Finite Group Databasebeta

← #773913

Subgroups — #773913

Order 512.

3992 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×#2409C211yesmaximal, characteristic, complemented
5C2×#2360C211yesmaximal, characteristic, complemented
6C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7#16296C212yesmaximal, complemented
8#15623C212yesmaximal, complemented
9#15429C212yesmaximal, complemented
10#15331C212yesmaximal, complemented
11#15309C212yesmaximal, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15179C211yesmaximal, characteristic, complemented
14#15131C211yesmaximal, characteristic, complemented
15#14770C212yesmaximal, complemented
16#14753C212yesmaximal, complemented
17#14207C212yesmaximal
18#14000C211yesmaximal, characteristic, complemented
19#13976C211yesmaximal, characteristic, complemented
20#13969C211yesmaximal, characteristic, complemented
21#13906C211yesmaximal, characteristic, complemented
22#13872C211yesmaximal, characteristic, complemented
23C4×#392C211yesmaximal, characteristic
24C24×Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2538—28no—
36#2417—28no—
37#2409—28no—
38#2409—28no—
39C2×#398C2212yes—
40C2×#396C2212yes—
41C2×#396C2212yes—
42C2×#396C2212yes—
43C2×#396C2212yes—
44C2×#395C2212yes—
45C2×#395C2212yes—
46C2×#393C2212yes—
47C2×#393C2212yes—
48C2×#392C2211yescharacteristic
49#2360—28no—
50Q8×C22⋊C4—28no—
51C2×#391C2212yes—
52C2×#391C2211yescharacteristic
53C2×#391C2212yes—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#390C2212yes—
60C2×#390C2212yes—
61C2×#389C2212yes—
62C2×#389C2212yes—
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#387C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#385C2212yes—
71C2×#385C2212yes—
72C2×#385C2212yes—
73C2×#384C2211yescharacteristic
74C2×#384C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2212yes—
80C2×#380C2212yes—
81C2×#380C2211yescharacteristic
82C2×#380C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2212yes—
87C2×C4×C22⋊C4C2212yes—
88C2×C4×C22⋊C4C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2212yes—
91#1444C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2212yes—
103#1439C2212yes—
104#1439C2211yescharacteristic
105#1439C2211yescharacteristic
106#1439C2211yescharacteristic
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1439C2212yes—
112#1439C2212yes—
113#1439C2212yes—
114#1438C2211yescharacteristic
115#1438C2211yescharacteristic
116#1438C2211yescharacteristic
117#1437C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121#1436C2212yes—
122#1436C2212yes—
123C4⋊#95C2212yes—
124C4⋊#95C2211yescharacteristic
125C4⋊#95C2211yescharacteristic
126C4⋊#95C2211yescharacteristic
127C22⋊#95C2212yes—
128C4×#95C2211yescharacteristic
129C23×Q8—24no—
130C23×Q8—24no—
131C23×Q8—24no—
132C23×Q8—24no—
133C23×Q8—24no—
134C23×Q8—42no—
135C23×Q8—42no—
136C23×Q8C2311yescharacteristic
137C23×Q8C2312yes—
138C23×Q8C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2312yes—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—42no—
157C2×C22⋊Q8—42no—
158C2×C22⋊Q8D418yescomplemented
159C2×C4×Q8—24no—
160C2×C4×Q8—24no—
161C2×C4×Q8—24no—
162C2×C4×Q8—24no—
163C2×C4×Q8—42no—
164C2×C4×Q8—42no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—24no—
171C2×C4×D4—42no—
172C2×C4×D4—42no—
173C2×C4×D4—42no—
174C22×C4⋊C4—24no—
175C22×C4⋊C4—24no—
176C22×C4⋊C4—42no—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228#398—28no—
229#396—28no—
230#396—28no—
231#396—28no—
232#396—44no—
233#395—28no—
234#395—28no—
235#393—28no—
236#393—28no—
237#392Q818yescomplemented
238#391—24no—
239#391—24no—
240#391—24no—
241#391—24no—
242#391—28no—
243#391—28no—
244#391D418yescomplemented
245#391D418yescomplemented
246#390—28no—
247#390—44no—
248#389—24no—
249#389—28no—
250#389—24no—
251#389—28no—
252#387—28no—
