Finite Group Databasebeta

← #238086

Subgroups — #238086

Order 512.

928 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37480C211yesmaximal, characteristic
2#20688C211yesmaximal, characteristic
3#20688C212yesmaximal
4#10393C214yesmaximal
5#10391C214yesmaximal
6#8102C212yesmaximal
7#8100C211yesmaximal, characteristic
8C22×#117C2211yescharacteristic
9#2842C2212yes—
10#2840C2212yes—
11#2665—24no—
12#2628—22no—
13#2607—22no—
14#2439—24no—
15#2280C2212yes—
16#2280C2211yescharacteristic
17#2280C2211yescharacteristic
18#2280C2212yes—
19#1820—22no—
20#1820—24no—
21#1819C2212yes—
22#1819C2218yes—
23#1819C2212yes—
24#1740—22no—
25#1740—24no—
26#1304C2212yes—
27#1304C2218yes—
28#1304C2212yes—
29C24×C4C2311yescharacteristic
30C2×C4⋊Q8—22no—
31C2×#117—21no—
32C2×#117—22no—
33C2×#117—22no—
34C2×#117—21no—
35C2×#117—21no—
36C2×#117—22no—
37C2×#117—22no—
38C2×#117—21no—
39C2×#117—22no—
40C2×#117—21no—
41C2×#117D412yes—
42C2×#117D414yes—
43C22×C4⋊C4Q812yescomplemented
44C22×C22⋊C4C2312yes—
45C22×C42Q812yescomplemented
46#400—24no—
47#399—24no—
48#396—28no—
49#395—24no—
50#393—24no—
51#393—28no—
52#391—28no—
53#389—24no—
54#387—28no—
55#382—22no—
56#381—21no—
57#381—22no—
58#381D412yes—
59#381D414yes—
60#380—22no—
61#380—22no—
62#380—22no—
63#380—22no—
64#380—22no—
65#380—22no—
66#379C2314yes—
67#379C2312yes—
68#379C2311yescharacteristic
69#379C2314yes—
70#379C2311yescharacteristic
71C4×C22⋊C4—22no—
72C4×C22⋊C4—22no—
73C4×C22⋊C4—22no—
74C4×C22⋊C4—22no—
75C4×C22⋊C4—22no—
76C4×C22⋊C4—22no—
77#342—24no—
78#342—216no—
79#342—24no—
80C25C2411yescharacteristic
81C22×Q8—24no—
82C23×C4—44no—
83C23×C4C2×D412yes—
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D412yes—
87C23×C4C2×Q814yes—
88C23×C4C2×Q811yescharacteristic
89C23×C4C2×Q811yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4112yes—
92C23×C4#4112yes—
93C23×C4#4111yescharacteristic
94C4⋊Q8—84no—
95#117—42no—
96#117—41no—
97#117—41no—
98#117—42no—
99#117—41no—
100#117—41no—
101#117—42no—
102#117—42no—
103#117—42no—
104#117—42no—
105#117—44no—
106#117—48no—
107#117—48no—
108#117—44no—
109C2×C4⋊C4—24no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—24no—
117C2×C4⋊C4—28no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—42no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—22no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4—24no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—24no—
129C2×C22⋊C4—24no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—24no—
132C2×C22⋊C4—24no—
133C2×C22⋊C4—24no—
134C2×C22⋊C4C2×D412yes—
135C2×C22⋊C4C2×D418yes—
136C2×C22⋊C4C2×D412yes—
137C2×C42—22no—
138C2×C42—24no—
139C2×C42—22no—
140C2×C42—22no—
141C2×C42—24no—
142C2×C42—24no—
143C2×C42—42no—
144C2×C42—41no—
145#95—24no—
146#95—24no—
147#95—28no—
148#95—24no—
149#95—24no—
150#95—24no—
151#95—42no—
152#95—42no—
153#95—42no—
154C24—42no—
155C24—82no—
156C24C22×D412yes—
157C24C22×D411yescharacteristic
158C24C22×Q811yescharacteristic
159C24C2×#4111yescharacteristic
160C24C2×#4112yes—
161C2×Q8—84no—
162C2×Q8—88no—
163C22×C4—28no—
164C22×C4—24no—
165C22×C4—22no—
166C22×C4—28no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—44no—
175C22×C4—44no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—44no—
179C22×C4—44no—
180C22×C4—42no—
181C22×C4—84no—
182C22×C4#12012yes—
183C22×C4#12011yescharacteristic
184C22×C4#12011yescharacteristic
185C22×C4C22⋊Q812yes—
186C22×C4C22⋊Q811yescharacteristic
187C22×C4C22⋊Q812yes—
188C22×C4C22⋊Q811yescharacteristic
189C22×C4C22⋊Q811yescharacteristic
190C22×C4C22⋊Q812yes—
191C22×C4C22⋊Q811yescharacteristic
192C22×C4C22⋊Q812yes—
193C22×C4#12412yes—
194C22×C4#12411yescharacteristic
195C22×C4#12411yescharacteristic
196C22×C4#12412yes—
197C22×C4#12412yes—
198C22×C4#12412yes—
199C22×C4#12412yes—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—48no—
205C4⋊C4—82no—
206C4⋊C4—84no—
207C4⋊C4—82no—
208C4⋊C4—88no—
209C4⋊C4—84no—
210C22⋊C4—42no—
211C22⋊C4—44no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—48no—
216C22⋊C4—44no—
217C22⋊C4—48no—
218C22⋊C4—82no—
219C22⋊C4—84no—
220C22⋊C4—84no—
221C22⋊C4—82no—
222C22⋊C4—84no—
223C22⋊C4—84no—
224C22⋊C4—84no—
225C42—44no—
226C42—42no—
227C42—42no—
228C42—44no—
229C42—84no—
230C42—84no—
231C42—82no—
232C23—22no—
233C23—24no—
234C23—41no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—41no—
243C23—42no—
244C23—88no—
245C23C2×#12011yescharacteristic
246C23C2×C22⋊Q812yes—
247C23C2×C22⋊Q811yescharacteristic
248C23C2×#12412yes—
249C23C2×#12411yescharacteristic
250Q8—168no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—48no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—48no—
276C2×C4—84no—
277C2×C4—84no—
278C2×C4—84no—
279C2×C4—84no—
280C2×C4—82no—
281C2×C4—84no—
282C2×C4—84no—
283C2×C4—84no—
284C2×C4#39312yes—
285C2×C4#39311yescharacteristic
286C2×C4#39312yes—
287C2×C4#39311yescharacteristic
288C2×C4#39311yescharacteristic
289C2×C4#39311yescharacteristic
290C2×C4#45814yes—
291C22—22no—
292C22—22no—
293C22—21no—
294C22—22no—
295C22—21no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—44no—
303C22—82no—
304C22—84no—
305C22—82no—
306C22—84no—
307C22C2×#39311yescharacteristic
308C22C2×#45812yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—82no—
314C4—88no—
315C4—82no—
316C4—84no—
317C4—164no—
318C4—162no—
319C4#203012yes—
320C4#203012yes—
321C2—22no—
322C2—42no—
323C2—41no—
324C2—42no—
325C2—41no—
326C2C2×#203011yescharacteristic
327C2#2347412yes—
subgroupG/H
center, socleC22C2×#393
commutator, Frattini, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C25 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
43. C22×C4⋊C4Q8semidirect
45. C22×C42Q8semidirect

Maximal subgroups

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

subgroupindex
#374802
#206882
#103932
#103912
#81022
#81002