Finite Group Databasebeta

← #6370413

Subgroups — #6370413

Order 512.

2482 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2981C211yesmaximal, characteristic
2C2×#2935C211yesmaximal, characteristic
3#34155C211yesmaximal, characteristic
4#20567C211yesmaximal, characteristic, complemented
5#20566C212yesmaximal, complemented
6#20565C211yesmaximal, characteristic, complemented
7#20562C211yesmaximal, characteristic, complemented
8#20559C212yesmaximal, complemented
9#20555C211yesmaximal, characteristic, complemented
10#20546C211yesmaximal, characteristic, complemented
11#20543C211yesmaximal, characteristic, complemented
12#20531C212yesmaximal, complemented
13#20530C212yesmaximal, complemented
14#20495C211yesmaximal, characteristic, complemented
15#20494C211yesmaximal, characteristic, complemented
16#20492C212yesmaximal, complemented
17C4×#435C212yesmaximal, complemented
18#20485C211yesmaximal, characteristic, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20#20480C211yesmaximal, characteristic, complemented
21#20472C211yesmaximal, characteristic, complemented
22#20387C212yesmaximal, complemented
23#20383C212yesmaximal, complemented
24C22×#131C2212yes—
25C2×#532C2211yescharacteristic
26#2981C4116yescomplemented
27#2935C4116yescomplemented
28C2×#436C2211yescharacteristic
29C2×#436C2211yescharacteristic
30C2×#436C2211yescharacteristic
31C2×#436C2211yescharacteristic
32C2×#435C2212yes—
33C2×#435C2212yes—
34C2×#435C2212yes—
35C2×#435C2212yes—
36C2×C8×D4C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C2×C8×D4C2211yescharacteristic
40C2×#432C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C2×#408C2212yes—
44C2×#408C2212yes—
45C2×#408C2212yes—
46C2×#405C2212yes—
47C2×#405C2212yes—
48C2×C4×M16C2212yes—
49C2×C4×M16C2211yescharacteristic
50C22×C4×C8C2212yes—
51#2372C414yes—
52#2369C412yes—
53#2366C412yes—
54#2363C412yes—
55#2363C412yes—
56#2363C414yes—
57#2297C2212yes—
58#2297C2212yes—
59#2293C2211yescharacteristic
60#2293C2212yes—
61#2293C2211yescharacteristic
62C42×D4C2211yescharacteristic
63C42×D4C2212yes—
64C42×D4C2211yescharacteristic
65C4×#117C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#1771C2211yescharacteristic
68#1771C2212yes—
69#1771C2211yescharacteristic
70#1771C2212yes—
71#1771C2211yescharacteristic
72#1771C2211yescharacteristic
73#1770C2211yescharacteristic
74#1770C2211yescharacteristic
75C8×C4⋊C4C2211yescharacteristic
76C8×C4⋊C4C2211yescharacteristic
77C8×C4⋊C4C2211yescharacteristic
78C8×C4⋊C4C2211yescharacteristic
79C8×C4⋊C4C2211yescharacteristic
80C8×C4⋊C4C2211yescharacteristic
81#1767C2211yescharacteristic
82#1767C2211yescharacteristic
83C4×C4⋊C8C2211yescharacteristic
84C4×C4⋊C8C2212yes—
85C4×C4⋊C8C2212yes—
86C4×C4⋊C8C2211yescharacteristic
87#1753C2212yes—
88#1753C2212yes—
89#1753C2212yes—
90#1753C2212yes—
91#1753C2212yes—
92#1753C2212yes—
93#1753C2212yes—
94#1753C2212yes—
95#1753C2211yescharacteristic
96#1753C2211yescharacteristic
97#1753C2212yes—
98#1753C2212yes—
99#1753C2211yescharacteristic
100#1753C2211yescharacteristic
101#1752C2212yes—
102#1752C2212yes—
103#1752C2212yes—
104C8×C22⋊C4C2212yes—
105C8×C22⋊C4C2212yes—
106C8×C22⋊C4C2212yes—
107C8×C22⋊C4C2212yes—
108C8×C22⋊C4C2212yes—
109C8×C22⋊C4C2212yes—
110C8×C22⋊C4C2212yes—
111C8×C22⋊C4C2212yes—