253#386—28no—
254#386—28no—
255#386—28no—
256#386—44no—
257#385—28no—
258#385—28no—
259#385—28no—
260#384—24no—
261#384—42no—
262#380—24no—
263#380—24no—
264#380—24no—
265#380—24no—
266#380—24no—
267#380—24no—
268#380—28no—
269#380—28no—
270C4×C4⋊C4—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—28no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4—42no—
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×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C22×Q8—232no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—24no—
321C22×Q8—24no—
322C22×Q8—24no—
323C22×Q8—22no—
324C22×Q8—24no—
325C22×Q8—24no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8—416no—
335C22×Q8—416no—
336C22×Q8—416no—
337C22×Q8—416no—
338C22×Q8—416no—
339C22×Q8—416no—
340C22×Q8C2×D414yes—
341C22×Q8C2×D414yes—
342C22×Q8C2×D414yes—
343C22×Q8#4114yes—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×Q814yes—
363C22×D4C2×Q814yes—
364C22×D4C2×Q814yescomplemented
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4C2×D414yes—
399C23×C4#4114yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C22⋊Q8—232no—
421C22⋊Q8—416no—
422C22⋊Q8—416no—
423C22⋊Q8—416no—
424C4×Q8—416no—
425C4×Q8—416no—
426C4×D4—416no—
427C4×D4—416no—
428C4×D4—416no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—416no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4C2×D414yes—
494C2×C4⋊C4C2×D414yes—
495C2×C4⋊C4C2×D418yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4C2×D418yes—
559C2×C22⋊C4C2×Q814yes—
560C2×C22⋊C4C2×Q814yescomplemented
561C2×C22⋊C4C2×Q814yescomplemented
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—24no—
568C2×C42—22no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—22no—
572C2×C42—24no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42C2×D414yes—
582C2×C42C2×D414yes—
583#95—22no—
584#95—24no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—42no—
607#95—42no—
608#95—41no—
609#95—42no—
610#95—41no—
611#95—41no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95C2×D418yes—
616#95C2×D418yes—
617#95C2×D418yes—
618#95C2×D418yes—
619#95C2×Q814yescomplemented
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—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C22×D412yes—
659C24C22×Q812yes—
660C24C22×Q812yes—
661C24C22×Q812yes—
662C24C2×#4112yes—
663C24H(5,𝔽2)12yes—
664C242−1+412yes—
665C24C2511yescharacteristic
666C2×Q8—216no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—48no—
678C2×Q8—48no—
679C2×Q8—48no—
680C2×Q8—48no—
681C2×Q8—4128no—
682C2×Q8—48no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8#121116yes—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—216no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4C22×D412yes—
859C22×C4C22×D414yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D414yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D414yes—
866C22×C4C22×D414yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×Q812yes—
873C22×C4C22×Q812yes—
874C22×C4C22×Q812yes—
875C22×C4C22×Q812yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4114yes—
878C22×C4C2×#4112yes—
879C22×C4C2×#4112yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C4H(5,𝔽2)12yes—
882C22×C42−1+412yes—
883C22×C42−1+412yes—
884C4⋊C4—28no—
885C4⋊C4—216no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—84no—
902C4⋊C4—84no—
903C4⋊C4—84no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C42—28no—
929C42—28no—
930C42—48no—
931C42—48no—
932C42—44no—
933C42—44no—
934C42—84no—
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—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
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—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23D4×Q814yes—
1039C23#55414yes—
1040C23C23×D411yescharacteristic
