Finite Group Databasebeta

← #6404667

Subgroups — #6404667

Order 512.

1442 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#34793C211yesmaximal, characteristic
2#23293C212yesmaximal, complemented
3#23257C212yesmaximal, complemented
4#23253C211yesmaximal, characteristic, complemented
5#23054C211yesmaximal, characteristic, complemented
6#22952C211yesmaximal, characteristic, complemented
7#22905C212yesmaximal
8#22748C211yesmaximal, characteristic
9#22735C211yesmaximal, characteristic, complemented
10#22639C211yesmaximal, characteristic, complemented
11#22600C211yesmaximal, characteristic, complemented
12#22597C212yesmaximal, complemented
13#22377C212yesmaximal, complemented
14#22352C212yesmaximal, complemented
15#22072C212yesmaximal
16#21675C211yesmaximal, characteristic, complemented
17#21598C211yesmaximal, characteristic, complemented
18C8×C22⋊Q8C211yesmaximal, characteristic, complemented
19#21349C211yesmaximal, characteristic, complemented
20#21343C211yesmaximal, characteristic, complemented
21#21145C211yesmaximal, characteristic, complemented
22#20552C212yesmaximal, complemented
23C4×#435C211yesmaximal, characteristic
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#435C2211yescharacteristic
27C2×#435C2211yescharacteristic
28C2×#433C2212yes—
29C2×#431C2211yescharacteristic
30C2×#424C2212yes—
31C22×C4⋊C8C2211yescharacteristic
32C2×C4×M16C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34#2530C412yes—
35#2528C412yes—
36#2517C412yes—
37#2511C411yescharacteristic
38#2506C411yescharacteristic
39#2499C411yescharacteristic
40#2494C411yescharacteristic
41#2489C411yescharacteristic
42#2485C411yescharacteristic
43#2460C412yes—
44#2441C411yescharacteristic
45#2415C411yescharacteristic
46#2401C2212yes—
47#2395C2212yes—
48C4×#125C2212yes—
49C4×#125C2211yescharacteristic
50C4×C22⋊Q8C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52#2298C2212yes—
53#2295C2211yescharacteristic
54#2285C2211yescharacteristic
55C42×D4C2211yescharacteristic
56C4×#117C2211yescharacteristic
57#1984C2211yescharacteristic
58#1984C2211yescharacteristic
59#1940C2212yes—
60#1940C2212yes—
61#1940C2212yes—
62#1939C2211yescharacteristic
63#1939C2212yes—
64#1939C2211yescharacteristic
65#1939C2211yescharacteristic
66#1939C2212yes—
67#1939C2211yescharacteristic
68#1939C2211yescharacteristic
69#1939C2211yescharacteristic
70#1939C2211yescharacteristic
71#1939C2212yes—
72#1939C2211yescharacteristic
73#1924C2212yes—
74#1924C2212yes—
75#1923C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1917C2212yes—
79#1917C2212yes—
80#1917C2212yes—
81#1917C2212yes—
82#1917C2212yes—
83#1917C2212yes—
84#1916C2212yes—
85#1916C2212yes—
86#1916C2212yes—
87#1916C2212yes—
88#1916C2212yes—
89#1916C2212yes—
90#1916C2212yes—
91#1869C2212yes—
92#1851C2212yes—
93#1850C2212yes—
94#1850C2212yes—
95#1850C2212yes—
96#1850C2212yes—
97#1839C2212yes—
98#1832C2212yes—
99#1831C2211yescharacteristic
100#1818C2212yes—
101#1797C2211yescharacteristic
102#1797C2211yescharacteristic
103#1771C2211yescharacteristic
104#1771C2211yescharacteristic
105#1771C2212yes—
106#1771C2212yes—
107#1770C2211yescharacteristic
108#1770C2212yes—
109#1770C2212yes—
110C8×C4⋊C4C2212yes—
111C8×C4⋊C4C2212yes—
112C8×C4⋊C4C2211yescharacteristic
113C8×C4⋊C4C2211yescharacteristic
114C8×C4⋊C4C2211yescharacteristic
115#1768C2212yes—
116#1768C2212yes—
117C4×C4⋊C8C2211yescharacteristic
118C4×C4⋊C8C2212yes—
119C4×C4⋊C8C2212yes—
120C4×C4⋊C8C2212yes—
121C4×C4⋊C8C2211yescharacteristic
122#1753C2211yescharacteristic
123#1753C2211yescharacteristic
124#1753C2212yes—
125#1752C2211yescharacteristic
126#1752C2211yescharacteristic
127C8×C22⋊C4C2212yes—
128C8×C22⋊C4C2212yes—
129C8×C22⋊C4C2212yes—
130C4×C22⋊C8C2211yescharacteristic
131C4×C22⋊C8C2211yescharacteristic
132#1746C2212yes—
133#1729C2212yes—
134C4×#97C2211yescharacteristic
135C22×M16C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2312yes—
140C2×#125C2×C411yescharacteristic
141C2×#125C2×C412yes—
142C2×C22⋊Q8C2×C411yescharacteristic
143C2×C22⋊Q8C2×C411yescharacteristic
144C2×C4×Q8C2311yescharacteristic
145C2×C4×D4C2×C411yescharacteristic
146C2×C4×D4C2×C411yescharacteristic
147C2×C4×D4C2311yescharacteristic
