Finite Group Databasebeta

← #6381008

Subgroups — #6381008

Order 512.

2275 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2924C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3C2×#2290C211yesmaximal, characteristic
4#22801C212yesmaximal, complemented
5#22755C212yesmaximal, complemented
6#22753C212yesmaximal, complemented
7#22649C212yesmaximal, complemented
8#22603C211yesmaximal, characteristic, complemented
9#22601C211yesmaximal, characteristic, complemented
10#22555C211yesmaximal, characteristic, complemented
11#22555C211yesmaximal, characteristic, complemented
12#22554C211yesmaximal, characteristic, complemented
13#22553C211yesmaximal, characteristic, complemented
14#22401C211yesmaximal, characteristic
15#22399C211yesmaximal, characteristic
16#21272C212yesmaximal, complemented
17#21109C212yesmaximal, complemented
18#21104C212yesmaximal, complemented
19#20814C211yesmaximal, characteristic, complemented
20#20717C211yesmaximal, characteristic, complemented
21#20715C211yesmaximal, characteristic, complemented
22#20487C212yesmaximal, complemented
23#20469C211yesmaximal, characteristic, complemented
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C2×#436C2212yes—
28C2×#435C2212yes—
29#2924—28no—
30#2920—28no—
31C2×#433C2212yescomplemented
32C2×#433C2212yescomplemented
33C2×#432C2211yescharacteristic
34C2×#432C2211yescharacteristic
35C2×#432C2211yescharacteristic
36C2×#432C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C2×#432C2212yescomplemented
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C2×#431C2212yescomplemented
43C2×#424C2212yescomplemented
44C2×#423C2212yescomplemented
45C2×#407C2211yescharacteristic
46C2×#407C2211yescharacteristic
47C2×#407C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C2×#405C2212yescomplemented
50C2×C4×M16C2212yescomplemented
51#2290C411yescharacteristic
52#2290C411yescharacteristic
53#2290C411yescharacteristic
54#2290C411yescharacteristic
55#2290C411yescharacteristic
56#2290C411yescharacteristic
57#2290C411yescharacteristic
58#2290C411yescharacteristic
59#2290C2211yescharacteristic
60#2290C2211yescharacteristic
61#2290C2211yescharacteristic
62#2290C2211yescharacteristic
63#2290C2211yescharacteristic
64#2290C2211yescharacteristic
65#2290C2211yescharacteristic
66#2290C2211yescharacteristic
67C2×#388C411yescharacteristic
68C2×#388C411yescharacteristic
69C2×#387C411yescharacteristic
70C2×#387C411yescharacteristic
71C2×#386C411yescharacteristic
72C2×#386C411yescharacteristic
73C2×#385C411yescharacteristic
74C2×#385C411yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×#376C2211yescharacteristic
79#1955C2212yes—
80#1954C2212yes—
81#1940C2212yescomplemented
82#1939C2212yescomplemented
83#1924C2212yescomplemented
84#1924C2212yescomplemented
85#1924C2212yescomplemented
86#1924C2212yescomplemented
87#1924C2212yescomplemented
88#1923C2212yescomplemented
89#1923C2212yescomplemented
90#1923C2212yescomplemented
91#1917C2212yescomplemented
92#1917C2212yescomplemented
93#1917C2212yescomplemented
