Finite Group Databasebeta

← #617007

Subgroups — #617007

Order 512.

4510 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×#2437C211yesmaximal, characteristic, complemented
3C2×#2308C211yesmaximal, characteristic
4C22×#390C211yesmaximal, characteristic
5#15962C212yesmaximal, complemented
6#15358C212yesmaximal, complemented
7#15355C212yesmaximal, complemented
8#15335C212yesmaximal, complemented
9#15334C212yesmaximal, complemented
10#15331C212yesmaximal, complemented
11#15309C212yesmaximal, complemented
12#15280C212yesmaximal, complemented
13#14734C211yesmaximal, characteristic, complemented
14#14726C211yesmaximal, characteristic, complemented
15#14726C211yesmaximal, characteristic, complemented
16#14717C211yesmaximal, characteristic, complemented
17#14705C211yesmaximal, characteristic, complemented
18#14339C211yesmaximal, characteristic, complemented
19#14335C211yesmaximal, characteristic
20#14263C211yesmaximal, characteristic, complemented
21#14127C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13877C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2855—28no—
36#2437—28no—
37C2×#399C2211yescharacteristic, complemented
38C2×#399C2212yescomplemented
39C2×#396C2211yescharacteristic, complemented
40C2×#396C2211yescharacteristic, complemented
41C2×#396C2212yescomplemented
42C2×#396C2212yescomplemented
43C2×#393C2211yescharacteristic, complemented
44C2×#393C2212yescomplemented
45#2308—28no—
46C2×#391C2212yescomplemented
47C2×#390—28no—
48C2×#390C2212yes—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#389C2212yescomplemented
53C2×#387C2212yescomplemented
54C2×#387C2212yescomplemented
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic, complemented
66C2×#385C2211yescharacteristic, complemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#381C2211yescharacteristic
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#381C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic, complemented
77C2×#380C2212yescomplemented
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84#1444C2212yescomplemented
85#1444C2212yescomplemented
86#1442C2212yescomplemented
87#1442C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4Q818yescomplemented
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—42no—
151C2×C22⋊Q8—44no—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—42no—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4D418yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C42—24no—
222C22×C42—24no—
223C22×C42—42no—
224C22×C42C2312yes—
225C22×C42C2312yes—
226#399—24no—
227#399—44no—
228#396—24no—
229#396—24no—
230#396—44no—
231#396—44no—
232#393—24no—
233#393—44no—
234#391—28no—
235#390—28no—
236#390—28no—
237#390—28no—
238#390—28no—
239#389—28no—
240#387—28no—
241#387—28no—
242#386—28no—
243#386—28no—
244#386—28no—
245#386—28no—
246#385—24no—
247#385—24no—
248#385—24no—
249#385—24no—
250#385—24no—
251#385—24no—
252#385—44no—
253#385—42no—
254#385—42no—
255#385—44no—
256#381—24no—
257#381—24no—
258#381—24no—
259#381D418yes—
260#380—24no—
261#380—24no—
262#380—24no—
263#380—44no—
264#380—42no—
265#379—24no—
266#379—24no—
267#379—24no—
268#379—24no—
269#379—42no—
270#379—42no—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
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×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25C2×D414yes—
322C25C2×Q814yes—
323C25C2×Q814yes—
324C25#4114yes—
325C25C2412yes—
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—24no—
332C22×Q8—41no—
333C22×Q8—42no—
334C22×D4—232no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—232no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—416no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—416no—
350C22×D4—416no—
351C22×D4—416no—
352C22×D4—416no—
353C22×D4C2×Q818yes—
354C22×D4C2×Q818yes—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—41no—
383C23×C4—41no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4C2×D414yes—
395C23×C4C2×D414yes—
396C23×C4C2×D414yes—
397C23×C4C2×Q814yes—
398C23×C4#4114yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C22⋊Q8—416no—
419C22⋊Q8—416no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—416no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
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—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
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—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
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—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—416no—
519C2×C22⋊C4—416no—
520C2×C22⋊C4—416no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—416no—
537C2×C22⋊C4—416no—
538C2×C22⋊C4—416no—
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—42no—
548C2×C22⋊C4—42no—
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—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4C2×D414yes—
564C2×C22⋊C4C2×D414yes—
565C2×C22⋊C4C2×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—42no—
574C2×C42—42no—
575C2×C42—416no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95C2×D418yes—
607#95C2×D418yes—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—28no—
633C24—28no—
634C24—28no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—28no—
650C24—28no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—48no—
665C24—44no—
666C24—48no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24C22⋊Q8116yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×Q814yes—
693C24C22×Q812yes—
694C24C22×Q812yes—
