Finite Group Databasebeta

← #99663

Subgroups — #99663

Order 512.

649 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 649 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C2×#2095C211yesmaximal, characteristic
2#14471C211yesmaximal, characteristic
3#11371C212yesmaximal
4C2×#1272C211yesmaximal, characteristic
5#7025C212yesmaximal
6C22×#107—21no—
7C22×#103—21no—
8C2×#391C2211yescharacteristic
9C2×#384C2211yescharacteristic
10#2095—22no—
11#2095C414yescomplemented
12C2×#340—22no—
13C2×#340—22no—
14C2×#336C2212yes—
15C2×#336C2211yescharacteristic
16#1446—21no—
17#1442—22no—
18#1436—21no—
19#1436—22no—
20C4⋊#95C2212yes—
21#1272—22no—
22C23×Q8D411yescharacteristic
23C23×C8—21no—
24C23×C8—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—22no—
27C22×C4⋊C4D412yes—
28C22×C4⋊C4D411yescharacteristic
29C22×C4⋊C4D412yes—
30C22×C42—21no—
31C22×C42C2311yescharacteristic
32C2×#107—24no—
33C2×#107—42no—
34C2×#107—42no—
35C2×#103—24no—
36C2×#103—42no—
37C2×#103—42no—
38#391—22no—
39#391C2×C412yes—
40#391D412yes—
41#384—21no—
42#384—22no—
43#384C2×C412yes—
44C2×#95—22no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—22no—
51C2×#95—21no—
52#340—44no—
53#340—44no—
54#336—21no—
55#336—22no—
56#336—22no—
57#336C2×C412yes—
58C22×Q8—21no—
59C22×Q8—22no—
60C22×Q8—22no—
61C22×Q8—42no—
62C22×Q8—41no—
63C22×Q8—41no—
64C22×Q8C22⋊C412yes—
65C23×C4—21no—
66C23×C4—22no—
67C23×C4—21no—
68C23×C4—22no—
69C23×C4—41no—
70C23×C4C2×D411yescharacteristic
71C23×C4C2×D412yes—
72C22×C8—22no—
73C22×C8—22no—
74C22×C8—22no—
75C22×C8—24no—
76C22×C8—42no—
77C22×C8—42no—
78C22×C8—42no—
79C22×C8—42no—
80C22×C8—42no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8—42no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4C22⋊C412yes—
107C2×C4⋊C4Q1614yes—
108C2×C42—42no—
109C2×C42—82no—
110C2×C42—81no—
111C2×C42C22×C411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42#4112yes—
114#107—48no—
115#103—48no—
116#95—24no—
117#95—24no—
118#95—42no—
119#95—42no—
120#95—42no—
121#95—42no—
122#95—81no—
123#95—82no—
124#95—81no—
125#95—81no—
126#95—82no—
127C24#12011yescharacteristic
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—42no—
131C2×Q8—42no—
132C2×Q8—44no—
133C2×Q8—44no—
134C2×Q8—42no—
135C2×Q8—81no—
136C2×Q8—81no—
137C2×Q8—82no—
138C2×Q8—82no—
139C22×C4—22no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—42no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—82no—
172C22×C4—81no—
173C22×C4—81no—
174C22×C4—82no—
175C22×C4C2×C22⋊C411yescharacteristic
176C22×C4C4×D412yes—
177C22×C4#12112yes—
178C22×C4#12311yescharacteristic
179C22×C4C2×Q1612yes—
180C22×C4#13512yes—
181C22×C4#13512yes—
182C22×C4#13712yes—
183C22×C4#13712yes—
184C22×C4#13712yes—
185C2×C8—24no—
186C2×C8—44no—
187C2×C8—44no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—44no—
191C2×C8—44no—
192C2×C8—44no—
193C2×C8—82no—
194C2×C8—82no—
195C2×C8—82no—
196C2×C8—82no—
197C4⋊C4—42no—
198C4⋊C4—44no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—44no—
203C4⋊C4—44no—
204C4⋊C4—82no—
205C4⋊C4—81no—
206C4⋊C4—82no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C42—41no—
212C42—41no—
213C42—42no—
214C42—84no—
215C23#38611yescharacteristic
216C23#45112yes—
217C23#45212yes—
218C23#45212yes—
219C23#45312yes—
220C23#45311yescharacteristic
221C23#45311yescharacteristic
222C23#45412yes—
223C23#45812yes—
224Q8—44no—
225Q8—82no—
226Q8—84no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—81no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—84no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—161no—
274C2×C4—162no—
275C2×C4—161no—
276C2×C4#41611yescharacteristic
277C2×C4#41911yescharacteristic
278C2×C4C4×Q1612yes—
279C2×C4#44112yes—
280C2×C4#46212yes—
281C2×C4#46412yes—
282C2×C4#48512yes—
283C8—44no—
284C8—84no—
285C22#161412yes—
286C22#161512yes—
287C22#161712yes—
288C22#161812yes—
289C22#161812yes—
290C22#161812yes—
291C22#163012yes—
292C22#163212yes—
293C22#163212yes—
294C22#163311yescharacteristic
295C22#163411yescharacteristic
296C22#163612yes—
297C22#163812yes—
298C22#165511yescharacteristic
299C22#165612yes—
300C22#165711yescharacteristic
301C22#187311yescharacteristic
302C22#187812yes—
303C22#188312yes—
304C22#188711yescharacteristic
305C22#189011yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—82no—
314C4—82no—
315C4—84no—
316C4—162no—
317C4—162no—
318C2#783312yes—
319C2#783412yes—
320C2#783512yes—
321C2#783612yes—
322C2#897412yes—
323C2#900111yescharacteristic
324C2#902411yescharacteristic
325C2#904612yes—
326C2#906611yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
11. #2095C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20952
#144712
#113712
C2×#12722
#70252