Finite Group Databasebeta

← #117245

Subgroups — #117245

Order 512.

572 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21799C211yesmaximal, characteristic
2#17821C211yesmaximal, characteristic
3#17742C211yesmaximal, characteristic
4C2×#1556C211yesmaximal, characteristic
5#8086C211yesmaximal, characteristic
6#8010C211yesmaximal, characteristic
7#7998C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14C2×#432C2211yescharacteristic
15#1966—22no—
16#1966—22no—
17#1784—22no—
18#1573—22no—
19#1572—22no—
20#1569—22no—
21#1556—22no—
22#1556—22no—
23#1556—22no—
24#1549C414yes—
25#1546—22no—
26C2×#332—22no—
27#1302—22no—
28#1293—22no—
29#1291—22no—
30C23×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⋊Q8—21no—
41C2×C4⋊Q8C2×C412yes—
42C2×C4⋊Q8D412yes—
43C22×C4⋊C4—21no—
44C22×C4⋊C4Q812yes—
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#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432D412yes—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431C2×C412yes—
69#431D412yes—
70#423—21no—
71#423—21no—
72#423C2×C412yes—
73#423D412yes—
74C2×C4⋊C8—21no—
75C2×C4⋊C8D412yes—
76C2×#101—28no—
77#407—21no—
78#407—21no—
79#407—21no—
80#407D412yes—
81C2×C22⋊C8—21no—
82C2×C22⋊C8—21no—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C2×#97—21no—
88C2×#97—21no—
89#335—24no—
90#334—24no—
91#332—28no—
92#332—28no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—41no—
99C22×Q8—84no—
100C23×C4—22no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×Q811yescharacteristic
103C23×C4#4111yescharacteristic
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—41no—
108C22×C8—22no—
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—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4C4⋊C414yes—
138C2×C42C22×C411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42#4111yescharacteristic
146C2×C42#4111yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—41no—
158C4⋊C8—41no—
159C4⋊C8—41no—
160C4⋊C8—41no—
161C4⋊C8C22⋊C414yes—
162#101—88no—
163C22⋊C8—22no—
164C22⋊C8—22no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C22⋊C8—41no—
172C22⋊C8—41no—
173C22⋊C8—41no—
174C22⋊C8—41no—
175#97—22no—
176#97—22no—
177#97—41no—
178#97—41no—
179#97—41no—
180#97—41no—
181#97—41no—
182#97—41no—
183C4×C8—22no—
184C4×C8—22no—
185C4×C8—41no—
186C4×C8—41no—
187C24C22⋊Q811yescharacteristic
188C2×Q8—48no—
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—84no—
194C2×Q8—84no—
195C2×Q8—84no—
196C2×Q8—84no—
197C2×Q8—84no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—84no—
205C22×C4C2×C4⋊C411yescharacteristic
206C22×C4C4×D411yescharacteristic
207C22×C4C4×D411yescharacteristic
208C22×C4#12011yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12611yescharacteristic
222C22×C4#12711yescharacteristic
223M16—44no—
224M16—44no—
225M16—82no—
226M16—82no—
227C2×C8—24no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—82no—
234C2×C8—82no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C42C2×C22⋊C411yescharacteristic
244C42#11711yescharacteristic
245C42C4×D411yescharacteristic
246C42C4×D411yescharacteristic
247C42#12011yescharacteristic
248C42#12011yescharacteristic
249C42#12111yescharacteristic
250C42#12111yescharacteristic
251C42#12111yescharacteristic
252C42#12111yescharacteristic
253C42#12111yescharacteristic
254C42#12311yescharacteristic
255C42#12411yescharacteristic
256C42#12411yescharacteristic
257C42#12411yescharacteristic
258C42#12611yescharacteristic
259C23—22no—
260C23—41no—
261C23—41no—
262C23#38511yescharacteristic
263C23#39611yescharacteristic
264C23#39911yescharacteristic
265Q8—84no—
266Q8—84no—
267Q8—84no—
268Q8—84no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—48no—
288C2×C4—44no—
289C2×C4—84no—
290C2×C4—84no—
291C2×C4#38011yescharacteristic
292C2×C4#38511yescharacteristic
293C2×C4#38611yescharacteristic
294C2×C4#38811yescharacteristic
295C2×C4#38811yescharacteristic
296C2×C4#39011yescharacteristic
297C2×C4#39211yescharacteristic
298C2×C4#39311yescharacteristic
299C2×C4#39411yescharacteristic
300C2×C4#39411yescharacteristic
301C2×C4#39611yescharacteristic
302C2×C4#39711yescharacteristic
303C8—44no—
304C8—82no—
305C8—82no—
306C8—82no—
307C8—82no—
308C8—82no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—44no—
318C22#143911yescharacteristic
319C22#207012yes—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—84no—
331C4#190212yes—
332C4#200812yes—
333C2—22no—
334C2—41no—
335C2—41no—
336C2#1105911yescharacteristic
337C2#1112911yescharacteristic
338C2#1114011yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
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
#217992
#178212
#177422
C2×#15562
#80862
#80102
#79982