Finite Group Databasebeta

← #1195937

Subgroups — #1195937

Order 512.

2364 conjugacy classes of subgroups.

The subgroup lattice has 1448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2729C211yesmaximal, characteristic
2C2×#2465C211yesmaximal, characteristic
3#17080C211yesmaximal, characteristic, complemented
4#16826C211yesmaximal, characteristic, complemented
5#16520C211yesmaximal, characteristic
6#15811C211yesmaximal, characteristic, complemented
7#15762C211yesmaximal, characteristic, complemented
8#15760C211yesmaximal, characteristic, complemented
9#15753C211yesmaximal, characteristic, complemented
10#15671C211yesmaximal, characteristic
11#15627C211yesmaximal, characteristic, complemented
12#15601C211yesmaximal, characteristic, complemented
13#15592C211yesmaximal, characteristic, complemented
14#15555C211yesmaximal, characteristic
15#15421C211yesmaximal, characteristic
16#15360C211yesmaximal, characteristic, complemented
17#15265C211yesmaximal, characteristic
18#15209C211yesmaximal, characteristic, complemented
19#15158C211yesmaximal, characteristic, complemented
20#14981C211yesmaximal, characteristic, complemented
21#14914C211yesmaximal, characteristic
22#14816C211yesmaximal, characteristic, complemented
23#14770C211yesmaximal, characteristic
24#14514C211yesmaximal, characteristic
25#14442C211yesmaximal, characteristic
26#14114C211yesmaximal, characteristic
27#14053C211yesmaximal, characteristic, complemented
28#14052C211yesmaximal, characteristic
29#14024C211yesmaximal, characteristic, complemented
30#14004C211yesmaximal, characteristic
31#13789C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2729—28no—
38#2465—28no—
39C2×#400C2211yescharacteristic
40C2×#398C2211yescharacteristic
41C2×#398C2211yescharacteristic
42C2×#396C2211yescharacteristic
43C2×#396C2211yescharacteristic
44C2×#395C2211yescharacteristic
45C2×#395C2211yescharacteristic
46C2×#395C2211yescharacteristic
47C2×#395C2211yescharacteristic
48C2×#395C2211yescharacteristic
49C2×#395C2211yescharacteristic
50C2×#395C2211yescharacteristic
51C2×#393C2211yescharacteristic
52C2×#393C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#388C2211yescharacteristic
64C2×#388C2211yescharacteristic
65C2×#388C2211yescharacteristic
66C2×#388C2211yescharacteristic
67C2×#387C2211yescharacteristic
68C2×#387C2211yescharacteristic
69C2×#387C2211yescharacteristic
70C2×#387C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#385C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2211yescharacteristic
82#1446C2211yescharacteristic
83#1446C2211yescharacteristic
84#1446C2211yescharacteristic
85#1446C2211yescharacteristic
86#1446C2211yescharacteristic
87#1446C2211yescharacteristic
88#1446C2211yescharacteristic
89#1445C2211yescharacteristic
90#1445C2211yescharacteristic
91#1445C2211yescharacteristic
92#1445C2211yescharacteristic
93#1445C2211yescharacteristic
94#1444C2211yescharacteristic
95#1444C2211yescharacteristic
96#1444C2211yescharacteristic
97#1444C2211yescharacteristic
98#1444C2211yescharacteristic
99#1444C2211yescharacteristic
100#1444C2211yescharacteristic
101#1444C2211yescharacteristic
102#1444C2211yescharacteristic
103#1444C2211yescharacteristic
104#1444C2211yescharacteristic
105#1442C2211yescharacteristic
106#1442C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1442C2211yescharacteristic
110#1442C2211yescharacteristic
111#1442C2211yescharacteristic
112#1442C2211yescharacteristic
113#1442C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1441C2211yescharacteristic
121#1441C2211yescharacteristic
122#1441C2211yescharacteristic