94#1916C2212yescomplemented
95#1870C2212yes—
96#1870C2212yes—
97#1870C2212yes—
98#1869C2212yes—
99#1851C2212yescomplemented
100#1851C2212yescomplemented
101#1851C2212yescomplemented
102#1850C2212yescomplemented
103#1843C2212yescomplemented
104#1832C2212yescomplemented
105#1817C2211yescharacteristic
106#1817C2211yescharacteristic
107#1817C2211yescharacteristic
108#1817C2211yescharacteristic
109#1798C2212yescomplemented
110#1798C2212yescomplemented
111#1797C2211yescharacteristic
112#1797C2211yescharacteristic
113#1797C2211yescharacteristic
114#1797C2211yescharacteristic
115#1797C2212yescomplemented
116#1797C2212yescomplemented
117#1779C2211yescharacteristic
118#1779C2211yescharacteristic
119#1779C2211yescharacteristic
120#1779C2211yescharacteristic
121#1771C2212yescomplemented
122#1770C2212yescomplemented
123#1768C2212yescomplemented
124#1768C2212yescomplemented
125#1768C2212yescomplemented
126#1768C2212yescomplemented
127#1753C2212yescomplemented
128#1753C2212yescomplemented
129#1753C2212yescomplemented
130#1752C2212yescomplemented
131#1750C2212yescomplemented
132#1750C2212yescomplemented
133#1749C2211yescharacteristic
134#1749C2211yescharacteristic
135#1749C2212yescomplemented
136#1749C2212yescomplemented
137C4×C22⋊C8C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139#1746C2212yescomplemented
140#1726C2212yescomplemented
141C23×D4C2×C411yescharacteristic
142C24×C4C2×C411yescharacteristic
143C24×C4C2×C411yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C22×M16C2312yes—
147C22×M16C2312yes—
148C22×M16C2312yes—
149C23×C8C2312yes—
150C2×C4×D4—28no—
151C2×C4×D4C2×C411yescharacteristic
152C2×C4×D4C2×C411yescharacteristic
153C2×C4×D4C2×C411yescharacteristic
154C2×C4×D4C2×C411yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×#117—24no—
160C2×#117—24no—
161C2×#117C2×C411yescharacteristic
162C2×#117C2×C411yescharacteristic
163C2×#117C2×C411yescharacteristic
164C2×#117C2×C411yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C22×C4⋊C4C2×C411yescharacteristic
170C22×C4⋊C4C2×C411yescharacteristic
171C22×C4⋊C4C2×C411yescharacteristic
172C22×C4⋊C4C2×C411yescharacteristic
173C22×C4⋊C4C2×C411yescharacteristic
174C22×C22⋊C4C2×C411yescharacteristic
175C22×C22⋊C4C2×C411yescharacteristic
176C22×C22⋊C4C2×C411yescharacteristic
177C22×C22⋊C4C2×C411yescharacteristic
178C22×C22⋊C4C2×C411yescharacteristic
179C22×C22⋊C4C2×C411yescharacteristic
180C22×C22⋊C4C2×C411yescharacteristic
181C22×C22⋊C4C2×C411yescharacteristic
182C22×C42—24no—
183C22×C42—24no—
184C22×C42C2×C411yescharacteristic
185C22×C42C2×C411yescharacteristic
186C22×C42C2×C411yescharacteristic
187C22×C42C2×C411yescharacteristic
188C22×C42C2×C411yescharacteristic
189C22×C42C2×C411yescharacteristic
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199#436—28no—
200#435—28no—
201#433—28no—
202#433—28no—
203#432—24no—
204#432—24no—
205#432—28no—
206#432—24no—
207#432—24no—
208#432—24no—
209#431—24no—
210#431—24no—
211#431—28no—
212#431D418yescomplemented
213#424—28no—
214#423—28no—
