Finite Group Databasebeta

← #647701

Subgroups — #647701

Order 512.

5736 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2534C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C2×#2358C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C22×#381C211yesmaximal, characteristic, complemented
7#15411C212yesmaximal, complemented
8#15369C212yesmaximal, complemented
9#15301C212yesmaximal, complemented
10#15299C212yesmaximal, complemented
11#14935C211yesmaximal, characteristic, complemented
12#14927C211yesmaximal, characteristic, complemented
13#14918C211yesmaximal, characteristic, complemented
14#14911C211yesmaximal, characteristic, complemented
15#14748C212yesmaximal, complemented
16#14747C212yesmaximal, complemented
17#14140C212yesmaximal, complemented
18#14023C212yesmaximal, complemented
19#13992C211yesmaximal, characteristic, complemented
20#13968C211yesmaximal, characteristic, complemented
21#13903C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#121C2212yes—
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic, complemented
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38#2849—28no—
39#2534—28no—
40#2410—28no—
41C2×#396C2212yescomplemented
42C2×#394C2212yes—
43C2×#394C2212yescomplemented
44C2×#392C2212yes—
45#2358—28no—
46C2×#390C2211yescharacteristic, complemented
47C2×#388C2212yescomplemented
48C2×#388C2211yescharacteristic, complemented
49C2×#388C2211yescharacteristic, complemented
50C2×#386—28no—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yescomplemented
61C2×#386C2212yescomplemented
62C2×#386C2212yescomplemented
63C2×#386C2211yescharacteristic, complemented
64C2×#386C2211yescharacteristic, complemented
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2211yescharacteristic, complemented
70C2×#385C2212yescomplemented
71C2×#381—28no—
72C2×#381C2211yescharacteristic
73C2×#381C2211yescharacteristic
74C2×#381C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#381C2212yescomplemented
79C2×#381C2212yescomplemented
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82C2×#379C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic, complemented
88C22×#95C2211yescharacteristic
89C22×#95C2211yescharacteristic
90C22×#95C2212yescomplemented
91C22×#95C2212yescomplemented
92#1443C2212yescomplemented
93#1443C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1440C2212yescomplemented
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yescomplemented
117#1438C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122#1434C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—28no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—24no—
147C24×C4—42no—
148C24×C4—42no—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2312yes—
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159C24×C4C2311yescharacteristic
160C2×#123—24no—
161C2×#123—24no—
162C2×#123—24no—
163C2×#123—24no—
164C2×#123—42no—
165C2×#123—42no—
166C2×#121—28no—
167C2×#121—28no—
168C2×#121—44no—
169C2×#120—24no—
170C2×#120—24no—
171C2×#120—24no—
172C2×#120—24no—
173C2×#120—42no—
174C2×#120D418yes—
175C2×C4×D4—24no—
176C2×C4×D4—24no—
177C2×C4×D4—24no—
178C2×C4×D4—42no—
179C2×C4×D4—44no—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—44no—
197C22×C22⋊C4—42no—
198C22×C22⋊C4—42no—
199C22×C22⋊C4—42no—
200C22×C22⋊C4—42no—
201C22×C22⋊C4D418yescomplemented
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⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240#396—28no—
241#394—28no—
242#394—28no—
243#392—28no—
244#390—24no—
245#388—24no—
246#388—24no—
247#388—28no—
248#386—28no—
249#386—28no—
250#386—24no—
251#386—28no—
252#386—24no—
253#386—24no—
254#386—24no—
255#386—28no—
256#386—28no—
