22⋊Q814yes—
786C22×C4C22⋊Q814yes—
787C22×C4C22⋊Q814yes—
788C22×C4C22⋊Q814yes—
789C22×C4C22⋊Q814yes—
790C22×C4#12314yes—
791C22×C4#12314yes—
792C22×C4#12314yes—
793C22×C4#12314yes—
794C22×C4#12314yes—
795C22×C4#12414yes—
796C22×C4#12414yes—
797C22×C4#12414yes—
798C22×C4#12414yes—
799C22×C4#12514yes—
800C22×C4#12514yes—
801C22×C4#12514yes—
802C22×C4#12514yes—
803C22×C4#12514yes—
804C22×C4#12514yes—
805C22×C4#12614yes—
806C22×C4#12614yes—
807C22×C4#12614yes—
808C22×C4#12614yes—
809C22×C4C4⋊Q814yes—
810C22×C4C4⋊Q814yes—
811C4⋊C4—232no—
812C4⋊C4—432no—
813C4⋊C4—416no—
814C4⋊C4—416no—
815C4⋊C4—416no—
816C42—416no—
817C42—416no—
818C42—416no—
819C23C22×C4⋊C411yescharacteristic
820C23C2×#11711yescharacteristic
821C23C2×#11711yescharacteristic
822C23C2×C4×D411yescharacteristic
823C23C2×C4×D411yescharacteristic
824C23C2×C4×D411yescharacteristic
825C23C2×C4×D411yescharacteristic
826C23C2×C4×Q811yescharacteristic
827C23C2×C4×Q811yescharacteristic
828C23C4×#4111yescharacteristic
829C23C4×#4111yescharacteristic
830C23#51811yescharacteristic
831C23#51911yescharacteristic
832C23#52011yescharacteristic
833C23#52011yescharacteristic
834C23C2×#12011yescharacteristic
835C23C2×#12111yescharacteristic
836C23C2×#12111yescharacteristic
837C23C2×#12111yescharacteristic
838C23C2×#12111yescharacteristic
839C23C2×C22⋊Q811yescharacteristic
840C23C2×C22⋊Q811yescharacteristic
841C23C2×C22⋊Q811yescharacteristic
842C23C2×C22⋊Q811yescharacteristic
843C23C2×C22⋊Q811yescharacteristic
844C23C2×C22⋊Q811yescharacteristic
845C23C2×#12311yescharacteristic
846C23C2×#12311yescharacteristic
847C23C2×#12311yescharacteristic
848C23C2×#12311yescharacteristic
849C23C2×#12311yescharacteristic
850C23#52511yescharacteristic
851C23#52511yescharacteristic
852C23C2×#12411yescharacteristic
853C23C2×#12411yescharacteristic
854C23C2×#12411yescharacteristic
855C23C2×#12411yescharacteristic
856C23C2×#12511yescharacteristic
857C23C2×#12511yescharacteristic
858C23C2×#12511yescharacteristic
859C23C2×#12511yescharacteristic
860C23C2×#12511yescharacteristic
861C23C2×#12511yescharacteristic
862C23C2×#12611yescharacteristic
863C23C2×#12611yescharacteristic
864C23C2×#12611yescharacteristic
865C23C2×#12611yescharacteristic
866C23#52911yescharacteristic
867C23#52911yescharacteristic
868C23#52911yescharacteristic
869C23#52911yescharacteristic
870C23#52911yescharacteristic
871C23#52911yescharacteristic
872C23#52911yescharacteristic
873C23#52911yescharacteristic
874C23C2×C4⋊Q811yescharacteristic
875C23C2×C4⋊Q811yescharacteristic
876C23#53211yescharacteristic
877C23#53211yescharacteristic
878C23#53211yescharacteristic
879C23#53211yescharacteristic
880C23#53311yescharacteristic
881C23#53311yescharacteristic
882C23#53311yescharacteristic
883C23#53311yescharacteristic
884C23#53311yescharacteristic
885C23#53311yescharacteristic
886C23#53511yescharacteristic
887C23#53611yescharacteristic
888C23#53711yescharacteristic
889C23#53711yescharacteristic
890C23#54011yescharacteristic
891C23#54011yescharacteristic
892C23#54011yescharacteristic
893C23#54011yescharacteristic
894C23#54111yescharacteristic
895C23#54111yescharacteristic
896C23#54111yescharacteristic
897C23#54111yescharacteristic