112C8×C22⋊C4C2212yes—
113#1750C2212yes—
114#1750C2212yes—
115#1750C2212yes—
116#1750C2212yes—
117#1749C2212yes—
118C4×C22⋊C8C2212yes—
119C4×C22⋊C8C2212yes—
120C4×C22⋊C8C2212yes—
121#1745C2212yes—
122#1744C2211yescharacteristic
123#1744C2211yescharacteristic
124#1729C2212yes—
125#1729C2212yes—
126#1728C2212yes—
127C2×#336C2212yes—
128C4×#97C2212yes—
129C4×#97C2211yescharacteristic
130C42×C8C2211yescharacteristic
131C22×#41C2312yes—
132C2×#131—44no—
133C2×#131—44no—
134C2×#131C2×C4116yescomplemented
135C22×M16C2312yes—
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2312yes—
139C22×M16C2312yes—
140C22×M16C2312yes—
141C23×C8C2312yes—
142C23×C8C2312yes—
143C23×C8C2312yes—
144C23×C8C2312yes—
145C23×C8C2312yes—
146#532C2×C418yes—
147#532C2×C418yes—
148C2×C4⋊Q8C2×C411yescharacteristic
149C2×#127C2×C411yescharacteristic
150C2×#124C2×C412yes—
151C2×#121C2×C411yescharacteristic
152C2×#121C2×C411yescharacteristic
153C2×#121C2×C412yes—
154C2×C4×D4C2×C412yes—
155C2×C4×D4C2×C412yes—
156C2×C4×D4C2×C414yes—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×C4×D4C2312yes—
160C2×#117C2×C412yes—
161C2×#117C2×C412yes—
162C2×#117C2312yes—
163C2×#117C2312yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167#436C2×C418yescomplemented
168#436C2×C418yescomplemented
169#436C2×C418yescomplemented
170#436C2×C418yescomplemented
171#435C2×C4116yescomplemented
172#435C2×C4116yescomplemented
173#435C2×C4116yescomplemented
174#435C2×C4116yescomplemented
175C8×D4C2×C418yescomplemented
176C8×D4C2×C418yescomplemented
177C8×D4C2×C418yescomplemented
178C8×D4C2×C418yescomplemented
179#432C2×C418yescomplemented
180#431C2×C418yescomplemented
181C2×C4⋊C8C2×C418yescomplemented
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189#408C2×C4116yescomplemented
190#408C2×C4116yescomplemented
191#408C2×C4116yescomplemented
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203#405—44no—
204#405—44no—
205C4×M16—44no—
206C4×M16C2×C418yescomplemented
207C2×#97C2311yescharacteristic
208C2×#97C2312yes—
209C2×#97C2311yescharacteristic
210C2×#97C2312yes—
211C2×#97C2312yes—
212C2×#97C2311yescharacteristic
213C2×#97C2312yes—
214C2×#97C2311yescharacteristic
215C2×#97C2311yescharacteristic
216C2×#97C2311yescharacteristic
217C2×#97C2312yes—
218C2×C4×C8—44no—
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2312yes—
221C2×C4×C8C2311yescharacteristic
222C2×C4×C8C2312yes—
223C2×C4×C8C2312yes—
224C2×C4×C8C2312yes—
225C2×C4×C8C2312yes—
226C2×C4×C8C2312yes—
227C2×C4×C8C2312yes—
228C2×C4×C8C2311yescharacteristic
229C2×C4×C8C2311yescharacteristic
230C2×C4×C8C2312yes—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233C2×C4×C8C2311yescharacteristic
234C2×C4×C8C2311yescharacteristic
235#391C2×C414yes—
236#391C2×C414yes—
237#390C2×C414yes—
238#390C2×C414yes—
239#390C2×C412yes—
240#390C2×C412yes—
241#390C2×C414yes—
242#389C2×C412yes—
243#389C2×C412yes—
244#389C2×C414yes—
245#388C2×C414yes—
246#388C2×C414yes—
247#388C2×C414yes—
248#388C2×C414yes—
249#386C2×C414yes—
250#386C2×C414yes—
251#386C2×C414yes—
252#386C2×C414yes—
253C4×C4⋊C4C2×C412yes—
254C4×C4⋊C4C2×C412yes—
255C4×C4⋊C4C2×C414yes—
256C4×C4⋊C4C2×C412yes—
257C4×C4⋊C4C2×C412yes—
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
260C4×C4⋊C4C2311yescharacteristic