148C2×#117C2×C411yescharacteristic
149C2×#117C2×C411yescharacteristic
150C2×#117C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#446—42no—
154C8×Q8—42no—
155#435—24no—
156#435—24no—
157#433—28no—
158#431—42no—
159#424—28no—
160C2×C4⋊C8—42no—
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2311yescharacteristic
180C2×C22⋊C8C2311yescharacteristic
181C2×C22⋊C8C2311yescharacteristic
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2311yescharacteristic
185C4×M16—42no—
186C2×#97C2312yes—
187C2×#97C2311yescharacteristic
188C2×#97C2311yescharacteristic
189C2×#97C2311yescharacteristic
190C2×#97C2311yescharacteristic
191C2×#97C2311yescharacteristic
192C2×#97C2312yes—
193C2×#97C2311yescharacteristic
194C2×C4×C8—42no—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207#401C2×C412yes—
208#400C2×C412yes—
209#400C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#399C2×C412yes—
213#398C2×C412yes—
214#397C2×C412yes—
215#397C2×C412yes—
216#397C2×C412yes—
217#397C2×C412yes—
218#397C2×C412yes—
219#397C2×C412yes—
220#396C2×C412yes—
221#394C2×C412yes—
222#394C2×C412yes—
223#391C2×C411yescharacteristic
224#391C2×C411yescharacteristic
225#391C2×C411yescharacteristic
226#391C2×C411yescharacteristic
227#389C2×C411yescharacteristic
228#389C2×C412yes—
229#389C2×C412yes—
230#389C2×C411yescharacteristic
231#389C2×C411yescharacteristic
232#389C2×C411yescharacteristic
233#389C2×C411yescharacteristic
234#389C2×C411yescharacteristic
235#388C2×C412yes—
236#388C2×C412yes—
237#388C2×C412yes—
238#388C2×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#387C2×C412yes—
248#387C2×C412yes—
249#387C2×C412yes—
250#387C2×C412yes—
251#387C2×C412yes—
252#387C2×C412yes—
253#385C2×C412yes—
254#385C2×C412yes—
255#384C2×C411yescharacteristic
256#384C2×C411yescharacteristic
257#382C2×C412yes—
258#382C2×C411yescharacteristic
259#382C2×C412yes—
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×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2311yescharacteristic
279C4×C22⋊C4C2×C411yescharacteristic
280C4×C22⋊C4C2×C412yes—
281C4×C22⋊C4C2×C411yescharacteristic
282C4×C22⋊C4C2×C411yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2311yescharacteristic
288C4×C22⋊C4C2311yescharacteristic
289#376C2×C412yes—
290#376C2312yes—
291C43C2311yescharacteristic
292C43C2312yes—
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#336C2312yes—
312#336C2312yes—
313#336C2311yescharacteristic
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—41no—
331C2×M16—41no—
332C2×M16—41no—
333C2×M16#4114yes—
334C22×C8—24no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—41no—
339C22×C8—41no—
340C22×C8—41no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8C2411yescharacteristic
344C22×C8C2412yes—
345C22×C8C2412yes—
346C22×C8C2411yescharacteristic
347C22×C8C2411yescharacteristic
348C22×C8C2412yes—
349C22×C8C2412yes—
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355#125—24no—
356#125—44no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—42no—
365#117—24no—
366#117—24no—
367#117—24no—
368#117—24no—
369C2×C4⋊C4C22×C411yescharacteristic
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C412yes—
373C2×C4⋊C4C22×C412yes—
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C412yes—
391C2×C4⋊C4C22×C412yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C412yes—
396C2×C22⋊C4C22×C412yes—
397C2×C22⋊C4C22×C412yes—
398C2×C22⋊C4C22×C411yescharacteristic
399C2×C22⋊C4C22×C411yescharacteristic
400C2×C22⋊C4C22×C411yescharacteristic
401C2×C22⋊C4C22×C411yescharacteristic
402C2×C22⋊C4C22×C411yescharacteristic
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C411yescharacteristic
406C2×C22⋊C4C22×C412yes—
407C2×C22⋊C4C22×C412yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42C22×C412yes—
413C2×C42C22×C412yes—
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C412yes—
417C2×C42C22×C411yescharacteristic
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C412yes—
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—24no—
437C4⋊C8—24no—
438C4⋊C8—24no—
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—24no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449C4⋊C8—42no—