215C2×C4⋊C8C2312yes—
216C2×C4⋊C8C2312yes—
217C2×C4⋊C8C2312yes—
218C2×C4⋊C8C2312yes—
219C2×C4⋊C8C2312yes—
220C2×C4⋊C8C2312yes—
221C2×C4⋊C8C2312yes—
222C2×C4⋊C8C2312yes—
223C2×C4⋊C8C2312yes—
224C2×C4⋊C8C2312yes—
225C2×C4⋊C8C2312yes—
226C2×C4⋊C8C2312yes—
227#407—24no—
228#407—24no—
229#407—24no—
230C2×C22⋊C8—24no—
231C2×C22⋊C8C2311yescharacteristic
232C2×C22⋊C8C2311yescharacteristic
233C2×C22⋊C8C2311yescharacteristic
234C2×C22⋊C8C2311yescharacteristic
235C2×C22⋊C8C2312yes—
236C2×C22⋊C8C2312yes—
237C2×C22⋊C8C2312yes—
238C2×C22⋊C8C2312yes—
239C2×C22⋊C8C2311yescharacteristic
240C2×C22⋊C8C2311yescharacteristic
241C2×C22⋊C8C2312yes—
242C2×C22⋊C8C2312yes—
243C2×C22⋊C8C2312yes—
244C2×C22⋊C8C2312yes—
245C2×C22⋊C8C2312yes—
246C2×C22⋊C8C2312yes—
247C2×C22⋊C8C2312yes—
248C2×C22⋊C8C2312yes—
249C2×C22⋊C8C2311yescharacteristic
250C2×C22⋊C8C2311yescharacteristic
251#405—28no—
252C4×M16—28no—
253C2×#97C2312yes—
254C2×#97C2312yes—
255C2×#97C2312yes—
256C2×#97C2312yes—
257C2×#97C2312yes—
258C2×#97C2312yes—
259C2×#97C2312yes—
260C2×C4×C8C2312yes—
261C2×C4×C8C2312yes—
262C2×C4×C8C2312yes—
263C2×C4×C8C2312yes—
264C2×C4×C8C2312yes—
265#388C2×C411yescharacteristic
266#388C2×C411yescharacteristic
267#388C2×C411yescharacteristic
268#388C2×C411yescharacteristic
269#388C2×C411yescharacteristic
270#388C2×C411yescharacteristic
271#388C2×C411yescharacteristic
272#388C2×C411yescharacteristic
273#388C2×C411yescharacteristic
274#388C2×C411yescharacteristic
275#388C2×C411yescharacteristic
276#388C2×C411yescharacteristic
277#388C2×C411yescharacteristic
278#388C2×C411yescharacteristic
279#388C2×C411yescharacteristic
280#388C2×C411yescharacteristic
281#387C2×C411yescharacteristic
282#387C2×C411yescharacteristic
283#387C2×C411yescharacteristic
284#387C2×C411yescharacteristic
285#387C2×C411yescharacteristic
286#387C2×C411yescharacteristic
287#387C2×C411yescharacteristic
288#387C2×C411yescharacteristic
289#387C2×C411yescharacteristic
290#387C2×C411yescharacteristic
291#387C2×C411yescharacteristic
292#387C2×C411yescharacteristic
293#387C2×C411yescharacteristic
294#387C2×C411yescharacteristic
295#387C2×C411yescharacteristic
296#387C2×C411yescharacteristic
297#386C2×C411yescharacteristic
298#386C2×C411yescharacteristic
299#386C2×C411yescharacteristic
300#386C2×C411yescharacteristic
301#386C2×C411yescharacteristic
302#386C2×C411yescharacteristic
303#386C2×C411yescharacteristic
304#386C2×C411yescharacteristic
305#386C2×C411yescharacteristic
306#386C2×C411yescharacteristic
307#386C2×C411yescharacteristic
308#386C2×C411yescharacteristic
309#386C2×C411yescharacteristic
310#386C2×C411yescharacteristic
311#386C2×C411yescharacteristic
312#386C2×C411yescharacteristic
313#385C2×C411yescharacteristic
314#385C2×C411yescharacteristic
315#385C2×C411yescharacteristic
316#385C2×C411yescharacteristic
317#385C2×C411yescharacteristic
318#385C2×C411yescharacteristic
319#385C2×C411yescharacteristic
320#385C2×C411yescharacteristic
321#385C2×C411yescharacteristic
322#385C2×C411yescharacteristic
323#385C2×C411yescharacteristic
