Finite Group Databasebeta

← #6405193

Subgroups — #6405193

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#554C211yesmaximal, characteristic
2#23257C211yesmaximal, characteristic, complemented
3#23254C211yesmaximal, characteristic, complemented
4#23248C211yesmaximal, characteristic, complemented
5#23054C212yesmaximal, complemented
6#23053C212yesmaximal, complemented
7#23053C212yesmaximal, complemented
8#22839C211yesmaximal, characteristic
9#22835C211yesmaximal, characteristic
10#22823C211yesmaximal, characteristic, complemented
11#22799C211yesmaximal, characteristic
12#22601C212yesmaximal, complemented
13#22325C212yesmaximal, complemented
14#22323C212yesmaximal, complemented
15#22108C212yesmaximal, complemented
16#21713C211yesmaximal, characteristic, complemented
17#21675C211yesmaximal, characteristic, complemented
18#21673C211yesmaximal, characteristic, complemented
19#21270C211yesmaximal, characteristic
20#21270C211yesmaximal, characteristic
21#21264C211yesmaximal, characteristic
22#20534C212yesmaximal, complemented
23C4×#446C211yesmaximal, characteristic, complemented
24C2×#554C411yescharacteristic
25C2×#446C2211yescharacteristic
26C2×#446C2211yescharacteristic
27C2×#446C2212yes—
28C2×#432C2212yes—
29C2×#432C2212yes—
30C2×#432C2212yes—
31C2×#431C2212yes—
32#2370C411yescharacteristic
33#2370C411yescharacteristic
34#2369C411yescharacteristic
35#2368C412yes—
36#2368C412yes—
37#2360C412yes—
38#2355C411yescharacteristic
39#2349C411yescharacteristic
40#2349C411yescharacteristic
41D4×C4⋊C4C411yescharacteristic
42#2345C412yes—
43C4×C4⋊Q8C2211yescharacteristic
44C4×#125C2211yescharacteristic
45C4×#125C2211yescharacteristic
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48C4×C22⋊Q8C2212yes—
49C42×Q8C2211yescharacteristic
50C42×D4C2211yescharacteristic
51C42×D4C2211yescharacteristic
52C42×D4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54#1985C2212yes—
55#1985C2212yes—
56#1985C2212yes—
57#1984C2212yes—
58#1954C2211yescharacteristic
59#1954C2211yescharacteristic
60#1954C2211yescharacteristic
61#1954C2211yescharacteristic
62#1940C2212yes—
63#1940C2212yes—
64#1940C2212yes—
65#1939C2212yes—
66#1939C2211yescharacteristic
67#1939C2211yescharacteristic
68#1939C2211yescharacteristic
69#1939C2211yescharacteristic
70#1939C2211yescharacteristic
71#1939C2211yescharacteristic
72#1924C2212yes—
73#1924C2212yes—
74#1924C2212yes—
75#1924C2212yes—
76#1924C2212yes—
77#1924C2212yes—
78#1924C2212yes—
79#1924C2212yes—
80#1923C2212yes—
81#1923C2212yes—
82#1923C2212yes—
83#1923C2212yes—
84#1917C2212yes—
85#1917C2212yes—
86#1917C2212yes—
87#1917C2212yes—
88#1917C2212yes—
89#1917C2212yes—
90#1916C2212yes—
91#1916C2212yes—
92#1916C2212yes—
93#1916C2212yes—
94#1842C2211yescharacteristic
95#1831C2211yescharacteristic
96#1831C2211yescharacteristic
97#1817C2212yes—
98#1817C2212yes—
99#1797C2212yes—
100#1771C2212yes—
101#1771C2212yes—
102#1771C2212yes—
103#1771C2211yescharacteristic
104#1771C2212yes—
105#1771C2211yescharacteristic
106#1771C2211yescharacteristic
107#1771C2211yescharacteristic
108#1771C2212yes—
109#1771C2212yes—
110#1771C2212yes—
111#1771C2212yes—
112#1770C2211yescharacteristic
113#1770C2212yes—
114#1770C2211yescharacteristic
115#1770C2211yescharacteristic
116#1770C2211yescharacteristic
117#1770C2211yescharacteristic
118#1770C2211yescharacteristic
119C8×C4⋊C4C2211yescharacteristic
120C8×C4⋊C4C2211yescharacteristic
121#1767C2211yescharacteristic
122#1767C2211yescharacteristic
123C4×C4⋊C8C2211yescharacteristic
124C4×C4⋊C8C2211yescharacteristic
125C4×C4⋊C8C2211yescharacteristic
126C4×C4⋊C8C2211yescharacteristic
127#1749C2212yes—
128#1749C2212yes—
129#1749C2212yes—
130C4×C22⋊C8C2212yes—
131C4×C22⋊C8C2212yes—
132C4×#97C2211yescharacteristic
133C4×#97C2211yescharacteristic
134C42×C8C2211yescharacteristic
135#554—28no—
136C2×C4⋊Q8C2×C411yescharacteristic
137C2×#125C2×C411yescharacteristic
138C2×#125C2×C411yescharacteristic
139C2×C22⋊Q8C2×C412yes—
140C2×C22⋊Q8C2×C412yes—
141C2×C22⋊Q8C2×C412yes—
142C2×C4×Q8C2×C411yescharacteristic
143C2×C4×Q8C2×C411yescharacteristic
144C2×C4×Q8C2311yescharacteristic
145C2×C4×Q8C2312yes—
146C2×C4×D4C2×C411yescharacteristic
147C2×C4×D4C2×C411yescharacteristic
148C2×C4×D4C2×C411yescharacteristic
149C2×C4×D4C2×C411yescharacteristic
150C2×C4×D4C2×C411yescharacteristic