898C23#54211yescharacteristic
899C23#54211yescharacteristic
900C23#54211yescharacteristic
901C23#54211yescharacteristic
902C23#54211yescharacteristic
903C23#54211yescharacteristic
904C23#54211yescharacteristic
905C23#54211yescharacteristic
906C23#54411yescharacteristic
907C23#54411yescharacteristic
908C23#54411yescharacteristic
909C23#54411yescharacteristic
910C23D4211yescharacteristic
911C23D4211yescharacteristic
912C23D4211yescharacteristic
913C23#54611yescharacteristic
914C23#54611yescharacteristic
915C23#54611yescharacteristic
916C23#54611yescharacteristic
917C23#54611yescharacteristic
918C23#54611yescharacteristic
919C23#54711yescharacteristic
920C23#54711yescharacteristic
921C23#54711yescharacteristic
922C23#54711yescharacteristic
923C23#54711yescharacteristic
924C23#54711yescharacteristic
925C23#54811yescharacteristic
926C23#54811yescharacteristic
927C23#54811yescharacteristic
928C23#54811yescharacteristic
929C23#54811yescharacteristic
930C23#54811yescharacteristic
931C23D4×Q811yescharacteristic
932C23D4×Q811yescharacteristic
933C23D4×Q811yescharacteristic
934C23D4×Q811yescharacteristic
935C23#55011yescharacteristic
936C23#55011yescharacteristic
937C23#55011yescharacteristic
938C23#55011yescharacteristic
939C23#55211yescharacteristic
940C23#55211yescharacteristic
941C23#55211yescharacteristic
942C23#55211yescharacteristic
943C23#55211yescharacteristic
944C23#55211yescharacteristic
945C23#55311yescharacteristic
946C23#55311yescharacteristic
947C23#55311yescharacteristic
948C23#55311yescharacteristic
949C23#55311yescharacteristic
950C23#55311yescharacteristic
951C23#55411yescharacteristic
952C23#55411yescharacteristic
953C23#55411yescharacteristic
954C23#55411yescharacteristic
955C23#55411yescharacteristic
956C23#55411yescharacteristic
957C23#55511yescharacteristic
958C23#55511yescharacteristic
959C23#55511yescharacteristic
960C23#55611yescharacteristic
961C23#55611yescharacteristic
962C23#55611yescharacteristic
963C23#55611yescharacteristic
964C23#55611yescharacteristic
965C23#55611yescharacteristic
966C23#55711yescharacteristic
967C23#55711yescharacteristic
968C23#55711yescharacteristic
969C23#55711yescharacteristic
970C23Q8211yescharacteristic
971C23#55911yescharacteristic
972C23#55911yescharacteristic
973C23#55911yescharacteristic
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—24no—
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—44no—
1004C2×C4—44no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—44no—
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—44no—
1024C2×C4—44no—
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—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—44no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—44no—
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—82no—
1111C2×C4—82no—
1112C2×C4—82no—
1113C2×C4—82no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4#38218yes—
1125C2×C4#38518yes—
1126C2×C4#38718yes—
1127C2×C4#38718yes—
1128C2×C4#38818yes—
1129C2×C4#38818yes—
1130C2×C4#38918yes—
1131C2×C4#39318yes—
1132C2×C4#39418yes—
1133C2×C4#39718yes—
1134C2×C4#39818yes—
1135C2×C4#39818yes—
1136C2×C4#40018yes—
1137C2×C4#40018yes—
1138C2×C4#40018yes—