324#385C2×C411yescharacteristic
325#385C2×C411yescharacteristic
326#385C2×C411yescharacteristic
327#385C2×C411yescharacteristic
328#385C2×C411yescharacteristic
329C4×C4⋊C4C2×C411yescharacteristic
330C4×C4⋊C4C2×C411yescharacteristic
331C4×C4⋊C4C2×C411yescharacteristic
332C4×C4⋊C4C2×C411yescharacteristic
333C4×C4⋊C4C2311yescharacteristic
334C4×C4⋊C4C2311yescharacteristic
335C4×C4⋊C4C2311yescharacteristic
336C4×C4⋊C4C2311yescharacteristic
337C4×C22⋊C4C2×C411yescharacteristic
338C4×C22⋊C4C2×C411yescharacteristic
339C4×C22⋊C4C2×C411yescharacteristic
340C4×C22⋊C4C2×C411yescharacteristic
341C4×C22⋊C4C2×C411yescharacteristic
342C4×C22⋊C4C2×C411yescharacteristic
343C4×C22⋊C4C2×C411yescharacteristic
344C4×C22⋊C4C2×C411yescharacteristic
345C4×C22⋊C4C2311yescharacteristic
346C4×C22⋊C4C2311yescharacteristic
347C4×C22⋊C4C2311yescharacteristic
348C4×C22⋊C4C2311yescharacteristic
349C4×C22⋊C4C2311yescharacteristic
350C4×C22⋊C4C2311yescharacteristic
351C4×C22⋊C4C2311yescharacteristic
352C4×C22⋊C4C2311yescharacteristic
353#376C2×C411yescharacteristic
354#376C2×C411yescharacteristic
355#376C2×C411yescharacteristic
356#376C2×C411yescharacteristic
357#376C2311yescharacteristic
358#376C2311yescharacteristic
359#376C2311yescharacteristic
360#376C2311yescharacteristic
361C2×#95C2×C411yescharacteristic
362C2×#95C2×C411yescharacteristic
363C2×#95C2×C411yescharacteristic
364C2×#95C2×C411yescharacteristic
365C2×#95C2×C411yescharacteristic
366C2×#95C2×C411yescharacteristic
367C2×#95C2×C411yescharacteristic
368C2×#95C2×C411yescharacteristic
369C2×#95C2×C411yescharacteristic
370C2×#95C2×C411yescharacteristic
371#336C2312yes—
372#336C2312yes—
373#336C2312yes—
374#336C2312yes—
375#336C2312yes—
376#336C2312yes—
377#336C2312yes—
378#336C2312yes—
379#336C2312yes—
380#336C2312yes—
381#336C2312yes—
382#336C2312yes—
383#336C2312yes—
384#336C2312yes—
385#336C2312yes—
386#336C2312yes—
387C25C22×C411yescharacteristic
388C25C22×C411yescharacteristic
389C22×D4—24no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4C22×C411yescharacteristic
393C22×D4C22×C411yescharacteristic
394C22×D4C22×C411yescharacteristic
395C22×D4C22×C411yescharacteristic
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4C22×C411yescharacteristic
411C23×C4C22×C411yescharacteristic
412C23×C4C22×C411yescharacteristic
413C23×C4C22×C411yescharacteristic
414C23×C4C22×C411yescharacteristic
415C23×C4C22×C411yescharacteristic
416C23×C4C22×C411yescharacteristic
417C23×C4C22×C411yescharacteristic
418C23×C4C22×C411yescharacteristic
419C23×C4C22×C411yescharacteristic
420C23×C4C22×C411yescharacteristic
421C23×C4C22×C411yescharacteristic
422C23×C4C22×C411yescharacteristic
423C23×C4C22×C411yescharacteristic
424C23×C4C22×C411yescharacteristic
425C23×C4C22×C411yescharacteristic
426C23×C4C22×C411yescharacteristic
427C23×C4C22×C411yescharacteristic
428C23×C4C22×C411yescharacteristic
429C23×C4C22×C411yescharacteristic
430C23×C4C22×C411yescharacteristic
431C23×C4C22×C411yescharacteristic
432C23×C4C22×C411yescharacteristic