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4C2×C412yes—
263C4×C22⋊C4C2×C412yes—
264C4×C22⋊C4C2×C414yes—
265C4×C22⋊C4C2×C414yes—
266C4×C22⋊C4C2×C414yes—
267C4×C22⋊C4C2×C414yes—
268C4×C22⋊C4C2312yes—
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2312yes—
271C4×C22⋊C4C2312yes—
272C4×C22⋊C4C2312yes—
273C4×C22⋊C4C2311yescharacteristic
274C4×C22⋊C4C2312yes—
275#376C2×C412yes—
276#376C2×C412yes—
277C43C2311yescharacteristic
278C43C2311yescharacteristic
279C43C2312yes—
280#336C2311yescharacteristic
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284#336C2311yescharacteristic
285#336C2312yes—
286#336C2312yes—
287#336C2311yescharacteristic
288#336C2311yescharacteristic
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2311yescharacteristic
295#336C2311yescharacteristic
296#336C2311yescharacteristic
297#336C2311yescharacteristic
298#336C2312yes—
299#336C2312yes—
300C2×#41—42no—
301C2×#41—42no—
302C2×#41—42no—
303C2×#41—42no—
304C2×#41C22×C418yes—
305C2×#41C22×C418yes—
306C22×Q8C22×C412yes—
307C22×D4C22×C411yescharacteristic
308C22×D4C22×C411yescharacteristic
309C22×D4C22×C412yes—
310C22×D4C22×C412yes—
311C22×D4C22×C412yes—
312C22×D4C22×C412yes—
313C23×C4C22×C414yes—
314C23×C4C22×C411yescharacteristic
315C23×C4C22×C414yes—
316C23×C4C22×C411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320#131—432no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—41no—
326C2×M16—41no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—42no—
332C2×M16—42no—
333C2×M16C22×C414yes—
334C2×M16C22×C418yes—
335C2×M16C22×C418yes—
336C2×M16C22×C414yes—
337C2×M16C22×C418yes—
338C2×M16C22×C418yes—
339C22×C8—24no—
340C22×C8—24no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8—42no—
344C22×C8—42no—
345C22×C8—42no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8—42no—
349C22×C8C22×C418yes—
350C22×C8C22×C418yes—
351C22×C8C22×C418yes—
352C22×C8C22×C418yes—
353C22×C8C22×C418yes—
354C22×C8C2412yes—
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C4⋊Q8C4218yes—
367#127C4218yes—
368#124C42116yes—
369#121C4218yes—
370#121C4218yes—
371#121C42116yes—
372C4×D4—28no—
373C4×D4—28no—
374C4×D4—48no—
375C4×D4C22×C414yes—
376C4×D4C22×C414yes—
377C4×D4C22×C414yes—
378C4×D4C22×C414yes—
379C4×D4C22×C418yes—
380C4×D4C22×C418yes—
381#117—28no—
382#117—42no—
383#117—42no—
384#117—42no—
385#117—42no—
386#117—44no—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C414yes—
391C2×C4⋊C4C22×C414yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C411yescharacteristic
395C2×C4⋊C4C22×C412yes—
396C2×C22⋊C4C22×C414yes—
397C2×C22⋊C4C22×C412yes—
398C2×C22⋊C4C22×C414yes—
399C2×C22⋊C4C22×C414yes—
400C2×C22⋊C4C22×C414yes—
401C2×C22⋊C4C22×C412yes—
402C2×C22⋊C4C22×C414yes—
403C2×C22⋊C4C22×C414yes—
404C2×C22⋊C4C22×C414yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C412yes—
407C2×C22⋊C4C22×C412yes—
408C2×C22⋊C4C22×C412yes—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42C22×C414yes—
414C2×C42C22×C412yes—
415C2×C42C22×C412yes—
416C2×C42C22×C412yes—
417C2×C42C22×C412yes—
418C2×C42C22×C414yes—
419C2×C42C22×C414yes—
420C2×C42C22×C414yes—
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C414yes—
424C2×C42C22×C414yes—
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2412yes—
428C2×C42C2412yes—
