Finite Group Databasebeta

← #6405155

Subgroups — #6405155

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34941C211yesmaximal, characteristic
2#23255C212yesmaximal, complemented
3#23248C211yesmaximal, characteristic, complemented
4#23059C212yesmaximal, complemented
5#23057C212yesmaximal, complemented
6#23051C211yesmaximal, characteristic, complemented
7#23050C211yesmaximal, characteristic, complemented
8#22838C212yesmaximal
9#22821C211yesmaximal, characteristic, complemented
10#22797C211yesmaximal, characteristic
11#22600C211yesmaximal, characteristic, complemented
12#22600C211yesmaximal, characteristic, complemented
13#22328C212yesmaximal, complemented
14#22324C212yesmaximal, complemented
15#22100C211yesmaximal, characteristic, complemented
16#22098C211yesmaximal, characteristic, complemented
17#21713C211yesmaximal, characteristic, complemented
18#21674C212yesmaximal, complemented
19#21269C212yesmaximal
20#21265C211yesmaximal, characteristic
21#20538C211yesmaximal, characteristic, complemented
22#20537C211yesmaximal, characteristic, complemented
23Q8×#97C211yesmaximal, characteristic, complemented
24C2×#446C2212yes—
25C2×C8×Q8C2211yescharacteristic
26C2×C8×Q8C2211yescharacteristic
27C2×#433C2212yes—
28C2×#433C2212yes—
29C2×#432C2211yescharacteristic
30C2×#431C2211yescharacteristic
31C2×#431C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2574C412yes—
34#2574C412yes—
35#2567C411yescharacteristic
36#2563C411yescharacteristic
37#2552C411yescharacteristic
38#2538C411yescharacteristic
39#2508C412yes—
40#2497C411yescharacteristic
41#2497C411yescharacteristic
42#2454C412yes—
43#2423C411yescharacteristic
44#2423C411yescharacteristic
45#2396C2212yes—
46#2396C2212yes—
47C4×C4⋊Q8C2211yescharacteristic
48C4×#125C2212yes—
49C4×C22⋊Q8C2211yescharacteristic
50C4×C22⋊Q8C2211yescharacteristic
51#2293C2212yes—
52#2285C2211yescharacteristic
53#2285C2211yescharacteristic
54C42×Q8C2211yescharacteristic
55C42×D4C2211yescharacteristic
56#1985C2212yes—
57#1985C2212yes—
58#1984C2211yescharacteristic
59#1984C2211yescharacteristic
60#1984C2212yes—
61#1955C2212yes—
62#1955C2211yescharacteristic
63#1955C2211yescharacteristic
64#1940C2211yescharacteristic
65#1940C2211yescharacteristic
66#1940C2212yes—
67#1940C2212yes—
68#1940C2212yes—
69#1939C2211yescharacteristic
70#1939C2211yescharacteristic
71#1939C2212yes—
72#1939C2211yescharacteristic
73#1939C2211yescharacteristic
74#1924C2212yes—
75#1924C2212yes—
76#1924C2211yescharacteristic
77#1924C2211yescharacteristic
78#1924C2211yescharacteristic
79#1924C2211yescharacteristic
80#1924C2212yes—
81#1923C2212yes—
82#1923C2212yes—
83#1923C2212yes—
84#1923C2212yes—
85#1923C2212yes—
86#1923C2212yes—
87#1923C2212yes—
88#1917C2212yes—
89#1917C2212yes—
90#1917C2212yes—
91#1916C2212yes—
92#1916C2212yes—
93#1916C2212yes—
94#1916C2212yes—
95#1916C2212yes—
96#1916C2212yes—
97#1916C2212yes—
98#1842C2211yescharacteristic
99#1831C2212yes—
100#1818C2212yes—
101#1818C2212yes—
102#1797C2211yescharacteristic
103#1797C2211yescharacteristic
104#1771C2212yes—
105#1771C2212yes—
106#1771C2212yes—
107#1771C2212yes—
108#1771C2212yes—
109#1771C2212yes—
110#1770C2211yescharacteristic
111#1770C2212yes—
112#1770C2212yes—
113#1770C2211yescharacteristic
114#1770C2211yescharacteristic
115#1770C2212yes—
116#1770C2211yescharacteristic
117C8×C4⋊C4C2212yes—
118C8×C4⋊C4C2211yescharacteristic
119C8×C4⋊C4C2212yes—
120C8×C4⋊C4C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123#1767C2211yescharacteristic
124#1767C2212yes—
125C4×C4⋊C8C2211yescharacteristic
126C4×C4⋊C8C2212yes—
127#1750C2212yes—
128#1750C2212yes—
129#1750C2212yes—
130#1750C2212yes—
131C4×C22⋊C8C2211yescharacteristic
132C4×C22⋊C8C2211yescharacteristic
133C4×#97C2211yescharacteristic
134C4×#97C2212yes—
135C2×C4⋊Q8C2×C411yescharacteristic
136C2×#125C2×C412yes—
137C2×C22⋊Q8C2×C411yescharacteristic
138C2×C22⋊Q8C2×C411yescharacteristic
139C2×C4×Q8C2×C411yescharacteristic
140C2×C4×Q8C2×C411yescharacteristic
141C2×C4×Q8C2311yescharacteristic
142C2×C4×Q8C2312yes—
143C2×C4×D4C2×C411yescharacteristic
144C2×C4×D4C2×C411yescharacteristic
145C2×C4×D4C2311yescharacteristic
146C2×#117C2312yes—
147C2×#117C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#446—44no—
151C8×Q8—24no—
152C8×Q8—24no—
153#433—44no—
154#433—44no—
155#432—24no—
156#431—24no—
157#431—24no—
158#431—24no—
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2311yescharacteristic
177C2×C22⋊C8C2311yescharacteristic
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2311yescharacteristic
