Finite Group Databasebeta

← #100297

Subgroups — #100297

Order 512.

375 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 88 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#33073C211yesmaximal, characteristic
2#22022C211yesmaximal, characteristic
3#9891C211yesmaximal, characteristic
4#8173C211yesmaximal, characteristic
5#7680C211yesmaximal, characteristic
6#7042C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C42×Q8C2211yescharacteristic
10#1984—21no—
11#1948C411yescharacteristic
12#1947C411yescharacteristic
13#1939—21no—
14#1920—21no—
15#1918—21no—
16#1917—22no—
17#1865—21no—
18#1863—21no—
19#1839—21no—
20#1831—21no—
21#1831C2211yescharacteristic
22#1803C411yescharacteristic
23#1803C411yescharacteristic
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26#1744C2211yescharacteristic
27C4×#97C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1295—22no—
30#1279—21no—
31#1271—21no—
32#1271—21no—
33C2×#125—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×#107—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8C2×C411yescharacteristic
43C2×C4⋊C8C2×C411yescharacteristic
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97D412yes—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384C2×C411yescharacteristic
57#384C2×C411yescharacteristic
58#382—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4C2×C411yescharacteristic
63C4×C4⋊C4D411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C43—21no—
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#336—22no—
72#336—22no—
73#336—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336D411yescharacteristic
80#336D411yescharacteristic
81Q8⋊C8—24no—
82C22×Q8C22⋊C411yescharacteristic
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—22no—
87C22×C8—21no—
88C22×C8—41no—
89C22×C8—41no—
90#125—81no—
91#125—81no—
92C4×Q8—22no—
93C4×Q8—22no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97C4×Q8—41no—
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—21no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4C22⋊C411yescharacteristic
110C2×C4⋊C4C22⋊C411yescharacteristic
111C2×C4⋊C4C22⋊C411yescharacteristic
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42C22×C411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125#107—42no—
126#106—42no—
127C4⋊C8—22no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—82no—
134#103—42no—
135#103—42no—
136#97—22no—
137#97—22no—
138#97—42no—
139#97—41no—
140#97—41no—
141#97—81no—
142C4×C8—22no—
143C4×C8—41no—
144C4×C8—41no—
145C4×C8—41no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—41no—
150#95—41no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8#10412yes—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4C2×C22⋊C411yescharacteristic
164C22×C4C4×D411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4#12011yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12311yescharacteristic
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—81no—
190C2×C8—81no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—82no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4#10112yes—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—41no—
225C42—42no—
226C42—42no—
227C42—42no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C23#38611yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—41no—
238Q8—41no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4C2×#10111yescharacteristic
273C2×C4#41311yescharacteristic
274C2×C4C2×#10411yescharacteristic
275C2×C4#42111yescharacteristic
276C2×C4#42111yescharacteristic
277C2×C4#42111yescharacteristic
278C2×C4#44311yescharacteristic
279C2×C4#44411yescharacteristic
280C2×C4#45511yescharacteristic
281C2×C4#45611yescharacteristic
282C2×C4#47111yescharacteristic
283C2×C4#47211yescharacteristic
284C8—44no—
285C8—81no—
286C8—82no—
287C8—81no—
288C8—82no—
289C8—81no—
290C8—81no—
291C22#187111yescharacteristic
292C22#187611yescharacteristic
293C22#188211yescharacteristic
294C22#189711yescharacteristic
295C22#190111yescharacteristic
296C22#190511yescharacteristic
297C22#190711yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—161no—
313C4#152811yescharacteristic
314C4#153211yescharacteristic
315C4#153511yescharacteristic
316C4#153711yescharacteristic
317C2#897211yescharacteristic
318C2#912511yescharacteristic
319C2#916411yescharacteristic
320C2#921311yescharacteristic
321C2#924611yescharacteristic
322C2#932811yescharacteristic
323C2#935511yescharacteristic
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

Maximal subgroups

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

subgroupindex
#330732
#220222
#98912
#81732
#76802
#70422
#70302