Finite Group Databasebeta

← #101482

Subgroups — #101482

Order 512.

355 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 355 conjugacy classes of subgroups — too many to draw. Only its 82 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#29370C211yesmaximal, characteristic
2#21342C211yesmaximal, characteristic
3#9877C211yesmaximal, characteristic
4#7644C211yesmaximal, characteristic
5#7622C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7019C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2100C411yescharacteristic
11#2095C411yescharacteristic
12#2043C411yescharacteristic
13#2016C411yescharacteristic
14#1985—21no—
15#1940—21no—
16#1928—21no—
17#1917—22no—
18#1878—21no—
19#1878—21no—
20#1863—21no—
21#1839C2211yescharacteristic
22#1839C2211yescharacteristic
23#1831C2211yescharacteristic
24#1768—21no—
25#1767C2211yescharacteristic
26#1746—21no—
27C4×#97C2211yescharacteristic
28#1279—21no—
29#1279—21no—
30#1272—21no—
31#1271—21no—
32#1271—22no—
33C22×Q16—21no—
34C2×C4⋊Q8C2×C411yescharacteristic
35C2×C4×Q8—21no—
36C2×C4×Q8D411yescharacteristic
37C2×#107—21no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#103—21no—
45C2×#97—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×C4×C8D411yescharacteristic
49C2×C4×C8D411yescharacteristic
50#391—21no—
51#391C2×C411yescharacteristic
52#391D411yescharacteristic
53#389—21no—
54#389—21no—
55#389C2×C411yescharacteristic
56#389D411yescharacteristic
57#387—21no—
58#387—21no—
59#384C2×C411yescharacteristic
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4D411yescharacteristic
64#376—21no—
65C43C2311yescharacteristic
66#340—21no—
67#340—21no—
68#336—22no—
69#336—22no—
70#336—22no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336C2×C411yescharacteristic
79#336C2×C411yescharacteristic
80#336D412yes—
81C22×Q8—21no—
82C22×Q8C22⋊C411yescharacteristic
83C2×Q16—42no—
84C2×Q16—42no—
85C2×Q16—81no—
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—41no—
92C22×C8—41no—
93C4⋊Q8—42no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—81no—
97C4×Q8—81no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4C22⋊C411yescharacteristic
108C2×C4⋊C4C22⋊C411yescharacteristic
109C2×C4⋊C4C22⋊C411yescharacteristic
110C2×C42—21no—
111C2×C42—21no—
112C2×C42—41no—
113C2×C42C22×C411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42#4111yescharacteristic
119C2×C42#4111yescharacteristic
120#107—81no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—44no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126#103—42no—
127#103—42no—
128#103—81no—
129#103—81no—
130#97—41no—
131#97—41no—
132#97—42no—
133#97—41no—
134#97—41no—
135C4×C8—21no—
136C4×C8—21no—
137C4×C8—21no—
138C4×C8Q1612yescomplemented
139#95—21no—
140#95—21no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—41no—
147#95—41no—
148C2×Q8—22no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4C2×C22⋊C411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12311yescharacteristic
171Q16—84no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—42no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—82no—
209C42—21no—
210C42—21no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42—41no—
216C42—42no—
217C42—42no—
218C42—82no—
219C42C2×Q1611yescharacteristic
220C42#13511yescharacteristic
221C42#13711yescharacteristic
222C42#13711yescharacteristic
223C23#38611yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—42no—
227Q8—81no—
228Q8—81no—
229Q8—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4#42111yescharacteristic
266C2×C4#42111yescharacteristic
267C2×C4C4×Q1611yescharacteristic
268C2×C4#44111yescharacteristic
269C2×C4#45111yescharacteristic
270C2×C4#45211yescharacteristic
271C2×C4#46211yescharacteristic
272C2×C4#46411yescharacteristic
273C8—42no—
274C8—42no—
275C8—82no—
276C8—81no—
277C8—81no—
278C8—161no—
279C8—161no—
280C22#187811yescharacteristic
281C22#188111yescharacteristic
282C22#189111yescharacteristic
283C22#189711yescharacteristic
284C22#190211yescharacteristic
285C22#190611yescharacteristic
286C22#191011yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—81no—
299C4—82no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—161no—
304C2#904811yescharacteristic
305C2#923611yescharacteristic
306C2#929011yescharacteristic
307C2#931411yescharacteristic
308C2#937011yescharacteristic
309C2#949411yescharacteristic
310C2#953111yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
138. C4×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#293702
#213422
#98772
#76442
#76222
#70412
#70192