Finite Group Databasebeta

← #119441

Subgroups — #119441

Order 512.

592 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21829C211yesmaximal, characteristic
2C2×#1993C211yesmaximal, characteristic
3#17742C211yesmaximal, characteristic
4#8088C211yesmaximal, characteristic
5#8088C211yesmaximal, characteristic
6#7959C211yesmaximal, characteristic
7#7959C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C22×#97C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1997—22no—
16#1997—22no—
17#1993—22no—
18#1993C414yes—
19#1821—22no—
20C2×#340—22no—
21#1556—22no—
22#1549—22no—
23#1546—22no—
24#1302—22no—
25#1302—22no—
26#1286—22no—
27#1286—22no—
28C23×Q8—21no—
29C23×C8—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—
42C22×C4⋊C4—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#431D412yes—
61#431D412yes—
62#423—21no—
63#423—21no—
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—
74C2×#97—21no—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97C2×C412yes—
80#382—21no—
81#382—21no—
82#382—21no—
83#382C2×C412yes—
84C2×#95—21no—
85C2×#95—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×C4—41no—
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—41no—
104C2×M16—41no—
105C22×C8—24no—
106C22×C8—22no—
107C22×C8—42no—
108C22×C8—41no—
109C22×C8—41no—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—22no—
114C4⋊Q8—22no—
115C4⋊Q8—22no—
116C4⋊Q8—22no—
117C4⋊Q8—22no—
118C4⋊Q8—41no—
119C4⋊Q8—41no—
120C4⋊Q8—41no—
121C4⋊Q8—41no—
122C4⋊Q8—41no—
123C4⋊Q8—41no—
124C4⋊Q8—41no—
125C4⋊Q8—41no—
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—44no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C22⋊C414yes—
141C2×C42C22×C411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—41no—
160C4⋊C8—41no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169#97—22no—
170#97—22no—
171#97—41no—
172#97—41no—
173#97—41no—
174#97—41no—
175#97—41no—
176#97—41no—
177C4×C8—22no—
178C4×C8—22no—
179C4×C8—41no—
180C4×C8—41no—
181#95—22no—
182#95—22no—
183#95—41no—
184#95—41no—
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×C4—82no—
206C22×C4—82no—
207C22×C4—82no—
208C22×C4C2×C22⋊C411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4#12011yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4#12111yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12411yescharacteristic
222C22×C4#12611yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4#12611yescharacteristic
225C22×C4#12611yescharacteristic
226M16—42no—
227M16—42no—
228M16—42no—
229M16—42no—
230M16—82no—
231M16—82no—
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—44no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—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—22no—
268C23—22no—
269C23—21no—
270C23—21no—
271C23#38611yescharacteristic
272C23#39711yescharacteristic
273C23#39711yescharacteristic
274Q8—84no—
275Q8—84no—
276Q8—84no—
277Q8—84no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
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—164no—
304C2×C4#38111yescharacteristic
305C2×C4#38611yescharacteristic
306C2×C4#38811yescharacteristic
307C2×C4#38811yescharacteristic
308C2×C4#38811yescharacteristic
309C2×C4#38811yescharacteristic
310C2×C4#39411yescharacteristic
311C2×C4#39411yescharacteristic
312C2×C4#39411yescharacteristic
313C2×C4#39411yescharacteristic
314C2×C4#39711yescharacteristic
315C2×C4#39711yescharacteristic
316C2×C4#45412yes—
317C2×C4#45612yes—
318C8—44no—
319C8—82no—
320C8—82no—
321C8—82no—
322C8—82no—
323C22—24no—
324C22—24no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22#144011yescharacteristic
332C22#188611yescharacteristic
333C22#188811yescharacteristic
334C22#208112yes—
335C22#208212yes—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—84no—
347C4—162no—
348C4#203812yes—
349C4#203812yes—
350C2—21no—
351C2—22no—
352C2—22no—
353C2—21no—
354C2#1116211yescharacteristic
355C2#1118111yescharacteristic
356C2#1118211yescharacteristic
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
C2×#19932
#177422
#80882
#79592