Finite Group Databasebeta

← #387154

Subgroups — #387154

Order 512.

1268 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2505C211yesmaximal, characteristic
2#13908C211yesmaximal, characteristic
3#13883C211yesmaximal, characteristic
4#11353C211yesmaximal, characteristic
5#11203C211yesmaximal, characteristic
6#11203C211yesmaximal, characteristic
7#11203C211yesmaximal, characteristic
8#11203C211yesmaximal, characteristic
9#11203C211yesmaximal, characteristic
10#10912C211yesmaximal, characteristic
11#10912C211yesmaximal, characteristic
12#10912C211yesmaximal, characteristic
13#10854C211yesmaximal, characteristic
14#10846C211yesmaximal, characteristic
15#10801C211yesmaximal, characteristic
16#2505—21no—
17#2505—21no—
18#2505—21no—
19#2505—21no—
20#2505—21no—
21#2505—21no—
22#2505—21no—
23#2505—21no—
24C2×#400C411yescharacteristic, complemented
25C2×#400C411yescharacteristic, complemented
26C2×#400C411yescharacteristic, complemented
27C2×#398C411yescharacteristic, complemented
28C2×#389C411yescharacteristic, complemented
29C2×#387C411yescharacteristic, complemented
30C2×#387C411yescharacteristic, complemented
31C2×#385C2211yescharacteristic
32C2×#385C2211yescharacteristic
33C2×#385C2211yescharacteristic
34C2×#385C2211yescharacteristic
35C2×#382C411yescharacteristic, complemented
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C2×#342C2211yescharacteristic
46C2×#342C2211yescharacteristic
47C2×#342C2211yescharacteristic
48C2×#342C2211yescharacteristic
49C2×#342C2211yescharacteristic
50C2×#342C2211yescharacteristic
51C2×#342C2211yescharacteristic
52C2×#342C2211yescharacteristic
53C2×#342C2211yescharacteristic
54C2×#342C2211yescharacteristic
55C2×#342C2211yescharacteristic
56C2×#342C2211yescharacteristic
57C2×#342C2211yescharacteristic
58C2×#342C2211yescharacteristic
59C2×#342C2211yescharacteristic
60C2×#342C2211yescharacteristic
61#1444—21no—
62#1443—21no—
63#1442—21no—
64#1442—21no—
65#1436—21no—
66#1436—21no—
67#1436—21no—
68#1434—21no—
69C22⋊#95C2211yescharacteristic
70C22⋊#95C2211yescharacteristic
71C22⋊#95C2211yescharacteristic
72C22⋊#95C2211yescharacteristic
73C22⋊#95C2211yescharacteristic
74C22⋊#95C2211yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4C2×C411yescharacteristic
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2311yescharacteristic
93C22×C22⋊C4C2311yescharacteristic
94C22×C22⋊C4C2311yescharacteristic
95C22×C22⋊C4C2311yescharacteristic
96C22×C22⋊C4C2311yescharacteristic
97C22×C22⋊C4C2311yescharacteristic
98C22×C22⋊C4C2311yescharacteristic
99C22×C22⋊C4C2311yescharacteristic
100C22×C22⋊C4C2311yescharacteristic
101C22×C22⋊C4C2311yescharacteristic
102C22×C22⋊C4C2311yescharacteristic
103C22×C22⋊C4C2311yescharacteristic
104C22×C42—21no—
105C22×C42—21no—
106C22×C42C2×C411yescharacteristic
107C22×C42C2×C411yescharacteristic
108#400—21no—
109#400—21no—
110#400—21no—
111#400—21no—
112#400—21no—
113#400—21no—
114#400—21no—
115#400—21no—
116#400—21no—
117#400—21no—
118#400—21no—
119#400—21no—
120#398—21no—
121#398—21no—
122#398—21no—
123#398—21no—
124#389—21no—
125#389—21no—
126#389—21no—
127#389—21no—
128#387—21no—
129#387—21no—
130#387—21no—
131#387—21no—
132#387—21no—
133#387—21no—
134#387—21no—
135#387—21no—
136#385—21no—
137#385—21no—
138#385—21no—
139#385—21no—
140#385—21no—
141#385—21no—
142#385—21no—
143#385—21no—
144#385—21no—
145#385—21no—
146#385—21no—
147#385—21no—
148#385—21no—
149#385—21no—
150#385—21no—
151#385—21no—
152#382—21no—
153#382—21no—
154#382—21no—
155#382—21no—
156#380—21no—
157#380—21no—
158#380—21no—
159#380—21no—
160#380—22no—
161#380—22no—
162#380—22no—
163#380—41no—
164#380—41no—
165#380—41no—
166#380—41no—
167#380—41no—
168C4×C22⋊C4—21no—
169C4×C22⋊C4—21no—
170C4×C22⋊C4—21no—
171C4×C22⋊C4—21no—
172C4×C22⋊C4—22no—
173C4×C22⋊C4—41no—