1139C22C2×#38211yescharacteristic
1140C22C2×#38511yescharacteristic
1141C22C2×#38711yescharacteristic
1142C22C2×#38711yescharacteristic
1143C22C2×#38811yescharacteristic
1144C22C2×#38811yescharacteristic
1145C22C2×#38911yescharacteristic
1146C22#229311yescharacteristic
1147C22#229511yescharacteristic
1148C22C4×#12111yescharacteristic
1149C22C4×C22⋊Q811yescharacteristic
1150C22C4×#12511yescharacteristic
1151C22C4×C4⋊Q811yescharacteristic
1152C22#231911yescharacteristic
1153C22#232011yescharacteristic
1154C22#232311yescharacteristic
1155C22#232411yescharacteristic
1156C22#233011yescharacteristic
1157C22#233111yescharacteristic
1158C22#234411yescharacteristic
1159C22#234511yescharacteristic
1160C22#234611yescharacteristic
1161C22#234711yescharacteristic
1162C22D4×C4⋊C411yescharacteristic
1163C22#234911yescharacteristic
1164C22Q8×C4⋊C411yescharacteristic
1165C22#235111yescharacteristic
1166C22#236011yescharacteristic
1167C22#236111yescharacteristic
1168C22#236211yescharacteristic
1169C22#236311yescharacteristic
1170C22#236511yescharacteristic
1171C22#236611yescharacteristic
1172C22#236711yescharacteristic
1173C22#236711yescharacteristic
1174C22C2×#39311yescharacteristic
1175C22C2×#39411yescharacteristic
1176C22C2×#39711yescharacteristic
1177C22C2×#39811yescharacteristic
1178C22C2×#39811yescharacteristic
1179C22C2×#40011yescharacteristic
1180C22C2×#40011yescharacteristic
1181C22C2×#40011yescharacteristic
1182C22#240711yescharacteristic
1183C22#240711yescharacteristic
1184C22#240811yescharacteristic
1185C22#240911yescharacteristic
1186C22#241411yescharacteristic
1187C22#241511yescharacteristic
1188C22#241611yescharacteristic
1189C22#241711yescharacteristic
1190C22#242011yescharacteristic
1191C22#242011yescharacteristic
1192C22#242111yescharacteristic
1193C22#242111yescharacteristic
1194C22#242211yescharacteristic
1195C22#242211yescharacteristic
1196C22#242311yescharacteristic
1197C22#242311yescharacteristic
1198C22#242611yescharacteristic
1199C22#242611yescharacteristic
1200C22#242711yescharacteristic
1201C22#242711yescharacteristic
1202C22#242811yescharacteristic
1203C22#242811yescharacteristic
1204C22#242911yescharacteristic
1205C22#242911yescharacteristic
1206C22#243911yescharacteristic
1207C22#243911yescharacteristic
1208C22#244011yescharacteristic
1209C22#244011yescharacteristic
1210C22#244111yescharacteristic
1211C22#244111yescharacteristic
1212C22#244211yescharacteristic
1213C22#244211yescharacteristic
1214C22#244511yescharacteristic
1215C22#244511yescharacteristic
1216C22#244611yescharacteristic
1217C22#244611yescharacteristic
1218C22#244711yescharacteristic
1219C22#244711yescharacteristic
1220C22#244811yescharacteristic
1221C22#244811yescharacteristic
1222C22#245111yescharacteristic
1223C22#245211yescharacteristic
1224C22#245311yescharacteristic
1225C22#245411yescharacteristic
1226C22#248911yescharacteristic
1227C22#248911yescharacteristic
1228C22#248911yescharacteristic
1229C22#249011yescharacteristic
1230C22#249011yescharacteristic
1231C22#249011yescharacteristic
1232C22#249111yescharacteristic
1233C22#249111yescharacteristic
1234C22#249111yescharacteristic
1235C22#249211yescharacteristic
1236C22#249211yescharacteristic
