Finite Group Databasebeta

← #6370387

Subgroups — #6370387

Order 512.

2454 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2981C211yesmaximal, characteristic
2C2×#2979C211yesmaximal, characteristic
3#34141C211yesmaximal, characteristic
4#20567C211yesmaximal, characteristic, complemented
5#20565C211yesmaximal, characteristic, complemented
6#20562C211yesmaximal, characteristic, complemented
7#20561C212yesmaximal, complemented
8#20557C212yesmaximal, complemented
9#20555C211yesmaximal, characteristic, complemented
10#20535C211yesmaximal, characteristic, complemented
11#20533C211yesmaximal, characteristic, complemented
12#20531C212yesmaximal, complemented
13#20530C212yesmaximal, complemented
14#20495C211yesmaximal, characteristic, complemented
15#20494C211yesmaximal, characteristic, complemented
16#20490C212yesmaximal, complemented
17#20485C211yesmaximal, characteristic, complemented
18#20484C212yesmaximal, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20#20470C211yesmaximal, characteristic, complemented
21#20462C211yesmaximal, characteristic, complemented
22#20378C212yesmaximal, complemented
23C4×#408C212yesmaximal, complemented
24C2×#532C2211yescharacteristic
25C2×C4×#41C2212yes—
26#2981C4116yescomplemented
27#2979C4116yescomplemented
28C2×#436C2211yescharacteristic
29C2×#436C2212yes—
30C2×#436C2211yescharacteristic
31C2×#436C2211yescharacteristic
32C2×#436C2211yescharacteristic
33C2×#435C2212yes—
34C2×#435C2212yes—
35C2×C8×D4C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×C8×D4C2212yes—
38C2×C8×D4C2211yescharacteristic
39C2×C8×D4C2211yescharacteristic
40C2×#432C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C2×#431C2211yescharacteristic
43C2×#431C2211yescharacteristic
44C2×#408C2212yes—
45C2×#408C2212yes—
46C2×#408C2212yes—
47C2×#408C2212yes—
48C2×#405C2212yes—
49C2×#405C2212yes—
50C2×C4×M16C2212yes—
51C22×C4×C8C2212yes—
52#2367C414yes—
53#2366C412yes—
54#2365C412yes—
55#2364C414yes—
56#2361C412yes—
57#2361C412yes—
58#2297C2212yes—
59#2293C2211yescharacteristic
60#2293C2211yescharacteristic
61#2290C2212yes—
62#2290C2212yes—
63C42×D4C2211yescharacteristic
64C42×D4C2211yescharacteristic
65C4×#117C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67#1771C2212yes—
68#1771C2212yes—
69#1770C2211yescharacteristic
70#1770C2211yescharacteristic
71C8×C4⋊C4C2211yescharacteristic
72C8×C4⋊C4C2211yescharacteristic
73C8×C4⋊C4C2212yes—
74C8×C4⋊C4C2211yescharacteristic
75C8×C4⋊C4C2212yes—
76C8×C4⋊C4C2211yescharacteristic
77C8×C4⋊C4C2211yescharacteristic
78C8×C4⋊C4C2211yescharacteristic
79#1768C2211yescharacteristic
80#1768C2211yescharacteristic
81#1768C2211yescharacteristic
82#1768C2211yescharacteristic
83#1767C2211yescharacteristic
84#1767C2211yescharacteristic
85C4×C4⋊C8C2211yescharacteristic
86C4×C4⋊C8C2211yescharacteristic
87#1753C2212yes—
88#1753C2212yes—
89#1753C2212yes—
90#1753C2212yes—
91#1753C2212yes—
92#1753C2212yes—
93#1753C2212yes—
94#1753C2212yes—
95#1752C2212yes—
96#1752C2212yes—
97C8×C22⋊C4C2212yes—
98C8×C22⋊C4C2212yes—
99C8×C22⋊C4C2212yes—
100C8×C22⋊C4C2212yes—
101C8×C22⋊C4C2212yes—
102C8×C22⋊C4C2212yes—
103#1750C2212yes—