433C23×C4C22×C411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C2×M16—24no—
440C2×M16—24no—
441C2×M16—24no—
442C2×M16—24no—
443C2×M16—24no—
444C2×M16—24no—
445C2×M16—42no—
446C2×M16—42no—
447C2×M16—42no—
448C22×C8—24no—
449C22×C8—24no—
450C22×C8—42no—
451C22×C8C2412yes—
452C22×C8C2412yes—
453C22×C8C2412yes—
454C22×C8C2412yes—
455C22×C8C2412yes—
456C22×C8C2412yes—
457C22×C8C2412yes—
458C22×C8C2412yes—
459C4×D4—24no—
460C4×D4—24no—
461C4×D4—24no—
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4#4118yes—
467#117—24no—
468#117—24no—
469#117—24no—
470#117—24no—
471#117—22no—
472#117—22no—
473#117—22no—
474#117—22no—
475#117—22no—
476#117—22no—
477#117—22no—
478#117—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4C22×C411yescharacteristic
485C2×C4⋊C4C22×C411yescharacteristic
486C2×C4⋊C4C22×C411yescharacteristic
487C2×C4⋊C4C22×C411yescharacteristic
488C2×C4⋊C4C22×C411yescharacteristic
489C2×C4⋊C4C22×C411yescharacteristic
490C2×C4⋊C4C22×C411yescharacteristic
491C2×C4⋊C4C22×C411yescharacteristic
492C2×C4⋊C4C22×C411yescharacteristic
493C2×C4⋊C4C22×C411yescharacteristic
494C2×C4⋊C4C22×C411yescharacteristic
495C2×C4⋊C4C22×C411yescharacteristic
496C2×C4⋊C4C22×C411yescharacteristic
497C2×C4⋊C4C22×C411yescharacteristic
498C2×C4⋊C4C22×C411yescharacteristic
499C2×C4⋊C4C22×C411yescharacteristic
500C2×C4⋊C4C22×C411yescharacteristic
501C2×C4⋊C4C22×C411yescharacteristic
502C2×C4⋊C4C22×C411yescharacteristic
503C2×C4⋊C4C22×C411yescharacteristic
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4C22×C411yescharacteristic
513C2×C22⋊C4C22×C411yescharacteristic
514C2×C22⋊C4C22×C411yescharacteristic
515C2×C22⋊C4C22×C411yescharacteristic
516C2×C22⋊C4C22×C411yescharacteristic
517C2×C22⋊C4C22×C411yescharacteristic
518C2×C22⋊C4C22×C411yescharacteristic
519C2×C22⋊C4C22×C411yescharacteristic
520C2×C22⋊C4C22×C411yescharacteristic
521C2×C22⋊C4C22×C411yescharacteristic
522C2×C22⋊C4C22×C411yescharacteristic
523C2×C22⋊C4C22×C411yescharacteristic
524C2×C22⋊C4C22×C411yescharacteristic
525C2×C22⋊C4C22×C411yescharacteristic
526C2×C22⋊C4C22×C411yescharacteristic
527C2×C22⋊C4C22×C411yescharacteristic
528C2×C22⋊C4C22×C411yescharacteristic
529C2×C22⋊C4C22×C411yescharacteristic
530C2×C22⋊C4C22×C411yescharacteristic
531C2×C22⋊C4C22×C411yescharacteristic
532C2×C22⋊C4C22×C411yescharacteristic
533C2×C22⋊C4C22×C411yescharacteristic
534C2×C22⋊C4C22×C411yescharacteristic
535C2×C22⋊C4C22×C411yescharacteristic
536C2×C22⋊C4C22×C411yescharacteristic
537C2×C22⋊C4C22×C411yescharacteristic
538C2×C22⋊C4C22×C411yescharacteristic
539C2×C22⋊C4C22×C411yescharacteristic
540C2×C22⋊C4C22×C411yescharacteristic
541C2×C22⋊C4C22×C411yescharacteristic
542C2×C22⋊C4C22×C411yescharacteristic
543C2×C22⋊C4C22×C411yescharacteristic
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—24no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—42no—
564C2×C42C22×C411yescharacteristic
565C2×C42C22×C411yescharacteristic
566C2×C42C22×C411yescharacteristic
567C2×C42C22×C411yescharacteristic