174C4×C22⋊C4—41no—
175C4×C22⋊C4—41no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95C2×C411yescharacteristic
195C2×#95C2×C411yescharacteristic
196C2×#95C2×C411yescharacteristic
197C2×#95C2×C411yescharacteristic
198C2×#95C2×C411yescharacteristic
199C2×#95C2×C411yescharacteristic
200C2×#95C2×C411yescharacteristic
201C2×#95C2×C411yescharacteristic
202C2×#95C2×C411yescharacteristic
203C2×#95C2×C411yescharacteristic
204C2×#95C2×C411yescharacteristic
205C2×#95C2×C411yescharacteristic
206C2×#95C2×C411yescharacteristic
207C2×#95C2×C411yescharacteristic
208C2×#95C2×C411yescharacteristic
209C2×#95C2×C411yescharacteristic
210C2×#95D411yescharacteristic
211C2×#95D411yescharacteristic
212C2×#95D411yescharacteristic
213C2×#95D411yescharacteristic
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218#342—22no—
219#342—22no—
220#342—22no—
221#342—22no—
222#342—22no—
223#342—41no—
224#342—41no—
225#342—41no—
226#342—41no—
227#342—41no—
228#342—41no—
229#342—41no—
230#342—41no—
231#342—41no—
232#342—41no—
233#342Q814yes—
234C25C2411yescharacteristic
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—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—81no—
258C23×C4—81no—
259C23×C4—81no—
260C23×C4—81no—
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C411yescharacteristic
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—81no—
318C2×C4⋊C4—81no—
319C2×C4⋊C4—81no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4—81no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4C2×Q812yes—
396C2×C22⋊C4C2×Q812yes—
397C2×C22⋊C4C2×Q812yes—
398C2×C22⋊C4#4112yes—
399C2×C22⋊C4#4112yes—
400C2×C22⋊C4#4112yes—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—81no—
410C2×C42—81no—
411C2×C42—81no—
412C2×C42—81no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—81no—
448#95—81no—
449#95—81no—
450#95—81no—
451#95—81no—
452#95—81no—
453#95—81no—
454#95—81no—
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C22⋊C411yescharacteristic
466#95C22⋊C411yescharacteristic
467#95C22⋊C411yescharacteristic
468#95C22⋊C411yescharacteristic
469#95C22⋊C411yescharacteristic
470#95C22⋊C411yescharacteristic
471C24—41no—
472C24—41no—
473C24—41no—
474C24—41no—
475C24C23×C411yescharacteristic
476C24C22×D411yescharacteristic
477C24C22×D411yescharacteristic
478C24C22×Q811yescharacteristic
479C24C2×#4111yescharacteristic
480C24C2×#4111yescharacteristic
481C24C2×#4111yescharacteristic
482C24H(5,𝔽2)11yescharacteristic
483C24H(5,𝔽2)11yescharacteristic
484C24H(5,𝔽2)11yescharacteristic
485C242−1+411yescharacteristic
486C242−1+411yescharacteristic
487C242−1+411yescharacteristic
488C242−1+411yescharacteristic
489C242−1+411yescharacteristic
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
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—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—82no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4—82no—
660C22×C4—82no—
661C22×C4—82no—
662C22×C4—82no—
663C22×C4—82no—
664C22×C4—82no—
665C22×C4—82no—
666C22×C4—82no—
667C22×C4—82no—
668C22×C4C2×C22⋊C411yescharacteristic
669C22×C4C2×C22⋊C411yescharacteristic
670C22×C4C2×C22⋊C411yescharacteristic
671C22×C4C2×C22⋊C411yescharacteristic
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C2×C22⋊C411yescharacteristic
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C4×Q812yes—
681C22×C4C4×Q812yes—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—81no—
697C4⋊C4—81no—
698C4⋊C4—81no—
699C4⋊C4—81no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—84no—
703C4⋊C4—84no—
704C4⋊C4—84no—
705C4⋊C4—84no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—41no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—41no—
724C22⋊C4—41no—
725C22⋊C4—41no—