257#386—28no—
258#386—28no—
259#386—28no—
260#386—28no—
261#386—44no—
262#385—24no—
263#385—28no—
264#385—28no—
265#385—24no—
266#385—24no—
267#385—44no—
268#381—24no—
269#381—24no—
270#381—24no—
271#381—24no—
272#381—24no—
273#381—28no—
274#381—28no—
275#381D418yescomplemented
276#380—24no—
277#380—42no—
278#379—24no—
279#379—24no—
280#379—24no—
281#379—42no—
282C4×C22⋊C4—24no—
283C4×C22⋊C4—24no—
284C2×#95—24no—
285C2×#95—24no—
286C2×#95—28no—
287C2×#95—28no—
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—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—22no—
323C25—22no—
324C25—24no—
325C25—22no—
326C25—22no—
327C25—24no—
328C25—22no—
329C25—24no—
330C25—22no—
331C25—22no—
332C25—22no—
333C25—22no—
334C25—22no—
335C25—22no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25—42no—
341C25C2×D414yes—
342C25C2×D414yes—
343C25#4114yes—
344C25C2411yescharacteristic
345C25C2412yes—
346C25C2411yescharacteristic
347C25C2411yescharacteristic
348C25C2411yescharacteristic
349C22×D4—232no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—24no—
373C22×D4—24no—
374C22×D4—24no—
375C22×D4—24no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—432no—
385C22×D4—432no—
386C22×D4—416no—
387C22×D4—416no—
388C22×D4C2×D414yes—
389C22×D4C2×D414yes—
390C22×D4C2×D414yes—
391C22×D4#4118yes—
392C23×C4—232no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—22no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—41no—
443C23×C4—42no—
444C23×C4—41no—
445C23×C4—42no—
446C23×C4—41no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—416no—
455C23×C4—416no—
456C23×C4—416no—
457C23×C4—416no—
458C23×C4—416no—
459C23×C4—416no—
460C23×C4C2×D414yes—
461C23×C4C2×D414yes—
462C23×C4C2×D414yes—
463C23×C4#4114yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2412yes—
482#123—416no—
483#123—416no—
484#121—432no—
485#120—232no—
486#120—416no—
487C4×D4—416no—
488C4×D4—416no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—42no—
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—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—416no—
573C2×C22⋊C4—416no—
574C2×C22⋊C4—416no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—416no—
595C2×C22⋊C4—416no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4C2×D414yes—
607C2×C22⋊C4C2×D414yes—
608C2×C22⋊C4C2×D414yes—
609C2×C22⋊C4C2×D414yes—
610C2×C22⋊C4C2×D414yes—
611C2×C22⋊C4C2×D414yes—
612C2×C22⋊C4C2×D414yes—
613C2×C22⋊C4C2×D414yes—
614C2×C22⋊C4C2×D414yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—41no—
620C2×C42—42no—
621C2×C42—42no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—24no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—24no—
641#95—22no—
642#95—22no—
643#95—24no—
644#95—24no—
645#95—24no—
646#95—24no—
647#95—42no—
648#95—42no—
649#95—42no—
650#95—42no—
651#95—42no—
652#95—42no—
653#95—42no—
654#95C2×D418yescomplemented
655#95C2×D418yescomplemented
656C24—21no—
657C24—21no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—28no—
667C24—28no—
668C24—28no—
669C24—28no—
670C24—28no—
671C24—28no—
672C24—28no—
673C24—28no—
674C24—216no—
675C24—216no—
676C24—21no—
677C24—21no—
678C24—22no—
679C24—21no—
680C24—21no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—28no—
685C24—22no—
686C24—22no—
687C24—21no—
688C24—21no—
689C24—22no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—21no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—21no—
698C24—22no—
699C24—22no—
700C24—21no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—44no—
710C24—44no—
711C24—48no—
712C24—48no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—44no—
728C24—44no—
729C24—44no—
730C24—44no—
