Finite Group Databasebeta

← #6385367

Subgroups — #6385367

Order 512.

1493 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34898C211yesmaximal, characteristic
2#23286C212yesmaximal, complemented
3#23267C212yesmaximal, complemented
4#23253C211yesmaximal, characteristic, complemented
5#23050C211yesmaximal, characteristic, complemented
6#22952C211yesmaximal, characteristic, complemented
7#22915C212yesmaximal
8#22832C211yesmaximal, characteristic, complemented
9#22748C211yesmaximal, characteristic
10#22633C211yesmaximal, characteristic, complemented
11#22600C211yesmaximal, characteristic, complemented
12#22597C212yesmaximal, complemented
13#21678C212yesmaximal, complemented
14#21673C211yesmaximal, characteristic, complemented
15#21666C212yesmaximal, complemented
16#21596C211yesmaximal, characteristic, complemented
17#21596C211yesmaximal, characteristic, complemented
18#21571C212yesmaximal
19C4×C8×Q8C211yesmaximal, characteristic, complemented
20C4×#436C211yesmaximal, characteristic
21#20482C211yesmaximal, characteristic, complemented
22#20474C212yesmaximal, complemented
23#20441C211yesmaximal, characteristic, complemented
24C2×C8×Q8C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#436C2211yescharacteristic
27C2×#436C2211yescharacteristic
28C2×#433C2212yes—
29C2×#431C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31C2×#405C2212yes—
32C2×C4×M16C2211yescharacteristic
33C2×C4×M16C2211yescharacteristic
34#2577C412yes—
35#2575C412yes—
36#2570C411yescharacteristic
37#2565C411yescharacteristic
38#2562C411yescharacteristic
39#2536C411yescharacteristic
40#2524C412yes—
41#2496C411yescharacteristic
42#2495C411yescharacteristic
43#2468C412yes—
44#2423C411yescharacteristic
45#2421C411yescharacteristic
46#2402C2212yes—
47#2395C2212yes—
48C4×#125C2211yescharacteristic
49C4×#126C2212yes—
50C4×C22⋊Q8C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52#2298C2212yes—
53#2285C2211yescharacteristic
54#2283C2211yescharacteristic
55C42×Q8C2211yescharacteristic
56C42×D4C2211yescharacteristic
57#1984C2211yescharacteristic
58#1984C2211yescharacteristic
59#1939C2211yescharacteristic
60#1939C2211yescharacteristic
61#1939C2211yescharacteristic
62#1939C2211yescharacteristic
63#1939C2212yes—
64#1939C2212yes—
65#1924C2212yes—
66#1923C2212yes—
67#1923C2212yes—
68#1923C2212yes—
69#1923C2212yes—
70#1917C2212yes—
71#1917C2212yes—
72#1917C2212yes—
73#1917C2212yes—
74#1917C2212yes—
75#1916C2212yes—
76#1916C2212yes—
77#1916C2212yes—
78#1916C2212yes—
79#1916C2212yes—
80#1916C2212yes—
81#1916C2212yes—
82#1916C2212yes—
83#1869C2212yes—
84#1851C2212yes—
85#1851C2212yes—
86#1850C2212yes—
87#1839C2212yes—
88#1832C2212yes—
89#1831C2211yescharacteristic
90#1818C2212yes—
91#1797C2211yescharacteristic
92#1797C2211yescharacteristic
93#1771C2212yes—
94#1771C2212yes—
95#1771C2212yes—
96#1771C2212yes—
97#1771C2212yes—
98#1771C2212yes—
99#1770C2211yescharacteristic
100#1770C2211yescharacteristic
101#1770C2211yescharacteristic
102#1770C2211yescharacteristic
103#1770C2211yescharacteristic
104#1770C2211yescharacteristic
105C8×C4⋊C4C2211yescharacteristic
106C8×C4⋊C4C2211yescharacteristic
107C8×C4⋊C4C2211yescharacteristic
108C8×C4⋊C4C2212yes—
109C8×C4⋊C4C2212yes—
110C8×C4⋊C4C2211yescharacteristic
111C8×C4⋊C4C2212yes—
112C8×C4⋊C4C2212yes—
113C4×C4⋊C8C2211yescharacteristic
114C4×C4⋊C8C2212yes—
115C4×C4⋊C8C2211yescharacteristic
116#1753C2212yes—
117#1753C2212yes—
118#1753C2211yescharacteristic
119#1753C2211yescharacteristic
