Finite Group Databasebeta

← #108321

Subgroups — #108321

Order 512.

696 conjugacy classes of subgroups.

The subgroup lattice has 379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60250C211yesmaximal, characteristic
2#17734C211yesmaximal, characteristic
3C2×#1515C211yesmaximal, characteristic
4#7975C211yesmaximal, characteristic
5#7967C211yesmaximal, characteristic
6#7921C211yesmaximal, characteristic
7#7916C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2986—22no—
10#2985—22no—
11#2984—22no—
12#2983C412yescomplemented
13#2982C412yescomplemented
14#2962—22no—
15#2960—22no—
16#2924—22no—
17#2920C2211yescharacteristic
18#2920C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#432C2211yescharacteristic
21C2×#431C2211yescharacteristic
22C2×#383C2211yescharacteristic
23#1559—22no—
24#1558C412yescomplemented
25#1556C412yescomplemented
26#1542—22no—
27#1515—22no—
28#1515—22no—
29C2×#328C414yes—
30#1288—22no—
31#1287—22no—
32#1281—22no—
33#1280—22no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533D412yes—
39#533D412yes—
40#533D412yes—
41#533Q812yes—
42C2×C4⋊Q8C2×C411yescharacteristic
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×#125—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8C2×C412yes—
47C2×C4×Q8—21no—
48C2×C4×Q8C2×C412yes—
49C2×#117—21no—
50C22×C42C2311yescharacteristic
51#446—24no—
52#446—28no—
53#446—24no—
54#446—24no—
55C8×Q8—24no—
56C8×Q8—24no—
57C8×Q8—24no—
58#433—28no—
59#432—21no—
60#432—21no—
61#432—24no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432—21no—
66#432—21no—
67#432—21no—
68#432—21no—
69#432—21no—
70#432C2×C412yes—
71#432C2×C412yes—
72#431—21no—
73#431—21no—
74#431—24no—
75#431—21no—
76#431—21no—
77#431C2×C411yescharacteristic
78#431C2×C411yescharacteristic
79#431C2×C412yes—
80#431D412yes—
81#431D412yes—
82#424—24no—
83#423—21no—
84#423—21no—
85C2×C4⋊C8—21no—
86C2×C4⋊C8—21no—
87C2×C4⋊C8—21no—
88#407—21no—
89#407—21no—
90C2×C22⋊C8—21no—
91C2×C22⋊C8C2×C412yes—
92C2×C22⋊C8D412yes—
93#405—24no—
94C4×M16—21no—
95C4×M16D412yes—
96C2×#97—21no—
97C2×#97—21no—
98C2×C4×C8—21no—
99#383—21no—
100#383—21no—
101#383—21no—
102#383—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95C2×C412yes—
106#333—24no—
107#332—24no—
108#328—28no—
109C22×Q8—21no—
110C22×Q8C4212yes—
111C23×C4—22no—
112C23×C4C22×C411yescharacteristic
113C23×C4C2×D411yescharacteristic
114C23×C4#4111yescharacteristic
115C2×M16—22no—
116C2×M16—41no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—41no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8C22⋊C412yes—
125C4⋊Q8C22⋊C412yes—
126C4⋊Q8C4⋊C412yes—
127C4⋊Q8C4⋊C412yes—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8C22⋊C414yes—
139C22⋊Q8C4⋊C414yes—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8C22⋊C414yes—
147C4×Q8C4⋊C414yes—
148#117—22no—
149#117—22no—
150#117—22no—
151#117—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4C4212yes—
158C2×C22⋊C4—22no—
159C2×C42—22no—
160C2×C42C22×C411yescharacteristic
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×Q811yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C4⋊C8—28no—
173C4⋊C8—28no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8C22⋊C412yes—
195C22⋊C8C22⋊C412yes—
196#97—28no—
197#97—22no—
198#97—22no—
199#97—22no—
200#97—41no—
201#97—41no—
202#97—41no—
203C4×C8—28no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—22no—
207C4×C8—41no—
208C4×C8C22⋊C414yes—
209#95—22no—
210#95—22no—
211#95—41no—
212#95—41no—
213#95—41no—
214#95—41no—
215C24C4×D411yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—82no—
221C2×Q8#9514yes—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—44no—
228C22×C4—81no—
229C22×C4—82no—
230C22×C4—82no—
231C22×C4C2×C4211yescharacteristic
232C22×C4C2×C22⋊C411yescharacteristic
233C22×C4C2×C22⋊C411yescharacteristic
234C22×C4C2×C4⋊C411yescharacteristic
235C22×C4#11711yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4C4×D411yescharacteristic
240C22×C4C4×D411yescharacteristic
241C22×C4#12011yescharacteristic
242C22×C4#12011yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4C22⋊Q811yescharacteristic
246C22×C4C22⋊Q811yescharacteristic
247C22×C4#12311yescharacteristic
248C22×C4#12311yescharacteristic
249M16—44no—
250M16—82no—
251C2×C8—22no—
252C2×C8—24no—
253C2×C8—22no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—82no—
260C4⋊C4—22no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—24no—
271C4⋊C4#9514yes—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C42—24no—
275C42—24no—
276C42C2×C22⋊C411yescharacteristic
277C42C2×C22⋊C411yescharacteristic
278C42C2×C22⋊C411yescharacteristic
279C42C2×C4⋊C411yescharacteristic
280C42C2×C4⋊C411yescharacteristic
281C42#11711yescharacteristic
282C42C4×D411yescharacteristic
283C42C4×D411yescharacteristic
284C42#12011yescharacteristic
285C42#12011yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42#12311yescharacteristic
291C42#12311yescharacteristic
292C23—22no—
293C23—22no—
294C23—41no—
295C23C4×C22⋊C411yescharacteristic
296C23#38511yescharacteristic
297C23#38611yescharacteristic
298Q8—44no—
299Q8—44no—
300Q8—44no—
301Q8—82no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—44no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—164no—
328C2×C4C2×#9511yescharacteristic
329C2×C4C4×C22⋊C411yescharacteristic
330C2×C4#37911yescharacteristic
331C2×C4#38011yescharacteristic
332C2×C4#38011yescharacteristic
333C2×C4#38111yescharacteristic
334C2×C4#38511yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38511yescharacteristic
337C2×C4#38611yescharacteristic
338C2×C4#38611yescharacteristic
339C2×C4#38611yescharacteristic
340C8—42no—
341C8—42no—
342C8—44no—
343C8—82no—
344C8—82no—
345C8—82no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—44no—
354C22C22⋊#9511yescharacteristic
355C22#175712yes—
356C22#190512yes—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—44no—
371C4—162no—
372C2—22no—
373C2—22no—
374C2—41no—
375C2#1076411yescharacteristic
376C2#1078611yescharacteristic
377C2#1078711yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. #2983C4semidirect
13. #2982C4semidirect
24. #1558C4semidirect
25. #1556C4semidirect

Maximal subgroups

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

subgroupindex
#602502
#177342
C2×#15152
#79752
#79672
#79212
#79162