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C4⋊C8C22×C414yes—
434C4⋊C8C22×C418yes—
435C4⋊C8C22×C414yes—
436C4⋊C8C22×C414yes—
437C4⋊C8C22×C414yes—
438C4⋊C8C22×C414yes—
439C4⋊C8C22×C414yes—
440C22⋊C8C22×C414yes—
441C22⋊C8C22×C414yes—
442C22⋊C8C22×C418yes—
443C22⋊C8C22×C418yes—
444C22⋊C8C22×C418yes—
445C22⋊C8C22×C418yes—
446C22⋊C8C22×C418yes—
447C22⋊C8C22×C418yes—
448C22⋊C8C22×C418yes—
449C22⋊C8C22×C418yes—
450C22⋊C8C22×C418yes—
451#97—22no—
452#97—22no—
453#97—24no—
454#97—41no—
455#97—41no—
456#97—42no—
457#97—42no—
458#97—42no—
459#97C22×C414yes—
460#97C22×C414yes—
461#97C22×C418yes—
462C4×C8—22no—
463C4×C8—24no—
464C4×C8—22no—
465C4×C8—42no—
466C4×C8—42no—
467C4×C8—42no—
468C4×C8—41no—
469C4×C8—41no—
470C4×C8—42no—
471C4×C8—42no—
472C4×C8—42no—
473C4×C8—42no—
474C4×C8C22×C414yes—
475C4×C8C22×C414yes—
476C4×C8C22×C414yes—
477C4×C8C22×C414yes—
478#95C22×C412yes—
479#95C22×C412yes—
480#95C22×C412yes—
481#95C22×C412yes—
482#95C22×C412yes—
483#95C22×C414yes—
484#95C22×C412yes—
485#95C22×C414yes—
486#95C22×C414yes—
487#95C22×C414yes—
488#95C22×C414yes—
489C24C23×C412yes—
490C24C23×C412yes—
491C24C23×C411yescharacteristic
492#41—48no—
493#41—48no—
494#41—48no—
495#41—48no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8C2×C4218yes—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—44no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4C2×C4214yes—
509C2×D4C2×C4214yes—
510C2×D4C2×C4218yes—
511C2×D4C2×C4218yes—
512C2×D4C2×C4218yes—
513C2×D4C2×C4218yes—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—44no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4C2×C4214yes—
535C22×C4C2×C4214yes—
536C22×C4C23×C412yes—
537C22×C4C23×C412yes—
538C22×C4C23×C412yes—
539C22×C4C23×C414yes—
540C22×C4C23×C414yes—
541C22×C4C23×C412yes—
542C22×C4C23×C412yes—
543C22×C4C23×C414yes—
544C22×C4C23×C414yes—
545C22×C4C23×C414yes—
546C22×C4C23×C414yes—
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C412yes—
552C22×C4C23×C412yes—
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C411yescharacteristic
555C22×C4C2511yescharacteristic
556M16—216no—
557M16—28no—
558M16—44no—
559M16—48no—
560M16—48no—
561M16—48no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—22no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—22no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—216no—
585C2×C8—48no—
586C2×C8—48no—
587C2×C8—48no—
588C2×C8—48no—
589C2×C8C23×C412yes—
590C2×C8C23×C412yes—
591C2×C8C23×C412yes—
592C2×C8C23×C412yes—
593C2×C8C23×C412yes—
594C2×C8C23×C412yes—
595C2×C8C23×C412yes—
596C2×C8C23×C414yes—
597C2×C8C23×C414yes—
598C2×C8C23×C414yes—
599C2×C8C23×C414yes—
600C2×C8C23×C412yes—
601C2×C8H(5,𝔽2)12yes—
602C2×C8H(5,𝔽2)12yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4C2×C4218yes—
609C4⋊C4C2×C4214yes—
610C4⋊C4C2×C4214yes—
611C4⋊C4#13118yescomplemented
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—24no—
616C22⋊C4—28no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—42no—
620C22⋊C4—44no—
621C22⋊C4C2×C4218yes—
622C22⋊C4C2×C4218yes—
623C22⋊C4C2×C4218yes—
624C22⋊C4C2×C4218yes—
625C42—28no—
626C42—24no—
627C42—24no—
628C42—24no—
629C42—21no—
630C42—22no—
631C42—21no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—22no—
641C42—44no—
642C42—44no—
643C42—42no—
644C42—44no—
645C42C2×C4214yes—
646C42C2×C4214yes—