731C24—44no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24—44no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24—84no—
742C24—84no—
743C24#121116yes—
744C24C22×D412yes—
745C24C22×D412yes—
746C24C22×D412yes—
747C24C22×D412yes—
748C24C22×D412yes—
749C24C22×D412yes—
750C24C22×D412yes—
751C24C22×D412yes—
752C24C2×#4114yes—
753C24C2×#4112yes—
754C24C2×#4112yes—
755C24C2×#4112yes—
756C24C2×#4112yes—
757C24C2×#4114yes—
758C24H(5,𝔽2)14yes—
759C24H(5,𝔽2)12yes—
760C24H(5,𝔽2)12yes—
761C24C2511yescharacteristic
762C2×D4—216no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—216no—
768C2×D4—216no—
769C2×D4—28no—
770C2×D4—216no—
771C2×D4—28no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—4128no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—48no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—84no—
795C2×D4—82no—
796C2×D4—82no—
797C2×D4—84no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C22×C4—216no—
802C22×C4—216no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—44no—
921C22×C4—48no—
922C22×C4—44no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—44no—
928C22×C4—4128no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—44no—
932C22×C4—48no—
933C22×C4—48no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—48no—
946C22×C4—82no—
947C22×C4—84no—
948C22×C4—82no—
949C22×C4—82no—
950C22×C4—84no—
951C22×C4—84no—
952C22×C4—84no—
953C22×C4—84no—
954C22×C4—84no—
955C22×C4—84no—
956C22×C4—84no—
957C22×C4—84no—
958C22×C4—84no—
959C22×C4—84no—
960C22×C4C22×D412yes—
961C22×C4C22×D412yes—
962C22×C4C22×D412yes—
963C22×C4C22×D414yes—
964C22×C4C22×D412yes—
965C22×C4C22×D412yes—
966C22×C4C22×D412yes—
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C22×D414yes—
970C22×C4C22×D412yes—
971C22×C4C2×#4114yes—
972C22×C4C2×#4114yes—
973C4⋊C4—44no—
974C4⋊C4—48no—
975C4⋊C4—48no—
976C4⋊C4—48no—
977C4⋊C4—44no—
978C4⋊C4—82no—
979C4⋊C4—84no—
980C4⋊C4—84no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—48no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—44no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—48no—
1004C22⋊C4—44no—
1005C22⋊C4—48no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—48no—
1010C22⋊C4—44no—
1011C22⋊C4—82no—
1012C22⋊C4—84no—
1013C22⋊C4—84no—
1014C22⋊C4—84no—
1015C22⋊C4—84no—
1016C42—44no—
1017C42—44no—
1018C42—82no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—232no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—24no—
1063C23—24no—
1064C23—24no—
1065C23—22no—
1066C23—22no—
1067C23—24no—
1068C23—232no—
1069C23—22no—
1070C23—24no—
1071C23—22no—
1072C23—22no—
1073C23—24no—
1074C23—24no—
1075C23—24no—
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—416no—
1082C23—416no—
1083C23—416no—
1084C23—416no—
1085C23—432no—
1086C23—432no—
1087C23—432no—
1088C23—432no—
1089C23—416no—
1090C23—416no—
1091C23—416no—
1092C23—416no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—41no—
1103C23—41no—
1104C23—42no—
1105C23—41no—
1106C23—42no—
1107C23—41no—
1108C23—42no—
1109C23—42no—
1110C23—41no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—41no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—41no—
1123C23—42no—
1124C23—41no—
1125C23—42no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—816no—
1148C23—816no—
1149C23—816no—
1150C23—816no—
1151C23—88no—
1152C23—88no—
1153C23—88no—
1154C23—88no—
1155C23C2×#12114yes—
1156C23C2×#12114yes—
1157C23C2×#12114yes—
1158C23#52514yes—
1159C23#52514yes—
1160C23#53414yes—
1161C23#53814yes—
1162C23D4214yes—
1163C23D4214yes—
1164C23#54614yes—
1165C23#54614yes—
1166C23#54618yes—
1167C23#55118yes—
1168C23C23×D411yescharacteristic
1169C23C23×D411yescharacteristic
1170C23C23×D411yescharacteristic
1171C23C22×#4111yescharacteristic
