Finite Group Databasebeta

← #6406716

Subgroups — #6406716

Order 512.

1448 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34918C211yesmaximal, characteristic
2#23304C212yesmaximal, complemented
3#23276C212yesmaximal, complemented
4#23209C211yesmaximal, characteristic, complemented
5#23208C211yesmaximal, characteristic, complemented
6#23174C211yesmaximal, characteristic
7#22903C212yesmaximal, complemented
8#22839C211yesmaximal, characteristic, complemented
9#22829C211yesmaximal, characteristic, complemented
10#22825C211yesmaximal, characteristic, complemented
11#22796C211yesmaximal, characteristic, complemented
12#22794C212yesmaximal, complemented
13#22390C212yesmaximal, complemented
14#22370C212yesmaximal, complemented
15#22264C211yesmaximal, characteristic
16#22210C211yesmaximal, characteristic, complemented
17#21634C211yesmaximal, characteristic, complemented
18#21562C212yesmaximal, complemented
19#21340C211yesmaximal, characteristic, complemented
20#21104C212yesmaximal, complemented
21#20574C211yesmaximal, characteristic, complemented
22#20562C211yesmaximal, characteristic, complemented
23#20494C211yesmaximal, characteristic, complemented
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#436C2211yescharacteristic
27C2×#436C2211yescharacteristic
28C2×#436C2211yescharacteristic
29C2×#435C2212yes—
30C2×C8×D4C2211yescharacteristic
31C2×#433C2212yes—
32C2×C4×M16C2212yes—
33#2597C412yes—
34#2595C412yes—
35#2592C411yescharacteristic
36#2580C411yescharacteristic
37#2570C411yescharacteristic
38#2544C411yescharacteristic
39#2516C412yes—
40#2513C411yescharacteristic
41#2511C411yescharacteristic
42#2458C412yes—
43#2447C411yescharacteristic
44#2445C411yescharacteristic
45#2398C2212yes—
46#2395C2212yes—
47C4×#127C2211yescharacteristic
48C4×#124C2211yescharacteristic
49C4×#124C2211yescharacteristic
50C4×#123C2212yes—
51#2295C2211yescharacteristic
52#2293C2211yescharacteristic
53#2290C2212yes—
54C42×Q8C2211yescharacteristic
55C42×D4C2211yescharacteristic
56#1985C2211yescharacteristic
57#1985C2211yescharacteristic
58#1984C2212yes—
59#1984C2211yescharacteristic
60#1984C2211yescharacteristic
61#1955C2212yes—
62#1954C2211yescharacteristic
63#1954C2211yescharacteristic
64#1954C2211yescharacteristic
65#1954C2211yescharacteristic
66#1940C2211yescharacteristic
67#1940C2211yescharacteristic
68#1924C2212yes—
69#1924C2212yes—
70#1924C2212yes—
71#1924C2212yes—
72#1924C2212yes—
73#1924C2212yes—
74#1924C2212yes—
75#1924C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1923C2212yes—
79#1923C2212yes—
80#1917C2211yescharacteristic
81#1917C2212yes—
82#1917C2211yescharacteristic
83#1917C2212yes—
84#1917C2212yes—
85#1917C2211yescharacteristic
86#1917C2211yescharacteristic
87#1916C2212yes—
88#1870C2212yes—
89#1870C2212yes—
90#1870C2212yes—
91#1870C2212yes—
92#1870C2212yes—
93#1869C2212yes—
94#1851C2212yes—
95#1851C2212yes—
96#1851C2212yes—
97#1850C2212yes—
98#1842C2211yescharacteristic
99#1840C2212yes—
100#1831C2211yescharacteristic
101#1831C2211yescharacteristic
102#1817C2212yes—
103#1798C2212yes—
104#1771C2212yes—
105#1770C2212yes—
106#1770C2212yes—
107#1770C2211yescharacteristic
108#1770C2211yescharacteristic
109C8×C4⋊C4C2211yescharacteristic
110C8×C4⋊C4C2211yescharacteristic
111#1768C2212yes—
112#1767C2211yescharacteristic
