Finite Group Databasebeta

← #118013

Subgroups — #118013

Order 512.

603 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21820C211yesmaximal, characteristic
2#17806C211yesmaximal, characteristic
3#17449C211yesmaximal, characteristic
4C2×#1479C211yesmaximal, characteristic
5#8058C211yesmaximal, characteristic
6#7966C211yesmaximal, characteristic
7#7884C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×#431C2211yescharacteristic
15#1985—22no—
16#1984—22no—
17#1817—22no—
18#1574—22no—
19#1573—22no—
20#1564—22no—
21#1491—22no—
22#1487—22no—
23#1479—22no—
24#1479—22no—
25#1479C414yes—
26C2×Q8⋊C8—22no—
27#1298—22no—
28#1287—22no—
29#1278—22no—
30C23×Q8Q811yescharacteristic
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×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8C2×C412yes—
42C2×C4×Q8D412yes—
43C22×C4⋊C4—21no—
44C22×C4⋊C4Q811yescharacteristic
45C22×C42—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#431—21no—
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#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431C2×C412yes—
69#431C2×C412yes—
70#431D412yes—
71#423—21no—
72#423D412yes—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8D412yes—
77#407—21no—
78#407—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C2×C22⋊C8D412yes—
83C4×M16—21no—
84C4×M16D412yes—
85C2×#97—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8D412yes—
89#336—28no—
90#335—24no—
91#334—24no—
92Q8⋊C8—28no—
93Q8⋊C8—28no—
94C22×Q8—21no—
95C22×Q8—24no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—42no—
101C22×Q8C4⋊C412yes—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4C2×D411yescharacteristic
105C23×C4C2×Q811yescharacteristic
106C23×C4#4111yescharacteristic
107C2×M16—22no—
108C2×M16—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—41no—
113C4×Q8—22no—
114C4×Q8—22no—
115C4×Q8—22no—
116C4×Q8—22no—
117C4×Q8—22no—
118C4×Q8—22no—
119C4×Q8—22no—
120C4×Q8—22no—
121C4×Q8—41no—
122C4×Q8—41no—
123C4×Q8—41no—
124C4×Q8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C4⋊C412yes—
141C2×C42—22no—
142C2×C42—22no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—41no—
146C2×C42—41no—
147C2×C42C22×C411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183#97—22no—
184#97—41no—
185#97—41no—
186#97—41no—
187C4×C8—22no—
188C4×C8—22no—
189C4×C8—22no—
190C4×C8—41no—
191C4×C8—41no—
192C4×C8—41no—
193C4×C8—41no—
194C4×C8C22⋊C414yes—
195C24C22⋊Q811yescharacteristic
196C2×Q8—22no—
197C2×Q8—24no—
198C2×Q8—24no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C2×Q8—44no—
205C2×Q8—44no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8#10814yes—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—44no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C2×C4⋊C411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4#12011yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12611yescharacteristic
240C22×C4#12711yescharacteristic
241M16—44no—
242M16—82no—
243C2×C8—24no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—82no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C42—42no—
262C42—42no—
263C42—42no—
264C42—42no—
265C42C2×C22⋊C411yescharacteristic
266C42#11711yescharacteristic
267C42C4×D411yescharacteristic
268C42C4×D411yescharacteristic
269C42#12011yescharacteristic
270C42#12011yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12111yescharacteristic
274C42#12111yescharacteristic
275C42#12111yescharacteristic
276C42#12311yescharacteristic
277C42#12411yescharacteristic
278C42#12411yescharacteristic
279C42#12411yescharacteristic
280C42#12611yescharacteristic
281C23—22no—
282C23—22no—
283C23—41no—
284C23#38511yescharacteristic
285C23#39611yescharacteristic
286C23#39911yescharacteristic
287Q8—24no—
288Q8—24no—
289Q8—44no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4#38011yescharacteristic
322C2×C4#38511yescharacteristic
323C2×C4#38611yescharacteristic
324C2×C4#38811yescharacteristic
325C2×C4#38811yescharacteristic
326C2×C4#39011yescharacteristic
327C2×C4#39211yescharacteristic
328C2×C4#39311yescharacteristic
329C2×C4#39411yescharacteristic
330C2×C4#39411yescharacteristic
331C2×C4#39611yescharacteristic
332C2×C4#39711yescharacteristic
333C2×C4C2×#10812yes—
334C2×C4#43012yes—
335C8—44no—
336C8—82no—
337C8—82no—
338C8—82no—
339C8—82no—
340C8—82no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—44no—
349C22#143911yescharacteristic
350C22#185512yes—
351C22#209812yes—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—44no—
362C4—82no—
363C4#181011yescharacteristic
364C4#181111yescharacteristic
365C4#185512yes—
366C4#200912yes—
367C2—22no—
368C2—22no—
369C2—41no—
370C2#1108411yescharacteristic
371C2#1109711yescharacteristic
372C2#1113011yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#218202
#178062
#174492
C2×#14792
#80582
#79662
#78842