123#1441C2211yescharacteristic
124#1441C2211yescharacteristic
125#1441C2211yescharacteristic
126#1441C2211yescharacteristic
127#1441C2211yescharacteristic
128#1441C2211yescharacteristic
129#1441C2211yescharacteristic
130#1441C2211yescharacteristic
131#1441C2211yescharacteristic
132#1441C2211yescharacteristic
133#1441C2211yescharacteristic
134#1441C2211yescharacteristic
135#1441C2211yescharacteristic
136#1441C2211yescharacteristic
137#1441C2211yescharacteristic
138#1441C2211yescharacteristic
139#1441C2211yescharacteristic
140#1439C2211yescharacteristic
141#1439C2211yescharacteristic
142#1439C2211yescharacteristic
143#1439C2211yescharacteristic
144#1439C2211yescharacteristic
145#1439C2211yescharacteristic
146#1437C2211yescharacteristic
147#1437C2211yescharacteristic
148#1436C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167#1436C2211yescharacteristic
168C4⋊#95C2211yescharacteristic
169C4⋊#95C2211yescharacteristic
170C4⋊#95C2211yescharacteristic
171C4⋊#95C2211yescharacteristic
172C4⋊#95C2211yescharacteristic
173C4⋊#95C2211yescharacteristic
174C4⋊#95C2211yescharacteristic
175C4⋊#95C2211yescharacteristic
176C4⋊#95C2211yescharacteristic
177C4⋊#95C2211yescharacteristic
178#1434C2211yescharacteristic
179#1434C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C22⋊#95C2211yescharacteristic
185C22⋊#95C2211yescharacteristic
186C22⋊#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C4×#95C2211yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192C23×Q8C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2311yescharacteristic
195C24×C4C2311yescharacteristic
196C2×C4⋊Q8—24no—
197C2×C4⋊Q8—24no—
198C2×C4⋊Q8—24no—
199C2×C4⋊Q8—42no—
200C2×C4⋊Q8—42no—
201C2×C4⋊Q8—42no—
202C2×C22⋊Q8—24no—
203C2×C22⋊Q8—24no—
204C2×C22⋊Q8—24no—
205C2×C22⋊Q8—42no—
206C2×C22⋊Q8—42no—
207C2×C22⋊Q8—42no—
208C2×C4×Q8—24no—
209C2×C4×Q8—42no—
210C2×C4×Q8—42no—
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2311yescharacteristic
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2311yescharacteristic
253C22×C22⋊C4C2311yescharacteristic
254C22×C22⋊C4C2311yescharacteristic
255C22×C22⋊C4C2311yescharacteristic
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269#400—24no—
270#398—24no—
271#398—24no—
272#396—24no—
273#396—24no—
274#395—24no—
275#395—24no—
276#395—24no—
277#395—42no—
278#395—42no—
279#395—42no—
280#395—42no—
281#393—24no—
282#393—24no—
283#391—24no—
284#391—24no—
285#391—42no—
286#391—42no—
287#391—42no—
288#389—24no—
289#389—24no—
290#389—42no—
291#389—42no—
292#389—42no—
293#388—24no—
294#388—24no—
295#388D418yes—
296#388Q818yescomplemented
297#387—24no—
298#387—24no—
299#387—24no—
300#387—24no—
301#385—24no—
302#385—24no—
303#385—24no—
304#385—42no—
305#385—42no—
306#385Q818yescomplemented
307#380—42no—
308C4×C4⋊C4—42no—
309C4×C22⋊C4—24no—
310C4×C22⋊C4—42no—
311C2×#95—42no—
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2311yescharacteristic
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2311yescharacteristic
384C2×#95C2311yescharacteristic
385C2×#95C2311yescharacteristic
386C2×#95C2311yescharacteristic
387C2×#95C2311yescharacteristic
388C2×#95C2311yescharacteristic
389C2×#95C2311yescharacteristic
390C2×#95C2311yescharacteristic
391C2×#95C2311yescharacteristic
392C2×#95C2311yescharacteristic
393C2×#95C2311yescharacteristic
394C2×#95C2311yescharacteristic
395C2×#95C2311yescharacteristic
396C2×#95C2311yescharacteristic
397C2×#95C2311yescharacteristic
398C2×#95C2311yescharacteristic
399C2×#95C2311yescharacteristic
400C2×#95C2311yescharacteristic
401C2×#95C2311yescharacteristic
