Finite Group Databasebeta

← #6408330

Subgroups — #6408330

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34909C211yesmaximal, characteristic
2#23325C211yesmaximal, characteristic, complemented
3#23319C212yesmaximal, complemented
4#23317C211yesmaximal, characteristic, complemented
5#22853C211yesmaximal, characteristic, complemented
6#22847C212yesmaximal, complemented
7#22845C211yesmaximal, characteristic, complemented
8#22752C212yesmaximal, complemented
9#22752C212yesmaximal, complemented
10#22649C212yesmaximal, complemented
11#22647C212yesmaximal, complemented
12#22289C212yesmaximal, complemented
13#22287C212yesmaximal, complemented
14#22174C212yesmaximal, complemented
15#22172C212yesmaximal, complemented
16#21928C212yesmaximal, complemented
17#21849C211yesmaximal, characteristic, complemented
18#21847C211yesmaximal, characteristic, complemented
19#20630C212yesmaximal, complemented
20C2×C4×#41C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C2×#436C2212yes—
23C2×#435C2212yes—
24C2×#435C2212yes—
25C2×C8×D4C2212yes—
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C2×#424C2212yes—
29C2×#424C2212yes—
30C2×#423C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C2×#408C2212yes—
33C2×#408C2212yes—
34#2600C412yes—
35#2600C412yes—
36#2599C411yescharacteristic
37#2599C411yescharacteristic
38#2598C411yescharacteristic
39#2598C411yescharacteristic
40#2581C411yescharacteristic
41#2580C411yescharacteristic
42#2536C411yescharacteristic
43#2535C411yescharacteristic
44#2485C412yes—
45#2407C412yes—
46#2395C2211yescharacteristic
47#2395C2211yescharacteristic
48#2388C2211yescharacteristic
49#2388C2211yescharacteristic
50C4×C22⋊Q8C2212yes—
51C4×#121C2212yes—
52#2290C2212yes—
53#2290C2212yes—
54#2283C2211yescharacteristic
55#1984C2211yescharacteristic
56#1984C2212yes—
57#1984C2211yescharacteristic
58#1954C2211yescharacteristic
59#1954C2212yes—
60#1954C2211yescharacteristic
61#1940C2212yes—
62#1940C2212yes—
63#1939C2212yes—
64#1939C2212yes—
65#1924C2212yes—
66#1924C2212yes—
67#1924C2212yes—
68#1924C2212yes—
69#1923C2212yes—
70#1923C2212yes—
71#1923C2212yes—
72#1923C2212yes—
73#1917C2212yes—
74#1917C2212yes—
75#1916C2212yes—
76#1916C2212yes—
77#1916C2212yes—
78#1916C2212yes—
79#1916C2212yes—
80#1916C2212yes—
81#1870C2211yescharacteristic
82#1870C2211yescharacteristic
83#1870C2212yes—
84#1870C2212yes—
85#1870C2211yescharacteristic
86#1870C2211yescharacteristic
87#1869C2212yes—
88#1869C2212yes—
89#1869C2212yes—
90#1869C2212yes—
91#1851C2212yes—
92#1851C2212yes—
93#1851C2212yes—
94#1851C2212yes—
95#1850C2212yes—
96#1850C2212yes—
97#1850C2212yes—
98#1850C2212yes—
99#1843C2212yes—
100#1832C2212yes—
101#1798C2212yes—
102#1798C2212yes—
103#1798C2212yes—
104#1798C2212yes—
105#1797C2212yes—
106#1797C2212yes—
107#1797C2212yes—
108#1797C2212yes—
109#1797C2212yes—
110#1797C2212yes—
111#1768C2212yes—
112#1768C2212yes—
113#1753C2212yes—
114#1753C2212yes—
115C8×C22⋊C4C2212yes—
116C8×C22⋊C4C2212yes—
117#1728C2212yes—
118C2×#336C2212yes—
119C22×#41C2×C411yescharacteristic
120C22×#41C2311yescharacteristic
121C22×M16C2312yes—
122C22×M16C2312yes—
123C22×M16C2311yescharacteristic
124C22×M16C2311yescharacteristic
125C23×C8C2312yes—
126C23×C8C2312yes—
127C23×C8C2312yes—
128C2×C22⋊Q8C2×C412yes—
129C2×#121C2×C412yes—
130C4×#41—42no—
131C4×#41—42no—
132C4×#41—42no—
133C4×#41—42no—