120#1753C2211yescharacteristic
121#1753C2211yescharacteristic
122#1753C2212yes—
123#1753C2212yes—
124C8×C22⋊C4C2212yes—
125C8×C22⋊C4C2212yes—
126C4×C22⋊C8C2211yescharacteristic
127C4×C22⋊C8C2211yescharacteristic
128#1746C2212yes—
129#1746C2212yes—
130#1745C2212yes—
131#1729C2212yes—
132#1726C2212yes—
133C42×C8C2211yescharacteristic
134C42×C8C2212yes—
135C22×M16C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2312yes—
140C2×#126C2×C412yes—
141C2×#125C2×C411yescharacteristic
142C2×C22⋊Q8C2×C411yescharacteristic
143C2×C22⋊Q8C2×C411yescharacteristic
144C2×C4×Q8C2×C411yescharacteristic
145C2×C4×Q8C2×C411yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×D4C2×C411yescharacteristic
148C2×C4×D4C2×C411yescharacteristic
149C2×C4×D4C2311yescharacteristic
150C2×#117C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C8×Q8—24no—
154C8×Q8—24no—
155#436—24no—
156#436—24no—
157#433—28no—
158#431—24no—
159C2×C4⋊C8—24no—
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2311yescharacteristic
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2311yescharacteristic
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2311yescharacteristic
177C2×C22⋊C8C2311yescharacteristic
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2311yescharacteristic
180#405—28no—
181C4×M16—24no—
182C4×M16—24no—
183C2×#97C2311yescharacteristic
184C2×#97C2311yescharacteristic
185C2×#97C2311yescharacteristic
186C2×#97C2311yescharacteristic
187C2×#97C2312yes—
188C2×#97C2312yes—
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2312yes—
194C2×C4×C8C2312yes—
195C2×C4×C8C2312yes—
196C2×C4×C8C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207#400C2×C412yes—
208#400C2×C412yes—
209#400C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#399C2×C412yes—
213#398C2×C412yes—
214#398C2×C412yes—
215#398C2×C412yes—
216#398C2×C412yes—
217#398C2×C412yes—
218#397C2×C412yes—
219#397C2×C412yes—
220#397C2×C412yes—
221#394C2×C412yes—
222#394C2×C412yes—
223#391C2×C411yescharacteristic
224#391C2×C411yescharacteristic
225#389C2×C411yescharacteristic
226#389C2×C411yescharacteristic
227#389C2×C411yescharacteristic
228#389C2×C411yescharacteristic
229#388C2×C412yes—
230#388C2×C412yes—
231#388C2×C412yes—
232#388C2×C412yes—
233#388C2×C412yes—
234#388C2×C412yes—
235#388C2×C412yes—
236#387C2×C412yes—
237#387C2×C412yes—
238#387C2×C412yes—
239#387C2×C412yes—
240#387C2×C412yes—
241#387C2×C412yes—
242#387C2×C412yes—
243#387C2×C412yes—
244#387C2×C412yes—
245#387C2×C412yes—
246#387C2×C412yes—
247#385C2×C412yes—
248#385C2×C412yes—
249#384C2×C411yescharacteristic
250#384C2×C411yescharacteristic
251#383C2×C412yes—
252#383C2×C412yes—
253#382C2×C411yescharacteristic
254#382C2×C411yescharacteristic
255#382C2×C411yescharacteristic
256#382C2×C412yes—
257#381C2×C412yes—
258#380C2×C411yescharacteristic
259#380C2×C411yescharacteristic
260#380C2×C411yescharacteristic
261#380C2×C411yescharacteristic
262#380C2×C412yes—
263#380C2×C411yescharacteristic
264#380C2×C411yescharacteristic
265C4×C4⋊C4C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C412yes—
268C4×C4⋊C4C2×C412yes—
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C22⋊C4C2×C411yescharacteristic
282C4×C22⋊C4C2×C411yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2×C411yescharacteristic
285C4×C22⋊C4C2311yescharacteristic
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C4×C22⋊C4C2312yes—
289C4×C22⋊C4C2311yescharacteristic
290#376C2312yes—
291C43C2312yes—
292C43C2311yescharacteristic
