Finite Group Databasebeta

← #515951

Subgroups — #515951

Order 512.

2566 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2429C211yesmaximal, characteristic
2#14237C211yesmaximal, characteristic, complemented
3#14222C211yesmaximal, characteristic
4#14217C211yesmaximal, characteristic, complemented
5#14212C211yesmaximal, characteristic, complemented
6#14210C211yesmaximal, characteristic
7#14210C211yesmaximal, characteristic
8#14198C211yesmaximal, characteristic
9#14179C211yesmaximal, characteristic, complemented
10#14162C211yesmaximal, characteristic, complemented
11#14114C211yesmaximal, characteristic
12#14112C211yesmaximal, characteristic
13#14099C211yesmaximal, characteristic
14#14099C211yesmaximal, characteristic
15#14092C211yesmaximal, characteristic, complemented
16#14083C211yesmaximal, characteristic, complemented
17#14060C211yesmaximal, characteristic, complemented
18#14057C211yesmaximal, characteristic, complemented
19#14053C211yesmaximal, characteristic, complemented
20#14053C211yesmaximal, characteristic, complemented
21#14052C211yesmaximal, characteristic
22#14052C211yesmaximal, characteristic
23#13948C211yesmaximal, characteristic
24#13927C211yesmaximal, characteristic, complemented
25#13793C211yesmaximal, characteristic, complemented
26#13792C211yesmaximal, characteristic, complemented
27#13788C211yesmaximal, characteristic
28C4×#391C211yesmaximal, characteristic, complemented
29C4×#389C211yesmaximal, characteristic, complemented
30C4×#388C211yesmaximal, characteristic
31#13749C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2429C4116yescomplemented
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#396C2211yescharacteristic
40C2×#396C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388C2211yescharacteristic
53C2×#388C2211yescharacteristic
54C2×#388C2211yescharacteristic
55C2×#388C2211yescharacteristic
56C2×#387C2211yescharacteristic
57C2×#387C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#387C2211yescharacteristic
60C2×#387C2211yescharacteristic
61C2×#387C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C22×#95C2211yescharacteristic
79C2×C43C2211yescharacteristic
80#1446C2211yescharacteristic
81#1446C2211yescharacteristic
82#1446C2211yescharacteristic
83#1446C2211yescharacteristic
84#1445C2211yescharacteristic
85#1445C2211yescharacteristic
86#1444C2211yescharacteristic
87#1442C2211yescharacteristic
88#1442C2211yescharacteristic
89#1442C2211yescharacteristic
90#1441C2211yescharacteristic
91#1441C2211yescharacteristic
92#1441C2211yescharacteristic
93#1441C2211yescharacteristic
94#1441C2211yescharacteristic
95#1441C2211yescharacteristic
96#1441C2211yescharacteristic
97#1441C2211yescharacteristic
98#1441C2211yescharacteristic
99#1441C2211yescharacteristic
100#1441C2211yescharacteristic
101#1441C2211yescharacteristic
102#1439C2211yescharacteristic
103#1439C2211yescharacteristic
104#1439C2211yescharacteristic
105#1439C2211yescharacteristic
106#1439C2211yescharacteristic
107#1439C2211yescharacteristic
108#1437C2211yescharacteristic
109#1437C2211yescharacteristic
110#1437C2211yescharacteristic
111#1437C2211yescharacteristic
112#1436C2211yescharacteristic
113#1436C2211yescharacteristic
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116#1436C2211yescharacteristic
117#1436C2211yescharacteristic
118#1436C2211yescharacteristic
119#1436C2211yescharacteristic
120#1436C2211yescharacteristic
121#1436C2211yescharacteristic
122#1436C2211yescharacteristic
123#1436C2211yescharacteristic
124#1436C2211yescharacteristic
125#1436C2211yescharacteristic
126#1436C2211yescharacteristic
127#1436C2211yescharacteristic
128#1436C2211yescharacteristic
