Finite Group Databasebeta

← #617427

Subgroups — #617427

Order 512.

5117 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2472C211yesmaximal, characteristic, complemented
3C2×#2626C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#15577C212yesmaximal, complemented
6#15468C212yesmaximal, complemented
7#15419C212yesmaximal, complemented
8#15370C212yesmaximal, complemented
9#15345C212yesmaximal, complemented
10#15314C212yesmaximal, complemented
11#15301C212yesmaximal, complemented
12#15272C212yesmaximal, complemented
13#14921C211yesmaximal, characteristic, complemented
14#14914C211yesmaximal, characteristic, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14693C211yesmaximal, characteristic, complemented
18#14259C211yesmaximal, characteristic, complemented
19#14255C211yesmaximal, characteristic, complemented
20#13995C211yesmaximal, characteristic, complemented
21#13991C211yesmaximal, characteristic, complemented
22#13873C211yesmaximal, characteristic, complemented
23#13782C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#124C2211yescharacteristic, complemented
27C22×#123C2212yescomplemented
28C22×C22⋊Q8C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2849—28no—
35#2626—28no—
36#2472—28no—
37C2×#399C2212yescomplemented
38C2×#397C2211yescharacteristic, complemented
39C2×#396C2212yescomplemented
40C2×#396C2212yescomplemented
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2211yescharacteristic, complemented
44C2×#394C2211yescharacteristic, complemented
45C2×#393C2211yescharacteristic, complemented
46C2×#393C2212yescomplemented
47C2×#392C2212yes—
48C2×#392C2212yes—
49C2×#390C2211yescharacteristic, complemented
50C2×#390C2212yescomplemented
51C2×#388C2211yescharacteristic, complemented
52C2×#388C2211yescharacteristic, complemented
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#386—28no—
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yescomplemented
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2212yescomplemented
72C2×#385C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#381C2212yescomplemented
75C2×#380C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C22×#95C2211yescharacteristic
85C22×#95C2211yescharacteristic
86#1446C2212yescomplemented
87#1444C2212yescomplemented
88#1443C2212yescomplemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117C4⋊#95C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C24×C4—24no—
142C24×C4—24no—
143C24×C4—44no—
144C24×C4—42no—
145C24×C4—44no—
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×#124—24no—
154C2×#124—44no—
155C2×#123—28no—
156C2×#123—44no—
157C2×#123—44no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—42no—
161C2×#120—24no—
162C2×#120—24no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—42no—
166C2×#120—42no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4D418yescomplemented
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225#399—28no—
226#397—24no—
227#396—28no—
228#396—28no—
229#394—24no—
230#394—24no—
231#394—44no—
232#394—44no—
233#393—24no—
234#393—28no—
235#392—44no—
236#392—44no—
237#390—24no—
238#390—44no—
239#388—24no—
240#388—24no—
241#388—44no—
242#388—44no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—24no—
247#386—24no—
248#386—28no—
249#386—28no—
250#386—28no—
251#386—28no—
252#386—28no—
253#385—24no—
254#385—24no—
255#385—28no—
256#385—24no—
257#385—44no—
258#385—42no—
259#385—44no—
260#385D418yescomplemented
261#381—28no—
262#380—24no—
263#379—24no—
264#379—24no—
265#379—24no—
266#379—24no—
267#379—24no—
268#379—24no—
269C4×C22⋊C4—24no—
270C4×C22⋊C4—24no—
271C2×#95—24no—
272C2×#95—24no—
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2×D414yes—
326C25#4114yes—
327C25C2411yescharacteristic
328C25C2412yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—41no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×D4—232no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—41no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—432no—
377C22×D4—432no—
378C22×D4—416no—
379C22×D4—416no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—416no—
416C23×C4—416no—
417C23×C4—432no—
418C23×C4—416no—
419C23×C4—432no—
420C23×C4C2×D414yes—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4#4114yes—
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442#124—416no—
443#123—432no—
444C22⋊Q8—416no—
445#120—416no—
446#120—416no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
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—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4C2×D418yescomplemented
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
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—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
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—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—416no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—416no—
558C2×C22⋊C4—416no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4C2×D414yes—
578C2×C22⋊C4C2×D414yes—
579C2×C22⋊C4C2×D414yes—
580C2×C22⋊C4C2×D414yes—
581C2×C22⋊C4#4114yes—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—24no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95C2×D418yescomplemented
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—216no—
626C24—216no—
627C24—28no—
628C24—28no—
629C24—28no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—28no—
666C24—28no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—44no—
679C24—44no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—48no—
696C24—44no—
697C24—48no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C2×#4114yes—