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2311yescharacteristic
302#336C2312yes—
303#336C2311yescharacteristic
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2311yescharacteristic
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2311yescharacteristic
317#336C2312yes—
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320C22×Q8C22×C411yescharacteristic
321C22×D4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C411yescharacteristic
325C23×C4C22×C411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—41no—
338C2×M16—41no—
339C2×M16#4114yes—
340C22×C8—24no—
341C22×C8—24no—
342C22×C8—42no—
343C22×C8C2412yes—
344C22×C8C2411yescharacteristic
345C22×C8C2411yescharacteristic
346C22×C8C2412yes—
347C22×C8C2411yescharacteristic
348C22×C8C2412yes—
349C22×C8C2412yes—
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355#126—44no—
356#125—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—24no—
366C4×D4—42no—
367#117—24no—
368#117—24no—
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C412yes—
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C411yescharacteristic
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C412yes—
391C2×C4⋊C4C22×C412yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C412yes—
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C412yes—
396C2×C22⋊C4C22×C411yescharacteristic
397C2×C22⋊C4C22×C411yescharacteristic
398C2×C22⋊C4C22×C411yescharacteristic
399C2×C22⋊C4C22×C411yescharacteristic
400C2×C22⋊C4C22×C411yescharacteristic
401C2×C22⋊C4C22×C411yescharacteristic
402C2×C22⋊C4C22×C412yes—
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C412yes—
407C2×C22⋊C4C22×C412yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C412yes—
415C2×C42C22×C412yes—
416C2×C42C22×C412yes—
417C2×C42C22×C411yescharacteristic
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C412yes—
423C2×C42C22×C411yescharacteristic
424C2×C42C2412yes—
425C2×C42C2412yes—
426C2×C42C2411yescharacteristic
427C2×C42C2412yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2412yes—
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8—24no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C4⋊C8#4114yes—
446C22⋊C8—24no—
447C22⋊C8—22no—
448C22⋊C8—24no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—42no—
452C22⋊C8#4114yes—
453#97—22no—
454#97—22no—
455#97—22no—
456#97—22no—
457#97—24no—
458#97—24no—
459#97—24no—
460#97—24no—
461C4×C8—24no—
462C4×C8—24no—
463C4×C8—24no—
464C4×C8—24no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—24no—
468C4×C8—24no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—42no—
474C4×C8—41no—
475C4×C8—42no—
476C4×C8#4114yes—
477#95C22×C412yes—
478#95C22×C412yes—
479#95C22×C412yes—
480#95C22×C412yes—
481#95C22×C411yescharacteristic
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
484#95C22×C411yescharacteristic
485#95C22×C411yescharacteristic
486#95C22×C411yescharacteristic
487#95C22×C412yes—
488#95C22×C412yes—
489#95C22×C412yes—
490#95C22×C412yes—
491#95C22×C412yes—
492#95C22×C412yes—
493#95C22×C412yes—
494#95C22×C412yes—
495#95C22×C412yes—
496#95C22×C412yes—
497#95C22×C412yes—
498#95C22×C412yes—
499#95C22×C412yes—
500#95C22×C412yes—
501#95C22×C412yes—
502#95C22×C412yes—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C412yes—
506#95C22×C412yes—
507#95C22×C412yes—
508C24C23×C411yescharacteristic
509C24C23×C411yescharacteristic
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8#13114yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C411yescharacteristic