568C2×C42C22×C411yescharacteristic
569C2×C42C22×C411yescharacteristic
570C2×C42C22×C411yescharacteristic
571C2×C42C22×C411yescharacteristic
572C2×C42C22×C411yescharacteristic
573C2×C42C22×C411yescharacteristic
574C2×C42C22×C411yescharacteristic
575C2×C42C22×C411yescharacteristic
576C2×C42C22×C411yescharacteristic
577C2×C42C22×C411yescharacteristic
578C2×C42C22×C411yescharacteristic
579C2×C42C22×C411yescharacteristic
580C2×C42C22×C411yescharacteristic
581C2×C42C22×C411yescharacteristic
582C2×C42C2×D414yes—
583C2×C42#4114yes—
584C2×C42C2411yescharacteristic
585C2×C42C2411yescharacteristic
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2411yescharacteristic
592C2×C42C2411yescharacteristic
593C2×C42C2411yescharacteristic
594C4⋊C8—24no—
595C4⋊C8—24no—
596C4⋊C8—24no—
597C4⋊C8—24no—
598C4⋊C8—24no—
599C4⋊C8—24no—
600C4⋊C8—24no—
601C4⋊C8—24no—
602C4⋊C8—24no—
603C4⋊C8—42no—
604C4⋊C8—42no—
605C4⋊C8C2×D418yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—22no—
611C22⋊C8—22no—
612C22⋊C8—24no—
613C22⋊C8—24no—
614C22⋊C8—24no—
615C22⋊C8—24no—
616C22⋊C8—24no—
617C22⋊C8—24no—
618C22⋊C8—24no—
619C22⋊C8—24no—
620C22⋊C8—42no—
621C22⋊C8—42no—
622C22⋊C8—42no—
623C22⋊C8—42no—
624C22⋊C8C2×D414yes—
625C22⋊C8C2×D414yes—
626#97—24no—
627#97—24no—
628#97—24no—
629#97—24no—
630#97—24no—
631#97—24no—
632#97—42no—
633C4×C8—24no—
634C4×C8—24no—
635C4×C8—24no—
636C4×C8—42no—
637C4×C8C2×D418yescomplemented
638#95C22×C411yescharacteristic
639#95C22×C411yescharacteristic
640#95C22×C411yescharacteristic
641#95C22×C411yescharacteristic
642#95C22×C411yescharacteristic
643#95C22×C411yescharacteristic
644#95C22×C411yescharacteristic
645#95C22×C411yescharacteristic
646#95C22×C411yescharacteristic
647#95C22×C411yescharacteristic
648#95C22×C411yescharacteristic
649#95C22×C411yescharacteristic
650#95C22×C411yescharacteristic
651#95C22×C411yescharacteristic
652#95C22×C411yescharacteristic
653#95C22×C411yescharacteristic
654#95C22×C411yescharacteristic
655#95C22×C411yescharacteristic
656#95C22×C411yescharacteristic
657#95C22×C411yescharacteristic
658#95C22×C411yescharacteristic
659#95C22×C411yescharacteristic
660#95C22×C411yescharacteristic
661#95C22×C411yescharacteristic
662#95C22×C411yescharacteristic
663#95C22×C411yescharacteristic
664#95C22×C411yescharacteristic
665#95C22×C411yescharacteristic
666#95C22×C411yescharacteristic
667#95C22×C411yescharacteristic
668#95C22×C411yescharacteristic
669#95C22×C411yescharacteristic
670#95C22×C411yescharacteristic
671#95C22×C411yescharacteristic
672#95C22×C411yescharacteristic
673#95C22×C411yescharacteristic
674#95C22×C411yescharacteristic
675#95C22×C411yescharacteristic
676#95C22×C411yescharacteristic
677#95C22×C411yescharacteristic
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—41no—
688C24—41no—
689C24—41no—
690C24—41no—
691C24—41no—
692C24C23×C411yescharacteristic
693C24C23×C411yescharacteristic
694C24C23×C411yescharacteristic
695C24C23×C411yescharacteristic
696C24C23×C411yescharacteristic
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—416no—