129#1436C2211yescharacteristic
130#1436C2211yescharacteristic
131#1436C2211yescharacteristic
132#1436C2211yescharacteristic
133#1436C2211yescharacteristic
134#1436C2211yescharacteristic
135#1436C2211yescharacteristic
136#1436C2211yescharacteristic
137#1436C2211yescharacteristic
138#1436C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
145#1436C2211yescharacteristic
146C4⋊#95C2211yescharacteristic
147C4⋊#95C2211yescharacteristic
148C4⋊#95C2211yescharacteristic
149C4⋊#95C2211yescharacteristic
150C4⋊#95C2211yescharacteristic
151C4⋊#95C2211yescharacteristic
152C4⋊#95C2211yescharacteristic
153C4⋊#95C2211yescharacteristic
154C4⋊#95C2211yescharacteristic
155C4⋊#95C2211yescharacteristic
156C4⋊#95C2211yescharacteristic
157#1434C2211yescharacteristic
158#1434C2211yescharacteristic
159#1434C2211yescharacteristic
160#1434C2211yescharacteristic
161#1434C2211yescharacteristic
162#1434C2211yescharacteristic
163#1434C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168C22⋊#95C2211yescharacteristic
169C22⋊#95C2211yescharacteristic
170C22⋊#95C2211yescharacteristic
171C22⋊#95C2211yescharacteristic
172C22⋊#95C2211yescharacteristic
173C22⋊#95C2211yescharacteristic
174C4×#95C2211yescharacteristic
175C4×#95C2211yescharacteristic
176C4×#95C2211yescharacteristic
177C4×#95C2211yescharacteristic
178C4×#95C2211yescharacteristic
179C4×#95C2211yescharacteristic
180C4×#95C2211yescharacteristic
181C4×#95C2211yescharacteristic
182C4×#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C2×C4⋊Q8—42no—
194C2×C4⋊Q8—42no—
195C2×C4⋊Q8C2×C418yescomplemented
196C2×C22⋊Q8—42no—
197C2×C22⋊Q8—42no—
198C2×C22⋊Q8—42no—
199C2×C22⋊Q8—42no—
200C2×C22⋊Q8C2×C418yes—
201C2×C22⋊Q8C2×C418yes—
202C2×C4×Q8—42no—
203C2×C4×Q8—42no—
204C2×C4×Q8C2×C418yescomplemented
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#398C2×C418yescomplemented
268#398C2×C418yescomplemented
269#396C2×C418yes—
270#396C2×C418yes—
271#391—24no—
272#391—24no—
273#391—24no—
274#391—24no—
275#391C2×C418yescomplemented
276#389—24no—
277#389—42no—
278#389—42no—
279#389C2×C418yescomplemented
280#389C2×C418yescomplemented
281#389C2×C418yescomplemented
282#388—24no—
283#388—24no—
284#388C2×C418yes—
285#388C2×C418yes—
286#387—24no—
287#387—24no—
288#387—42no—
289#387—42no—
290#387—42no—
291#387—42no—
292#385—42no—
293#385—42no—
294C4×C4⋊C4—24no—
295C4×C4⋊C4—42no—
296C4×C4⋊C4—42no—
297C4×C4⋊C4—42no—
298C4×C4⋊C4—42no—
299C4×C4⋊C4—42no—
300C4×C22⋊C4—24no—
301C4×C22⋊C4—24no—
302C4×C22⋊C4—24no—
303C4×C22⋊C4—24no—
304C4×C22⋊C4—42no—
305C4×C22⋊C4—42no—
306C4×C22⋊C4C2×C418yes—
307C4×C22⋊C4Q818yescomplemented
308C2×#95—24no—
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
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
397C43—42no—
398C25C2411yescharacteristic
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—22no—
403C22×Q8—22no—
404C22×Q8—22no—
405C22×Q8—41no—
406C22×Q8—41no—
407C22×Q8—41no—
408C22×Q8—41no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8C22×C414yes—
412C22×Q8C22×C414yes—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4C22×C414yes—
433C23×C4C2×Q814yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C4⋊Q8—416no—
465C22⋊Q8—416no—
466C22⋊Q8—416no—
467C4×Q8—416no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
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—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4C22×C414yes—
533C2×C4⋊C4C22×C414yes—
534C2×C4⋊C4C22×C414yes—
535C2×C4⋊C4C22×C414yes—
536C2×C4⋊C4C22×C414yes—
537C2×C4⋊C4C22×C414yes—
538C2×C4⋊C4C22×C414yes—
539C2×C4⋊C4C22×C414yes—
540C2×C4⋊C4C22×C414yes—
541C2×C4⋊C4C22×C414yes—
542C2×C4⋊C4C22×C414yes—
543C2×C4⋊C4C22×C414yes—