695C24C22×Q812yes—
696C24C2×#4112yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24H(5,𝔽2)12yes—
701C24H(5,𝔽2)12yes—
702C24C2511yescharacteristic
703C2×Q8—44no—
704C2×Q8—48no—
705C2×Q8—44no—
706C2×Q8—82no—
707C2×Q8—84no—
708C2×D4—216no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—216no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—4128no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
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—21no—
797C22×C4—22no—
798C22×C4—21no—
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—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—82no—
853C22×C4—82no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4C22⋊Q8116yescomplemented
864C22×C4C22×D412yes—
865C22×C4C22×D414yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D414yes—
871C22×C4C22×D412yes—
872C22×C4C22×Q814yes—
873C22×C4C2×#4114yes—
874C22×C4H(5,𝔽2)14yes—
875C22×C4H(5,𝔽2)14yes—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—82no—
888C4⋊C4—82no—
889C4⋊C4—82no—
890C4⋊C4—84no—
891C4⋊C4—84no—
892C4⋊C4—84no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—82no—
922C22⋊C4—82no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C42—48no—
929C42—48no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
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—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—232no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—416no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—416no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—816no—
1032C23—816no—
1033C23—88no—
1034C23—88no—
1035C23—88no—
1036C23—88no—
1037C23—816no—
1038C23—816no—
1039C23—816no—
1040C23—816no—
1041C23—88no—
1042C23—88no—
1043C23—88no—
1044C23—88no—
1045C23—816no—
1046C23—816no—
1047C23C2×C22⋊Q814yes—
1048C23C2×C22⋊Q814yes—
1049C23C2×C22⋊Q814yes—
1050C23C2×C22⋊Q814yes—
1051C23#54314yes—
1052C23D4214yes—
1053C23#54614yes—
1054C23#54614yes—
1055C23#55114yes—
1056C23C23×D411yescharacteristic
1057C23C23×D411yescharacteristic
1058C23C23×Q811yescharacteristic
1059C23C22×#4111yescharacteristic
1060C23C22×#4111yescharacteristic
1061C23C2×H(5,𝔽2)12yes—
1062C23C2×H(5,𝔽2)11yescharacteristic
1063C23C2×H(5,𝔽2)11yescharacteristic
1064C23C2×H(5,𝔽2)12yes—
1065C23#58512yes—
1066C23#58512yes—
1067Q8—88no—
1068D4—432no—
1069D4—432no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—232no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—416no—
1101C2×C4—416no—
1102C2×C4—41no—
1103C2×C4—42no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
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—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—88no—
1181C2×C4—88no—
1182C2×C4—88no—
1183C2×C4—816no—
1184C2×C4—88no—
1185C2×C4C2×C22⋊Q818yes—
1186C2×C4#53414yes—
1187C22—28no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—28no—
1193C22—28no—
1194C22—24no—
1195C22—28no—
1196C22—24no—
1197C22—24no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—832no—
1227C22—832no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22#243718yes—
1237C22C22×C22⋊Q811yescharacteristic
1238C22C22×C22⋊Q811yescharacteristic
1239C22C2×#53411yescharacteristic
1240C22#344911yescharacteristic
1241C22C2×#54311yescharacteristic
1242C22#345912yes—
1243C22C2×D4211yescharacteristic
1244C22C2×#54611yescharacteristic
1245C22C2×#54611yescharacteristic
1246C22C2×#55111yescharacteristic
1247C22#348411yescharacteristic
1248C22#348511yescharacteristic
1249C22#348812yes—
1250C22#348812yes—
1251C22#350112yes—
1252C22#350112yes—
1253C22#350512yes—
1254C22#350812yes—
1255C22#351012yes—
1256C22#353412yes—
1257C22#353412yes—
1258C22#354312yes—
1259C22#354512yes—
1260C4—24no—
1261C4—28no—
1262C4—42no—
1263C4—42no—
1264C4—44no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—44no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—82no—
1276C4—82no—
1277C4—82no—
1278C4—82no—
1279C2—28no—
1280C2—44no—
1281C2—44no—
1282C2—84no—
1283C2C2×#243711yescharacteristic
1284C2#3498511yescharacteristic
1285C2#3501011yescharacteristic
1286C2#3551512yes—
1287C2#3713412yes—
1288C2#3764611yescharacteristic
1289C2#3765211yescharacteristic
1290C2#3777812yes—
1291C2#3946111yescharacteristic
1292C2#3946411yescharacteristic
1293C2#3955812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2855C2semidirect
2. C2×#2437C2semidirect
5. #15962C2semidirect
6. #15358C2semidirect
7. #15355C2semidirect
8. #15335C2semidirect
9. #15334C2semidirect
10. #15331C2semidirect
11. #15309C2semidirect
12. #15280C2semidirect
13. #14734C2semidirect
14. #14726C2semidirect
15. #14726C2semidirect
16. #14717C2semidirect
17. #14705C2semidirect
18. #14339C2semidirect
20. #14263C2semidirect
21. #14127C2semidirect
22. #13877C2semidirect
23. #13877C2semidirect
26. C22×C22⋊Q8C22semidirect
37. C2×#399C22semidirect
38. C2×#399C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#393C22semidirect
44. C2×#393C22semidirect
46. C2×#391C22semidirect
52. C2×#389C22semidirect
53. C2×#387C22semidirect
54. C2×#387C22semidirect
65. C2×#385C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
76. C2×#380C22semidirect
77. C2×#380C22semidirect
84. #1444C22semidirect
85. #1444C22semidirect
86. #1442C22semidirect
87. #1442C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
136. C23×D4Q8semidirect
863. C22×C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×#24372
C2×#23082
C22×#3902
#159622
#153582
#153552
#153352
#153342
#153312
#153092
#152802
#147342
#147262
#147172
#147052
#143392
#143352
#142632
#141272
#138772