719C24C2×#4112yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24H(5,𝔽2)14yes—
723C24H(5,𝔽2)14yes—
724C24H(5,𝔽2)12yes—
725C242−1+412yes—
726C24C2511yescharacteristic
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—82no—
730C2×Q8—84no—
731C2×Q8—84no—
732C2×D4—216no—
733C2×D4—216no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—4128no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—48no—
898C22×C4—4128no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—44no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D414yes—
912C22×C4C22×D414yes—
913C22×C4C22×D412yes—
914C22×C4C2×#4114yes—
915C22×C4C2×#4114yes—
916C22×C4H(5,𝔽2)14yes—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—84no—
923C4⋊C4—84no—
924C4⋊C4—84no—
925C4⋊C4—84no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—84no—
956C22⋊C4—82no—
957C22⋊C4—84no—
958C22⋊C4—82no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C22⋊C4—82no—
963C22⋊C4—82no—
964C22⋊C4—84no—
965C42—44no—
966C42—82no—
967C42—84no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—232no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—416no—
1017C23—416no—
1018C23—416no—
1019C23—416no—
1020C23—432no—
1021C23—432no—
1022C23—432no—
1023C23—416no—
1024C23—432no—
1025C23—416no—
1026C23—416no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—416no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—416no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—42no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—42no—
1088C23—41no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—816no—
1101C23—816no—
1102C23—88no—
1103C23—88no—
1104C23—816no—
1105C23—88no—
1106C23—88no—
1107C23—816no—
1108C23#52514yes—
1109C23#53214yes—
1110C23#53414yes—
1111C23#53514yes—
1112C23#54214yes—
1113C23D4214yes—
1114C23#54714yes—
1115C23#54814yes—
1116C23#55114yes—
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C22×#4111yescharacteristic
1121C23C22×#4111yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23C2×H(5,𝔽2)12yes—
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)12yes—
1126C23C2×2−1+411yescharacteristic
1127C23#58512yes—
1128Q8—88no—
1129D4—432no—
1130D4—432no—
1131D4—88no—
1132D4—88no—
1133D4—816no—
1134D4—88no—
1135C2×C4—24no—
1136C2×C4—24no—
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—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—416no—
1167C2×C4—416no—
1168C2×C4—432no—
1169C2×C4—416no—
1170C2×C4—432no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C22—24no—
1249C22—24no—
1250C22—28no—
1251C22—28no—
1252C22—28no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—28no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—464no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—42no—
1270C22—42no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—832no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—82no—
1300C22—81no—
1301C22—82no—
1302C22—82no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—82no—
1307C22—81no—
1308C22#246118yes—
1309C22C2×#52511yescharacteristic
1310C22C2×#53211yescharacteristic
1311C22C2×#53411yescharacteristic
1312C22C2×#53511yescharacteristic
1313C22C2×#54211yescharacteristic
1314C22#345912yes—
1315C22C2×D4211yescharacteristic
1316C22C2×#54711yescharacteristic
1317C22C2×#54811yescharacteristic
1318C22C2×#55111yescharacteristic
1319C22#348412yes—
1320C22#348411yescharacteristic
1321C22#348511yescharacteristic
1322C22#348812yes—
1323C22#349012yes—
1324C22#349012yes—
1325C22#350612yes—
1326C22#351312yes—
1327C22#351912yes—
1328C22#353212yes—
1329C22#353412yes—
1330C22#353512yes—
1331C22#353612yes—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—81no—
1344C4—81no—
1345C4—82no—
1346C4—81no—
1347C4—82no—
1348C4—81no—
1349C4—81no—
1350C2—28no—
1351C2—44no—
1352C2—44no—
1353C2—84no—
1354C2—161no—
1355C2C2×#246111yescharacteristic
1356C2#3498611yescharacteristic
1357C2#3505011yescharacteristic
1358C2#3539212yes—
1359C2#3679312yes—
1360C2#3764511yescharacteristic
1361C2#3764611yescharacteristic
1362C2#3775212yes—
1363C2#3803611yescharacteristic
1364C2#3803911yescharacteristic
1365C2#3903612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2849C2semidirect
2. C2×#2472C2semidirect
3. C2×#2626C2semidirect
4. C22×#386C2semidirect
5. #15577C2semidirect
6. #15468C2semidirect
7. #15419C2semidirect
8. #15370C2semidirect
9. #15345C2semidirect
10. #15314C2semidirect
11. #15301C2semidirect
12. #15272C2semidirect
13. #14921C2semidirect
14. #14914C2semidirect
15. #14724C2semidirect
17. #14693C2semidirect
18. #14259C2semidirect
19. #14255C2semidirect
20. #13995C2semidirect
21. #13991C2semidirect
22. #13873C2semidirect
23. #13782C2semidirect
26. C22×#124C22semidirect
27. C22×#123C22semidirect
37. C2×#399C22semidirect
38. C2×#397C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
45. C2×#393C22semidirect
46. C2×#393C22semidirect
49. C2×#390C22semidirect
50. C2×#390C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
65. C2×#386C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
74. C2×#381C22semidirect
86. #1446C22semidirect
87. #1444C22semidirect
88. #1443C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. C4⋊#95C22semidirect
118. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
182. C22×C22⋊C4D4semidirect
260. #385D4semidirect
473. C2×C4⋊C4C2×D4semidirect
620. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#24722
C2×#26262
C22×#3862
#155772
#154682
#154192
#153702
#153452
#153142
#153012
#152722
#149212
#149142
#147242
#147152
#146932
#142592
#142552
#139952
#139912
#138732
#137822