104#1750C2212yes—
105#1750C2211yescharacteristic
106#1750C2212yes—
107#1750C2211yescharacteristic
108#1750C2212yes—
109#1750C2212yes—
110#1750C2211yescharacteristic
111#1750C2212yes—
112#1750C2211yescharacteristic
113#1749C2212yes—
114#1749C2212yes—
115C4×C22⋊C8C2212yes—
116C4×C22⋊C8C2212yes—
117C4×C22⋊C8C2212yes—
118C4×C22⋊C8C2212yes—
119C4×C22⋊C8C2212yes—
120C4×C22⋊C8C2212yes—
121#1746C2212yes—
122#1744C2211yescharacteristic
123#1744C2211yescharacteristic
124#1729C2212yes—
125#1729C2212yes—
126#1728C2212yes—
127C2×#336C2212yes—
128#1726C2212yes—
129C4×#97C2211yescharacteristic
130C42×C8C2211yescharacteristic
131C22×#41C2312yes—
132C22×M16C2312yes—
133C22×M16C2312yes—
134C22×M16C2312yes—
135C22×M16C2312yes—
136C23×C8C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139C23×C8C2312yes—
140#532C2×C418yes—
141#532C2×C418yes—
142C2×C4⋊Q8C2×C411yescharacteristic
143C2×#127C2×C411yescharacteristic
144C2×#124C2×C412yes—
145C2×#121C2×C411yescharacteristic
146C2×#121C2×C411yescharacteristic
147C2×#121C2×C412yes—
148C4×#41—44no—
149C4×#41—44no—
150C2×C4×Q8C2×C414yes—
151C2×C4×D4C2×C412yes—
152C2×C4×D4C2×C412yes—
153C2×C4×D4C2×C414yes—
154C2×C4×D4C2×C414yes—
155C2×C4×D4C2×C414yes—
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2312yes—
159C2×#117C2312yes—
160C2×#117C2311yescharacteristic
161C2×#117C2312yes—
162C2×#117C2311yescharacteristic
163C22×C4⋊C4C2×C412yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168#436C2×C418yescomplemented
169#436C2×C4116yescomplemented
170#436C2×C418yescomplemented
171#436C2×C418yescomplemented
172#436C2×C418yescomplemented
173#435C2×C4116yescomplemented
174#435C2×C4116yescomplemented
175C8×D4C2×C418yescomplemented
176C8×D4C2×C4116yescomplemented
177C8×D4C2×C418yescomplemented
178C8×D4C2×C418yescomplemented
179C8×D4C2×C418yescomplemented
180#432C2×C418yescomplemented
181#431C2×C418yescomplemented
182#431C2×C418yescomplemented
183#431C2×C418yescomplemented
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192#408C2×C4116yescomplemented
193#408C2×C4116yescomplemented
194#408C2×C4116yescomplemented
195#408C2×C4116yescomplemented
196C2×C22⋊C8C2311yescharacteristic
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2311yescharacteristic
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210#405—44no—
211#405—44no—
212C4×M16—44no—
213C2×#97C2311yescharacteristic
214C2×#97C2312yes—
215C2×#97C2311yescharacteristic
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×#97C2311yescharacteristic
219C2×#97C2311yescharacteristic
220C2×#97C2312yes—
221C2×#97C2312yes—
222C2×C4×C8—44no—
223C2×C4×C8C2311yescharacteristic
224C2×C4×C8C2312yes—
225C2×C4×C8C2311yescharacteristic
226C2×C4×C8C2312yes—
227C2×C4×C8C2312yes—
228C2×C4×C8C2312yes—
229C2×C4×C8C2312yes—
230C2×C4×C8C2312yes—
231C2×C4×C8C2312yes—
232C2×C4×C8C2311yescharacteristic
233C2×C4×C8C2311yescharacteristic
234C2×C4×C8C2312yes—
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2312yes—
239C2×C4×C8C2311yescharacteristic
240#391C2×C414yes—
241#390C2×C412yes—
242#390C2×C412yes—
243#390C2×C414yes—
244#389C2×C412yes—
245#389C2×C412yes—
246#388C2×C414yes—