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C412yes—
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C412yes—
549C22×C4C23×C412yes—
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C412yes—
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2511yescharacteristic
561M16—28no—
562M16—44no—
563M16—44no—
564M16—44no—
565C2×C8—21no—
566C2×C8—22no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—22no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8—21no—
591C2×C8—22no—
592C2×C8—21no—
593C2×C8—48no—
594C2×C8C2×#4112yes—
595C2×C8C2×#4112yes—
596C2×C8C2×#4114yes—
597C2×C8C2×#4112yes—
598C2×C8C2×#4112yes—
599C2×C8C2×#4112yes—
600C2×C8C2×#4112yes—
601C2×C82−1+412yes—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—24no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—41no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—24no—
646C42—22no—
647C42—24no—
648C42—22no—
649C42—24no—
650C42—21no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—22no—
657C42—22no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—22no—
662C42—21no—
663C42—22no—
664C42—21no—
665C42—22no—
666C42—41no—
667C42—42no—
668C42#13114yes—
669C42C2×#4112yes—
670C42C2×#4112yes—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23C4×#4112yes—
685C23C24×C411yescharacteristic
686Q8—28no—
687D4—44no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4C4×#4112yes—
752C2×C4C4×#4112yes—
753C2×C4C4×#4112yes—
754C2×C4C2×#13112yes—
755C2×C4C2×#13114yes—
756C2×C4C2×#13112yes—
757C2×C4C2×#13112yes—
758C2×C4C2×#13112yes—
759C2×C4#56812yes—
760C2×C4C22×#4111yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C22×#4111yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C2×2−1+411yescharacteristic
765C2×C4#58511yescharacteristic
766C8—22no—
767C8—24no—
768C8—22no—
769C8—22no—
770C8—22no—
771C8—41no—
772C8—41no—
773C8—42no—
774C8—42no—
775C8—41no—
776C8—42no—
777C8#55214yes—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22C2×C4×#4111yescharacteristic
793C22C2×C4×#4111yescharacteristic
794C22C4×2−1+411yescharacteristic
795C22C22×#13111yescharacteristic
796C22C22×#13111yescharacteristic
797C22C2×#56811yescharacteristic
798C22#357311yescharacteristic
799C4—24no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—42no—
817C4—42no—
818C4#296614yes—
819C4C2×#55211yescharacteristic
820C4#347511yescharacteristic
821C4#347511yescharacteristic
822C4#348211yescharacteristic
823C2—42no—
824C2—81no—
825C2C4×#55211yescharacteristic
826C2C2×#296611yescharacteristic
827C2#6021011yescharacteristic
828C2#6021711yescharacteristic
829C2#6021811yescharacteristic
830C2#6033411yescharacteristic
831C2#6033511yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC22×D4C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #23286C2semidirect
3. #23267C2semidirect
4. #23253C2semidirect
5. #23050C2semidirect
6. #22952C2semidirect
8. #22832C2semidirect
10. #22633C2semidirect
11. #22600C2semidirect
12. #22597C2semidirect
13. #21678C2semidirect
14. #21673C2semidirect
15. #21666C2semidirect
16. #21596C2semidirect
17. #21596C2semidirect
19. C4×C8×Q8C2semidirect
21. #20482C2semidirect
22. #20474C2semidirect
23. #20441C2semidirect

Maximal subgroups

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

subgroupindex
#348982
#232862
#232672
#232532
#230502
#229522
#229152
#228322
#227482
#226332
#226002
#225972
#216782
#216732
#216662
#215962
#215712
C4×C8×Q82
C4×#4362
#204822
#204742
#204412