180C2×C22⋊C8C2311yescharacteristic
181C2×C22⋊C8C2311yescharacteristic
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×#97C2311yescharacteristic
192C2×#97C2311yescharacteristic
193C2×#97C2311yescharacteristic
194C2×#97C2312yes—
195C2×#97C2311yescharacteristic
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2311yescharacteristic
210#400C2×C412yes—
211#400C2×C412yes—
212#399C2×C412yes—
213#399C2×C412yes—
214#398C2×C412yes—
215#398C2×C412yes—
216#398C2×C412yes—
217#398C2×C412yes—
218#396C2×C412yes—
219#396C2×C412yes—
220#396C2×C412yes—
221#396C2×C412yes—
222#395C2×C412yes—
223#395C2×C412yes—
224#393C2×C412yes—
225#393C2×C412yes—
226#391C2×C412yes—
227#391C2×C411yescharacteristic
228#391C2×C411yescharacteristic
229#390C2×C412yes—
230#390C2×C412yes—
231#389C2×C412yes—
232#389C2×C412yes—
233#389C2×C411yescharacteristic
234#389C2×C411yescharacteristic
235#389C2×C412yes—
236#389C2×C412yes—
237#389C2×C411yescharacteristic
238#389C2×C411yescharacteristic
239#389C2×C412yes—
240#388C2×C412yes—
241#388C2×C412yes—
242#388C2×C412yes—
243#388C2×C412yes—
244#387C2×C412yes—
245#387C2×C412yes—
246#387C2×C412yes—
247#387C2×C412yes—
248#387C2×C412yes—
249#387C2×C412yes—
250#385C2×C412yes—
251#385C2×C412yes—
252#384C2×C411yescharacteristic
253#384C2×C411yescharacteristic
254#384C2×C411yescharacteristic
255#384C2×C411yescharacteristic
256#384C2×C411yescharacteristic
257#382C2×C412yes—
258#382C2×C412yes—
259#382C2×C412yes—
260#380C2×C411yescharacteristic
261#380C2×C411yescharacteristic
262#380C2×C411yescharacteristic
263#380C2×C411yescharacteristic
264#380C2×C412yes—
265#380C2×C412yes—
266#380C2×C411yescharacteristic
267#380C2×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C412yes—
271C4×C4⋊C4C2×C412yes—
272C4×C4⋊C4C2×C411yescharacteristic
273C4×C4⋊C4C2×C411yescharacteristic
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2311yescharacteristic
284C4×C22⋊C4C2×C411yescharacteristic
285C4×C22⋊C4C2×C411yescharacteristic
286C4×C22⋊C4C2×C411yescharacteristic
287C4×C22⋊C4C2×C411yescharacteristic
288C4×C22⋊C4C2311yescharacteristic
289C4×C22⋊C4C2311yescharacteristic
290C4×C22⋊C4C2312yes—
291C4×C22⋊C4C2312yes—
292C43C2312yes—
293C43C2311yescharacteristic
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304#336C2312yes—
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2312yes—
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2311yescharacteristic
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×Q8C22×C412yes—
321C22×D4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C411yescharacteristic
325C23×C4C22×C411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2411yescharacteristic
330C22×C8C2411yescharacteristic
331C22×C8C2411yescharacteristic
332C22×C8C2411yescharacteristic
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C22×C8C2412yes—
337C22×C8C2411yescharacteristic
338C22×C8C2411yescharacteristic
339C22×C8C2411yescharacteristic
340C4⋊Q8—42no—
341#125—44no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—42no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—42no—
353C4×D4—42no—
354#117—42no—
355#117—42no—
356#117—42no—
357#117—42no—
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C4⋊C4C22×C411yescharacteristic
362C2×C4⋊C4C22×C412yes—
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C412yes—
368C2×C4⋊C4C22×C412yes—
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C412yes—
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C412yes—
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C411yescharacteristic
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×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C22⋊C4C22×C411yescharacteristic
389C2×C22⋊C4C22×C411yescharacteristic
390C2×C22⋊C4C22×C411yescharacteristic
391C2×C22⋊C4C22×C412yes—
392C2×C22⋊C4C22×C412yes—
393C2×C22⋊C4C22×C412yes—
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C412yes—
396C2×C22⋊C4C22×C412yes—
397C2×C22⋊C4C22×C411yescharacteristic
398C2×C22⋊C4C22×C411yescharacteristic
399C2×C22⋊C4C22×C411yescharacteristic
400C2×C22⋊C4C22×C412yes—
401C2×C22⋊C4C22×C412yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C22×C412yes—
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C412yes—
415C2×C42C22×C412yes—
416C2×C42C22×C411yescharacteristic
417C2×C42C22×C412yes—
418C2×C42C2412yes—
419C2×C42C2412yes—
420C2×C42C2412yes—
421C2×C42C2411yescharacteristic
422C2×C42C2412yes—
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8—22no—
440C4⋊C8—24no—