247#388C2×C414yes—
248#388C2×C414yes—
249#388C2×C414yes—
250#387C2×C414yes—
251#387C2×C414yes—
252#386C2×C414yes—
253#386C2×C414yes—
254#386C2×C414yes—
255#386C2×C414yes—
256#385C2×C414yes—
257#385C2×C414yes—
258C4×C4⋊C4C2×C412yes—
259C4×C4⋊C4C2×C412yes—
260C4×C4⋊C4C2×C412yes—
261C4×C4⋊C4C2×C412yes—
262C4×C4⋊C4C2×C412yes—
263C4×C4⋊C4C2×C412yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C4⋊C4C2311yescharacteristic
266C4×C4⋊C4C2312yes—
267C4×C22⋊C4C2×C412yes—
268C4×C22⋊C4C2×C412yes—
269C4×C22⋊C4C2×C414yes—
270C4×C22⋊C4C2×C414yes—
271C4×C22⋊C4C2312yes—
272C4×C22⋊C4C2312yes—
273C4×C22⋊C4C2312yes—
274C4×C22⋊C4C2312yes—
275#376C2311yescharacteristic
276#376C2311yescharacteristic
277C2×#95C2×C412yes—
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280#336C2311yescharacteristic
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284#336C2311yescharacteristic
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288#336C2311yescharacteristic
289#336C2311yescharacteristic
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×C414yes—
317C23×C4C22×C411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2412yes—
320C23×C4C2412yes—
321C2×M16—42no—
322C2×M16—42no—
323C2×M16—42no—
324C2×M16—42no—
325C2×M16—42no—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16C22×C418yes—
330C2×M16C22×C418yes—
331C2×M16C22×C418yes—
332C2×M16C22×C418yes—
333C22×C8—42no—
334C22×C8—42no—
335C22×C8—42no—
336C22×C8—42no—
337C22×C8—42no—
338C22×C8—42no—
339C22×C8—42no—
340C22×C8—42no—
341C22×C8C22×C418yes—
342C22×C8C22×C418yes—
343C22×C8C22×C418yes—
344C22×C8C22×C418yes—
345C22×C8C2411yescharacteristic
346C22×C8C2412yes—
347C22×C8C2411yescharacteristic
348C22×C8C2411yescharacteristic
349C22×C8C2411yescharacteristic
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C4⋊Q8C4218yes—
358#127C4218yes—
359#124C42116yes—
360#121C4218yes—
361#121C4218yes—
362#121C42116yes—
363C4×Q8—48no—
364C4×D4—28no—
365C4×D4—28no—
366C4×D4—48no—
367C4×D4—48no—
368C4×D4—48no—
369C4×D4C22×C414yes—
370C4×D4C22×C414yes—
371C4×D4C22×C414yes—
372C4×D4C22×C414yes—
373C4×D4C22×C418yes—
374C4×D4C22×C418yes—
375#117—22no—
376#117—22no—
377#117—24no—
378#117—24no—
379#117—41no—
380#117—41no—
381#117—42no—
382#117—42no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4C22×C414yes—
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C414yes—
388C2×C4⋊C4C22×C414yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C411yescharacteristic
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C412yes—
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C414yes—
396C2×C22⋊C4C22×C414yes—
397C2×C22⋊C4C22×C414yes—
398C2×C22⋊C4C22×C414yes—
399C2×C22⋊C4C22×C412yes—
400C2×C22⋊C4C22×C414yes—
401C2×C22⋊C4C22×C414yes—
402C2×C22⋊C4C22×C412yes—
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42C22×C414yes—
413C2×C42C22×C412yes—
414C2×C42C22×C412yes—
415C2×C42C22×C414yes—
416C2×C42C22×C414yes—
417C2×C42C22×C412yes—
418C2×C42C22×C412yes—
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C414yes—
422C2×C42C22×C414yes—
423C2×C42C2411yescharacteristic
424C2×C42C2412yes—