151C2×C4×D4C2×C411yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C22×C4⋊C4C2×C412yes—
154C22×C4⋊C4C2×C412yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158#446—24no—
159#446—24no—
160#446—44no—
161#432—28no—
162#432—28no—
163#432—44no—
164#431—44no—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2311yescharacteristic
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×#97C2311yescharacteristic
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×#97C2311yescharacteristic
196C2×#97C2311yescharacteristic
197C2×#97C2311yescharacteristic
198C2×#97C2311yescharacteristic
199C2×#97C2312yes—
200C2×#97C2311yescharacteristic
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×#97C2311yescharacteristic
204C2×#97C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2312yes—
213C2×C4×C8C2312yes—
214C2×C4×C8C2312yes—
215C2×C4×C8C2311yescharacteristic
216#391C2×C412yes—
217#391C2×C412yes—
218#391C2×C412yes—
219#391C2×C412yes—
220#389C2×C411yescharacteristic
221#389C2×C411yescharacteristic
222#389C2×C411yescharacteristic
223#389C2×C411yescharacteristic
224#389C2×C412yes—
225#389C2×C411yescharacteristic
226#389C2×C411yescharacteristic
227#389C2×C412yes—
228#389C2×C412yes—
229#389C2×C412yes—
230#387C2×C412yes—
231#387C2×C412yes—
232#387C2×C412yes—
233#387C2×C412yes—
234#387C2×C412yes—
235#387C2×C412yes—
236#387C2×C412yes—
237#387C2×C412yes—
238#387C2×C412yes—
239#387C2×C412yes—
240#385C2×C412yes—
241#385C2×C412yes—
242#385C2×C412yes—
243#385C2×C412yes—
244#385C2×C412yes—
245#385C2×C412yes—
246#384C2×C411yescharacteristic
247#382C2×C411yescharacteristic
248#382C2×C411yescharacteristic
249#380C2×C412yes—
250#380C2×C412yes—
251#380C2×C412yes—
252C4×C4⋊C4C2×C411yescharacteristic
253C4×C4⋊C4C2×C412yes—
254C4×C4⋊C4C2×C411yescharacteristic
255C4×C4⋊C4C2×C411yescharacteristic
256C4×C4⋊C4C2×C411yescharacteristic
257C4×C4⋊C4C2×C411yescharacteristic
258C4×C4⋊C4C2×C411yescharacteristic
259C4×C4⋊C4C2×C411yescharacteristic
260C4×C4⋊C4C2×C412yes—
261C4×C4⋊C4C2×C411yescharacteristic
262C4×C4⋊C4C2×C411yescharacteristic
263C4×C4⋊C4C2×C412yes—
264C4×C4⋊C4C2×C412yes—
265C4×C4⋊C4C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2311yescharacteristic
269C4×C4⋊C4C2311yescharacteristic
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×C412yes—
280C4×C22⋊C4C2×C412yes—
281C4×C22⋊C4C2×C412yes—
282C4×C22⋊C4C2×C412yes—
283C4×C22⋊C4C2×C412yes—
284C4×C22⋊C4C2×C412yes—
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C2×#95C2×C412yes—
289C2×#95C2×C412yes—
290C43C2311yescharacteristic
291C43C2311yescharacteristic
292C43C2311yescharacteristic
293#336C2312yes—
294#336C2312yes—
295#336C2311yescharacteristic
296#336C2311yescharacteristic
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2311yescharacteristic
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318C22×Q8C22×C411yescharacteristic
319C22×Q8C22×C412yes—
320C22×D4C22×C411yescharacteristic
321C23×C4C22×C412yes—
322C23×C4C22×C412yes—
323C23×C4C22×C412yes—
324C23×C4C22×C412yes—
325C23×C4C22×C412yes—
326C23×C4C22×C412yes—
327C23×C4C2412yes—
328C22×C8C2412yes—
329C22×C8C2411yescharacteristic
330C22×C8C2411yescharacteristic
331C22×C8C2412yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2411yescharacteristic
335C22×C8C2411yescharacteristic
336C22×C8C2411yescharacteristic
337C22×C8C2411yescharacteristic
338C22×C8C2411yescharacteristic
339C22×C8C2411yescharacteristic
340C4⋊Q8—24no—
341#125—24no—
342#125—24no—
343C22⋊Q8—28no—
344C22⋊Q8—28no—
345C22⋊Q8—28no—
346C4×Q8—24no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—42no—
350C4×Q8—42no—
351C4×Q8—42no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4—42no—
359C4×D4M1618yes—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C22×C412yes—
367C2×C4⋊C4C22×C412yes—
368C2×C4⋊C4C22×C411yescharacteristic
369C2×C4⋊C4C22×C411yescharacteristic
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊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×C412yes—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—42no—
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×C412yes—
411C2×C42C22×C412yes—
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C411yescharacteristic
417C2×C42C22×C412yes—
418C2×C42C22×C412yes—
419C2×C42C22×C412yes—
420C2×C42C22×C412yes—
421C2×C42C22×C411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2412yes—
