Finite Group Databasebeta

← #119448

Subgroups — #119448

Order 512.

582 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21829C211yesmaximal, characteristic
2#21324C211yesmaximal, characteristic
3#17742C211yesmaximal, characteristic
4#8094C211yesmaximal, characteristic
5#8094C211yesmaximal, characteristic
6#8064C211yesmaximal, characteristic
7#8064C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2285C2211yescharacteristic
15#1997—22no—
16#1997—22no—
17#1993C414yes—
18#1990—22no—
19#1821—22no—
20#1736—22no—
21#1556—22no—
22#1549—22no—
23#1546—22no—
24#1303—22no—
25#1303—22no—
26#1299—22no—
27#1299—22no—
28C23×Q8—21no—
29C22×M16—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⋊Q8—21no—
39C2×C4⋊Q8—21no—
40C2×C4⋊Q8C2×C412yes—
41C2×C4⋊Q8D412yes—
42C2×#117—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4D412yes—
45C22×C42C2311yescharacteristic
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#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#423D412yes—
63#423D412yes—
64#423D412yes—
65#423D412yes—
66#407—21no—
67#407—21no—
68#407—21no—
69#407—21no—
70C4×M16—21no—
71C4×M16—21no—
72C4×M16—21no—
73C4×M16—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16—21no—
78C2×#97C2×C412yes—
79C2×C4×C8—21no—
80#384—21no—
81#382C2×C412yes—
82#380—21no—
83#380—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86#343—28no—
87#340—28no—
88#332—28no—
89C22×Q8—22no—
90C22×Q8—22no—
91C22×Q8—41no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8—41no—
95C22×Q8—84no—
96C23×C4—22no—
97C23×C4C2×D411yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—24no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—42no—
106C2×M16—41no—
107C2×M16—41no—
108C22×C8—22no—
109C4⋊Q8—22no—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—22no—
114C4⋊Q8—22no—
115C4⋊Q8—22no—
116C4⋊Q8—22no—
117C4⋊Q8—41no—
118C4⋊Q8—41no—
119C4⋊Q8—41no—
120C4⋊Q8—41no—
121C4⋊Q8—41no—
122C4⋊Q8—41no—
123C4⋊Q8—41no—
124C4⋊Q8—41no—
125#117—44no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C22⋊C414yes—
141C2×C22⋊C4—41no—
142C2×C42—41no—
143C2×C42C22×C411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171#97—22no—
172#97—22no—
173#97—41no—
174#97—41no—
175#97—41no—
176#97—41no—
177C4×C8—41no—
178C4×C8—41no—
179C4×C8—41no—
180C4×C8—41no—
181C4×C8—41no—
182C4×C8—41no—
183#95—22no—
184#95—22no—
185C24#12311yescharacteristic
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×Q8—84no—
191C2×Q8—84no—
192C2×Q8—84no—
193C2×Q8—84no—
194C2×Q8—84no—
195C2×Q8—84no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—84no—
205C22×C4C2×C22⋊C411yescharacteristic
206C22×C4C4×D411yescharacteristic
207C22×C4C4×D411yescharacteristic
208C22×C4#12011yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12311yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12411yescharacteristic
218C22×C4#12411yescharacteristic
219C22×C4#12611yescharacteristic
220C22×C4#12611yescharacteristic
221C22×C4#12611yescharacteristic
222C22×C4#12611yescharacteristic
223M16—44no—
224M16—44no—
225M16—42no—
226M16—42no—
227M16—42no—
228M16—42no—
229M16—82no—
230M16—82no—
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—44no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C22⋊C4—82no—
250C42—82no—
251C42#11711yescharacteristic
252C42#11711yescharacteristic
253C42C4×D411yescharacteristic
254C42C4×D411yescharacteristic
255C42#12011yescharacteristic
256C42#12111yescharacteristic
257C42#12111yescharacteristic
258C42#12111yescharacteristic
259C42#12111yescharacteristic
260C42#12311yescharacteristic
261C42#12311yescharacteristic
262C42#12311yescharacteristic
263C42#12311yescharacteristic
264C42#12311yescharacteristic
265C42#12411yescharacteristic
266C42#12411yescharacteristic
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23#38611yescharacteristic
272C23#39711yescharacteristic
273C23#39711yescharacteristic
274Q8—84no—
275Q8—84no—
276Q8—84no—
277Q8—84no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—84no—
298C2×C4—84no—
299C2×C4—84no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4#38111yescharacteristic
304C2×C4#38611yescharacteristic
305C2×C4#38811yescharacteristic
306C2×C4#38811yescharacteristic
307C2×C4#38811yescharacteristic
308C2×C4#38811yescharacteristic
309C2×C4#39411yescharacteristic
310C2×C4#39411yescharacteristic
311C2×C4#39411yescharacteristic
312C2×C4#39411yescharacteristic
313C2×C4#39711yescharacteristic
314C2×C4#39711yescharacteristic
315C2×C4#45412yes—
316C2×C4#45612yes—
317C8—44no—
318C8—82no—
319C8—82no—
320C8—82no—
321C8—82no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—42no—
331C22—42no—
332C22#144011yescharacteristic
333C22#188611yescharacteristic
334C22#188811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—84no—
344C4—162no—
345C4#203812yes—
346C4#203812yes—
347C4#204812yes—
348C4#204912yes—
349C2—21no—
350C2—21no—
351C2—41no—
352C2—41no—
353C2#1116211yescharacteristic
354C2#1118711yescharacteristic
355C2#1118811yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
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
#218292
#213242
#177422
#80942
#80642