Finite Group Databasebeta

← #100660

Subgroups — #100660

Order 512.

368 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 86 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#30091C211yesmaximal, characteristic
2#22244C211yesmaximal, characteristic
3#9690C211yesmaximal, characteristic
4#8236C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7023C211yesmaximal, characteristic
8C2×#446—21no—
9#2859C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2099—21no—
12#2099C411yescharacteristic
13#2099C411yescharacteristic
14#2083C411yescharacteristic
15#2083C411yescharacteristic
16#2057—21no—
17#1985—21no—
18#1918—21no—
19#1918—21no—
20#1917—21no—
21#1917—21no—
22#1916—21no—
23#1916—21no—
24#1839C2211yescharacteristic
25#1831C2211yescharacteristic
26#1767C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×#332—21no—
30C2×#330—21no—
31C2×#330—21no—
32#1296—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8D411yescharacteristic
36C2×#125—21no—
37C2×C4×Q8—21no—
38#446—42no—
39#446—42no—
40C2×#107—21no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97D411yescharacteristic
50C2×#97D411yescharacteristic
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#391—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389C2×C411yescharacteristic
60#389C2×C411yescharacteristic
61#384C2×C411yescharacteristic
62#384C2×C411yescharacteristic
63#384D411yescharacteristic
64#382—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4D411yescharacteristic
67C4×C4⋊C4D411yescharacteristic
68C43C2311yescharacteristic
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336C2×C411yescharacteristic
87#336C2×C411yescharacteristic
88#336D411yescharacteristic
89#336D411yescharacteristic
90#332—24no—
91#330—42no—
92#330—42no—
93C22×Q8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—41no—
101C22×C8—41no—
102C4⋊Q8—22no—
103C4⋊Q8—41no—
104#125—41no—
105#125—41no—
106#125—41no—
107#125—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
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—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C42—21no—
130C2×C42—21no—
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42#4111yescharacteristic
137C2×C42#4111yescharacteristic
138#107—42no—
139#107—42no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—42no—
145C4⋊C8—42no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148#97—21no—
149#97—21no—
150#97—21no—
151#97—42no—
152#97—41no—
153#97—41no—
154#97D812yes—
155C4×C8—42no—
156C4×C8—81no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—41no—
162#95—41no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4C2×C22⋊C411yescharacteristic
174C22×C4C4×D411yescharacteristic
175C22×C4C4×D411yescharacteristic
176C22×C4#12011yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12311yescharacteristic
180C2×C8—22no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—42no—
184C2×C8—42no—
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—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
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—81no—
231C4⋊C4#10412yes—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42C2×D811yescharacteristic
245C42#13511yescharacteristic
246C42AGL(1,ℤ/8)11yescharacteristic
247C42AGL(1,ℤ/8)11yescharacteristic
248C23#38611yescharacteristic
249Q8—82no—
250Q8—82no—
251C2×C4—21no—
252C2×C4—21no—
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—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
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—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4C2×#10411yescharacteristic
286C2×C4#42111yescharacteristic
287C2×C4C4×D811yescharacteristic
288C2×C4#44211yescharacteristic
289C2×C4#44711yescharacteristic
290C2×C4#44911yescharacteristic
291C2×C4#45911yescharacteristic
292C2×C4#46311yescharacteristic
293C2×C4#47111yescharacteristic
294C2×C4#47311yescharacteristic
295C8—42no—
296C8—81no—
297C8—81no—
298C8—81no—
299C8—81no—
300C8—81no—
301C8—82no—
302C8—82no—
303C22#187111yescharacteristic
304C22#187911yescharacteristic
305C22#188111yescharacteristic
306C22#190511yescharacteristic
307C22#190811yescharacteristic
308C22#191211yescharacteristic
309C22#191511yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—42no—
321C4—41no—
322C4—41no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—161no—
327C4—161no—
328C2#899111yescharacteristic
329C2#916611yescharacteristic
330C2#919011yescharacteristic
331C2#927111yescharacteristic
332C2#930011yescharacteristic
333C2#933611yescharacteristic
334C2#937411yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#300912
#222442
#96902
#82362
#76602
#70412
#70232