Finite Group Databasebeta

← #535967

Subgroups — #535967

Order 512.

3834 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#2317C211yesmaximal, characteristic, complemented
6#14549C212yesmaximal, complemented
7#14548C212yesmaximal, complemented
8#14535C212yesmaximal, complemented
9#14526C212yesmaximal, complemented
10#14204C212yesmaximal, complemented
11#14185C212yesmaximal, complemented
12#14176C212yesmaximal, complemented
13#14171C212yesmaximal
14#13909C211yesmaximal, characteristic, complemented
15#13905C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13876C211yesmaximal, characteristic, complemented
19#13875C211yesmaximal, characteristic, complemented
20#13872C211yesmaximal, characteristic, complemented
21#13871C211yesmaximal, characteristic, complemented
22C4⋊C42C211yesmaximal, characteristic, complemented
23#13777C211yesmaximal, characteristic, complemented
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2212yes—
28C22×C4×D4C2212yes—
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2392C4116yescomplemented
35C2×#398C2211yescharacteristic
36C2×#397C2211yescharacteristic
37C2×#396C2211yescharacteristic
38C2×#396C2211yescharacteristic
39C2×#394C2211yescharacteristic
40C2×#394C2211yescharacteristic
41C2×#394C2211yescharacteristic
42C2×#392C2211yescharacteristic
43#2352—28no—
44D4×C4⋊C4—28no—
45D4×C4⋊C4—28no—
46#2317—28no—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#387C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×#385C2212yes—
59C2×#385C2212yes—
60C2×#385C2212yes—
61C2×#385C2212yes—
62C2×#385C2212yes—
63C2×#385C2212yes—
64C2×#384C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C2×#384C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#382C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87#1445C2212yes—
88#1444C2212yes—
89#1444C2212yes—
90#1443C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1440C2212yes—
98#1440C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123C4⋊#95C2212yes—
124#1434C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—28no—
142C2×C4×D4—28no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—44no—
146C2×C4×D4—44no—
147C2×C4×D4—44no—
148C2×C4×D4—44no—
149C2×C4×D4C2×C418yescomplemented
150C2×C4×D4C2×C418yescomplemented
151C2×C4×D4C2×C418yescomplemented
152C2×#117—24no—
153C2×#117—24no—
154C2×#117—24no—
155C2×#117—24no—
156C2×#117—42no—
157C2×#117C2×C418yescomplemented
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—42no—
165C22×C4⋊C4—42no—
166C22×C4⋊C4—42no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221#398C2×C418yescomplemented
222#397C2×C418yescomplemented
223#396C2×C418yescomplemented
224#396C2×C418yescomplemented
225#394C2×C418yescomplemented
226#394C2×C418yescomplemented
227#394C2×C418yescomplemented
228#392C2×C418yes—
229#389—28no—
230#389—28no—
231#389—28no—
232#389—28no—
233#388—28no—
234#388—44no—
235#387—28no—
236#386—28no—
237#386—44no—
238#385—28no—
239#385—28no—
240#385—28no—
241#385—28no—
242#385—28no—
243#385—28no—
244#385—44no—
245#385—44no—
246#384—24no—
247#384—24no—
248#384D418yescomplemented
249#382—24no—
250#382—24no—
251#382—24no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—24no—
256#380—24no—
257#380—42no—
258#380—42no—
259#380D418yescomplemented
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4—24no—
264C4×C4⋊C4—44no—
265C4×C4⋊C4C2×C418yescomplemented
266C4×C22⋊C4—28no—
267C4×C22⋊C4C2×C418yescomplemented
268C4×C22⋊C4C2×C418yescomplemented
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C25C2411yescharacteristic
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4C22×C414yes—
327C22×D4C22×C414yes—
