Finite Group Databasebeta

← #100657

Subgroups — #100657

Order 512.

354 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 86 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#30079C211yesmaximal, characteristic
2#22315C211yesmaximal, characteristic
3#9894C211yesmaximal, characteristic
4#8235C211yesmaximal, characteristic
5#7663C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7023C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2095C411yescharacteristic
11#2095C411yescharacteristic
12#2083—21no—
13#2072C411yescharacteristic
14#2072C411yescharacteristic
15#2043—21no—
16#1985—21no—
17#1984—21no—
18#1940—21no—
19#1917—21no—
20#1916—21no—
21#1863—21no—
22#1863—21no—
23#1839C2211yescharacteristic
24#1831C2211yescharacteristic
25#1771—21no—
26#1767C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×#333—21no—
30#1296—21no—
31#1295—21no—
32#1295—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8D411yescharacteristic
36C2×#125—21no—
37C2×C4×Q8D411yescharacteristic
38C2×C4×Q8D411yescharacteristic
39C2×#107—21no—
40C2×#107—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×#103—21no—
47C2×#103—21no—
48C2×#103—21no—
49C2×#103—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×#97D411yescharacteristic
53C2×#97D411yescharacteristic
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391C2×C411yescharacteristic
57#391C2×C411yescharacteristic
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#384C2×C411yescharacteristic
65#384C2×C411yescharacteristic
66#384D411yescharacteristic
67#382—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C43C2311yescharacteristic
71#340—21no—
72#340—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#333—24no—
89C22×Q8C22⋊C411yescharacteristic
90C22×Q8C22⋊C411yescharacteristic
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—41no—
98C22×C8—41no—
99C4⋊Q8—22no—
100C4⋊Q8—41no—
101#125—81no—
102#125—81no—
103C4×Q8—81no—
104C4×Q8—81no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42C22×C411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129C2×C42#4111yescharacteristic
130#107—81no—
131#107—81no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—81no—
139C4⋊C8—81no—
140#103—42no—
141#103—42no—
142#103—81no—
143#103—81no—
144#97—21no—
145#97—21no—
146#97—21no—
147#97—41no—
148#97—41no—
149#97—81no—
150#97Q1612yes—
151C4×C8—81no—
152C4×C8—81no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—21no—
157#95—41no—
158#95—41no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8#10412yes—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4C2×C22⋊C411yescharacteristic
174C22×C4C4×D411yescharacteristic
175C22×C4C4×D411yescharacteristic
176C22×C4#12011yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12311yescharacteristic
180C2×C8—22no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—82no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42C2×Q1611yescharacteristic
237C42#13511yescharacteristic
238C42#13711yescharacteristic
239C42#13711yescharacteristic
240C23#38611yescharacteristic
241Q8—42no—
242Q8—42no—
243Q8—81no—
244Q8—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4C2×#10411yescharacteristic
280C2×C4#42111yescharacteristic
281C2×C4C4×Q1611yescharacteristic
282C2×C4#44111yescharacteristic
283C2×C4#45111yescharacteristic
284C2×C4#45211yescharacteristic
285C2×C4#46211yescharacteristic
286C2×C4#46411yescharacteristic
287C2×C4#47111yescharacteristic
288C2×C4#47211yescharacteristic
289C8—42no—
290C8—81no—
291C8—81no—
292C8—81no—
293C8—81no—
294C8—81no—
295C8—82no—
296C8—82no—
297C22#187111yescharacteristic
298C22#187811yescharacteristic
299C22#188111yescharacteristic
300C22#190511yescharacteristic
301C22#190711yescharacteristic
302C22#191111yescharacteristic
303C22#191511yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—42no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—161no—
321C4—161no—
322C2#899011yescharacteristic
323C2#916411yescharacteristic
324C2#918911yescharacteristic
325C2#927011yescharacteristic
326C2#929711yescharacteristic
327C2#933611yescharacteristic
328C2#937111yescharacteristic
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
#300792
#223152
#98942
#82352
#76632
#70412
#70232