647C42C23×C412yes—
648C42C23×C412yes—
649C42C23×C412yes—
650C42C23×C412yes—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23C22×C4214yes—
664C23C22×C4214yes—
665C23C22×C4212yes—
666C23C24×C411yescharacteristic
667Q8—48no—
668D4—28no—
669D4—28no—
670D4—48no—
671D4—48no—
672D4—48no—
673D4—48no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—28no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—416no—
714C2×C4—88no—
715C2×C4C22×C4212yes—
716C2×C4C22×C4212yes—
717C2×C4C22×C4212yes—
718C2×C4C22×C4212yes—
719C2×C4C22×C4214yes—
720C2×C4C22×C4214yes—
721C2×C4C22×C4212yes—
722C2×C4C2×#13118yes—
723C2×C4C2×#13114yes—
724C2×C4#56814yes—
725C2×C4C24×C411yescharacteristic
726C2×C4C24×C411yescharacteristic
727C2×C4C2×H(5,𝔽2)11yescharacteristic
728C2×C4C2×H(5,𝔽2)11yescharacteristic
729C2×C4#58511yescharacteristic
730C2×C4#58511yescharacteristic
731C8—24no—
732C8—22no—
733C8—24no—
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C8—24no—
739C8—24no—
740C8—22no—
741C8—22no—
742C8#51814yes—
743C22—22no—
744C22—24no—
745C22—24no—
746C22—22no—
747C22—24no—
748C22—24no—
749C22—22no—
750C22—24no—
751C22—24no—
752C22—44no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—44no—
757C22—42no—
758C22C23×C4211yescharacteristic
759C22C4×H(5,𝔽2)11yescharacteristic
760C22C4×H(5,𝔽2)11yescharacteristic
761C22C22×#13112yes—
762C22C2×#56812yes—
763C4—22no—
764C4—24no—
765C4—28no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—44no—
775C4C4×#13114yes—
776C4C2×#51811yescharacteristic
777C4#342811yescharacteristic
778C4C4×H(5,𝔽2)11yescharacteristic
779C4C4×H(5,𝔽2)11yescharacteristic
780C2—42no—
781C2—44no—
782C2—44no—
783C2C4×#51811yescharacteristic
784C2C2×C4×#13111yescharacteristic
785C2C4×#56811yescharacteristic
786C2#6031112yes—
787C2#6032812yes—
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutatorC22C23×C42
socleC23C24×C4
prime radicalC2×#532C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #20567C2semidirect
5. #20566C2semidirect
6. #20565C2semidirect
7. #20562C2semidirect
8. #20559C2semidirect
9. #20555C2semidirect
10. #20546C2semidirect
11. #20543C2semidirect
12. #20531C2semidirect
13. #20530C2semidirect
14. #20495C2semidirect
15. #20494C2semidirect
16. #20492C2semidirect
17. C4×#435C2semidirect
18. #20485C2semidirect
19. C4×C8×D4C2semidirect
20. #20480C2semidirect
21. #20472C2semidirect
22. #20387C2semidirect
23. #20383C2semidirect
26. #2981C4semidirect
27. #2935C4semidirect
134. C2×#131C2×C4semidirect
167. #436C2×C4semidirect
168. #436C2×C4semidirect
169. #436C2×C4semidirect
170. #436C2×C4semidirect
171. #435C2×C4semidirect
172. #435C2×C4semidirect
173. #435C2×C4semidirect
174. #435C2×C4semidirect
175. C8×D4C2×C4semidirect
176. C8×D4C2×C4semidirect
177. C8×D4C2×C4semidirect
178. C8×D4C2×C4semidirect
179. #432C2×C4semidirect
180. #431C2×C4semidirect
181. C2×C4⋊C8C2×C4semidirect
189. #408C2×C4semidirect
190. #408C2×C4semidirect
191. #408C2×C4semidirect
206. C4×M16C2×C4semidirect
611. C4⋊C4#131semidirect

Maximal subgroups

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

subgroupindex
C2×#29812
C2×#29352
#341552
#205672
#205662
#205652
#205622
#205592
#205552
#205462
#205432
#205312
#205302
#204952
#204942
#204922
C4×#4352
#204852
C4×C8×D42
#204802
#204722
#203872
#203832