Finite Group Databasebeta

← #122140

Subgroups — #122140

Order 512.

536 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37564C211yesmaximal, characteristic
2#8113C211yesmaximal, characteristic
3#8096C211yesmaximal, characteristic
4#7978C211yesmaximal, characteristic
5#7977C211yesmaximal, characteristic
6#7958C211yesmaximal, characteristic
7#7926C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12#2845—22no—
13#2667—22no—
14#2667—22no—
15#2667C414yes—
16#2606—22no—
17#2606—22no—
18#2606—22no—
19#2283C2211yescharacteristic
20#2283C2211yescharacteristic
21#2283C2211yescharacteristic
22#1306—22no—
23#1303—22no—
24#1288—22no—
25#1288—22no—
26#1286—22no—
27#1282—22no—
28C22×C42C2311yescharacteristic
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431Q812yes—
43#431Q812yes—
44#431Q812yes—
45#423—21no—
46#423—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49#407—21no—
50#407—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C4×M16—21no—
54C4×M16—21no—
55C2×#97Q812yes—
56C2×C4×C8—21no—
57#399—24no—
58#398—24no—
59#398—24no—
60#398—24no—
61#398—24no—
62#398—24no—
63#398—24no—
64#396—24no—
65#389—24no—
66#389—24no—
67#389—24no—
68#387—24no—
69#387—24no—
70#387—24no—
71#383—21no—
72#383D412yes—
73#383D412yes—
74#382—21no—
75#382—21no—
76#382D412yes—
77#381—21no—
78#381C2×C412yes—
79#381D412yes—
80#380—21no—
81#380—21no—
82#380C2×C412yes—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4D412yes—
86C4×C22⋊C4—21no—
87C4×C22⋊C4C2×C412yes—
88C4×C22⋊C4D412yes—
89#376—21no—
90#376—21no—
91#376—21no—
92C23×C4C22×C411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C2×M16—41no—
96C2×M16—41no—
97C22×C8—22no—
98C22×C8—41no—
99C2×C4⋊C4—24no—
100C2×C4⋊C4—24no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C22⋊C4—22no—
109C2×C22⋊C4—22no—
110C2×C22⋊C4C22⋊C414yes—
111C2×C42—22no—
112C2×C42—22no—
113C2×C42—22no—
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×Q811yescharacteristic
119C2×C42C2×Q811yescharacteristic
120C2×C42C2×Q811yescharacteristic
121C2×C42C2×Q811yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125C2×C42#4111yescharacteristic
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C22⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—22no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142#97—22no—
143#97—22no—
144#97—41no—
145#97—41no—
146C4×C8—22no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—41no—
150#95—24no—
151#95—24no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95—22no—
156#95—22no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162#95C22⋊C414yes—
163#95C22⋊C414yes—
164C24C2×C22⋊C411yescharacteristic
165C22×C4—24no—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—42no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4C2×C22⋊C411yescharacteristic
172C22×C4C2×C22⋊C411yescharacteristic
173C22×C4C4×Q811yescharacteristic
174C22×C4C4×Q811yescharacteristic
175C22×C4C4×Q811yescharacteristic
176C22×C4C4×Q811yescharacteristic
177C22×C4#12011yescharacteristic
178C22×C4#12011yescharacteristic
179C22×C4#12011yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4C22⋊Q811yescharacteristic
182C22×C4C22⋊Q811yescharacteristic
183C22×C4C22⋊Q811yescharacteristic
184C22×C4C22⋊Q811yescharacteristic
185C22×C4#12411yescharacteristic
186C22×C4#12411yescharacteristic
187C22×C4C4⋊Q811yescharacteristic
188C22×C4C4⋊Q811yescharacteristic
189M16—82no—
190M16—82no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—82no—
196C2×C8—82no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C4⋊C4—84no—
201C4⋊C4—84no—
202C4⋊C4—84no—
203C4⋊C4—84no—
204C4⋊C4—84no—
205C4⋊C4—84no—
206C22⋊C4—44no—
207C22⋊C4—82no—
208C22⋊C4—82no—
209C42—82no—
210C42—82no—
211C42—82no—
212C42C22⋊Q811yescharacteristic
213C42C22⋊Q811yescharacteristic
214C42C22⋊Q811yescharacteristic
215C42C22⋊Q811yescharacteristic
216C42C22⋊Q811yescharacteristic
217C42C22⋊Q811yescharacteristic
218C42C22⋊Q811yescharacteristic
219C42C22⋊Q811yescharacteristic
220C42#12411yescharacteristic
221C42#12411yescharacteristic
222C42#12411yescharacteristic
223C42#12411yescharacteristic
224C42C4⋊Q811yescharacteristic
225C42C4⋊Q811yescharacteristic
226C42C4⋊Q811yescharacteristic
227C42C4⋊Q811yescharacteristic
228C23—22no—
229C23—41no—
230C23—41no—
231C23#37911yescharacteristic
232C23#39111yescharacteristic
233C23#39111yescharacteristic
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
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×C4—41no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4#39111yescharacteristic
262C2×C4#39111yescharacteristic
263C2×C4#39111yescharacteristic
264C2×C4#39111yescharacteristic
265C2×C4#39311yescharacteristic
266C2×C4#39311yescharacteristic
267C2×C4#39311yescharacteristic
268C2×C4#39311yescharacteristic
269C2×C4#39511yescharacteristic
270C2×C4#39511yescharacteristic
271C2×C4#39511yescharacteristic
272C2×C4#39511yescharacteristic
273C8—82no—
274C8—82no—
275C8—82no—
276C8—82no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—82no—
286C22#144611yescharacteristic
287C22#179412yes—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—84no—
301C4—84no—
302C4—84no—
303C2—22no—
304C2—41no—
305C2—41no—
306C2#1138911yescharacteristic
307C2#1139311yescharacteristic
308C2#1139511yescharacteristic
subgroupG/H
center, socleC22#1446
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#375642
#81132
#80962
#79782
#79772
#79582
#79262