Finite Group Databasebeta

← #100686

Subgroups — #100686

Order 512.

365 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 365 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29971C211yesmaximal, characteristic
2#21919C211yesmaximal, characteristic
3#7725C211yesmaximal, characteristic
4#7667C211yesmaximal, characteristic
5#7579C211yesmaximal, characteristic
6#7044C211yesmaximal, characteristic
7#7020C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9#2296C2211yescharacteristic
10#2099C411yescharacteristic
11#2099C411yescharacteristic
12#2088—21no—
13#2087—21no—
14#2058C411yescharacteristic
15#2057C411yescharacteristic
16#1917—21no—
17#1917—21no—
18#1916—21no—
19#1916—21no—
20#1854—21no—
21#1825—21no—
22#1818—21no—
23#1817C2211yescharacteristic
24#1797C2211yescharacteristic
25#1797C2211yescharacteristic
26#1797C2211yescharacteristic
27#1750—21no—
28C2×#336C2211yescharacteristic
29#1272—21no—
30#1272—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C23×C8—21no—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×#117D411yescharacteristic
39C2×#117D411yescharacteristic
40C22×C42C2311yescharacteristic
41C2×#107—21no—
42C2×#106—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×#97—21no—
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389C2×C411yescharacteristic
56#389C2×C411yescharacteristic
57#389D411yescharacteristic
58#389D411yescharacteristic
59#385—21no—
60#385—21no—
61#384C2×C411yescharacteristic
62#380—21no—
63#380—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336C2×C411yescharacteristic
83#336C2×C411yescharacteristic
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×Q8—21no—
89C23×C4C2×D411yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—22no—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—81no—
103C22×C8—81no—
104C4⋊Q8—81no—
105C22⋊Q8—82no—
106#117—21no—
107#117—21no—
108#117—21no—
109#117—21no—
110#117—81no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C22⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—41no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—81no—
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135#107—81no—
136#106—81no—
137C4⋊C8—81no—
138C4⋊C8—81no—
139C4⋊C8—81no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—81no—
147#97—81no—
148C4×C8—81no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—41no—
154#95—41no—
155C24#12311yescharacteristic
156C2×Q8—42no—
157C2×Q8—81no—
158C2×Q8—81no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4C2×C22⋊C411yescharacteristic
176C22×C4C4×D411yescharacteristic
177C22×C4C4×D411yescharacteristic
178C22×C4#12011yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4#13511yescharacteristic
182C22×C4#13511yescharacteristic
183C22×C4#13711yescharacteristic
184C22×C4#13711yescharacteristic
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—81no—
205C2×C8—82no—
206C2×C8—81no—
207C2×C8—82no—
208C2×C8—81no—
209C2×C8—81no—
210C2×C8—81no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—82no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—81no—
234C22⋊C4—82no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23#38611yescharacteristic
250C23#48511yescharacteristic
251C23#48511yescharacteristic
252Q8—162no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
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—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#41611yescharacteristic
295C2×C4#41911yescharacteristic
296C2×C4#44311yescharacteristic
297C2×C4#44411yescharacteristic
298C2×C4#45211yescharacteristic
299C2×C4#45211yescharacteristic
300C2×C4#47111yescharacteristic
301C2×C4#47311yescharacteristic
302C8—81no—
303C8—81no—
304C8—81no—
305C8—81no—
306C8—81no—
307C8—81no—
308C8—82no—
309C8—161no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#187311yescharacteristic
321C22#187611yescharacteristic
322C22#188111yescharacteristic
323C22#190311yescharacteristic
324C22#190811yescharacteristic
325C22#191211yescharacteristic
326C22#191311yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—161no—
342C4—161no—
343C2—41no—
344C2—41no—
345C2#899411yescharacteristic
346C2#917011yescharacteristic
347C2#920211yescharacteristic
348C2#926311yescharacteristic
349C2#928411yescharacteristic
350C2#933211yescharacteristic
351C2#937411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#299712
#219192
#77252
#76672
#75792
#70442
#70202