113#1767C2211yescharacteristic
114C4×C4⋊C8C2211yescharacteristic
115C4×C4⋊C8C2211yescharacteristic
116C4×C4⋊C8C2211yescharacteristic
117C4×C4⋊C8C2211yescharacteristic
118#1753C2212yes—
119#1753C2212yes—
120#1753C2212yes—
121#1753C2212yes—
122#1753C2212yes—
123#1753C2212yes—
124#1752C2212yes—
125C8×C22⋊C4C2212yes—
126#1750C2212yes—
127#1749C2212yes—
128#1749C2212yes—
129#1746C2212yes—
130#1746C2212yes—
131#1744C2211yescharacteristic
132#1744C2211yescharacteristic
133#1729C2212yes—
134C4×#97C2211yescharacteristic
135C22×M16C2312yes—
136C22×M16C2312yes—
137C22×M16C2312yes—
138C23×C8C2312yes—
139C2×#127C2×C411yescharacteristic
140C2×#124C2×C411yescharacteristic
141C2×#124C2×C411yescharacteristic
142C2×#123C2×C412yes—
143C2×C4×Q8C2×C411yescharacteristic
144C2×C4×Q8C2×C411yescharacteristic
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×D4C2×C411yescharacteristic
148C2×C4×D4C2×C411yescharacteristic
149C2×C4×D4C2311yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×#117C2312yes—
154C22×C42C2312yes—
155#446—24no—
156C8×Q8—24no—
157#436—24no—
158#436—24no—
159#436—24no—
160#435—44no—
161C8×D4—24no—
162#433—44no—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C4×M16—44no—
190C2×#97C2311yescharacteristic
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×#97C2311yescharacteristic
196C2×#97C2312yes—
197C2×#97C2311yescharacteristic
198C2×#97C2311yescharacteristic
199C2×C4×C8C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207#400C2×C412yes—
208#400C2×C412yes—
209#400C2×C412yes—
210#399C2×C412yes—
211#398C2×C412yes—
212#397C2×C412yes—
213#397C2×C412yes—
214#397C2×C412yes—
215#397C2×C412yes—
216#397C2×C412yes—
217#394C2×C412yes—
218#394C2×C412yes—
219#394C2×C412yes—
220#394C2×C412yes—
221#393C2×C412yes—
222#393C2×C412yes—
223#391C2×C411yescharacteristic
224#391C2×C411yescharacteristic
225#391C2×C411yescharacteristic
226#391C2×C411yescharacteristic
227#390C2×C411yescharacteristic
228#390C2×C411yescharacteristic
229#390C2×C412yes—
230#390C2×C412yes—
231#390C2×C411yescharacteristic
232#390C2×C411yescharacteristic
233#390C2×C411yescharacteristic
234#390C2×C411yescharacteristic
235#389C2×C411yescharacteristic
236#389C2×C411yescharacteristic
237#389C2×C411yescharacteristic
238#389C2×C411yescharacteristic
239#388C2×C412yes—
240#388C2×C412yes—
241#388C2×C412yes—
242#388C2×C412yes—
243#388C2×C412yes—
244#388C2×C412yes—
245#388C2×C412yes—
246#388C2×C412yes—
247#388C2×C412yes—
248#388C2×C412yes—
249#387C2×C412yes—
250#387C2×C412yes—
251#387C2×C412yes—
252#387C2×C412yes—
253#387C2×C412yes—
254#387C2×C412yes—
255#386C2×C412yes—
256#386C2×C412yes—
257#386C2×C412yes—
258#385C2×C412yes—
259#385C2×C412yes—
260#385C2×C412yes—
261#384C2×C411yescharacteristic
262#382C2×C411yescharacteristic
263#382C2×C411yescharacteristic
264#381C2×C412yes—
265C4×C4⋊C4C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2×C411yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4C2×C412yes—
279C4×C22⋊C4C2×C412yes—
280C4×C22⋊C4C2312yes—
281C4×C22⋊C4C2312yes—
282C4×C22⋊C4C2312yes—
283C4×C22⋊C4C2312yes—
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2312yes—
286#376C2312yes—
287C43C2311yescharacteristic
288C43C2311yescharacteristic
289C43C2311yescharacteristic
290#336C2312yes—
291#336C2312yes—
292#336C2311yescharacteristic
