Finite Group Databasebeta

← #118354

Subgroups — #118354

Order 512.

592 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20727C211yesmaximal, characteristic
2#20727C211yesmaximal, characteristic
3#17823C211yesmaximal, characteristic
4#17365C211yesmaximal, characteristic
5#8062C211yesmaximal, characteristic
6#7996C211yesmaximal, characteristic
7#7969C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13#2920C2211yescharacteristic
14#2920C2211yescharacteristic
15#1821—21no—
16#1821—21no—
17#1801—22no—
18#1801—22no—
19#1784—21no—
20#1784—21no—
21C4×#101—22no—
22C4×#101—22no—
23#1574—22no—
24#1572—22no—
25#1569—22no—
26#1467—22no—
27#1463C414yes—
28#1461—22no—
29#1299—22no—
30#1291—22no—
31#1287—22no—
32C23×Q8D411yescharacteristic
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×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C22×C4⋊C4C2×C412yes—
46C22×C4⋊C4D411yescharacteristic
47C22×C42Q812yes—
48C22×C42C2311yescharacteristic
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#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#431—21no—
70#431—21no—
71#431—21no—
72#431D412yes—
73#423—21no—
74#423—21no—
75#423—21no—
76#423—21no—
77#423D412yes—
78#423D412yes—
79C2×#101—24no—
80C2×#101—24no—
81#407—21no—
82#407—21no—
83#407—21no—
84#407—21no—
85#407C2×C412yes—
86#407C2×C412yes—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16—21no—
90C4×M16—21no—
91C4×M16D412yes—
92C4×M16D412yes—
93#343—24no—
94#343—24no—
95#335—24no—
96#334—24no—
97#324—28no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—44no—
105C23×C4C4⋊C412yes—
106C23×C4C4⋊C412yes—
107C23×C4C22×C411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4C2×Q811yescharacteristic
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—22no—
116C4×Q8—41no—
117C4×Q8—41no—
118C4×Q8—41no—
119C4×Q8—41no—
120C4×Q8—41no—
121C4×Q8—41no—
122C4×Q8—41no—
123C4×Q8—41no—
124C4×Q8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C42—22no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174#101—48no—
175#101—48no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8C22⋊C414yes—
188#97—22no—
189#97—22no—
190#97—22no—
191#97—41no—
192#97—41no—
193#97—41no—
194C4×C8—22no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—41no—
198C4×C8—41no—
199C4×C8—41no—
200C24C2×C4⋊C411yescharacteristic
201C2×Q8—24no—
202C2×Q8—24no—
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—44no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—41no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—44no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—81no—
224C22×C4—82no—
225C22×C4C2×C22⋊C411yescharacteristic
226C22×C4#11711yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4C4×D411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12011yescharacteristic
232C22×C4#12011yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12311yescharacteristic
243M16—44no—
244M16—44no—
245M16—44no—
246M16—44no—
247M16—82no—
248M16—82no—
249C2×C8—24no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C42—42no—
264C42—42no—
265C42—42no—
266C42—42no—
267C42#12011yescharacteristic
268C42#12111yescharacteristic
269C42#12111yescharacteristic
270C42#12111yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12111yescharacteristic
274C42#12311yescharacteristic
275C42#12311yescharacteristic
276C42#12311yescharacteristic
277C42#12411yescharacteristic
278C42#12411yescharacteristic
279C42#12411yescharacteristic
280C42#12611yescharacteristic
281C42#12611yescharacteristic
282C42#12711yescharacteristic
283C23—41no—
284C23—41no—
285C23—41no—
286C23#38011yescharacteristic
287C23#38511yescharacteristic
288C23#38511yescharacteristic
289Q8—44no—
290Q8—44no—
291Q8—44no—
292Q8—44no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
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—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4#38611yescharacteristic
323C2×C4#38811yescharacteristic
324C2×C4#38811yescharacteristic
325C2×C4#39011yescharacteristic
326C2×C4#39211yescharacteristic
327C2×C4#39311yescharacteristic
328C2×C4#39411yescharacteristic
329C2×C4#39411yescharacteristic
330C2×C4#39611yescharacteristic
331C2×C4#39611yescharacteristic
332C2×C4#39711yescharacteristic
333C2×C4#39911yescharacteristic
334C8—44no—
335C8—82no—
336C8—82no—
337C8—82no—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—44no—
350C22#143911yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—44no—
362C4—82no—
363C4#201012yes—
364C4#207012yes—
365C2—41no—
366C2—41no—
367C2—41no—
368C2#1109011yescharacteristic
369C2#1110011yescharacteristic
370C2#1114011yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C4⋊C4
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
#207272
#178232
#173652
#80622
#79962
#79692