450C22⋊C8—24no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—22no—
454C22⋊C8—42no—
455C22⋊C8—42no—
456C22⋊C8#4114yes—
457#97—24no—
458#97—22no—
459#97—22no—
460#97—22no—
461#97—41no—
462#97—41no—
463#97—41no—
464#97—42no—
465C4×C8—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8—41no—
471C4×C8—41no—
472C4×C8—42no—
473C4×C8—42no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477#95C22×C412yes—
478#95C22×C412yes—
479#95C22×C412yes—
480#95C22×C412yes—
481#95C22×C412yes—
482#95C22×C412yes—
483#95C22×C412yes—
484#95C22×C412yes—
485#95C22×C411yescharacteristic
486#95C22×C411yescharacteristic
487#95C22×C411yescharacteristic
488#95C22×C411yescharacteristic
489#95C22×C411yescharacteristic
490#95C22×C411yescharacteristic
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—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4#13114yes—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C412yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
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×C411yescharacteristic
555C22×C4C23×C412yes—
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2511yescharacteristic
561M16—44no—
562M16—44no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—22no—
574C2×C8—21no—
575C2×C8—22no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8—44no—
596C2×C8—84no—
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—22no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4#13114yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—24no—
635C22⋊C4—22no—
636C22⋊C4—24no—
637C22⋊C4—22no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—41no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—24no—
646C42—24no—
647C42—22no—
648C42—22no—
649C42—24no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—21no—
657C42—22no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—21no—
662C42—21no—
663C42—22no—
664C42—21no—
665C42—22no—
666C42—42no—
667C42—41no—
668C42—41no—
669C42H(5,𝔽2)12yes—
670C422−1+412yes—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23C4×#4112yes—
684C23C2×#13112yes—
685C23C24×C411yescharacteristic
686Q8—44no—
687D4—44no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—82no—
752C2×C4C4×#4112yes—
753C2×C4#52012yes—
754C2×C4#52012yes—
755C2×C4C2×#13112yes—
756C2×C4C2×#13114yes—
757C2×C4C2×#13112yes—
758C2×C4C2×#13112yes—
759C2×C4#56812yes—
760C2×C4C22×#4111yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4C2×2−1+411yescharacteristic
764C2×C4C2×2−1+411yescharacteristic
765C2×C4#58511yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C8—22no—
771C8—41no—
772C8—42no—
773C8—42no—
774C8—41no—
775C8—42no—
776C8—42no—
777C8—41no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22C2×C4×#4111yescharacteristic
793C22C2×#52011yescharacteristic
794C22C4×2−1+411yescharacteristic
795C22C22×#13111yescharacteristic
796C22C22×#13111yescharacteristic
797C22C2×#56811yescharacteristic
798C22#357311yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—24no—
804C4—41no—
805C4—42no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—41no—
818C4#299414yes—
819C4#350511yescharacteristic
820C4#350911yescharacteristic
821C4#351511yescharacteristic
822C4#352011yescharacteristic
823C2—42no—
824C2—42no—
825C2#3431411yescharacteristic
826C2#6021011yescharacteristic
827C2#6021811yescharacteristic
828C2C2×#299411yescharacteristic
829C2#6027211yescharacteristic
830C2#6033411yescharacteristic
831C2#6034111yescharacteristic
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. #23293C2semidirect
3. #23257C2semidirect
4. #23253C2semidirect
5. #23054C2semidirect
6. #22952C2semidirect
9. #22735C2semidirect
10. #22639C2semidirect
11. #22600C2semidirect
12. #22597C2semidirect
13. #22377C2semidirect
14. #22352C2semidirect
16. #21675C2semidirect
17. #21598C2semidirect
18. C8×C22⋊Q8C2semidirect
19. #21349C2semidirect
20. #21343C2semidirect
21. #21145C2semidirect
22. #20552C2semidirect

Maximal subgroups

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

subgroupindex
#347932
#232932
#232572
#232532
#230542
#229522
#229052
#227482
#227352
#226392
#226002
#225972
#223772
#223522
#220722
#216752
#215982
C8×C22⋊Q82
#213492
#213432
#211452
#205522
C4×#4352