Finite Group Databasebeta

← #110499

Subgroups — #110499

Order 512.

538 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17747C211yesmaximal, characteristic
2#17479C211yesmaximal, characteristic
3#17404C211yesmaximal, characteristic
4#17324C211yesmaximal, characteristic
5#8126C211yesmaximal, characteristic
6#7998C211yesmaximal, characteristic
7#7863C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14C2×#431C2211yescharacteristic
15#1559—22no—
16#1554—22no—
17#1549C412yes—
18#1548C412yes—
19#1497—22no—
20#1493—21no—
21#1493—21no—
22#1479C414yes—
23#1472C414yes—
24#1470—22no—
25#1467—22no—
26#1454—22no—
27#1453—22no—
28#1451—21no—
29C8×M16—21no—
30#1308—22no—
31#1291—22no—
32#1275—22no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41C2×C4⋊Q8C2×C411yescharacteristic
42C2×C4⋊Q8C2×C411yescharacteristic
43C2×#125—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8C2×C412yes—
46C2×C4×Q8—21no—
47C2×C4×Q8C2×C412yes—
48C2×#117—21no—
49C22×C42C2311yescharacteristic
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#431C2×C412yes—
70#431C2×C412yes—
71#431D412yes—
72#431D412yes—
73#431D412yes—
74#423—21no—
75#423—21no—
76#423—21no—
77#423C2×C412yes—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80#407—21no—
81#407—21no—
82#407—21no—
83#407C2×C412yes—
84C2×C22⋊C8—21no—
85C2×C22⋊C8C2×C412yes—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16—21no—
90C2×#97—21no—
91C2×C4×C8D411yescharacteristic
92C2×C4×C8D411yescharacteristic
93#333—24no—
94#332—24no—
95Q8⋊C8—24no—
96Q8⋊C8—24no—
97#324—28no—
98#322—22no—
99#322—24no—
100C82—22no—
101C22×Q8—21no—
102C22×Q8C4212yes—
103C23×C4C22×C411yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—41no—
109C2×M16—41no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—22no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121#125—41no—
122#125—41no—
123#125—41no—
124#125—41no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C22⋊Q8—22no—
129C22⋊Q8—41no—
130C22⋊Q8—41no—
131C22⋊Q8—41no—
132C22⋊Q8—41no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141#117—41no—
142#117—41no—
143#117—41no—
144#117—41no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4C4212yes—
151C2×C22⋊C4—22no—
152C2×C42—22no—
153C2×C42C22×C411yescharacteristic
154C2×C42C22×C411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8C22⋊C414yes—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8C22⋊C414yes—
189#97—22no—
190#97—22no—
191#97—41no—
192#97—41no—
193#97—41no—
194#97—41no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—21no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—21no—
201C4×C8C22⋊C412yes—
202C4×C8C22⋊C412yes—
203C24#11711yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—44no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—82no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—81no—
215C22×C4C2×C4211yescharacteristic
216C22×C4C2×C22⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4#12611yescharacteristic
233M16—44no—
234M16—82no—
235M16—82no—
236M16—82no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—24no—
240C2×C8—24no—
241C2×C8—44no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—81no—
246C2×C8—81no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—42no—
262C42—42no—
263C42C2×C22⋊C411yescharacteristic
264C42C2×C22⋊C411yescharacteristic
265C42#11711yescharacteristic
266C42#11711yescharacteristic
267C42C4×D411yescharacteristic
268C42C4×D411yescharacteristic
269C42C4×D411yescharacteristic
270C42C4×D411yescharacteristic
271C42#12011yescharacteristic
272C42#12111yescharacteristic
273C42#12111yescharacteristic
274C42#12111yescharacteristic
275C42#12111yescharacteristic
276C42#12311yescharacteristic
277C42#12411yescharacteristic
278C42#12711yescharacteristic
279C23—41no—
280C23—41no—
281C23—41no—
282C23C4×C22⋊C411yescharacteristic
283C23#38811yescharacteristic
284C23#38811yescharacteristic
285Q8—44no—
286Q8—82no—
287Q8—82no—
288Q8—82no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4C4×C22⋊C411yescharacteristic
312C2×C4C4×C22⋊C411yescharacteristic
313C2×C4#38611yescharacteristic
314C2×C4#38611yescharacteristic
315C2×C4#38611yescharacteristic
316C2×C4#38811yescharacteristic
317C2×C4#38811yescharacteristic
318C2×C4#38811yescharacteristic
319C2×C4#38811yescharacteristic
320C2×C4#39011yescharacteristic
321C2×C4#39011yescharacteristic
322C2×C4#39011yescharacteristic
323C8—42no—
324C8—42no—
325C8—44no—
326C8—44no—
327C8—82no—
328C8—82no—
329C8—82no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—82no—
340C22#143711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—82no—
353C4#175712yes—
354C4#190212yes—
355C2—41no—
356C2—41no—
357C2—41no—
358C2#1095011yescharacteristic
359C2#1095211yescharacteristic
360C2#1096111yescharacteristic
subgroupG/H
center, socleC22#1437
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C22×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
#177472
#174792
#174042
#173242
#81262
#79982
#78632