1237C22#249211yescharacteristic
1238C22#249411yescharacteristic
1239C22#249511yescharacteristic
1240C22#249611yescharacteristic
1241C22#249711yescharacteristic
1242C22#250611yescharacteristic
1243C22#250611yescharacteristic
1244C22#250611yescharacteristic
1245C22#250711yescharacteristic
1246C22#250711yescharacteristic
1247C22#250711yescharacteristic
1248C22#250811yescharacteristic
1249C22#250811yescharacteristic
1250C22#250811yescharacteristic
1251C22#250911yescharacteristic
1252C22#250911yescharacteristic
1253C22#250911yescharacteristic
1254C22#251111yescharacteristic
1255C22#251111yescharacteristic
1256C22#251211yescharacteristic
1257C22#251211yescharacteristic
1258C22#251311yescharacteristic
1259C22#251311yescharacteristic
1260C22#251411yescharacteristic
1261C22#251411yescharacteristic
1262C22#253811yescharacteristic
1263C22#254711yescharacteristic
1264C22#255011yescharacteristic
1265C22#255011yescharacteristic
1266C22#255111yescharacteristic
1267C22#255211yescharacteristic
1268C22#255211yescharacteristic
1269C22#256211yescharacteristic
1270C22#256211yescharacteristic
1271C22#256311yescharacteristic
1272C22#257011yescharacteristic
1273C22#257011yescharacteristic
1274C22#257111yescharacteristic
1275C22#258011yescharacteristic
1276C22#258111yescharacteristic
1277C22#258211yescharacteristic
1278C22#262411yescharacteristic
1279C22#262511yescharacteristic
1280C22#262811yescharacteristic
1281C22#262911yescharacteristic
1282C22#264411yescharacteristic
1283C22#264511yescharacteristic
1284C22#264711yescharacteristic
1285C22#264711yescharacteristic
1286C22#285111yescharacteristic
1287C22#285411yescharacteristic
1288C22#285511yescharacteristic
1289C22#285711yescharacteristic
1290C22#285911yescharacteristic
1291C22#286011yescharacteristic
1292C22#286311yescharacteristic
1293C22#286411yescharacteristic
1294C4—44no—
1295C4—44no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—48no—
1301C4—84no—
1302C4—84no—
1303C4—84no—
1304C4#1442116yescomplemented
1305C2C2×#144211yescharacteristic
1306C2#1391811yescharacteristic
1307C2#1393311yescharacteristic
1308C2#1397311yescharacteristic
1309C2#1397411yescharacteristic
1310C2#1400511yescharacteristic
1311C2#1400611yescharacteristic
1312C2#1401711yescharacteristic
1313C2#1401811yescharacteristic
1314C2#1402911yescharacteristic
1315C2#1403011yescharacteristic
1316C2#1414111yescharacteristic
1317C2#1414211yescharacteristic
1318C2#1426611yescharacteristic
1319C2#1469911yescharacteristic
1320C2#1512511yescharacteristic
1321C2#1512611yescharacteristic
1322C2#1513311yescharacteristic
1323C2#1513711yescharacteristic
1324C2#1513811yescharacteristic
1325C2#1513911yescharacteristic
1326C2#1514611yescharacteristic
1327C2#1515611yescharacteristic
1328C2#1517911yescharacteristic
1329C2#1518611yescharacteristic
1330C2#1518711yescharacteristic
1331C2#1520011yescharacteristic
1332C2#1521611yescharacteristic
1333C2#1522111yescharacteristic
1334C2#1522511yescharacteristic
1335C2#1523211yescharacteristic
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
43. C4⋊#95C4semidirect
1304. C4#1442semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C2×#14422
C2×C4⋊#952
C2×C4×#952
#75572
#75562