328C22×D4C22×C414yes—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C2×D414yes—
370C23×C4#4114yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C4×D4—232no—
392C4×D4—232no—
393C4×D4—232no—
394C4×D4—432no—
395C4×D4—432no—
396#117—232no—
397#117—416no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—416no—
442C2×C4⋊C4—416no—
443C2×C4⋊C4—416no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4C22×C414yes—
461C2×C4⋊C4C22×C414yes—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C414yes—
465C2×C4⋊C4C22×C414yes—
466C2×C4⋊C4C22×C414yes—
467C2×C4⋊C4C2×D414yes—
468C2×C4⋊C4C2×D414yes—
469C2×C4⋊C4C2×D414yes—
470C2×C4⋊C4C2×D414yes—
471C2×C4⋊C4C2×D418yes—
472C2×C4⋊C4C2×D418yes—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4C22×C414yes—
524C2×C22⋊C4C22×C414yes—
525C2×C22⋊C4C22×C414yes—
526C2×C22⋊C4C22×C414yes—
527C2×C22⋊C4C22×C414yes—
528C2×C22⋊C4C22×C414yes—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C22×C414yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C2×D418yes—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—42no—
553C2×C42—42no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42C22×C414yes—
558C2×C42C22×C414yes—
559C2×C42C22×C414yes—
560C2×C42C22×C414yes—
561C2×C42C2×D414yes—
562C2×C42#4114yes—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95C22×C414yes—
593#95C22×C414yes—
594#95C22×C414yes—
595#95C22×C414yes—
596#95C22×C414yes—
597#95C22×C414yes—
598#95C2×D418yes—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24C23×C412yes—
636C24C23×C412yes—
637C24C23×C412yes—
638C24C22×D412yes—
639C24C2×#4112yes—
640C24H(5,𝔽2)12yes—
641C24H(5,𝔽2)12yes—
642C242−1+412yes—
643C242−1+412yes—
644C24C2511yescharacteristic
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—84no—
805C22×C4—84no—
806C22×C4—84no—
807C22×C4—84no—
808C22×C4—84no—
809C22×C4—84no—
810C22×C4—84no—
811C22×C4—84no—
812C22×C4—84no—
813C22×C4—84no—
814C22×C4—84no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4C4×D4116yescomplemented
818C22×C4C23×C412yes—
819C22×C4C23×C412yes—
820C22×C4C23×C412yes—
821C22×C4C23×C412yes—
822C22×C4C23×C412yes—
823C22×C4C23×C412yes—
824C22×C4C23×C412yes—
825C22×C4C23×C412yes—
826C22×C4C23×C412yes—
827C22×C4C23×C412yes—
828C22×C4C23×C412yes—
829C22×C4C23×C412yes—
830C22×C4C22×D414yes—
831C22×C4C22×D414yes—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D412yes—
835C22×C4C22×D412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C2×#4112yes—
840C22×C4C2×#4112yes—
841C22×C4C2×#4112yes—
842C22×C4C2×#4112yes—
843C22×C4C2×#4112yes—
844C22×C4H(5,𝔽2)12yes—
845C22×C4H(5,𝔽2)12yes—
846C22×C42−1+412yes—
847C22×C42−1+412yes—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—84no—
870C4⋊C4—84no—
871C4⋊C4—84no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—84no—
893C42—28no—
894C42—28no—
895C42—28no—
896C42—48no—
897C42—48no—
898C42—48no—
899C42—48no—
900C42—84no—
901C42C4×D4116yescomplemented
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23C2×C4×D414yes—
1005C23#52014yes—
1006C23#52014yes—
1007C23C24×C411yescharacteristic
1008C23C23×D411yescharacteristic
1009C23C23×D411yescharacteristic
1010C23C22×#4111yescharacteristic
1011C23C22×#4111yescharacteristic
1012C23C2×H(5,𝔽2)11yescharacteristic
1013C23C2×H(5,𝔽2)11yescharacteristic
1014C23C2×H(5,𝔽2)11yescharacteristic
1015C23C2×H(5,𝔽2)11yescharacteristic
1016C23C2×2−1+411yescharacteristic
1017C23C2×2−1+411yescharacteristic
1018C23C2×2−1+411yescharacteristic
1019C23C2×2−1+411yescharacteristic
1020C23#58511yescharacteristic
1021C23#58511yescharacteristic
1022D4—232no—
1023D4—232no—
1024D4—416no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—232no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—41no—