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2412yes—
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449C4⋊C8#4114yes—
450C22⋊C8—24no—
451C22⋊C8—24no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—42no—
456C22⋊C8—42no—
457C22⋊C8—42no—
458#97—24no—
459#97—24no—
460#97—22no—
461#97—22no—
462#97—22no—
463#97—22no—
464#97—24no—
465#97—22no—
466#97—41no—
467#97—42no—
468#97—41no—
469#97—42no—
470#97—42no—
471#97#4114yes—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—22no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—41no—
480C4×C8—42no—
481C4×C8—42no—
482C4×C8—42no—
483#95C22×C411yescharacteristic
484#95C22×C411yescharacteristic
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×C411yescharacteristic
501#95C22×C411yescharacteristic
502#95C22×C411yescharacteristic
503#95C22×C411yescharacteristic
504#95C22×C412yes—
505#95C22×C412yes—
506#95C22×C412yes—
507#95C22×C412yes—
508C24C23×C412yes—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—24no—
512C2×Q8—41no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4C2×M1614yes—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×M1618yes—
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C412yes—
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C2511yescharacteristic
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—21no—
574C2×C8—21no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—21no—
595C2×C8C2×#4112yes—
596C2×C8C2×#4112yes—
597C2×C8C2×#4112yes—
598C2×C8C2×#4112yes—
599C2×C8H(5,𝔽2)12yes—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—41no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C2×M1614yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4C2×M1618yes—
636C42—24no—
637C42—24no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—22no—
647C42—21no—
648C42—21no—
649C42—22no—
650C42—21no—
651C42—22no—
652C42—21no—
653C42—21no—
654C42—22no—
655C42—21no—
656C42—22no—
657C42—21no—
658C42—22no—
659C42—21no—
660C42—42no—
661C42—42no—
662C42—42no—
663C42—42no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42C2×M1614yes—
670C42C2×#4112yes—
671C42C2×#4112yes—
672C422−1+412yes—
673C422−1+412yes—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23C22×M1614yes—
681C23C24×C411yescharacteristic
682Q8—44no—
683Q8—84no—
684D4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4C4×#4112yes—
749C2×C4C4×#4112yes—
750C2×C4#51912yes—
751C2×C4#51912yes—
752C2×C4C22×M1612yes—
753C2×C4C22×M1612yes—
754C2×C4C22×M1614yes—
755C2×C4C22×M1612yes—
756C2×C4#56812yes—
757C2×C4#56812yes—
758C2×C4C22×#4111yescharacteristic
759C2×C4C22×#4111yescharacteristic
760C2×C4C2×H(5,𝔽2)11yescharacteristic
761C2×C4C2×2−1+411yescharacteristic
762C2×C4C2×2−1+411yescharacteristic
763C2×C4#58511yescharacteristic
764C8—22no—
765C8—22no—
766C8—22no—
767C8—22no—
768C8—22no—
769C8—42no—
770C8—41no—
771C8—42no—
772C8—41no—
773C8—41no—
774C8—42no—
775C8—42no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22C2×C4×#4111yescharacteristic
784C22C2×#51911yescharacteristic
785C22C4×H(5,𝔽2)11yescharacteristic
786C22C23×M1611yescharacteristic
787C22C2×#56811yescharacteristic
788C22C2×#56811yescharacteristic
789C22#357311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—24no—
796C4—22no—
797C4—42no—
798C4—42no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4#298314yes—
811C4#350711yescharacteristic
812C4#351111yescharacteristic
813C4#351511yescharacteristic
814C4#352211yescharacteristic
815C2—44no—
816C2#3431711yescharacteristic
817C2M16×#4111yescharacteristic
818C2#6021711yescharacteristic
819C2C2×#298311yescharacteristic
820C2#6025411yescharacteristic
821C2#6030911yescharacteristic
822C2#6032411yescharacteristic
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. #23257C2semidirect
3. #23254C2semidirect
4. #23248C2semidirect
5. #23054C2semidirect
6. #23053C2semidirect
7. #23053C2semidirect
10. #22823C2semidirect
12. #22601C2semidirect
13. #22325C2semidirect
14. #22323C2semidirect
15. #22108C2semidirect
16. #21713C2semidirect
17. #21675C2semidirect
18. #21673C2semidirect
22. #20534C2semidirect
23. C4×#446C2semidirect

Maximal subgroups

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

subgroupindex
C4×#5542
#232572
#232542
#232482
#230542
#230532
#228392
#228352
#228232
#227992
#226012
#223252
#223232
#221082
#217132
#216752
#216732
#212702
#212642
#205342
C4×#4462