Finite Group Databasebeta

← #6424511

Subgroups — #6424511

Order 512.

1363 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34772C211yesmaximal, characteristic
2#23345C212yesmaximal, complemented
3#23341C212yesmaximal, complemented
4#23262C212yesmaximal, complemented
5#23247C211yesmaximal, characteristic, complemented
6#23055C211yesmaximal, characteristic, complemented
7#23051C211yesmaximal, characteristic, complemented
8#22800C212yesmaximal
9#22799C211yesmaximal, characteristic
10#22721C211yesmaximal, characteristic, complemented
11#22600C211yesmaximal, characteristic, complemented
12#22599C211yesmaximal, characteristic, complemented
13#22302C212yesmaximal, complemented
14#22109C212yesmaximal, complemented
15#22104C212yesmaximal, complemented
16#22102C211yesmaximal, characteristic, complemented
17#22098C211yesmaximal, characteristic, complemented
18#22017C212yesmaximal
19#21954C211yesmaximal, characteristic, complemented
20#21953C211yesmaximal, characteristic, complemented
21#21713C211yesmaximal, characteristic, complemented
22#21343C211yesmaximal, characteristic, complemented
23#21265C211yesmaximal, characteristic
24C2×#446C2211yescharacteristic
25C2×#446C2212yes—
26C2×C8×Q8C2211yescharacteristic
27C2×#433C2212yes—
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#431C2212yes—
31C2×#431C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2522C412yes—
34#2520C412yes—
35#2511C411yescharacteristic
36#2507C411yescharacteristic
37#2505C412yes—
38#2502C411yescharacteristic
39#2497C411yescharacteristic
40#2492C411yescharacteristic
41#2487C411yescharacteristic
42#2450C412yes—
43#2440C411yescharacteristic
44#2417C411yescharacteristic
45#2402C2212yes—
46#2396C2212yes—
47C4×C4⋊Q8C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×C22⋊Q8C2212yes—
51#2295C2211yescharacteristic
52#2290C2212yes—
53#2285C2211yescharacteristic
54C42×D4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56#1985C2212yes—
57#1984C2211yescharacteristic
58#1984C2212yes—
59#1984C2212yes—
60#1984C2211yescharacteristic
61#1955C2211yescharacteristic
62#1955C2211yescharacteristic
63#1954C2212yes—
64#1940C2212yes—
65#1940C2211yescharacteristic
66#1940C2211yescharacteristic
67#1940C2212yes—
68#1940C2212yes—
69#1940C2212yes—
70#1940C2212yes—
71#1940C2212yes—
72#1939C2212yes—
73#1939C2211yescharacteristic
74#1939C2211yescharacteristic
75#1939C2212yes—
76#1939C2212yes—
77#1939C2212yes—
78#1939C2211yescharacteristic
79#1939C2211yescharacteristic
80#1939C2211yescharacteristic
81#1939C2211yescharacteristic
82#1939C2211yescharacteristic
83#1939C2211yescharacteristic
84#1924C2212yes—
85#1924C2212yes—
86#1924C2212yes—
87#1924C2212yes—
88#1924C2212yes—
89#1924C2211yescharacteristic
90#1924C2211yescharacteristic
91#1924C2211yescharacteristic
92#1924C2211yescharacteristic
93#1923C2212yes—
94#1923C2212yes—
95#1923C2212yes—
96#1923C2212yes—
97#1923C2212yes—
98#1917C2212yes—
99#1917C2212yes—
100#1917C2212yes—
101#1917C2212yes—
102#1917C2212yes—
103#1917C2212yes—
104#1916C2212yes—
105#1916C2212yes—
106#1916C2212yes—
107#1916C2212yes—
108#1843C2212yes—
109#1842C2211yescharacteristic
110#1818C2212yes—
111#1817C2212yes—
112#1798C2212yes—
113#1798C2212yes—
114#1797C2212yes—
115#1797C2211yescharacteristic
116#1797C2211yescharacteristic
117#1797C2212yes—
118#1771C2212yes—
119#1771C2212yes—
120#1770C2211yescharacteristic
121#1770C2212yes—
122#1770C2212yes—
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2212yes—
125C8×C4⋊C4C2211yescharacteristic
126C8×C4⋊C4C2211yescharacteristic
127#1768C2212yes—
128#1768C2212yes—
129C4×C4⋊C8C2211yescharacteristic
130C4×C4⋊C8C2211yescharacteristic
131C4×C22⋊C8C2211yescharacteristic
132C4×C22⋊C8C2211yescharacteristic
133#1746C2212yes—
134C4×#97C2211yescharacteristic
135C2×C4⋊Q8C2×C411yescharacteristic
136C2×C22⋊Q8C2×C411yescharacteristic
137C2×C22⋊Q8C2×C411yescharacteristic
138C2×C22⋊Q8C2×C412yes—
139C2×C4×Q8C2311yescharacteristic
140C2×C4×Q8C2312yes—
141C2×C4×D4C2×C411yescharacteristic
142C2×C4×D4C2×C411yescharacteristic
143C2×C4×D4C2311yescharacteristic
144C2×#117C2312yes—
145C22×C4⋊C4C2×C411yescharacteristic
146C22×C4⋊C4C2×C411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150#446—44no—
151#446—42no—
152C8×Q8—42no—
153#433—44no—
154#432—42no—
155#432—42no—
156#431—42no—
157#431—42no—
158#431—44no—
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