544C2×C4⋊C4C22×C414yes—
545C2×C4⋊C4C22×C414yes—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4C22×C414yes—
574C2×C22⋊C4C22×C414yes—
575C2×C22⋊C4C22×C414yes—
576C2×C22⋊C4C22×C414yes—
577C2×C22⋊C4C22×C414yes—
578C2×C22⋊C4C22×C414yes—
579C2×C22⋊C4C2×Q814yes—
580C2×C22⋊C4C2×Q814yes—
581C2×C22⋊C4#4114yes—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—41no—
622C2×C42—41no—
623C2×C42—41no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42—41no—
639C2×C42—41no—
640C2×C42—41no—
641C2×C42—41no—
642C2×C42—41no—
643C2×C42—41no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42—41no—
647C2×C42C22×C414yes—
648C2×C42C22×C414yes—
649C2×C42C22×C414yes—
650C2×C42C22×C414yes—
651C2×C42C2×Q814yes—
652C2×C42C2×Q814yes—
653C2×C42#4114yes—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
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—22no—
694#95—22no—
695#95—22no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
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#95C22×C414yes—
730#95C22×C414yes—
731#95C22×C414yes—
732#95C22×C414yes—
733#95C22×C414yes—
734#95C22×C414yes—
735#95C22×C414yes—
736#95C22×C414yes—
737#95C2×Q814yes—
738#95C2×Q814yes—
739#95#4114yes—
740#95#4114yes—
741#95#4114yes—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24C23×C412yes—
755C24C22×Q812yes—
756C24C2×#4112yes—
757C24C2511yescharacteristic
758C2×Q8—28no—
759C2×Q8—28no—
760C2×Q8—28no—
761C2×Q8—44no—
762C2×Q8—44no—
763C2×Q8—44no—
764C2×Q8—44no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—82no—
769C2×Q8—82no—
770C2×Q8—82no—
771C2×Q8—82no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
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—28no—
901C22×C4—28no—
902C22×C4—28no—
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—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—82no—
950C22×C4—82no—
951C22×C4—82no—
952C22×C4—82no—
953C22×C4—82no—
954C22×C4—82no—
955C22×C4—82no—
956C22×C4—82no—
957C22×C4—82no—
958C22×C4—82no—
959C22×C4—82no—
960C22×C4—82no—
961C22×C4—82no—
962C22×C4—82no—
963C22×C4C23×C412yes—
964C22×C4C23×C412yes—
965C22×C4C23×C412yes—
966C22×C4C23×C412yes—
967C22×C4C23×C412yes—
968C22×C4C23×C412yes—
969C22×C4C23×C412yes—
970C22×C4C23×C412yes—
971C22×C4C23×C412yes—
972C22×C4C23×C412yes—
973C22×C4C23×C412yes—
974C22×C4C23×C412yes—
975C22×C4C23×C412yes—
976C22×C4C23×C412yes—
977C22×C4C22×Q812yes—
978C22×C4C22×Q812yes—
979C22×C4C22×Q812yes—
980C22×C4C22×Q812yes—
981C22×C4C22×Q812yes—
982C22×C4C22×Q812yes—
983C22×C4C2×#4112yes—
984C22×C4C2×#4112yes—
985C22×C4C2×#4112yes—
986C22×C4C2×#4112yes—
987C22×C4C2×#4112yes—
988C22×C4C2×#4112yes—
989C22×C4C2×#4112yes—
990C22×C4C2×#4112yes—
991C22×C4C2×#4112yes—
992C22×C4C2×#4112yes—
993C22×C4C2×#4112yes—
994C22×C4C2×#4112yes—
995C22×C4C2×#4112yes—
996C22×C4C2×#4112yes—
997C22×C4H(5,𝔽2)12yes—
998C22×C4H(5,𝔽2)12yes—
999C22×C4H(5,𝔽2)12yes—
1000C22×C4H(5,𝔽2)12yes—
1001C22×C42−1+412yes—
1002C22×C42−1+412yes—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—82no—
1025C4⋊C4—82no—
1026C4⋊C4—82no—
1027C4⋊C4—82no—
1028C4⋊C4—82no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—82no—
1039C22⋊C4—82no—
1040C22⋊C4C4×Q8116yes—
1041C42—28no—
1042C42—28no—
1043C42—44no—
1044C42—44no—
1045C42—44no—
1046C42—44no—
1047C42—44no—
1048C42—44no—
1049C42—44no—
1050C42—44no—
1051C42—44no—
1052C42—44no—
1053C42—44no—
1054C42—82no—
1055C42—82no—
1056C42—82no—
1057C42—82no—
1058C42—82no—
1059C42—82no—
1060C42—82no—
1061C42—82no—
1062C42—82no—
1063C42—82no—
1064C42—82no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23C2×C4×Q814yes—
1100C23C24×C411yescharacteristic
1101C23C23×Q811yescharacteristic