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2412yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C4⋊C8C22×C414yes—
432C4⋊C8C22×C414yes—
433C4⋊C8C22×C414yes—
434C4⋊C8C22×C414yes—
435C4⋊C8C22×C414yes—
436C4⋊C8C22×C414yes—
437C4⋊C8C22×C414yes—
438C4⋊C8C22×C414yes—
439C22⋊C8C22×C414yes—
440C22⋊C8C22×C418yes—
441C22⋊C8C22×C414yes—
442C22⋊C8C22×C414yes—
443C22⋊C8C22×C414yes—
444C22⋊C8C22×C418yes—
445C22⋊C8C22×C418yes—
446C22⋊C8C22×C418yes—
447C22⋊C8C22×C418yes—
448C22⋊C8C22×C418yes—
449C22⋊C8C22×C418yes—
450C22⋊C8C22×C418yes—
451C22⋊C8C22×C418yes—
452C22⋊C8C22×C418yes—
453#97—22no—
454#97—24no—
455#97—22no—
456#97—41no—
457#97—41no—
458#97—42no—
459#97—42no—
460#97—42no—
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×C418yes—
478C4×C8C22×C414yes—
479#95C22×C412yes—
480#95C22×C414yes—
481#95C22×C412yes—
482#95C22×C412yes—
483#95C22×C412yes—
484#95C22×C412yes—
485#95C22×C412yes—
486#95C22×C414yes—
487#95C22×C414yes—
488#95C22×C414yes—
489#95C22×C414yes—
490C24C23×C412yes—
491C24C23×C412yes—
492C24C23×C411yescharacteristic
493#41—48no—
494#41—48no—
495#41—48no—
496#41—48no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8C2×C4218yes—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×C4214yes—
510C2×D4C2×C4214yes—
511C2×D4C2×C4218yes—
512C2×D4C2×C4218yes—
513C2×D4C2×C4218yes—
514C2×D4C2×C4218yes—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4C2×C4214yes—
539C22×C4C2×C4214yes—
540C22×C4C23×C412yes—
541C22×C4C23×C412yes—
542C22×C4C23×C414yes—
543C22×C4C23×C412yes—
544C22×C4C23×C412yes—
545C22×C4C23×C414yes—
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C414yes—
549C22×C4C23×C414yes—
550C22×C4C23×C414yes—
551C22×C4C23×C414yes—
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C412yes—
555C22×C4C23×C412yes—
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C2511yescharacteristic
560M16—48no—
561M16—48no—
562M16—48no—
563M16—48no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—22no—
567C2×C8—21no—
568C2×C8—22no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—22no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—21no—
576C2×C8—22no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—22no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—22no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—48no—
589C2×C8—48no—
590C2×C8—48no—
591C2×C8—48no—
592C2×C8C23×C412yes—
593C2×C8C23×C412yes—
594C2×C8C23×C412yes—
595C2×C8C23×C414yes—
596C2×C8C23×C412yes—
597C2×C8C23×C412yes—
598C2×C8C23×C412yes—
599C2×C8C23×C414yes—
600C2×C8C23×C412yes—
601C2×C8C23×C412yes—
602C2×C8C23×C414yes—
603C2×C8C23×C414yes—
604C4⋊C4—24no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4C2×C4218yes—
611C4⋊C4C2×C4214yes—
612C4⋊C4C2×C4214yes—
613C4⋊C4#13118yes—
614C22⋊C4—28no—
615C22⋊C4—24no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—42no—
621C22⋊C4—44no—
622C22⋊C4C2×C4218yes—
623C22⋊C4C2×C4218yes—
624C22⋊C4C2×C4218yes—
625C22⋊C4C2×C4218yes—
626C42—28no—
627C42—24no—
628C42—24no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—44no—
640C42—44no—
641C42—42no—
642C42—42no—
643C42C2×C4214yes—
644C42C2×C4214yes—
645C42C23×C412yes—
646C42C23×C412yes—
647C42C23×C412yes—