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⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C22⋊C8C2311yescharacteristic
182C2×C22⋊C8C2311yescharacteristic
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×#97C2312yes—
194C2×#97C2311yescharacteristic
195C2×#97C2311yescharacteristic
196C2×#97C2311yescharacteristic
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×#97C2311yescharacteristic
200C2×#97C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#400C2×C412yes—
213#400C2×C412yes—
214#400C2×C412yes—
215#399C2×C412yes—
216#398C2×C412yes—
217#398C2×C412yes—
218#398C2×C412yes—
219#398C2×C412yes—
220#398C2×C412yes—
221#398C2×C412yes—
222#396C2×C412yes—
223#396C2×C412yes—
224#395C2×C412yes—
225#393C2×C412yes—
226#391C2×C412yes—
227#391C2×C411yescharacteristic
228#391C2×C411yescharacteristic
229#391C2×C411yescharacteristic
230#391C2×C412yes—
231#391C2×C411yescharacteristic
232#389C2×C411yescharacteristic
233#389C2×C411yescharacteristic
234#389C2×C412yes—
235#389C2×C411yescharacteristic
236#389C2×C411yescharacteristic
237#389C2×C411yescharacteristic
238#389C2×C411yescharacteristic
239#389C2×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#387C2×C412yes—
249#387C2×C412yes—
250#386C2×C412yes—
251#386C2×C412yes—
252#385C2×C412yes—
253#385C2×C412yes—
254#385C2×C412yes—
255#385C2×C412yes—
256#385C2×C412yes—
257#385C2×C412yes—
258#384C2×C411yescharacteristic
259#384C2×C411yescharacteristic
260#384C2×C411yescharacteristic
261#382C2×C412yes—
262#380C2×C411yescharacteristic
263#380C2×C412yes—
264#380C2×C411yescharacteristic
265#380C2×C412yes—
266#380C2×C411yescharacteristic
267#380C2×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2×C412yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2312yes—
282C4×C4⋊C4C2311yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2×C411yescharacteristic
285C4×C22⋊C4C2×C411yescharacteristic
286C4×C22⋊C4C2×C411yescharacteristic
287C4×C22⋊C4C2311yescharacteristic
288C4×C22⋊C4C2312yes—
289C4×C22⋊C4C2312yes—
290C4×C22⋊C4C2311yescharacteristic
291#376C2312yes—
292C2×#95C2×C412yes—
293C43C2311yescharacteristic
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2311yescharacteristic
318#336C2311yescharacteristic
319C22×Q8C22×C411yescharacteristic
320C22×Q8C22×C412yes—
321C22×D4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C412yes—
325C23×C4C22×C411yescharacteristic
326C23×C4C22×C411yescharacteristic
327C23×C4C22×C412yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C22×C8C2411yescharacteristic
331C22×C8C2412yes—
332C22×C8C2411yescharacteristic
333C22×C8C2411yescharacteristic
334C22×C8C2411yescharacteristic
335C22×C8C2412yes—
336C22×C8C2411yescharacteristic
337C22×C8C2411yescharacteristic
338C22×C8C2411yescharacteristic
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2411yescharacteristic
342C4⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—44no—
345C22⋊Q8—42no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—42no—
353C4×D4—42no—
354#117—42no—
355#117—42no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C4⋊C4C22×C412yes—
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C412yes—
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C412yes—
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C412yes—
371C2×C4⋊C4C22×C412yes—
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C412yes—
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C22×C411yescharacteristic
386C2×C22⋊C4C22×C411yescharacteristic
387C2×C22⋊C4C22×C411yescharacteristic
388C2×C22⋊C4C22×C411yescharacteristic
389C2×C22⋊C4C22×C412yes—
390C2×C22⋊C4C22×C412yes—
391C2×C22⋊C4C22×C412yes—
392C2×C22⋊C4C22×C412yes—
393C2×C22⋊C4C22×C411yescharacteristic
394C2×C22⋊C4C22×C411yescharacteristic
395C2×C22⋊C4C22×C411yescharacteristic
396C2×C22⋊C4C22×C412yes—
397C2×C22⋊C4C22×C412yes—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C412yes—
413C2×C42C22×C412yes—
414C2×C42C2412yes—
415C2×C42C2412yes—
416C2×C42C2411yescharacteristic
417C2×C42C2412yes—
418C2×C42C2412yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C4⋊C8—24no—
424C4⋊C8—22no—
425C4⋊C8—22no—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—24no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—42no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434C4⋊C8—41no—
435C4⋊C8—41no—
436C4⋊C8—41no—
437C4⋊C8—41no—
438C4⋊C8—42no—
439C4⋊C8—42no—
440C4⋊C8—42no—