709C2×D4#11714yes—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—416no—
801C22×C4—416no—
802C22×C4C4×D414yes—
803C22×C4C4×D414yes—
804C22×C4C23×C411yescharacteristic
805C22×C4C23×C411yescharacteristic
806C22×C4C23×C411yescharacteristic
807C22×C4C23×C411yescharacteristic
808C22×C4C23×C411yescharacteristic
809C22×C4C23×C411yescharacteristic
810C22×C4C23×C411yescharacteristic
811C22×C4C23×C411yescharacteristic
812C22×C4C23×C411yescharacteristic
813C22×C4C23×C411yescharacteristic
814C22×C4C23×C411yescharacteristic
815C22×C4C23×C411yescharacteristic
816C22×C4C23×C411yescharacteristic
817C22×C4C23×C411yescharacteristic
818C22×C4C23×C411yescharacteristic
819C22×C4C23×C411yescharacteristic
820C22×C4C23×C411yescharacteristic
821C22×C4C23×C411yescharacteristic
822C22×C4C23×C411yescharacteristic
823C22×C4C23×C411yescharacteristic
824C22×C4C23×C411yescharacteristic
825C22×C4C23×C411yescharacteristic
826C22×C4C23×C411yescharacteristic
827C22×C4C23×C411yescharacteristic
828C22×C4C23×C411yescharacteristic
829C22×C4C22×D412yes—
830C22×C4C2×#4114yes—
831C22×C4C2×#4114yes—
832C22×C4C2×#4112yes—
833C22×C4C2511yescharacteristic
834M16—48no—
835M16—48no—
836M16—48no—
837C2×C8—22no—
838C2×C8—22no—
839C2×C8—22no—
840C2×C8—22no—
841C2×C8—22no—
842C2×C8—22no—
843C2×C8—22no—
844C2×C8—22no—
845C2×C8—22no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—22no—
849C2×C8—22no—
850C2×C8—22no—
851C2×C8—22no—
852C2×C8—22no—
853C2×C8—22no—
854C2×C8—22no—
855C2×C8—22no—
856C2×C8—22no—
857C2×C8—22no—
858C2×C8—22no—
859C2×C8—48no—
860C2×C8C22×D414yes—
861C2×C8C22×D414yes—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4#11714yes—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—41no—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—41no—
905C22⋊C4—41no—
906C22⋊C4—41no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4#11714yes—
913C22⋊C4#11714yes—
914C42—22no—
915C42—22no—
916C42—22no—
917C42—22no—
918C42—22no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—41no—
940C42—41no—
941C42C4×D414yes—
942C42C4×D414yes—
943C42C22×D412yes—
944C42C22×D412yes—
945C42C2×#4114yes—
946C42C2×#4112yes—
947C42C2×#4112yes—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—28no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—44no—
979C23—44no—
980C23—44no—
981C23—44no—
982C23—44no—
983C23—44no—
984C23—44no—
985C23—44no—
986C23—44no—
987C23—44no—
988C23—82no—
989C23—82no—
990C23—82no—
991C23C2×#11712yes—
992C23C2×#11712yes—
993C23C2×C4×D412yes—
994C23#56812yes—
995C23#56812yes—
996C23#56812yes—
997C23C24×C411yescharacteristic
998D4—44no—
999D4—44no—
1000D4—44no—
1001D4—44no—
1002C2×C4—28no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—28no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4C2×#11712yes—
1102C2×C4C2×#11712yes—
1103C2×C4C2×#11712yes—
1104C2×C4C2×#11712yes—
1105C2×C4C2×C4×D412yes—
1106C2×C4C2×C4×D412yes—
1107C2×C4C2×C4×D412yes—
1108C2×C4C2×C4×D412yes—
1109C2×C4C2×C4×D412yes—
1110C2×C4#56812yes—
1111C2×C4C23×D411yescharacteristic
