Finite Group Databasebeta

← #118271

Subgroups — #118271

Order 512.

512 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17808C211yesmaximal, characteristic
2#17491C211yesmaximal, characteristic
3#17479C211yesmaximal, characteristic
4#17404C211yesmaximal, characteristic
5#8118C211yesmaximal, characteristic
6#7996C211yesmaximal, characteristic
7#7921C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14C2×#431C2211yescharacteristic
15#1574—22no—
16#1572—22no—
17#1565—22no—
18#1497—22no—
19#1497—22no—
20#1493—22no—
21#1487—22no—
22#1485—22no—
23#1479—22no—
24#1472C414yes—
25#1470—22no—
26#1467—22no—
27#1307—22no—
28#1291—22no—
29#1281—22no—
30#533—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38C2×C4⋊Q8Q811yescharacteristic
39C2×C4⋊Q8Q811yescharacteristic
40C2×#125—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8C2×C412yes—
43C2×C4×Q8—21no—
44C2×C4×Q8D412yes—
45C2×#117—21no—
46C22×C42C2311yescharacteristic
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#432D412yes—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431D412yes—
68#431D412yes—
69#431D412yes—
70#431D412yes—
71#423—21no—
72#423—21no—
73#423—21no—
74#423D412yes—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77#407—21no—
78#407—21no—
79#407—21no—
80#407C2×C412yes—
81C2×C22⋊C8—21no—
82C2×C22⋊C8C2×C412yes—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C2×#97—21no—
88C2×C4×C8—21no—
89#335—24no—
90#334—24no—
91Q8⋊C8—28no—
92Q8⋊C8—28no—
93#324—28no—
94C22×Q8—21no—
95C22×Q8C4⋊C412yes—
96C23×C4C22×C411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—41no—
102C2×M16—41no—
103C22×C8—22no—
104C22×C8—41no—
105C4⋊Q8—21no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113#125—41no—
114#125—41no—
115#125—41no—
116#125—41no—
117C22⋊Q8—22no—
118C22⋊Q8—22no—
119C22⋊Q8—22no—
120C22⋊Q8—22no—
121C22⋊Q8—41no—
122C22⋊Q8—41no—
123C22⋊Q8—41no—
124C22⋊Q8—41no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133#117—41no—
134#117—41no—
135#117—41no—
136#117—41no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4C4⋊C412yes—
143C2×C22⋊C4—22no—
144C2×C42—22no—
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×Q811yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8C22⋊C414yes—
181#97—22no—
182#97—41no—
183#97—41no—
184#97—41no—
185#97—41no—
186#97—41no—
187C4×C8—22no—
188C4×C8—22no—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—41no—
192C4×C8—41no—
193C24#11711yescharacteristic
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—44no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—82no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—81no—
205C22×C4C2×C22⋊C411yescharacteristic
206C22×C4C2×C4⋊C411yescharacteristic
207C22×C4C4×D411yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12411yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12611yescharacteristic
222C22×C4#12611yescharacteristic
223M16—44no—
224M16—82no—
225M16—82no—
226M16—82no—
227C2×C8—24no—
228C2×C8—44no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—82no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C42—42no—
250C42—42no—
251C42#12011yescharacteristic
252C42#12011yescharacteristic
253C42#12011yescharacteristic
254C42#12111yescharacteristic
255C42#12111yescharacteristic
256C42#12111yescharacteristic
257C42#12111yescharacteristic
258C42C22⋊Q811yescharacteristic
259C42C22⋊Q811yescharacteristic
260C42C22⋊Q811yescharacteristic
261C42C22⋊Q811yescharacteristic
262C42#12311yescharacteristic
263C42#12311yescharacteristic
264C42#12311yescharacteristic
265C42#12411yescharacteristic
266C42#12711yescharacteristic
267C23—41no—
268C23—41no—
269C23—41no—
270C23#38011yescharacteristic
271C23#38811yescharacteristic
272C23#38811yescharacteristic
273Q8—44no—
274Q8—44no—
275Q8—82no—
276Q8—82no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—82no—
299C2×C4#38511yescharacteristic
300C2×C4#38511yescharacteristic
301C2×C4#38611yescharacteristic
302C2×C4#39011yescharacteristic
303C2×C4#39211yescharacteristic
304C2×C4#39311yescharacteristic
305C2×C4#39411yescharacteristic
306C2×C4#39411yescharacteristic
307C2×C4#39611yescharacteristic
308C2×C4#39611yescharacteristic
309C2×C4#39711yescharacteristic
310C2×C4#39911yescharacteristic
311C8—44no—
312C8—82no—
313C8—82no—
314C8—82no—
315C8—82no—
316C8—82no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22#143911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—82no—
339C4—82no—
340C4#186812yes—
341C4#204912yes—
342C2—41no—
343C2—41no—
344C2—41no—
345C2#1108811yescharacteristic
346C2#1110911yescharacteristic
347C2#1114311yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
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
#178082
#174912
#174792
#174042
#81182
#79962
#79212