441C4⋊C8—42no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—41no—
448C22⋊C8—41no—
449C22⋊C8—41no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453C22⋊C8—42no—
454C22⋊C8—42no—
455C22⋊C8—42no—
456C22⋊C8—42no—
457#97—24no—
458#97—22no—
459#97—22no—
460#97—22no—
461#97—41no—
462#97—42no—
463#97—42no—
464#97—42no—
465C4×C8—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—24no—
470C4×C8—22no—
471C4×C8—42no—
472C4×C8—42no—
473C4×C8—42no—
474#95C22×C412yes—
475#95C22×C412yes—
476#95C22×C412yes—
477#95C22×C412yes—
478#95C22×C412yes—
479#95C22×C412yes—
480#95C22×C412yes—
481#95C22×C412yes—
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
484#95C22×C411yescharacteristic
485#95C22×C411yescharacteristic
486#95C22×C411yescharacteristic
487#95C22×C411yescharacteristic
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—
503C24C23×C411yescharacteristic
504C24C23×C411yescharacteristic
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—41no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—42no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—42no—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C412yes—
547C22×C4C23×C411yescharacteristic
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C412yes—
550C22×C4C23×C412yes—
551C22×C4C23×C412yes—
552C22×C4C23×C412yes—
553C22×C4C23×C412yes—
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C412yes—
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C412yes—
563C22×C4C23×C411yescharacteristic
564C22×C4C2511yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—22no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—21no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—22no—
600C2×C8H(5,𝔽2)12yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4#13114yes—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—42no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—22no—
657C42—21no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—42no—
662C42—42no—
663C42—41no—
664C42—41no—
665C42H(5,𝔽2)12yes—
666C422−1+412yes—
667C422−1+412yes—
668C422−1+412yes—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23#56812yes—
683C23C24×C411yescharacteristic
684Q8—44no—
685Q8—84no—
686D4—44no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
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—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—82no—
753C2×C4—84no—
754C2×C4#51912yes—
755C2×C4#51912yes—
756C2×C4#52012yes—
757C2×C4#52012yes—
758C2×C4C2×#13114yes—
759C2×C4C2×#13112yes—
760C2×C4#56812yes—
761C2×C4C2×H(5,𝔽2)11yescharacteristic
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4C2×2−1+411yescharacteristic
764C2×C4C2×2−1+411yescharacteristic
765C2×C4C2×2−1+411yescharacteristic
766C2×C4#58511yescharacteristic
767C8—22no—
768C8—42no—
769C8—41no—
770C8—41no—
771C8—41no—
772C8—42no—
773C8—41no—
774C8—41no—
775C8—41no—
776C8—42no—
777C8—42no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×#51911yescharacteristic
794C22C2×#52011yescharacteristic
795C22C4×H(5,𝔽2)11yescharacteristic
796C22C22×#13111yescharacteristic
797C22C2×#56811yescharacteristic
798C22C2×#56811yescharacteristic
799C22#357311yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—24no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4#299314yes—
820C4#354411yescharacteristic
821C4#354711yescharacteristic
822C4#354811yescharacteristic
823C4#355511yescharacteristic
824C2—42no—
825C2—81no—
826C2#3448411yescharacteristic
827C2#6025111yescharacteristic
828C2#6025311yescharacteristic
829C2C2×#299311yescharacteristic
830C2#6027211yescharacteristic
831C2#6031111yescharacteristic
832C2#6032611yescharacteristic
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. #23345C2semidirect
3. #23341C2semidirect
4. #23262C2semidirect
5. #23247C2semidirect
6. #23055C2semidirect
7. #23051C2semidirect
10. #22721C2semidirect
11. #22600C2semidirect
12. #22599C2semidirect
13. #22302C2semidirect
14. #22109C2semidirect
15. #22104C2semidirect
16. #22102C2semidirect
17. #22098C2semidirect
19. #21954C2semidirect
20. #21953C2semidirect
21. #21713C2semidirect
22. #21343C2semidirect

Maximal subgroups

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

subgroupindex
#347722
#233452
#233412
#232622
#232472
#230552
#230512
#228002
#227992
#227212
#226002
#225992
#223022
#221092
#221042
#221022
#220982
#220172
#219542
#219532
#217132
#213432
#212652