134C2×C4×Q8C2×C411yescharacteristic
135C2×C4×Q8C2×C411yescharacteristic
136C2×C4×Q8C2×C411yescharacteristic
137C2×C4×Q8C2311yescharacteristic
138C2×C4×D4C2×C411yescharacteristic
139C2×C4×D4C2×C411yescharacteristic
140C2×C4×D4C2×C411yescharacteristic
141C2×C4×D4C2×C411yescharacteristic
142C2×C4×D4C2×C412yes—
143C2×C4×D4C2×C412yes—
144C2×C4×D4C2×C411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2312yes—
147C2×C4×D4C2311yescharacteristic
148C2×C4×D4C2311yescharacteristic
149C2×C4×D4C2311yescharacteristic
150C2×#117C2×C411yescharacteristic
151C2×#117C2×C411yescharacteristic
152C2×#117C2×C411yescharacteristic
153C2×#117C2312yes—
154C2×#117C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159#436—44no—
160#435—44no—
161#435—44no—
162C8×D4—44no—
163#431—42no—
164#431—42no—
165#424—44no—
166#424—44no—
167#423—42no—
168C2×C4⋊C8—42no—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2311yescharacteristic
184#408—44no—
185#408—44no—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208#400C2×C411yescharacteristic
209#400C2×C411yescharacteristic
210#399C2×C411yescharacteristic
211#399C2×C411yescharacteristic
212#398C2×C411yescharacteristic
213#398C2×C411yescharacteristic
214#397C2×C411yescharacteristic
215#397C2×C411yescharacteristic
216#397C2×C412yes—
217#397C2×C412yes—
218#395C2×C411yescharacteristic
219#395C2×C411yescharacteristic
220#394C2×C411yescharacteristic
221#394C2×C411yescharacteristic
222#394C2×C412yes—
223#394C2×C412yes—
224#394C2×C412yes—
225#394C2×C412yes—
226#393C2×C411yescharacteristic
227#393C2×C411yescharacteristic
228#392C2×C411yescharacteristic
229#392C2×C411yescharacteristic
230#392C2×C412yes—
231#392C2×C412yes—
232#391C2×C412yes—
233#390C2×C412yes—
234#389C2×C412yes—
235#389C2×C412yes—
236#388C2×C412yes—
237#388C2×C412yes—
238#388C2×C412yes—
239#388C2×C412yes—
240#388C2×C412yes—
241#388C2×C412yes—
242#387C2×C412yes—
243#387C2×C412yes—
244#387C2×C412yes—
245#387C2×C412yes—
246#387C2×C412yes—
247#387C2×C412yes—
248#386C2×C412yes—
249#386C2×C412yes—
250#386C2×C412yes—
251#386C2×C412yes—
252#386C2×C412yes—
253#386C2×C412yes—
254#385C2×C412yes—
255#385C2×C412yes—
256#385C2×C412yes—
257#385C2×C412yes—
258#385C2×C412yes—
259#385C2×C412yes—
260#383C2×C411yescharacteristic
261#383C2×C411yescharacteristic
262#382C2×C411yescharacteristic
263#382C2×C411yescharacteristic
264#381C2×C412yes—
265#380C2×C412yes—
266#380C2×C412yes—
267#380C2×C412yes—
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2312yes—
271C4×C22⋊C4C2312yes—
272C4×C22⋊C4C2312yes—
273C4×C22⋊C4C2312yes—
274C4×C22⋊C4C2312yes—
275C4×C22⋊C4C2311yescharacteristic
276C4×C22⋊C4C2311yescharacteristic
277#376C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284#336C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298C2×#41—24no—
299C2×#41—24no—
300C2×#41—24no—
301C2×#41—42no—
302C2×#41—41no—
303C2×#41—41no—
304C2×#41—42no—
305C22×Q8C22×C411yescharacteristic
306C22×Q8C22×C411yescharacteristic
307C22×D4C22×C411yescharacteristic
308C22×D4C22×C412yes—
309C22×D4C22×C411yescharacteristic
310C22×D4C22×C411yescharacteristic
311C22×D4C22×C412yes—
312C22×D4C22×C411yescharacteristic
313C22×D4C22×C412yes—
314C23×C4C22×C411yescharacteristic
315C23×C4C22×C411yescharacteristic
316C23×C4C22×C411yescharacteristic
317C23×C4C22×C411yescharacteristic
318C23×C4C22×C412yes—