441C4⋊C8—42no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444C4⋊C8#4114yes—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—24no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—24no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455C22⋊C8—42no—
456C22⋊C8—42no—
457#97—24no—
458#97—24no—
459#97—22no—
460#97—22no—
461#97—24no—
462#97—22no—
463#97—42no—
464#97—42no—
465#97—41no—
466#97—42no—
467C4×C8—24no—
468C4×C8—24no—
469C4×C8—24no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—42no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477C4×C8#4114yes—
478#95C22×C411yescharacteristic
479#95C22×C411yescharacteristic
480#95C22×C411yescharacteristic
481#95C22×C411yescharacteristic
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
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×C412yes—
502#95C22×C412yes—
503C24C23×C411yescharacteristic
504C24C23×C411yescharacteristic
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8#13114yes—
511C2×D4—22no—
512C2×D4—41no—
513C2×D4—41no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
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—22no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C412yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C412yes—
544C22×C4C23×C412yes—
545C22×C4C23×C412yes—
546C22×C4C23×C412yes—
547C22×C4C23×C411yescharacteristic
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C412yes—
551C22×C4C23×C412yes—
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C412yes—
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C2511yescharacteristic
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—22no—
564C2×C8—21no—
565C2×C8—22no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8C2×#4112yes—
592C2×C8C2×#4114yes—
593C2×C8C2×#4112yes—
594C2×C8H(5,𝔽2)12yes—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—41no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—22no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—24no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—22no—
648C42—22no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42—42no—
662C42—41no—
663C42—42no—
664C42—42no—
665C42C2×#4112yes—
666C42C2×#4112yes—
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—21no—
683C23C24×C411yescharacteristic
684Q8—28no—
685Q8—84no—
686D4—44no—
687C2×C4—21no—
688C2×C4—22no—
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—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
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—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—82no—
751C2×C4C4×#4112yes—
752C2×C4C4×#4112yes—
753C2×C4#51912yes—
754C2×C4#51912yes—
755C2×C4C2×#13114yes—
756C2×C4C2×#13112yes—
757C2×C4#56812yes—
758C2×C4#56812yes—
759C2×C4C22×#4111yescharacteristic
760C2×C4C22×#4111yescharacteristic
761C2×C4C2×H(5,𝔽2)11yescharacteristic
762C2×C4C2×2−1+411yescharacteristic
763C2×C4C2×2−1+411yescharacteristic
764C2×C4#58511yescharacteristic
765C8—22no—
766C8—22no—
767C8—24no—
768C8—22no—
769C8—41no—
770C8—41no—
771C8—41no—
772C8—41no—
773C8—42no—
774C8—41no—
775C8—42no—
776C8—42no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22C2×C4×#4111yescharacteristic
792C22C2×#51911yescharacteristic
793C22C4×H(5,𝔽2)11yescharacteristic
794C22C22×#13111yescharacteristic
795C22C2×#56811yescharacteristic
796C22C2×#56811yescharacteristic
797C22#357311yescharacteristic
798C4—24no—
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—41no—
817C4#296814yes—
818C4#350711yescharacteristic
819C4#351111yescharacteristic
820C4#351511yescharacteristic
821C4#352211yescharacteristic
822C2—81no—
823C2—81no—
824C2#3431711yescharacteristic
825C2C2×#296811yescharacteristic
826C2#6021611yescharacteristic
827C2#6024911yescharacteristic
828C2#6025311yescharacteristic
829C2#6032611yescharacteristic
830C2#6032811yescharacteristic
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. #23255C2semidirect
3. #23248C2semidirect
4. #23059C2semidirect
5. #23057C2semidirect
6. #23051C2semidirect
7. #23050C2semidirect
9. #22821C2semidirect
11. #22600C2semidirect
12. #22600C2semidirect
13. #22328C2semidirect
14. #22324C2semidirect
15. #22100C2semidirect
16. #22098C2semidirect
17. #21713C2semidirect
18. #21674C2semidirect
21. #20538C2semidirect
22. #20537C2semidirect
23. Q8×#97C2semidirect

Maximal subgroups

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

subgroupindex
#349412
#232552
#232482
#230592
#230572
#230512
#230502
#228382
#228212
#227972
#226002
#223282
#223242
#221002
#220982
#217132
#216742
#212692
#212652
#205382
#205372
Q8×#972