726C22⋊C4—41no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—41no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C22⋊C4—41no—
733C22⋊C4—41no—
734C22⋊C4—41no—
735C22⋊C4—41no—
736C22⋊C4—41no—
737C22⋊C4—41no—
738C22⋊C4—41no—
739C22⋊C4—41no—
740C22⋊C4—41no—
741C22⋊C4—41no—
742C22⋊C4—41no—
743C22⋊C4—41no—
744C22⋊C4—41no—
745C22⋊C4—41no—
746C22⋊C4—41no—
747C22⋊C4—41no—
748C22⋊C4—41no—
749C22⋊C4—41no—
750C22⋊C4—41no—
751C22⋊C4—41no—
752C22⋊C4—41no—
753C22⋊C4—41no—
754C42—42no—
755C42—42no—
756C42—81no—
757C42—81no—
758C42—84no—
759C42—84no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×C22⋊C411yescharacteristic
797C23C2×C4×Q811yescharacteristic
798C23C4×#4111yescharacteristic
799C23#51911yescharacteristic
800C23#52011yescharacteristic
801C23#52011yescharacteristic
802C23#52011yescharacteristic
803C23#53511yescharacteristic
804C23#53611yescharacteristic
805C23#53711yescharacteristic
806C23#53711yescharacteristic
807C23#53911yescharacteristic
808C23#53911yescharacteristic
809C23#54011yescharacteristic
810C23#54111yescharacteristic
811C23#54111yescharacteristic
812C23#54111yescharacteristic
813C23#54411yescharacteristic
814C23#54411yescharacteristic
815C23#54611yescharacteristic
816C23#54611yescharacteristic
817C23#54711yescharacteristic
818C23#54711yescharacteristic
819C23#54811yescharacteristic
820C23#54811yescharacteristic
821C23D4×Q811yescharacteristic
822C23D4×Q811yescharacteristic
823C23#55211yescharacteristic
824C23#55311yescharacteristic
825C23#55411yescharacteristic
826C23#55711yescharacteristic
827C23#56211yescharacteristic
828C23#56311yescharacteristic
829C23#56311yescharacteristic
830C23#56411yescharacteristic
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—81no—
952C2×C4—81no—
953C2×C4—81no—
954C2×C4—81no—
955C2×C4—81no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—81no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4—81no—
973C2×C4—81no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—81no—
982C2×C4—81no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—81no—
992C2×C4—81no—
993C2×C4—81no—
994C2×C4—81no—
995C2×C4—81no—
996C2×C4—81no—
997C2×C4#41012yes—
998C2×C4#41012yes—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22#231111yescharacteristic
1052C22#233011yescharacteristic
1053C22#233611yescharacteristic
1054C22#233911yescharacteristic
1055C22Q8×C22⋊C411yescharacteristic
1056C22#237011yescharacteristic
1057C22#238211yescharacteristic
1058C22#270411yescharacteristic
1059C22#270711yescharacteristic
1060C22#271111yescharacteristic
1061C22#271311yescharacteristic
1062C22#271911yescharacteristic
1063C22#272011yescharacteristic
1064C22#272511yescharacteristic
1065C22#272611yescharacteristic
1066C22C2×#41011yescharacteristic
1067C22C2×#41011yescharacteristic
1068C22#288311yescharacteristic
1069C22#288311yescharacteristic
1070C4—22no—
1071C4—22no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—82no—
1085C4—82no—
1086C4—82no—
1087C4—82no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—161no—
1095C4—161no—
1096C4—161no—
1097C4—161no—
1098C2—21no—
1099C2—21no—
1100C2—21no—
1101C2—21no—
1102C2—21no—
1103C2—21no—
1104C2—21no—
1105C2—21no—
1106C2—21no—
1107C2—21no—
1108C2—21no—
1109C2—21no—
1110C2#1445111yescharacteristic
1111C2#2187511yescharacteristic
1112C2#2187611yescharacteristic
1113C2#2247711yescharacteristic
1114C2#2247711yescharacteristic
1115C2#2251311yescharacteristic
1116C2#2251311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#95 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
24. C2×#400C4semidirect
25. C2×#400C4semidirect
26. C2×#400C4semidirect
27. C2×#398C4semidirect
28. C2×#389C4semidirect
29. C2×#387C4semidirect
30. C2×#387C4semidirect
35. C2×#382C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25052
#139082
#138832
#113532
#112032
#109122
#108542
#108462
#108012