1102C23C22×#4111yescharacteristic
1103C23C22×#4111yescharacteristic
1104C23C22×#4111yescharacteristic
1105C23C22×#4111yescharacteristic
1106C23C22×#4111yescharacteristic
1107C23C2×H(5,𝔽2)11yescharacteristic
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×2−1+411yescharacteristic
1112C23C2×2−1+411yescharacteristic
1113C23#58511yescharacteristic
1114C23#58511yescharacteristic
1115Q8—416no—
1116Q8—88no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
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—22no—
1211C2×C4—22no—
1212C2×C4—22no—
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—88no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4C2×C4×Q814yes—
1323C2×C4C2×C4×Q814yes—
1324C2×C4C4×#4114yes—
1325C2×C4C4×#4114yes—
1326C2×C4#51814yes—
1327C2×C4#51814yes—
1328C2×C4#53314yes—
1329C2×C4#53314yes—
1330C22—24no—
1331C22—24no—
1332C22—24no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22C22×C4×Q811yescharacteristic
1346C22C2×C4×#4111yescharacteristic
1347C22C2×C4×#4111yescharacteristic
1348C22C2×#51811yescharacteristic
1349C22C2×#51811yescharacteristic
1350C22C4×2−1+411yescharacteristic
1351C22C4×2−1+411yescharacteristic
1352C22C2×#53311yescharacteristic
1353C22C2×#53311yescharacteristic
1354C22#344411yescharacteristic
1355C22#344411yescharacteristic
1356C22#349211yescharacteristic
1357C22#349411yescharacteristic
1358C22#350111yescharacteristic
1359C22#350111yescharacteristic
1360C22#350311yescharacteristic
1361C22#350311yescharacteristic
1362C22#350511yescharacteristic
1363C22#351111yescharacteristic
1364C22#351311yescharacteristic
1365C22#351411yescharacteristic
1366C22#351411yescharacteristic
1367C22#351411yescharacteristic
1368C22#351511yescharacteristic
1369C22#351611yescharacteristic
1370C22#351911yescharacteristic
1371C22#351911yescharacteristic
1372C22#351911yescharacteristic
1373C22#351911yescharacteristic
1374C22#352011yescharacteristic
1375C22#352011yescharacteristic
1376C22#352011yescharacteristic
1377C22#352111yescharacteristic
1378C22#352211yescharacteristic
1379C22#352311yescharacteristic
1380C4—24no—
1381C4—24no—
1382C4—24no—
1383C4—24no—
1384C4—24no—
1385C4—24no—
1386C4—24no—
1387C4—24no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C2—44no—
1411C2C4×#53311yescharacteristic
1412C2#3424611yescharacteristic
1413C2#3428611yescharacteristic
1414C2#3429811yescharacteristic
1415C2#3432711yescharacteristic
1416C2#3433411yescharacteristic
1417C2#3433411yescharacteristic
1418C2#3540011yescharacteristic
1419C2#3540211yescharacteristic
1420C2#3541311yescharacteristic
1421C2#3542411yescharacteristic
1422C2#3547511yescharacteristic
1423C2#3547811yescharacteristic
1424C2#3557811yescharacteristic
1425C2#3558111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14237C2semidirect
4. #14217C2semidirect
5. #14212C2semidirect
9. #14179C2semidirect
10. #14162C2semidirect
15. #14092C2semidirect
16. #14083C2semidirect
17. #14060C2semidirect
18. #14057C2semidirect
19. #14053C2semidirect
20. #14053C2semidirect
24. #13927C2semidirect
25. #13793C2semidirect
26. #13792C2semidirect
28. C4×#391C2semidirect
29. C4×#389C2semidirect
36. #2429C4semidirect
195. C2×C4⋊Q8C2×C4semidirect
204. C2×C4×Q8C2×C4semidirect
267. #398C2×C4semidirect
268. #398C2×C4semidirect
275. #391C2×C4semidirect
279. #389C2×C4semidirect
280. #389C2×C4semidirect
281. #389C2×C4semidirect
307. C4×C22⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24292
#142372
#142222
#142172
#142122
#142102
#141982
#141792
#141622
#141142
#141122
#140992
#140922
#140832
#140602
#140572
#140532
#140522
#139482
#139272
#137932
#137922
#137882
C4×#3912
C4×#3892
C4×#3882
#137492