Finite Group Databasebeta

← #115808

Subgroups — #115808

Order 512.

576 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21954C211yesmaximal, characteristic
2#21870C211yesmaximal, characteristic
3C2×#1537C211yesmaximal, characteristic
4C2×#1481C211yesmaximal, characteristic
5#8044C211yesmaximal, characteristic
6C2×#1290C211yesmaximal, characteristic
7C2×#1287C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15#1993C412yes—
16#1960C412yes—
17#1940—22no—
18#1939—22no—
19#1873—22no—
20#1803—22no—
21#1798—22no—
22#1537—22no—
23#1537—22no—
24C2×#330—22no—
25#1481—22no—
26#1481—22no—
27C2×Q8⋊C8—22no—
28#1296—22no—
29#1290—22no—
30#1287—22no—
31C23×C8—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533D412yes—
39#533Q812yes—
40C2×C4⋊Q8C2×C411yescharacteristic
41C2×C4⋊Q8C2×C411yescharacteristic
42C2×#125—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×#117—21no—
48C2×#117D412yes—
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#432—21no—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—24no—
76C2×C4⋊C8D412yes—
77C2×#103—24no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C2×#97—21no—
83C2×#97C2×C412yes—
84C2×#97D412yes—
85C2×C4×C8D412yes—
86#384D412yes—
87#382C2×C412yes—
88#380—21no—
89#380—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92#340—24no—
93#336—24no—
94#330—28no—
95Q8⋊C8—28no—
96C22×Q8—21no—
97C22×Q8—21no—
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—82no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8C4⋊C412yes—
116C4⋊Q8C4⋊C412yes—
117#125—22no—
118#125—22no—
119#125—41no—
120#125—41no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C22⋊Q8—22no—
124C22⋊Q8—22no—
125C22⋊Q8—41no—
126C22⋊Q8—41no—
127C22⋊Q8—41no—
128C22⋊Q8—41no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136C4×Q8—41no—
137#117—22no—
138#117—22no—
139#117—41no—
140#117—41no—
141#117—82no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4C22⋊C414yes—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—41no—
153C2×C42—22no—
154C2×C42—41no—
155C2×C42C22×C411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—84no—
180#103—84no—
181C22⋊C8—22no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189#97—22no—
190#97—22no—
191#97—22no—
192#97—22no—
193#97—22no—
194#97—41no—
195C4×C8—22no—
196C4×C8—22no—
197#95—22no—
198#95—22no—
199C24#12311yescharacteristic
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—42no—
203C2×Q8—44no—
204C2×Q8—42no—
205C2×Q8—41no—
206C2×Q8—41no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C2×C22⋊C411yescharacteristic
216C22×C4C4×D411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4#12011yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4C22⋊Q811yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12611yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4#12711yescharacteristic
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—82no—
245C2×C8—82no—
246C2×C8—82no—
247C2×C8—82no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—44no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—82no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—82no—
267C42—44no—
268C42—42no—
269C42—42no—
270C42C2×C4⋊C411yescharacteristic
271C42#11711yescharacteristic
272C42C4×D411yescharacteristic
273C42C4×D411yescharacteristic
274C42#12011yescharacteristic
275C42#12011yescharacteristic
276C42#12111yescharacteristic
277C42#12111yescharacteristic
278C42#12111yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42C22⋊Q811yescharacteristic
282C42C22⋊Q811yescharacteristic
283C42C22⋊Q811yescharacteristic
284C42#12411yescharacteristic
285C42#12411yescharacteristic
286C23—22no—
287C23—22no—
288C23—21no—
289C23—21no—
290C23#38611yescharacteristic
291C23#39711yescharacteristic
292C23#39911yescharacteristic
293Q8—44no—
294Q8—44no—
295Q8—82no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4#38011yescharacteristic
327C2×C4#38511yescharacteristic
328C2×C4#38511yescharacteristic
329C2×C4#38811yescharacteristic
330C2×C4#38811yescharacteristic
331C2×C4#39011yescharacteristic
332C2×C4#39211yescharacteristic
333C2×C4#39311yescharacteristic
334C2×C4#39411yescharacteristic
335C2×C4#39411yescharacteristic
336C2×C4#39611yescharacteristic
337C2×C4#39611yescharacteristic
338C2×C4#47112yes—
339C2×C4#47312yes—
340C8—82no—
341C8—82no—
342C8—82no—
343C8—82no—
344C8—82no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—42no—
352C22—42no—
353C22#143911yescharacteristic
354C22#188112yes—
355C22#190812yes—
356C22#191111yescharacteristic
357C22#191211yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—82no—
370C4—84no—
371C4#204611yescharacteristic
372C4#204711yescharacteristic
373C4#206412yes—
374C2—41no—
375C2—41no—
376C2#937312yes—
377C2#937412yes—
378C2#1106211yescharacteristic
379C2#1106511yescharacteristic
380C2#1107211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
#219542
#218702
C2×#15372
C2×#14812
#80442
C2×#12902
C2×#12872