Finite Group Databasebeta

← #107675

Subgroups — #107675

Order 512.

671 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60251C211yesmaximal, characteristic
2#17755C211yesmaximal, characteristic
3#17715C211yesmaximal, characteristic
4#8124C211yesmaximal, characteristic
5#7995C211yesmaximal, characteristic
6C2×#1287C211yesmaximal, characteristic
7#7922C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2987—22no—
10#2985—22no—
11#2984—22no—
12#2983—22no—
13#2962—22no—
14#2961—22no—
15#2924C414yes—
16#2920C2211yescharacteristic
17#2920C2211yescharacteristic
18C2×#432C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#432C2211yescharacteristic
21C2×#431C2211yescharacteristic
22#1556—21no—
23#1556—21no—
24#1552—22no—
25#1552—22no—
26#1552C414yes—
27#1549—21no—
28#1546—21no—
29#1544C414yes—
30#1308—22no—
31#1291—22no—
32#1287—22no—
33#1281—22no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533C2×C412yes—
39#533C2×C412yes—
40#533D412yes—
41#533D412yes—
42C2×C4⋊Q8D411yescharacteristic
43C2×C4⋊Q8D411yescharacteristic
44C2×#125Q812yes—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8—21no—
49C2×#117C2×C412yes—
50C22×C42C2311yescharacteristic
51#446—28no—
52#446—28no—
53#446—28no—
54#446—24no—
55C8×Q8—24no—
56#433—28no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—24no—
61#432—21no—
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#432D412yes—
72#432D412yes—
73#432D412yes—
74#431—21no—
75#431—24no—
76#431—21no—
77#431—21no—
78#431—21no—
79#431—21no—
80#431C2×C412yes—
81#431C2×C412yes—
82#431D412yes—
83#424—24no—
84#423—21no—
85#423—21no—
86C2×C4⋊C8—21no—
87C2×C4⋊C8—21no—
88C2×C4⋊C8—21no—
89C2×C4⋊C8C2×C412yes—
90#407—21no—
91#407C2×C412yes—
92C2×C22⋊C8—21no—
93C2×C22⋊C8—21no—
94C2×C22⋊C8—21no—
95C2×C22⋊C8C2×C412yes—
96#405—24no—
97C4×M16—21no—
98C4×M16—21no—
99C2×#97—21no—
100C2×#97—21no—
101C2×#97—21no—
102C2×C4×C8—21no—
103#332—24no—
104#332—24no—
105#332—24no—
106#332—24no—
107C22×Q8—21no—
108C22×Q8—21no—
109C23×C4C22×C411yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—22no—
113C2×M16—41no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—41no—
117C22×C8—41no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8C22⋊C412yes—
123C4⋊Q8C22⋊C412yes—
124C4⋊Q8C22⋊C412yes—
125C4⋊Q8C22⋊C412yes—
126#125—22no—
127#125—22no—
128#125C4⋊C414yes—
129#125C4⋊C414yes—
130C22⋊Q8—22no—
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146#117—22no—
147#117—22no—
148#117C4214yes—
149#117C22⋊C414yes—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4C4⋊C412yes—
155C2×C4⋊C4C4⋊C412yes—
156C2×C22⋊C4—22no—
157C2×C42—22no—
158C2×C42C22×C411yescharacteristic
159C2×C42C22×C411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×Q811yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C4⋊C8—28no—
171C4⋊C8—28no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8C22⋊C414yes—
195C22⋊C8C22⋊C414yes—
196#97—28no—
197#97—22no—
198#97—22no—
199#97—22no—
200#97—22no—
201#97—41no—
202#97—41no—
203#97—41no—
204#97—41no—
205C4×C8—28no—
206C4×C8—22no—
207C4×C8—22no—
208C4×C8—22no—
209C4×C8—41no—
210C24#11711yescharacteristic
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—82no—
216C2×Q8—82no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—81no—
222C22×C4C2×C4211yescharacteristic
223C22×C4C2×C22⋊C411yescharacteristic
224C22×C4C2×C22⋊C411yescharacteristic
225C22×C4C2×C22⋊C411yescharacteristic
226C22×C4C2×C4⋊C411yescharacteristic
227C22×C4#11711yescharacteristic
228C22×C4C4×D411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12311yescharacteristic
240M16—44no—
241M16—82no—
242C2×C8—24no—
243C2×C8—24no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—82no—
251C2×C8—82no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4#9514yes—
263C4⋊C4#9514yes—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C42—24no—
267C42—24no—
268C42C2×C22⋊C411yescharacteristic
269C42C2×C22⋊C411yescharacteristic
270C42C2×C4⋊C411yescharacteristic
271C42C2×C4⋊C411yescharacteristic
272C42C4×D411yescharacteristic
273C42C4×D411yescharacteristic
274C42C4×D411yescharacteristic
275C42C4×D411yescharacteristic
276C42#12011yescharacteristic
277C42#12011yescharacteristic
278C42#12011yescharacteristic
279C42#12011yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42C22⋊Q811yescharacteristic
283C42C22⋊Q811yescharacteristic
284C23—22no—
285C23—41no—
286C23—41no—
287C23C4×C22⋊C411yescharacteristic
288C23#38011yescharacteristic
289C23#38111yescharacteristic
290Q8—44no—
291Q8—82no—
292Q8—82no—
293Q8—82no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—44no—
315C2×C4—82no—
316C2×C4C2×#9511yescharacteristic
317C2×C4C4×C22⋊C411yescharacteristic
318C2×C4#37911yescharacteristic
319C2×C4#38011yescharacteristic
320C2×C4#38511yescharacteristic
321C2×C4#38511yescharacteristic
322C2×C4#38511yescharacteristic
323C2×C4#38511yescharacteristic
324C2×C4#38611yescharacteristic
325C2×C4#38611yescharacteristic
326C2×C4#38611yescharacteristic
327C2×C4#38611yescharacteristic
328C8—44no—
329C8—44no—
330C8—82no—
331C8—82no—
332C8—82no—
333C8—82no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—82no—
343C22C22⋊#9511yescharacteristic
344C22#183012yes—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—44no—
357C4—44no—
358C4#188112yes—
359C2—22no—
360C2—41no—
361C2—41no—
362C2#1077011yescharacteristic
363C2#1078211yescharacteristic
364C2#1079311yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#602512
#177552
#177152
#81242
#79952
C2×#12872
#79222