Finite Group Databasebeta

← #101310

Subgroups — #101310

Order 512.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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#23839C211yesmaximal, characteristic
2#23364C211yesmaximal, characteristic
3#8233C211yesmaximal, characteristic
4#7625C211yesmaximal, characteristic
5#7624C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7043C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2084C411yescharacteristic
11#2084C411yescharacteristic
12#2083—21no—
13#2058—21no—
14#2057C411yescharacteristic
15#2057C411yescharacteristic
16#1985—21no—
17#1984—21no—
18#1917—21no—
19#1917—21no—
20#1916—21no—
21#1916—21no—
22#1839C2211yescharacteristic
23#1839C2211yescharacteristic
24#1776—21no—
25#1776—21no—
26#1767C2211yescharacteristic
27#1767C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×#332—21no—
30#1296—21no—
31#1272—21no—
32#1272—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×#107—21no—
40C2×#107—21no—
41C2×#106—21no—
42C2×#106—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97—21no—
50C2×#97—21no—
51C2×C4×C8—21no—
52#391—21no—
53#391—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389C2×C411yescharacteristic
58#389C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#384D411yescharacteristic
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#336—21no—
72#336—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#336C2×C411yescharacteristic
83#336C2×C411yescharacteristic
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#332—24no—
89C22×Q8—21no—
90C22×Q8—21no—
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—
101C4⋊Q8—42no—
102C4×Q8—81no—
103C4×Q8—81no—
104C4×Q8—81no—
105C4×Q8—81no—
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—41no—
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#107—42no—
132#107—42no—
133#106—42no—
134#106—42no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—81no—
140C4⋊C8—81no—
141#97—22no—
142#97—22no—
143#97—81no—
144#97—81no—
145#97—81no—
146C4×C8—81no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—41no—
152#95—41no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—81no—
159C2×Q8—81no—
160C2×Q8—81no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4C2×C22⋊C411yescharacteristic
168C22×C4C4×D411yescharacteristic
169C22×C4C4×D411yescharacteristic
170C22×C4#12011yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12311yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C4⋊C4—21no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4#10412yes—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—82no—
236C23#38611yescharacteristic
237Q8—82no—
238Q8—82no—
239Q8—82no—
240Q8—82no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
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—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4C2×#10411yescharacteristic
277C2×C4#42111yescharacteristic
278C2×C4#45611yescharacteristic
279C2×C4#45611yescharacteristic
280C2×C4#47111yescharacteristic
281C2×C4#47111yescharacteristic
282C2×C4#47211yescharacteristic
283C2×C4#47311yescharacteristic
284C8—42no—
285C8—42no—
286C8—81no—
287C8—81no—
288C8—81no—
289C8—81no—
290C8—82no—
291C8—82no—
292C22#187111yescharacteristic
293C22#188611yescharacteristic
294C22#189111yescharacteristic
295C22#190411yescharacteristic
296C22#190511yescharacteristic
297C22#190711yescharacteristic
298C22#190811yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—82no—
314C4—81no—
315C4—161no—
316C2#903011yescharacteristic
317C2#916411yescharacteristic
318C2#916511yescharacteristic
319C2#942711yescharacteristic
320C2#943411yescharacteristic
321C2#952811yescharacteristic
322C2#952911yescharacteristic
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
#238392
#233642
#82332
#76252
#76242
#70432