Finite Group Databasebeta

← #119308

Subgroups — #119308

Order 512.

562 conjugacy classes of subgroups.

The subgroup lattice has 341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21829C211yesmaximal, characteristic
2#21811C211yesmaximal, characteristic
3#17746C211yesmaximal, characteristic
4#8118C211yesmaximal, characteristic
5#8116C211yesmaximal, characteristic
6#8070C211yesmaximal, characteristic
7#7970C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14#2283C2211yescharacteristic
15#1997—22no—
16#1997—22no—
17#1981—22no—
18#1960—22no—
19#1821—22no—
20#1787C414yes—
21#1558—22no—
22#1548—22no—
23#1548—22no—
24#1307—22no—
25#1306—22no—
26#1300—22no—
27#1287—22no—
28C23×Q8C2×C412yes—
29C2×C4⋊Q8—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⋊Q8D412yes—
40C2×C4⋊Q8D412yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C42C2311yescharacteristic
44#432—21no—
45#432—21no—
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#432D412yes—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423D412yes—
68C2×C4⋊C8—21no—
69C2×#103—28no—
70#407—21no—
71#407—21no—
72#407—21no—
73#407D412yes—
74C2×C22⋊C8C2×C412yes—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16—21no—
78C4×M16D412yes—
79C2×#97—21no—
80#383—21no—
81#382—21no—
82#381—21no—
83#380C2×C412yes—
84C4×C4⋊C4—21no—
85C4×C22⋊C4—21no—
86#376—21no—
87#343—28no—
88#333—28no—
89C22×Q8—22no—
90C22×Q8—22no—
91C22×Q8—22no—
92C22×Q8—22no—
93C22×Q8—22no—
94C22×Q8—84no—
95C22×Q8C22⋊C414yes—
96C23×C4—22no—
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—41no—
104C22×C8—22no—
105C4⋊Q8—22no—
106C4⋊Q8—22no—
107C4⋊Q8—22no—
108C4⋊Q8—22no—
109C4⋊Q8—22no—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—41no—
114C4⋊Q8—41no—
115C4⋊Q8—41no—
116C4⋊Q8—41no—
117C4⋊Q8—41no—
118C4⋊Q8—41no—
119C4⋊Q8—41no—
120C4⋊Q8—41no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C22⋊C4—22no—
135C2×C42—41no—
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146C2×C42#4111yescharacteristic
147C2×C42#4111yescharacteristic
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—22no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158#103—88no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—22no—
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—
175C4×C8—22no—
176C4×C8—41no—
177C4×C8—41no—
178C4×C8—41no—
179#95—22no—
180#95—41no—
181#95—41no—
182#95—41no—
183C24C4×D411yescharacteristic
184C2×Q8—24no—
185C2×Q8—24no—
186C2×Q8—48no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—84no—
190C2×Q8—84no—
191C2×Q8—84no—
192C2×Q8—84no—
193C2×Q8—84no—
194C22×C4—24no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—84no—
202C22×C4C2×C22⋊C411yescharacteristic
203C22×C4#11711yescharacteristic
204C22×C4#11711yescharacteristic
205C22×C4C4×D411yescharacteristic
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#12411yescharacteristic
217C22×C4#12411yescharacteristic
218C22×C4#12611yescharacteristic
219C22×C4#12611yescharacteristic
220M16—44no—
221M16—44no—
222M16—82no—
223M16—82no—
224C2×C8—44no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C4⋊C4—44no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C22⋊C4—82no—
240C42—82no—
241C42#12011yescharacteristic
242C42#12111yescharacteristic
243C42#12111yescharacteristic
244C42#12111yescharacteristic
245C42#12111yescharacteristic
246C42#12311yescharacteristic
247C42#12311yescharacteristic
248C42#12311yescharacteristic
249C42#12311yescharacteristic
250C42#12311yescharacteristic
251C42#12311yescharacteristic
252C42#12311yescharacteristic
253C42#12411yescharacteristic
254C42#12411yescharacteristic
255C42#12611yescharacteristic
256C42#12611yescharacteristic
257C23—22no—
258C23—41no—
259C23—41no—
260C23#38611yescharacteristic
261C23#38811yescharacteristic
262C23#38811yescharacteristic
263Q8—48no—
264Q8—84no—
265Q8—84no—
266Q8—84no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
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—44no—
286C2×C4—84no—
287C2×C4—84no—
288C2×C4—84no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4#38111yescharacteristic
293C2×C4#38611yescharacteristic
294C2×C4#38811yescharacteristic
295C2×C4#38811yescharacteristic
296C2×C4#39411yescharacteristic
297C2×C4#39411yescharacteristic
298C2×C4#39411yescharacteristic
299C2×C4#39411yescharacteristic
300C2×C4#39711yescharacteristic
301C2×C4#39711yescharacteristic
302C2×C4#39711yescharacteristic
303C2×C4#39711yescharacteristic
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#144011yescharacteristic
319C22#190512yes—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—84no—
331C4—162no—
332C4#182912yes—
333C4#204912yes—
334C2—22no—
335C2—41no—
336C2—41no—
337C2#1117011yescharacteristic
338C2#1118411yescharacteristic
339C2#1118811yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
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
#218292
#218112
#177462
#81182
#81162
#80702
#79702