1112C2×C4C22×#4112yes—
1113C2×C4C22×#4111yescharacteristic
1114C2×C4#58512yes—
1115C8—24no—
1116C8—24no—
1117C8—42no—
1118C8—42no—
1119C8—42no—
1120C8—42no—
1121C8—42no—
1122C8—42no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—416no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—88no—
1159C22#293014yes—
1160C22C22×#11711yescharacteristic
1161C22C22×C4×D411yescharacteristic
1162C22#342811yescharacteristic
1163C22C2×#56811yescharacteristic
1164C22C2×#56811yescharacteristic
1165C22C2×#56811yescharacteristic
1166C22C2×#56811yescharacteristic
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—22no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4D4×#4112yes—
1193C4#347512yes—
1194C2—24no—
1195C2—42no—
1196C2—42no—
1197C2—42no—
1198C2—81no—
1199C2D4×#11711yescharacteristic
1200C2#6012411yescharacteristic
1201C2#6012811yescharacteristic
1202C2C2×#293011yescharacteristic
1203C2#6014111yescharacteristic
1204C2#6028911yescharacteristic
1205C2#6029111yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC23×D4C2×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
1. C2×#2924C2semidirect
2. C2×#2920C2semidirect
4. #22801C2semidirect
5. #22755C2semidirect
6. #22753C2semidirect
7. #22649C2semidirect
8. #22603C2semidirect
9. #22601C2semidirect
10. #22555C2semidirect
11. #22555C2semidirect
12. #22554C2semidirect
13. #22553C2semidirect
16. #21272C2semidirect
17. #21109C2semidirect
18. #21104C2semidirect
19. #20814C2semidirect
20. #20717C2semidirect
21. #20715C2semidirect
22. #20487C2semidirect
23. #20469C2semidirect
31. C2×#433C22semidirect
32. C2×#433C22semidirect
38. C2×#432C22semidirect
42. C2×#431C22semidirect
43. C2×#424C22semidirect
44. C2×#423C22semidirect
49. C2×#405C22semidirect
50. C2×C4×M16C22semidirect
81. #1940C22semidirect
82. #1939C22semidirect
83. #1924C22semidirect
84. #1924C22semidirect
85. #1924C22semidirect
86. #1924C22semidirect
87. #1924C22semidirect
88. #1923C22semidirect
89. #1923C22semidirect
90. #1923C22semidirect
91. #1917C22semidirect
92. #1917C22semidirect
93. #1917C22semidirect
94. #1916C22semidirect
99. #1851C22semidirect
100. #1851C22semidirect
101. #1851C22semidirect
102. #1850C22semidirect
103. #1843C22semidirect
104. #1832C22semidirect
109. #1798C22semidirect
110. #1798C22semidirect
115. #1797C22semidirect
116. #1797C22semidirect
121. #1771C22semidirect
122. #1770C22semidirect
123. #1768C22semidirect
124. #1768C22semidirect
125. #1768C22semidirect
126. #1768C22semidirect
127. #1753C22semidirect
128. #1753C22semidirect
129. #1753C22semidirect
130. #1752C22semidirect
131. #1750C22semidirect
132. #1750C22semidirect
135. #1749C22semidirect
136. #1749C22semidirect
139. #1746C22semidirect
140. #1726C22semidirect
212. #431D4semidirect
605. C4⋊C8C2×D4semidirect
637. C4×C8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#29242
C2×#29202
C2×#22902
#228012
#227552
#227532
#226492
#226032
#226012
#225552
#225542
#225532
#224012
#223992
#212722
#211092
#211042
#208142
#207172
#207152
#204872
#204692