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2311yescharacteristic
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2311yescharacteristic
303#336C2311yescharacteristic
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2311yescharacteristic
314#336C2311yescharacteristic
315#336C2311yescharacteristic
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×Q8C22×C411yescharacteristic
321C22×D4C22×C411yescharacteristic
322C22×D4C22×C411yescharacteristic
323C22×D4C22×C412yes—
324C22×D4C22×C412yes—
325C23×C4C22×C412yes—
326C23×C4C22×C412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—24no—
339C22×C8—42no—
340C22×C8—42no—
341C22×C8C2411yescharacteristic
342C22×C8C2412yes—
343C22×C8C2412yes—
344C22×C8C2411yescharacteristic
345C22×C8C2411yescharacteristic
346C22×C8C2411yescharacteristic
347C22×C8C2412yes—
348C22×C8C2411yescharacteristic
349C22×C8C2412yes—
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353#127—42no—
354#124—42no—
355#124—42no—
356#123—44no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—42no—
360C4×Q8—41no—
361C4×Q8—41no—
362C4×Q8—42no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—42no—
373#117—42no—
374#117—42no—
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C411yescharacteristic
387C2×C4⋊C4C22×C411yescharacteristic
388C2×C4⋊C4C22×C411yescharacteristic
389C2×C4⋊C4C22×C411yescharacteristic
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C411yescharacteristic
392C2×C4⋊C4C22×C411yescharacteristic
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C412yes—
395C2×C4⋊C4C22×C412yes—
396C2×C22⋊C4C22×C412yes—
397C2×C22⋊C4C22×C412yes—
398C2×C22⋊C4C22×C412yes—
399C2×C22⋊C4C22×C412yes—
400C2×C22⋊C4C22×C412yes—
401C2×C22⋊C4C22×C412yes—
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×C22⋊C4C22×C412yes—
409C2×C22⋊C4C22×C412yes—
410C2×C22⋊C4C22×C412yes—
411C2×C22⋊C4C22×C412yes—
412C2×C22⋊C4C22×C412yes—
413C2×C22⋊C4C22×C412yes—
414C2×C22⋊C4C22×C412yes—
415C2×C22⋊C4C22×C412yes—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C411yescharacteristic
424C2×C42C22×C411yescharacteristic
425C2×C42C22×C411yescharacteristic
426C2×C42C22×C411yescharacteristic
427C2×C42C22×C411yescharacteristic
428C2×C42C22×C411yescharacteristic
429C2×C42C22×C411yescharacteristic
430C2×C42C22×C412yes—
431C2×C42C22×C412yes—
432C2×C42C2411yescharacteristic
433C2×C42C2412yes—
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2412yes—
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C4⋊C8—24no—
442C4⋊C8—24no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C4⋊C8—22no—
448C4⋊C8—41no—
449C4⋊C8—41no—
450C4⋊C8—42no—
451C4⋊C8—41no—
452C4⋊C8—41no—
453C4⋊C8—42no—
454C4⋊C8#4114yes—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C22⋊C8—42no—
461C22⋊C8—42no—
462C22⋊C8—42no—
463C22⋊C8—42no—
464C22⋊C8—42no—
465C22⋊C8—42no—
466C22⋊C8—42no—
467#97—24no—
468#97—22no—
469#97—41no—
470#97—41no—
471#97—41no—
472#97—42no—
473#97—42no—
474#97—42no—
475#97—42no—
476C4×C8—24no—
477C4×C8—24no—
478C4×C8—22no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—42no—
482C4×C8—42no—
483C4×C8#4114yes—
484#95C22×C412yes—
485#95C22×C412yes—
486#95C22×C412yes—
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×C411yescharacteristic
502#95C22×C411yescharacteristic
503#95C22×C411yescharacteristic