402C25C2411yescharacteristic
403C22×Q8—22no—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—22no—
414C22×Q8—41no—
415C22×Q8—41no—
416C22×Q8—41no—
417C22×Q8—41no—
418C22×Q8—41no—
419C22×Q8—41no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8—41no—
423C22×Q8—41no—
424C22×Q8—41no—
425C22×Q8—41no—
426C22×Q8—41no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8—41no—
430C22×Q8#4114yes—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—41no—
437C23×C4—41no—
438C23×C4—41no—
439C23×C4—41no—
440C23×C4—41no—
441C23×C4—41no—
442C23×C4—41no—
443C23×C4—41no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4—41no—
448C23×C4—41no—
449C23×C4—41no—
450C23×C4—41no—
451C23×C4C2×Q814yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C4⋊Q8—416no—
483C4⋊Q8—416no—
484C22⋊Q8—416no—
485C22⋊Q8—416no—
486C4×Q8—416no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4C2×D414yes—
592C2×C4⋊C4C2×Q814yes—
593C2×C4⋊C4C2×Q814yes—
594C2×C4⋊C4C2×Q814yes—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4C2×D414yes—
624C2×C22⋊C4C2×D414yes—
625C2×C22⋊C4C2×D414yes—
626C2×C22⋊C4C2×Q814yes—
627C2×C22⋊C4C2×Q814yes—
628C2×C22⋊C4C2×Q814yes—
629C2×C22⋊C4C2×Q814yes—
630C2×C22⋊C4C2×Q814yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—41no—
641C2×C42—41no—
642C2×C42—41no—
643C2×C42—41no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42—41no—
647C2×C42—41no—
648C2×C42—41no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42—41no—
653C2×C42—41no—
654C2×C42—41no—
655C2×C42—41no—
656C2×C42—41no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42C2×D414yes—
660C2×C42C2×Q814yes—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732#95—41no—
733#95—41no—
734#95—41no—
735#95—41no—
736#95—41no—
737#95—41no—
738#95—41no—
739#95—41no—
740#95—41no—
741#95—41no—
742#95—41no—
743#95—41no—
744#95—41no—
745#95C2×D414yes—
746#95C2×D414yes—
747#95C2×Q814yes—
748#95C2×Q814yes—
749#95C2×Q814yes—
750#95C2×Q814yes—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24C22×D412yes—
764C24C22×Q812yes—
765C24C22×Q812yes—
766C24C2511yescharacteristic
767C2×Q8—28no—
768C2×Q8—28no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—82no—
782C2×Q8—82no—
783C2×Q8—82no—
784C2×Q8—82no—
785C2×Q8—82no—
786C2×Q8—82no—
787C2×Q8—82no—
788C2×Q8—82no—
789C2×Q8—82no—
790C2×Q8—82no—
791C2×Q8—82no—
792C2×Q8—82no—
793C2×Q8—82no—
794C2×Q8—82no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—82no—
987C22×C4—82no—
988C22×C4—82no—
989C22×C4—82no—
990C22×C4—82no—
991C22×C4—82no—
992C22×C4—82no—
993C22×C4—82no—
994C22×C4—82no—
995C22×C4—82no—
996C22×C4—82no—
997C22×C4—82no—
998C22×C4—82no—
999C22×C4C22×D412yes—
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D412yes—
1004C22×C4C22×D412yes—
1005C22×C4C22×Q812yes—
1006C22×C4C22×Q812yes—
1007C22×C4C22×Q812yes—
1008C22×C4C22×Q812yes—
1009C22×C4C22×Q812yes—
1010C22×C4C22×Q812yes—
1011C22×C4C22×Q812yes—
1012C22×C4C22×Q812yes—
1013C22×C4C22×Q812yes—
1014C22×C4C22×Q812yes—
1015C22×C4C22×Q812yes—
1016C22×C4C22×Q812yes—
1017C22×C4C2×#4112yes—
1018C22×C4C2×#4112yes—
1019C22×C4C2×#4112yes—
1020C22×C4H(5,𝔽2)12yes—
1021C22×C4H(5,𝔽2)12yes—
1022C22×C4H(5,𝔽2)12yes—
1023C22×C4H(5,𝔽2)12yes—
1024C22×C42−1+412yes—
1025C22×C42−1+412yes—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—82no—
1051C4⋊C4—82no—
1052C4⋊C4—82no—
1053C4⋊C4—82no—
1054C4⋊C4—82no—
1055C4⋊C4—82no—
1056C4⋊C4—82no—
1057C4⋊C4—82no—
1058C4⋊C4—82no—
1059C4⋊C4—82no—
1060C4⋊C4—82no—
1061C4⋊C4—82no—
1062C22⋊C4—28no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—82no—
1072C22⋊C4—82no—
1073C22⋊C4C4⋊Q8116yescomplemented
