Finite Group Databasebeta

← #107229

Subgroups — #107229

Order 512.

702 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60249C211yesmaximal, characteristic
2#21425C211yesmaximal, characteristic
3#17404C211yesmaximal, characteristic
4#8087C211yesmaximal, characteristic
5#8086C211yesmaximal, characteristic
6#7996C211yesmaximal, characteristic
7#7992C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2987—22no—
10#2986—22no—
11#2985—22no—
12#2985—22no—
13Q8×M16—22no—
14Q8×M16—22no—
15#2921C414yes—
16#2920C2211yescharacteristic
17#2920C2211yescharacteristic
18#2920C2211yescharacteristic
19#2920C2211yescharacteristic
20C2×#432C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22#1997C412yes—
23#1966C412yes—
24#1901—22no—
25C4×#101—22no—
26#1472—22no—
27#1470C414yes—
28#1467—22no—
29#1302—22no—
30#1302—22no—
31#1291—22no—
32#1291—22no—
33C22×M16—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42C2×C4⋊Q8C2×C411yescharacteristic
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×#125C2×C412yes—
45C2×C22⋊Q8D412yes—
46C2×C22⋊Q8Q812yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8D412yes—
49C2×#117C2×C412yes—
50C22×C42C2311yescharacteristic
51#446—24no—
52#446—24no—
53#446—28no—
54#446—28no—
55C8×Q8—24no—
56C8×Q8—24no—
57#433—28no—
58#433—28no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432—21no—
66#432—21no—
67#432—21no—
68#432C2×C412yes—
69#432D412yes—
70#432D412yes—
71#431—21no—
72#431—21no—
73#431—21no—
74#431—21no—
75#431—21no—
76#431C2×C412yes—
77#431D412yes—
78#431D412yes—
79#423—24no—
80#423—21no—
81#423—21no—
82#423—21no—
83#423C2×C412yes—
84C2×C4⋊C8—21no—
85C2×#101—24no—
86#407—21no—
87#407—21no—
88#407C2×C412yes—
89#407C2×C412yes—
90C2×C22⋊C8—21no—
91C4×M16—24no—
92C4×M16—21no—
93C4×M16—21no—
94C4×M16—21no—
95C4×M16—21no—
96C4×M16—21no—
97C4×M16—21no—
98C4×M16—21no—
99C4×M16C2×C412yes—
100C2×#97—21no—
101C2×#97—21no—
102C2×C4×C8—21no—
103#343—24no—
104#324—28no—
105C22×Q8C22⋊C412yes—
106C22×Q8C4⋊C412yes—
107C23×C4C22×C411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4C2×Q811yescharacteristic
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—44no—
115C2×M16—41no—
116C2×M16—41no—
117C22×C8—41no—
118C22×C8—41no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127#125—22no—
128#125—22no—
129#125—22no—
130#125—22no—
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147#117—22no—
148#117—22no—
149#117—22no—
150#117—22no—
151C2×C4⋊C4C4212yes—
152C2×C4⋊C4C4212yes—
153C2×C4⋊C4C22⋊C414yes—
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C4⋊C414yes—
156C2×C4⋊C4C4⋊C412yes—
157C2×C22⋊C4C4⋊C414yes—
158C2×C42C22⋊C414yes—
159C2×C42C22×C411yescharacteristic
160C2×C42C22×C411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C4⋊C8—28no—
172C4⋊C8—28no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183#101—48no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8C22⋊C414yes—
193C22⋊C8C22⋊C414yes—
194#97—28no—
195#97—22no—
196#97—22no—
197#97—22no—
198#97—22no—
199#97—41no—
200#97—41no—
201#97—41no—
202#97—41no—
203C4×C8—28no—
204C4×C8—22no—
205C4×C8—22no—
206C4×C8—22no—
207C4×C8—22no—
208C4×C8—41no—
209C4×C8—41no—
210C24C2×C4⋊C411yescharacteristic
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—44no—
216C2×Q8—82no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—81no—
220C22×C4#9514yes—
221C22×C4#9514yes—
222C22×C4C2×C4211yescharacteristic
223C22×C4C2×C22⋊C411yescharacteristic
224C22×C4C2×C22⋊C411yescharacteristic
225C22×C4C2×C22⋊C411yescharacteristic
226C22×C4C2×C22⋊C411yescharacteristic
227C22×C4C2×C22⋊C411yescharacteristic
228C22×C4C2×C4⋊C411yescharacteristic
229C22×C4C2×C4⋊C411yescharacteristic
230C22×C4#11711yescharacteristic
231C22×C4#11711yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240M16—24no—
241M16—44no—
242M16—44no—
243M16—42no—
244M16—44no—
245M16—44no—
246M16—82no—
247C2×C8—24no—
248C2×C8—24no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—82no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C22⋊C4—24no—
268C22⋊C4—24no—
269C42—24no—
270C42—24no—
271C42C4×D411yescharacteristic
272C42C4×D411yescharacteristic
273C42C4×D411yescharacteristic
274C42C4×D411yescharacteristic
275C42C4×D411yescharacteristic
276C42C4×D411yescharacteristic
277C42C4×D411yescharacteristic
278C42C4×D411yescharacteristic
279C42#12011yescharacteristic
280C42#12011yescharacteristic
281C42#12011yescharacteristic
282C42#12011yescharacteristic
283C42#12311yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C42#12311yescharacteristic
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×#9511yescharacteristic
291C23#38011yescharacteristic
292C23#38011yescharacteristic
293Q8—44no—
294Q8—44no—
295Q8—82no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4C4×C22⋊C411yescharacteristic
320C2×C4C4×C22⋊C411yescharacteristic
321C2×C4#37911yescharacteristic
322C2×C4#38111yescharacteristic
323C2×C4#38511yescharacteristic
324C2×C4#38511yescharacteristic
325C2×C4#38511yescharacteristic
326C2×C4#38511yescharacteristic
327C2×C4#38611yescharacteristic
328C2×C4#38611yescharacteristic
329C2×C4#38611yescharacteristic
330C2×C4#38611yescharacteristic
331C8—44no—
332C8—44no—
333C8—44no—
334C8—82no—
335C8—82no—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—82no—
347C22C22⋊#9511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—44no—
359C4—44no—
360C4#183012yes—
361C4#188412yes—
362C2—41no—
363C2—41no—
364C2—41no—
365C2#1074411yescharacteristic
366C2#1075111yescharacteristic
367C2#1077011yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C2×C4⋊C4
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
#602492
#214252
#174042
#80872
#80862
#79962
#79922