504#95C22×C411yescharacteristic
505#95C22×C411yescharacteristic
506#95C22×C411yescharacteristic
507#95C22×C412yes—
508#95C22×C412yes—
509C24C23×C412yes—
510C24C23×C412yes—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—41no—
516C2×Q8—41no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C412yes—
552C22×C4C23×C412yes—
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C412yes—
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C23×C411yescharacteristic
564C22×C4C23×C411yescharacteristic
565C22×C4C23×C411yescharacteristic
566C22×C4C23×C411yescharacteristic
567C22×C4C2511yescharacteristic
568M16—48no—
569M16—48no—
570M16—84no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—22no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—22no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—22no—
602C2×C8—21no—
603C2×C8—84no—
604C2×C8C2×#4112yes—
605C2×C8C2×#4112yes—
606C2×C8C2×#4114yes—
607C2×C8H(5,𝔽2)12yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—42no—
673C42—42no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42C2×#4112yes—
680C42C2×#4112yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23C24×C411yescharacteristic
696Q8—44no—
697Q8—44no—
698D4—44no—
699D4—44no—
700D4—84no—
701D4—84no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4C4×#4112yes—
768C2×C4C4×#4112yes—
769C2×C4#56812yes—
770C2×C4#56812yes—
771C2×C4#56812yes—
772C2×C4C22×#4111yescharacteristic
773C2×C4C22×#4111yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4#58511yescharacteristic
776C2×C4#58511yescharacteristic
777C2×C4#58511yescharacteristic
778C8—22no—
779C8—22no—
780C8—24no—
781C8—22no—
782C8—42no—
783C8—42no—
784C8—42no—
785C8—41no—
786C8—41no—
787C8—41no—
788C8—41no—
789C8—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22C2×C4×#4111yescharacteristic
805C22#342811yescharacteristic
806C22C4×H(5,𝔽2)11yescharacteristic
807C22C2×#56811yescharacteristic
808C22C2×#56811yescharacteristic
809C22C2×#56811yescharacteristic
810C22#357311yescharacteristic
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4#296714yes—
831C4#350611yescharacteristic
832C4#351011yescharacteristic
833C4#351311yescharacteristic
834C4#352411yescharacteristic
835C2—82no—
836C2—82no—
837C2#3432911yescharacteristic
838C2C2×#296711yescharacteristic
839C2#6021911yescharacteristic
840C2#6028511yescharacteristic
841C2#6030011yescharacteristic
842C2#6031711yescharacteristic
843C2#6032611yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#127C2×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. #23304C2semidirect
3. #23276C2semidirect
4. #23209C2semidirect
5. #23208C2semidirect
7. #22903C2semidirect
8. #22839C2semidirect
9. #22829C2semidirect
10. #22825C2semidirect
11. #22796C2semidirect
12. #22794C2semidirect
13. #22390C2semidirect
14. #22370C2semidirect
16. #22210C2semidirect
17. #21634C2semidirect
18. #21562C2semidirect
19. #21340C2semidirect
20. #21104C2semidirect
21. #20574C2semidirect
22. #20562C2semidirect
23. #20494C2semidirect

Maximal subgroups

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

subgroupindex
#349182
#233042
#232762
#232092
#232082
#231742
#229032
#228392
#228292
#228252
#227962
#227942
#223902
#223702
#222642
#222102
#216342
#215622
#213402
#211042
#205742
#205622
#204942