1074C42—44no—
1075C42—44no—
1076C42—44no—
1077C42—44no—
1078C42—44no—
1079C42—44no—
1080C42—82no—
1081C42—82no—
1082C42—82no—
1083C42—82no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23C2×C4⋊Q814yes—
1119C23C23×D411yescharacteristic
1120C23C23×Q811yescharacteristic
1121C23C23×Q811yescharacteristic
1122C23C22×#4111yescharacteristic
1123C23C2×H(5,𝔽2)11yescharacteristic
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×2−1+411yescharacteristic
1128C23C2×2−1+411yescharacteristic
1129C23#58511yescharacteristic
1130C23#58511yescharacteristic
1131C23#58511yescharacteristic
1132C23#58511yescharacteristic
1133C23#58511yescharacteristic
1134Q8—416no—
1135Q8—88no—
1136Q8—88no—
1137Q8—88no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—41no—
1342C2×C4—41no—
1343C2×C4—41no—
1344C2×C4—41no—
1345C2×C4—88no—
1346C2×C4—88no—
1347C2×C4—88no—
1348C2×C4C2×C4⋊Q814yes—
1349C2×C4C2×C4⋊Q814yes—
1350C2×C4#54614yes—
1351C22—24no—
1352C22—24no—
1353C22—24no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22C22×C4⋊Q811yescharacteristic
1367C22#345911yescharacteristic
1368C22C2×#54611yescharacteristic
1369C22Q8×#4111yescharacteristic
1370C22Q8×#4111yescharacteristic
1371C22#348411yescharacteristic
1372C22#348811yescharacteristic
1373C22#348911yescharacteristic
1374C22#348911yescharacteristic
1375C22#349011yescharacteristic
1376C22#350011yescharacteristic
1377C22#350111yescharacteristic
1378C22#350111yescharacteristic
1379C22#350111yescharacteristic
1380C22#350111yescharacteristic
1381C22#350111yescharacteristic
1382C22#350211yescharacteristic
1383C22#350311yescharacteristic
1384C22#350311yescharacteristic
1385C22#350311yescharacteristic
1386C22#350411yescharacteristic
1387C22#351611yescharacteristic
1388C22#351811yescharacteristic
1389C22#353411yescharacteristic
1390C22#353511yescharacteristic
1391C22#353711yescharacteristic
1392C22#354011yescharacteristic
1393C22#355111yescharacteristic
1394C22#355211yescharacteristic
1395C22#355411yescharacteristic
1396C22#356011yescharacteristic
1397C22#356111yescharacteristic
1398C22#356211yescharacteristic
1399C22#356511yescharacteristic
1400C22#356811yescharacteristic
1401C4—24no—
1402C4—24no—
1403C4—24no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—81no—
1423C4—81no—
1424C4—81no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C2—44no—
1432C2#3556611yescharacteristic
1433C2#3592811yescharacteristic
1434C2#3627611yescharacteristic
1435C2#3774411yescharacteristic
1436C2#3970711yescharacteristic
1437C2#3971111yescharacteristic
1438C2#4313511yescharacteristic
1439C2#4423311yescharacteristic
1440C2#4530711yescharacteristic
1441C2#4643511yescharacteristic
1442C2#4644411yescharacteristic
1443C2#4772311yescharacteristic
1444C2#4795611yescharacteristic
1445C2#4795911yescharacteristic
1446C2#5069711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #17080C2semidirect
4. #16826C2semidirect
6. #15811C2semidirect
7. #15762C2semidirect
8. #15760C2semidirect
9. #15753C2semidirect
11. #15627C2semidirect
12. #15601C2semidirect
13. #15592C2semidirect
16. #15360C2semidirect
18. #15209C2semidirect
19. #15158C2semidirect
20. #14981C2semidirect
22. #14816C2semidirect
27. #14053C2semidirect
29. #14024C2semidirect
296. #388Q8semidirect
306. #385Q8semidirect
1073. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#27292
C2×#24652
#170802
#168262
#165202
#158112
#157622
#157602
#157532
#156712
#156272
#156012
#155922
#155552
#154212
#153602
#152652
#152092
#151582
#149812
#149142
#148162
#147702
#145142
#144422
#141142
#140532
#140522
#140242
#140042
#137892