Finite Group Databasebeta

← #99400

Subgroups — #99400

Order 512.

338 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 102 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#23249C211yesmaximal, characteristic
2#9643C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#9604C211yesmaximal, characteristic
5#7571C211yesmaximal, characteristic
6#7027C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#1985—21no—
10#1984—21no—
11#1940—21no—
12#1940—21no—
13#1842C2211yescharacteristic
14#1771—21no—
15#1771—21no—
16#1767C2211yescharacteristic
17#1767C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20#1744C2211yescharacteristic
21C2×#335—21no—
22C2×#334—21no—
23C2×Q8⋊C8—21no—
24C2×Q8⋊C8—21no—
25#1277—21no—
26#1277—21no—
27#1272C411yescharacteristic
28#1272C411yescharacteristic
29#1272C411yescharacteristic
30#1272C411yescharacteristic
31C2×C4⋊Q8Q811yescharacteristic
32C2×C4×Q8D411yescharacteristic
33C2×C4×Q8D411yescharacteristic
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×#97—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52#391C2×C411yescharacteristic
53#391C2×C411yescharacteristic
54#389—21no—
55#389—21no—
56#384Q811yescharacteristic
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C43C2311yescharacteristic
60#336—21no—
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336C2×C411yescharacteristic
69#336C2×C411yescharacteristic
70#336C2×C411yescharacteristic
71#336C2×C411yescharacteristic
72#335—42no—
73#334—42no—
74Q8⋊C8—42no—
75Q8⋊C8—42no—
76C22×Q8C4⋊C411yescharacteristic
77C22×Q8C4⋊C411yescharacteristic
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—41no—
87C22×C8—41no—
88C4⋊Q8—22no—
89C4⋊Q8—41no—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4C4⋊C411yescharacteristic
101C2×C4⋊C4C4⋊C411yescharacteristic
102C2×C42—21no—
103C2×C42—21no—
104C2×C42C22×C411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×Q811yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—21no—
114C4⋊C8—21no—
115C4⋊C8—21no—
116C4⋊C8—21no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—42no—
120C4⋊C8—42no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—81no—
126C4⋊C8—81no—
127C4⋊C8SD1612yes—
128C4⋊C8Q1612yes—
129#97—41no—
130#97—41no—
131#97—41no—
132#97—41no—
133#97—81no—
134C4×C8—22no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—81no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8#10812yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4C2×C4⋊C411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4C4×D411yescharacteristic
160C22×C4#12011yescharacteristic
161C22×C4C22⋊Q811yescharacteristic
162C22×C4C22⋊Q811yescharacteristic
163C22×C4#12311yescharacteristic
164C2×C8—22no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C2×C8—81no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—41no—
207C42—41no—
208C42—41no—
209C42—41no—
210C42—41no—
211C42—41no—
212C42—41no—
213C42C2×SD1611yescharacteristic
214C42C2×Q1611yescharacteristic
215C42#13511yescharacteristic
216C42#13511yescharacteristic
217C42AGL(1,ℤ/8)11yescharacteristic
218C42#13711yescharacteristic
219C42#13711yescharacteristic
220C42#13711yescharacteristic
221C23#38511yescharacteristic
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4C2×#10811yescharacteristic
252C2×C4#43011yescharacteristic
253C2×C4C4×SD1611yescharacteristic
254C2×C4C4×Q1611yescharacteristic
255C2×C4#44011yescharacteristic
256C2×C4#44111yescharacteristic
257C2×C4#44811yescharacteristic
258C2×C4#44911yescharacteristic
259C2×C4#45111yescharacteristic
260C2×C4#45211yescharacteristic
261C2×C4#45311yescharacteristic
262C2×C4#45511yescharacteristic
263C2×C4#47511yescharacteristic
264C2×C4#47711yescharacteristic
265C2×C4#47911yescharacteristic
266C2×C4#47911yescharacteristic
267C8—42no—
268C8—42no—
269C8—42no—
270C8—42no—
271C8—81no—
272C8—81no—
273C8—82no—
274C8—81no—
275C8—81no—
276C8—161no—
277C22#185511yescharacteristic
278C22#185611yescharacteristic
279C22#186111yescharacteristic
280C22#186111yescharacteristic
281C22#186311yescharacteristic
282C22#186511yescharacteristic
283C22#186811yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4#162211yescharacteristic
300C4#163211yescharacteristic
301C4#164511yescharacteristic
302C4#164611yescharacteristic
303C2#886411yescharacteristic
304C2#887911yescharacteristic
305C2#888111yescharacteristic
306C2#890711yescharacteristic
307C2#890911yescharacteristic
308C2#891811yescharacteristic
309C2#892711yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#232492
#96432
#96052
#96042
#75712
#70272