1094C2×C4—42no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—416no—
1128C2×C4—416no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—816no—
1158C2×C4—816no—
1159C2×C4—816no—
1160C2×C4C2×C4×D414yes—
1161C2×C4C2×C4×D414yes—
1162C2×C4C2×C4×D414yes—
1163C2×C4C2×C4×D414yes—
1164C2×C4C2×C4×D414yes—
1165C2×C4#52014yes—
1166C2×C4#52014yes—
1167C2×C4D4214yes—
1168C2×C4#54714yes—
1169C2×C4#54814yes—
1170C2×C4#55314yes—
1171C22—24no—
1172C22—24no—
1173C22—24no—
1174C22—24no—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22C22×C4×D411yescharacteristic
1217C22C22×C4×D411yescharacteristic
1218C22C2×#52011yescharacteristic
1219C22C2×#52011yescharacteristic
1220C22C2×#52011yescharacteristic
1221C22C2×#52011yescharacteristic
1222C22#342811yescharacteristic
1223C22C2×D4211yescharacteristic
1224C22C2×#54711yescharacteristic
1225C22C2×#54811yescharacteristic
1226C22C2×#55311yescharacteristic
1227C22#348411yescharacteristic
1228C22#348411yescharacteristic
1229C22#348611yescharacteristic
1230C22#348611yescharacteristic
1231C22#348811yescharacteristic
1232C22#348911yescharacteristic
1233C22#349211yescharacteristic
1234C22#349211yescharacteristic
1235C22#349211yescharacteristic
1236C22#349211yescharacteristic
1237C22#349411yescharacteristic
1238C22#349511yescharacteristic
1239C22#349611yescharacteristic
1240C22#349711yescharacteristic
1241C22#350611yescharacteristic
1242C22#350711yescharacteristic
1243C22#354311yescharacteristic
1244C22#354411yescharacteristic
1245C22#355211yescharacteristic
1246C22#355211yescharacteristic
1247C22#355811yescharacteristic
1248C22#355911yescharacteristic
1249C22#356111yescharacteristic
1250C22#356311yescharacteristic
1251C4—24no—
1252C4—24no—
1253C4—24no—
1254C4—24no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—44no—
1266C4—82no—
1267C4—82no—
1268C4—82no—
1269C4—82no—
1270C4#236118yes—
1271C2—44no—
1272C2—44no—
1273C2—44no—
1274C2C2×#236111yescharacteristic
1275C2#3420011yescharacteristic
1276C2#3420011yescharacteristic
1277C2#3420211yescharacteristic
1278C2#3420611yescharacteristic
1279C2#3438211yescharacteristic
1280C2#3438411yescharacteristic
1281C2#4487711yescharacteristic
1282C2#4487811yescharacteristic
1283C2#4492111yescharacteristic
1284C2#4492211yescharacteristic
1285C2#4510911yescharacteristic
1286C2#4512011yescharacteristic
1287C2#4524811yescharacteristic
1288C2#4525511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2352C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C2×#2317C2semidirect
6. #14549C2semidirect
7. #14548C2semidirect
8. #14535C2semidirect
9. #14526C2semidirect
10. #14204C2semidirect
11. #14185C2semidirect
12. #14176C2semidirect
14. #13909C2semidirect
15. #13905C2semidirect
16. #13881C2semidirect
17. #13880C2semidirect
18. #13876C2semidirect
19. #13875C2semidirect
20. #13872C2semidirect
21. #13871C2semidirect
22. C4⋊C42C2semidirect
23. #13777C2semidirect
34. #2392C4semidirect
149. C2×C4×D4C2×C4semidirect
150. C2×C4×D4C2×C4semidirect
151. C2×C4×D4C2×C4semidirect
157. C2×#117C2×C4semidirect
221. #398C2×C4semidirect
222. #397C2×C4semidirect
223. #396C2×C4semidirect
224. #396C2×C4semidirect
225. #394C2×C4semidirect
226. #394C2×C4semidirect
227. #394C2×C4semidirect
248. #384D4semidirect
259. #380D4semidirect
265. C4×C4⋊C4C2×C4semidirect
267. C4×C22⋊C4C2×C4semidirect
268. C4×C22⋊C4C2×C4semidirect
817. C22×C4C4×D4semidirect
901. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23922
C2×#23522
C2×D4×C4⋊C42
C2×#23172
#145492
#145482
#145352
#145262
#142042
#141852
#141762
#141712
#139092
#139052
#138812
#138802
#138762
#138752
#138722
#138712
C4⋊C422
#137772