319C23×C4C22×C411yescharacteristic
320C23×C4C22×C411yescharacteristic
321C23×C4C22×C412yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2412yes—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—41no—
331C2×M16—41no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C22×C8—24no—
337C22×C8—24no—
338C22×C8—42no—
339C22×C8—42no—
340C22×C8—42no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8—42no—
344C22×C8—42no—
345C22×C8C2412yes—
346C22×C8C2412yes—
347C22×C8C2412yes—
348C22×C8C2412yes—
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22⋊Q8—28no—
354#121—44no—
355C4×Q8—42no—
356C4×Q8—41no—
357C4×Q8—41no—
358C4×Q8—42no—
359C4×Q8—42no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—42no—
365C4×D4—42no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—41no—
370C4×D4—41no—
371C4×D4—41no—
372C4×D4—41no—
373C4×D4—41no—
374C4×D4—41no—
375C4×D4—44no—
376C4×D4—44no—
377#117—24no—
378#117—24no—
379#117—42no—
380#117—42no—
381#117—42no—
382#117—41no—
383#117—41no—
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×C411yescharacteristic
392C2×C4⋊C4C22×C411yescharacteristic
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C411yescharacteristic
395C2×C4⋊C4C22×C411yescharacteristic
396C2×C4⋊C4C22×C411yescharacteristic
397C2×C4⋊C4C22×C411yescharacteristic
398C2×C4⋊C4C22×C411yescharacteristic
399C2×C4⋊C4C22×C412yes—
400C2×C4⋊C4C22×C412yes—
401C2×C4⋊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×C411yescharacteristic
412C2×C22⋊C4C22×C411yescharacteristic
413C2×C22⋊C4C22×C411yescharacteristic
414C2×C22⋊C4C22×C411yescharacteristic
415C2×C22⋊C4C22×C411yescharacteristic
416C2×C22⋊C4C22×C411yescharacteristic
417C2×C22⋊C4C22×C412yes—
418C2×C22⋊C4C22×C412yes—
419C2×C22⋊C4C22×C412yes—
420C2×C22⋊C4C22×C412yes—
421C2×C22⋊C4C22×C412yes—
422C2×C22⋊C4C22×C412yes—
423C2×C22⋊C4C22×C412yes—
424C2×C22⋊C4C22×C412yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C411yescharacteristic
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C22×C411yescharacteristic
438C2×C42C22×C411yescharacteristic
439C2×C42C22×C412yes—
440C2×C42C22×C412yes—
441C2×C42C2412yes—
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2412yes—
446C2×C42C2412yes—
447C2×C42C2411yescharacteristic
448C4⋊C8—24no—
449C4⋊C8—24no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452C4⋊C8—41no—
453C4⋊C8—41no—
454C4⋊C8—42no—
455C4⋊C8—42no—
456C4⋊C8—42no—
457C4⋊C8—42no—
458C4⋊C8—42no—
459C4⋊C8—42no—
460C4⋊C8—42no—
461C4⋊C8—42no—
462C4⋊C8—42no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469C22⋊C8—42no—
470C22⋊C8—42no—
471C22⋊C8—41no—
472C22⋊C8—42no—
473C22⋊C8—41no—
474C22⋊C8—42no—
475C22⋊C8—42no—
476C22⋊C8—42no—
477C22⋊C8—42no—
478#97—42no—
479#97—42no—
480C4×C8—41no—
481C4×C8—42no—
482C4×C8—41no—
483C4×C8—42no—
484C4×C8—42no—
485#95C22×C412yes—
486#95C22×C412yes—
487#95C22×C412yes—
488#95C22×C412yes—
489#95C22×C412yes—
490#95C22×C412yes—
491#95C22×C411yescharacteristic
492#95C22×C411yescharacteristic
493#95C22×C411yescharacteristic
494#95C22×C411yescharacteristic
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—
507C24C23×C411yescharacteristic
508C24C23×C411yescharacteristic
509C24C23×C412yes—
510C24C23×C411yescharacteristic
511#41—48no—
512#41—44no—
513#41—44no—
514#41—416no—
515C2×Q8—24no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—41no—