1172C23C22×#4111yescharacteristic
1173C23C22×#4112yes—
1174C23C2×H(5,𝔽2)12yes—
1175C23C2×H(5,𝔽2)11yescharacteristic
1176C23C2×H(5,𝔽2)11yescharacteristic
1177C23#58512yes—
1178C23#58512yes—
1179D4—432no—
1180D4—416no—
1181D4—416no—
1182D4—432no—
1183D4—88no—
1184D4—816no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—432no—
1221C2×C4—432no—
1222C2×C4—416no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—42no—
1232C2×C4—416no—
1233C2×C4—416no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—816no—
1302C22—24no—
1303C22—24no—
1304C22—24no—
1305C22—24no—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—24no—
1310C22—28no—
1311C22—28no—
1312C22—24no—
1313C22—24no—
1314C22—28no—
1315C22—28no—
1316C22—28no—
1317C22—28no—
1318C22—28no—
1319C22—28no—
1320C22—24no—
1321C22—24no—
1322C22—24no—
1323C22—24no—
1324C22—24no—
1325C22—464no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—832no—
1347C22—81no—
1348C22—81no—
1349C22—82no—
1350C22—81no—
1351C22—82no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22—82no—
1356C22—82no—
1357C22—82no—
1358C22—82no—
1359C22—81no—
1360C22—82no—
1361C22#242418yes—
1362C22#253418yescomplemented
1363C22C22×#12111yescharacteristic
1364C22C2×#52511yescharacteristic
1365C22C2×#52511yescharacteristic
1366C22C2×#53411yescharacteristic
1367C22C2×#53811yescharacteristic
1368C22C2×D4211yescharacteristic
1369C22C2×D4211yescharacteristic
1370C22C2×#54612yes—
1371C22C2×#54611yescharacteristic
1372C22C2×#54611yescharacteristic
1373C22D4×#4112yes—
1374C22C2×#55112yes—
1375C22#347512yes—
1376C22#348511yescharacteristic
1377C22#348511yescharacteristic
1378C22#348512yes—
1379C22#348812yes—
1380C22#349112yes—
1381C22#349412yes—
1382C22#351312yes—
1383C22#351312yes—
1384C22#353412yes—
1385C22#353412yes—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—81no—
1400C4—81no—
1401C4—82no—
1402C4—82no—
1403C4—82no—
1404C2—28no—
1405C2—28no—
1406C2—44no—
1407C2—82no—
1408C2—84no—
1409C2C2×#242411yescharacteristic
1410C2C2×#253411yescharacteristic
1411C2#3544711yescharacteristic
1412C2#3609911yescharacteristic
1413C2#3615911yescharacteristic
1414C2#3622212yes—
1415C2#3764611yescharacteristic
1416C2#3783411yescharacteristic
1417C2#3805312yes—
1418C2#5899412yes—
1419C2#5900912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2534C2semidirect
4. C2×#2358C2semidirect
5. C22×#386C2semidirect
6. C22×#381C2semidirect
7. #15411C2semidirect
8. #15369C2semidirect
9. #15301C2semidirect
10. #15299C2semidirect
11. #14935C2semidirect
12. #14927C2semidirect
13. #14918C2semidirect
14. #14911C2semidirect
15. #14748C2semidirect
16. #14747C2semidirect
17. #14140C2semidirect
18. #14023C2semidirect
19. #13992C2semidirect
20. #13968C2semidirect
21. #13903C2semidirect
22. #13877C2semidirect
23. #13867C2semidirect
32. C22×C4×D4C22semidirect
41. C2×#396C22semidirect
43. C2×#394C22semidirect
46. C2×#390C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
60. C2×#386C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
78. C2×#381C22semidirect
79. C2×#381C22semidirect
87. C2×C4×C22⋊C4C22semidirect
90. C22×#95C22semidirect
91. C22×#95C22semidirect
92. #1443C22semidirect
93. #1443C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1440C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1434C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
201. C22×C22⋊C4D4semidirect
275. #381D4semidirect
654. #95C2×D4semidirect
655. #95C2×D4semidirect
1362. C22#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#25342
C2×#24102
C2×#23582
C22×#3862
C22×#3812
#154112
#153692
#153012
#152992
#149352
#149272
#149182
#149112
#147482
#147472
#141402
#140232
#139922
#139682
#139032
#138772
#138672