1041C23C23×D411yescharacteristic
1042C23C23×D411yescharacteristic
1043C23C23×Q811yescharacteristic
1044C23C22×#4111yescharacteristic
1045C23C22×#4111yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23C2×2−1+411yescharacteristic
1050C23C2×2−1+411yescharacteristic
1051C23C2×2−1+411yescharacteristic
1052C23#58511yescharacteristic
1053C23#58511yescharacteristic
1054C23#58511yescharacteristic
1055Q8—232no—
1056Q8—432no—
1057Q8—416no—
1058D4—416no—
1059D4—416no—
1060D4—416no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—432no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—416no—
1151C2×C4—416no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—816no—
1195C2×C4—88no—
1196C2×C4C2×#12118yes—
1197C2×C4C2×#12114yes—
1198C2×C4#52514yes—
1199C2×C4#53814yes—
1200C2×C4D4214yes—
1201C2×C4D4214yes—
1202C2×C4#54614yes—
1203C2×C4#54614yes—
1204C2×C4D4×Q814yes—
1205C2×C4D4×Q814yes—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22C22×#12111yescharacteristic
1252C22C2×#52511yescharacteristic
1253C22C2×#53811yescharacteristic
1254C22C2×D4211yescharacteristic
1255C22C2×D4211yescharacteristic
1256C22C2×#54611yescharacteristic
1257C22C2×#54611yescharacteristic
1258C22C2×D4×Q811yescharacteristic
1259C22C2×D4×Q811yescharacteristic
1260C22C2×D4×Q811yescharacteristic
1261C22C2×#55411yescharacteristic
1262C22Q8×#4111yescharacteristic
1263C22#348811yescharacteristic
1264C22#348811yescharacteristic
1265C22#348811yescharacteristic
1266C22#348911yescharacteristic
1267C22#348911yescharacteristic
1268C22#348911yescharacteristic
1269C22#349511yescharacteristic
1270C22#349511yescharacteristic
1271C22#349711yescharacteristic
1272C22#349711yescharacteristic
1273C22#349711yescharacteristic
1274C22#350111yescharacteristic
1275C22#350111yescharacteristic
1276C22#350711yescharacteristic
1277C22#352211yescharacteristic
1278C22#352311yescharacteristic
1279C22#352411yescharacteristic
1280C22#353611yescharacteristic
1281C22#353611yescharacteristic
1282C22#353811yescharacteristic
1283C22#354011yescharacteristic
1284C22#355011yescharacteristic
1285C22#355111yescharacteristic
1286C4—28no—
1287C4—24no—
1288C4—24no—
1289C4—42no—
1290C4—42no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—44no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—82no—
1303C4—82no—
1304C4—82no—
1305C4#242418yes—
1306C2—44no—
1307C2—44no—
1308C2—82no—
1309C2C2×#242411yescharacteristic
1310C2#3583111yescharacteristic
1311C2#3583211yescharacteristic
1312C2Q8×#12111yescharacteristic
1313C2#3654411yescharacteristic
1314C2#3966611yescharacteristic
1315C2#4286211yescharacteristic
1316C2#4511311yescharacteristic
1317C2#4524411yescharacteristic
1318C2#4532511yescharacteristic
1319C2#4542211yescharacteristic
1320C2#5899811yescharacteristic
1321C2#5901611yescharacteristic
1322C2#5901611yescharacteristic
1323C2#5981711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2538C2semidirect
2. C2×#2417C2semidirect
3. C2×#2409C2semidirect
4. C2×#2409C2semidirect
5. C2×#2360C2semidirect
6. C2×Q8×C22⋊C4C2semidirect
7. #16296C2semidirect
8. #15623C2semidirect
9. #15429C2semidirect
10. #15331C2semidirect
11. #15309C2semidirect
12. #15182C2semidirect
13. #15179C2semidirect
14. #15131C2semidirect
15. #14770C2semidirect
16. #14753C2semidirect
18. #14000C2semidirect
19. #13976C2semidirect
20. #13969C2semidirect
21. #13906C2semidirect
22. #13872C2semidirect
158. C2×C22⋊Q8D4semidirect
237. #392Q8semidirect
244. #391D4semidirect
245. #391D4semidirect
364. C22×D4C2×Q8semidirect
560. C2×C22⋊C4C2×Q8semidirect
561. C2×C22⋊C4C2×Q8semidirect
619. #95C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24172
C2×#24092
C2×#23602
C2×Q8×C22⋊C42
#162962
#156232
#154292
#153312
#153092
#151822
#151792
#151312
#147702
#147532
#142072
#140002
#139762
#139692
#139062
#138722
C4×#3922