648C42C23×C412yes—
649C42H(5,𝔽2)12yes—
650C42H(5,𝔽2)12yes—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—21no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23C22×C4214yes—
664C23C22×C4214yes—
665C23C22×C4212yes—
666C23C24×C411yescharacteristic
667Q8—48no—
668D4—28no—
669D4—28no—
670D4—48no—
671D4—48no—
672D4—48no—
673D4—48no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—28no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—416no—
714C2×C4—88no—
715C2×C4—88no—
716C2×C4C22×C4212yes—
717C2×C4C22×C4212yes—
718C2×C4C22×C4212yes—
719C2×C4C22×C4212yes—
720C2×C4C22×C4214yes—
721C2×C4C22×C4214yes—
722C2×C4C22×C4212yes—
723C2×C4#51814yes—
724C2×C4C2×#13118yes—
725C2×C4C2×#13114yes—
726C2×C4C24×C411yescharacteristic
727C2×C4C24×C411yescharacteristic
728C2×C4C2×H(5,𝔽2)11yescharacteristic
729C2×C4C2×H(5,𝔽2)11yescharacteristic
730C2×C4#58511yescharacteristic
731C2×C4#58511yescharacteristic
732C8—22no—
733C8—24no—
734C8—22no—
735C8—22no—
736C8—22no—
737C8—24no—
738C8—24no—
739C8—22no—
740C8—22no—
741C8—22no—
742C8—22no—
743C8—24no—
744C22—22no—
745C22—24no—
746C22—24no—
747C22—22no—
748C22—24no—
749C22—24no—
750C22—22no—
751C22—24no—
752C22—24no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22C23×C4211yescharacteristic
760C22C2×#51811yescharacteristic
761C22#342811yescharacteristic
762C22C22×#13112yes—
763C22#357312yes—
764C4—24no—
765C4—28no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—24no—
771C4—24no—
772C4—44no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4C4×#13114yes—
777C4C4×H(5,𝔽2)11yescharacteristic
778C4C4×H(5,𝔽2)11yescharacteristic
779C4C4×H(5,𝔽2)11yescharacteristic
780C4C4×H(5,𝔽2)11yescharacteristic
781C2—42no—
782C2—44no—
783C2—44no—
784C2C4×#51811yescharacteristic
785C2C2×C4×#13111yescharacteristic
786C2#6005811yescharacteristic
787C2#6023912yes—
788C2#6030112yes—
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. #20565C2semidirect
6. #20562C2semidirect
7. #20561C2semidirect
8. #20557C2semidirect
9. #20555C2semidirect
10. #20535C2semidirect
11. #20533C2semidirect
12. #20531C2semidirect
13. #20530C2semidirect
14. #20495C2semidirect
15. #20494C2semidirect
16. #20490C2semidirect
17. #20485C2semidirect
18. #20484C2semidirect
19. C4×C8×D4C2semidirect
20. #20470C2semidirect
21. #20462C2semidirect
22. #20378C2semidirect
23. C4×#408C2semidirect
26. #2981C4semidirect
27. #2979C4semidirect
168. #436C2×C4semidirect
169. #436C2×C4semidirect
170. #436C2×C4semidirect
171. #436C2×C4semidirect
172. #436C2×C4semidirect
173. #435C2×C4semidirect
174. #435C2×C4semidirect
175. C8×D4C2×C4semidirect
176. C8×D4C2×C4semidirect
177. C8×D4C2×C4semidirect
178. C8×D4C2×C4semidirect
179. C8×D4C2×C4semidirect
180. #432C2×C4semidirect
181. #431C2×C4semidirect
182. #431C2×C4semidirect
183. #431C2×C4semidirect
192. #408C2×C4semidirect
193. #408C2×C4semidirect
194. #408C2×C4semidirect
195. #408C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29812
C2×#29792
#341412
#205672
#205652
#205622
#205612
#205572
#205552
#205352
#205332
#205312
#205302
#204952
#204942
#204902
#204852
#204842
C4×C8×D42
#204702
#204622
#203782
C4×#4082