Finite Group Databasebeta

← #118923

Subgroups — #118923

Order 512.

528 conjugacy classes of subgroups.

The subgroup lattice has 335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17742C211yesmaximal, characteristic
2#17742C211yesmaximal, characteristic
3C2×#1558C211yesmaximal, characteristic
4#8118C211yesmaximal, characteristic
5#8086C211yesmaximal, characteristic
6#7970C211yesmaximal, characteristic
7#7968C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14C2×#432C2211yescharacteristic
15#1558—22no—
16#1558C414yes—
17#1556—22no—
18#1556—22no—
19#1549—22no—
20#1549—22no—
21#1546—22no—
22#1546—22no—
23C2×#333—22no—
24#1307—22no—
25#1302—22no—
26#1287—22no—
27#1287—22no—
28C23×Q8—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4⋊Q8C2×C412yes—
39C2×C4⋊Q8D412yes—
40C2×C4⋊Q8D412yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C42C2311yescharacteristic
44#432—21no—
45#432—21no—
46#432—21no—
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432C2×C412yes—
58#432C2×C412yes—
59#432D412yes—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431D412yes—
67#431D412yes—
68#423—21no—
69#423—21no—
70#423—21no—
71#423D412yes—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74#407—21no—
75#407—21no—
76#407—21no—
77#407—21no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C2×#97—21no—
85C2×#97—21no—
86#333—28no—
87#332—28no—
88#332—28no—
89C22×Q8—22no—
90C22×Q8—22no—
91C22×Q8—22no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8—41no—
95C22×Q8—84no—
96C23×C4—41no—
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—22no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C22×C8—41no—
105C22×C8—41no—
106C4⋊Q8—22no—
107C4⋊Q8—22no—
108C4⋊Q8—22no—
109C4⋊Q8—22no—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—22no—
114C4⋊Q8—22no—
115C4⋊Q8—41no—
116C4⋊Q8—41no—
117C4⋊Q8—41no—
118C4⋊Q8—41no—
119C4⋊Q8—41no—
120C4⋊Q8—41no—
121C4⋊Q8C22⋊C414yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C22⋊C8—22no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169C22⋊C8—41no—
170#97—22no—
171#97—22no—
172#97—22no—
173#97—41no—
174#97—41no—
175#97—41no—
176#97—41no—
177#97—41no—
178C4×C8—22no—
179C4×C8—22no—
180C4×C8—41no—
181C4×C8—41no—
182C24#12611yescharacteristic
183C2×Q8—24no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—42no—
187C2×Q8—84no—
188C2×Q8—84no—
189C2×Q8—84no—
190C2×Q8—84no—
191C2×Q8—84no—
192C2×Q8—84no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—84no—
200C22×C4#11711yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4C4×D411yescharacteristic
203C22×C4#12111yescharacteristic
204C22×C4#12111yescharacteristic
205C22×C4#12111yescharacteristic
206C22×C4#12311yescharacteristic
207C22×C4#12311yescharacteristic
208C22×C4#12311yescharacteristic
209C22×C4#12311yescharacteristic
210C22×C4#12311yescharacteristic
211C22×C4#12311yescharacteristic
212C22×C4#12311yescharacteristic
213C22×C4#12411yescharacteristic
214C22×C4#12411yescharacteristic
215C22×C4#12411yescharacteristic
216C22×C4#12611yescharacteristic
217C22×C4#12611yescharacteristic
218M16—82no—
219M16—82no—
220M16—82no—
221M16—82no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—82no—
229C2×C8—82no—
230C4⋊C4—24no—
231C4⋊C4—24no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C42C2×C22⋊C411yescharacteristic
239C42#11711yescharacteristic
240C42C4×D411yescharacteristic
241C42C4×D411yescharacteristic
242C42#12011yescharacteristic
243C42#12011yescharacteristic
244C42#12111yescharacteristic
245C42#12111yescharacteristic
246C42#12111yescharacteristic
247C42#12111yescharacteristic
248C42#12111yescharacteristic
249C42#12311yescharacteristic
250C42#12311yescharacteristic
251C42#12311yescharacteristic
252C42#12411yescharacteristic
253C42#12611yescharacteristic
254C23—22no—
255C23—41no—
256C23—41no—
257C23#38811yescharacteristic
258C23#39711yescharacteristic
259C23#39711yescharacteristic
260Q8—84no—
261Q8—84no—
262Q8—84no—
263Q8—84no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—44no—
283C2×C4—84no—
284C2×C4—84no—
285C2×C4—84no—
286C2×C4#38111yescharacteristic
287C2×C4#38611yescharacteristic
288C2×C4#38611yescharacteristic
289C2×C4#38811yescharacteristic
290C2×C4#38811yescharacteristic
291C2×C4#38811yescharacteristic
292C2×C4#39411yescharacteristic
293C2×C4#39411yescharacteristic
294C2×C4#39411yescharacteristic
295C2×C4#39411yescharacteristic
296C2×C4#39711yescharacteristic
297C2×C4#39711yescharacteristic
298C8—82no—
299C8—82no—
300C8—82no—
301C8—82no—
302C8—82no—
303C8—82no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—44no—
313C22#144011yescharacteristic
314C22#208112yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—84no—
326C4#204912yes—
327C4#208212yes—
328C2—22no—
329C2—41no—
330C2—41no—
331C2#1115711yescharacteristic
332C2#1118211yescharacteristic
333C2#1118811yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ 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
#177422
C2×#15582
#81182
#80862
#79702
#79682