519C2×Q8#13114yes—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—22no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—42no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—42no—
539C2×D4—42no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4C23×C412yes—
578C22×C4C23×C412yes—
579C22×C4C23×C412yes—
580C22×C4C23×C412yes—
581C22×C4C23×C411yescharacteristic
582C22×C4C23×C411yescharacteristic
583C22×C4C23×C411yescharacteristic
584C22×C4C23×C411yescharacteristic
585C22×C4C23×C411yescharacteristic
586C22×C4C23×C411yescharacteristic
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C411yescharacteristic
590C22×C4C23×C411yescharacteristic
591C22×C4C23×C412yes—
592C22×C4C23×C411yescharacteristic
593C22×C4C23×C411yescharacteristic
594C22×C4C23×C411yescharacteristic
595C22×C4H(5,𝔽2)14yes—
596C22×C42−1+414yes—
597C22×C4C2511yescharacteristic
598M16—84no—
599M16—84no—
600M16—82no—
601M16—82no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—84no—
627C2×C8—84no—
628C2×C8—84no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—42no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—21no—
677C42—21no—
678C42—22no—
679C42—22no—
680C42—21no—
681C42—21no—
682C42—22no—
683C42—22no—
684C42—21no—
685C42—21no—
686C42—22no—
687C42—22no—
688C42—42no—
689C42—42no—
690C42H(5,𝔽2)12yes—
691C42H(5,𝔽2)12yes—
692C23—22no—
693C23—21no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23#52014yes—
713C23#56812yes—
714C23C24×C411yescharacteristic
715Q8—44no—
716Q8—44no—
717D4—48no—
718D4—44no—
719D4—44no—
720D4—44no—
721D4—48no—
722D4—44no—
723D4—84no—
724C2×C4—28no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—84no—
786C2×C4#51812yes—
787C2×C4#51812yes—
788C2×C4#52014yes—
789C2×C4C2×#13112yes—
790C2×C4C2×#13112yes—
791C2×C4C2×#13112yes—
792C2×C4C2×H(5,𝔽2)11yescharacteristic
793C2×C4C2×H(5,𝔽2)12yes—
794C2×C4C2×H(5,𝔽2)11yescharacteristic
795C2×C4C2×2−1+412yes—
796C8—42no—
797C8—42no—
798C8—42no—
799C8—42no—
800C8—42no—
801C8—42no—
802C8—42no—
803C8—42no—
804C22—24no—
805C22—22no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22C2×#51811yescharacteristic
827C22C2×#52012yes—
828C22C22×#13111yescharacteristic
829C22C2×#56811yescharacteristic
830C22#357312yes—
831C4—24no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—42no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4#353612yes—
850C4#353711yescharacteristic
851C4#353811yescharacteristic
852C2—44no—
853C2—42no—
854C2—81no—
855C2—81no—
856C2#3436011yescharacteristic
857C2#6023311yescharacteristic
858C2#6023511yescharacteristic
859C2#6027212yes—
860C2#6027412yes—
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radical#34909C2
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. #23325C2semidirect
3. #23319C2semidirect
4. #23317C2semidirect
5. #22853C2semidirect
6. #22847C2semidirect
7. #22845C2semidirect
8. #22752C2semidirect
9. #22752C2semidirect
10. #22649C2semidirect
11. #22647C2semidirect
12. #22289C2semidirect
13. #22287C2semidirect
14. #22174C2semidirect
15. #22172C2semidirect
16. #21928C2semidirect
17. #21849C2semidirect
18. #21847C2semidirect
19. #20630C2semidirect

Maximal subgroups

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

subgroupindex
#349092
#233252
#233192
#233172
#228532
#228472
#228452
#227522
#226492
#226472
#222892
#222872
#221742
#221722
#219282
#218492
#218472
#206302