Finite Group Databasebeta

← #101849

Subgroups — #101849

Order 512.

381 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 102 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#29218C211yesmaximal, characteristic
2#23152C211yesmaximal, characteristic
3#9903C211yesmaximal, characteristic
4#9903C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7022C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#446—21no—
9#2868C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100—21no—
12#2100—21no—
13#1990C412yes—
14#1987—21no—
15#1987—21no—
16#1985—21no—
17#1940—21no—
18#1917—21no—
19#1916—21no—
20#1834C412yes—
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1771—21no—
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1296—21no—
28#1296—21no—
29#1296—21no—
30#1296—21no—
31#1271—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C4×Q8—21no—
38#446—42no—
39#446—42no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×#97—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×C4×C8—21no—
53C2×C4×C8C2×C412yes—
54#391—21no—
55#389—21no—
56#389D411yescharacteristic
57#389D411yescharacteristic
58#384—21no—
59#384—21no—
60#384—21no—
61#384C2×C412yes—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—22no—
68#340—22no—
69#340—22no—
70#340—22no—
71#336—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—
82C22×Q8—21no—
83C22×Q8—41no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—22no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—41no—
90C22×C8—41no—
91C4⋊Q8—22no—
92C4⋊Q8—41no—
93C4⋊Q8—42no—
94C4⋊Q8—42no—
95C4⋊Q8—82no—
96C4⋊Q8—82no—
97C4×Q8—41no—
98C4×Q8—41no—
99C4×Q8—41no—
100C4×Q8—41no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4C22⋊C411yescharacteristic
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C42—21no—
117C2×C42—21no—
118C2×C42C22×C411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125C4⋊C8—21no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—21no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8SD1612yes—
140C4⋊C8Q1612yes—
141#97—42no—
142#97—41no—
143#97—41no—
144#97—41no—
145#97—41no—
146C4×C8—42no—
147C4×C8—42no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—21no—
152C2×Q8—42no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—81no—
156C2×Q8—82no—
157C2×Q8—82no—
158C2×Q8—82no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4C2×C22⋊C411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12311yescharacteristic
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—44no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—81no—
206C4⋊C4—82no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4#10112yes—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42C2×SD1611yescharacteristic
225C42C2×Q1611yescharacteristic
226C42#13511yescharacteristic
227C42#13511yescharacteristic
228C42AGL(1,ℤ/8)11yescharacteristic
229C42#13711yescharacteristic
230C42#13711yescharacteristic
231C42#13711yescharacteristic
232C23#38611yescharacteristic
233Q8—82no—
234Q8—82no—
235Q8—164no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4C2×#10111yescharacteristic
265C2×C4#41311yescharacteristic
266C2×C4C4×SD1611yescharacteristic
267C2×C4C4×Q1611yescharacteristic
268C2×C4#44011yescharacteristic
269C2×C4#44111yescharacteristic
270C2×C4#45011yescharacteristic
271C2×C4#45111yescharacteristic
272C2×C4#45211yescharacteristic
273C2×C4#45211yescharacteristic
274C2×C4#45411yescharacteristic
275C2×C4#45411yescharacteristic
276C2×C4#46111yescharacteristic
277C2×C4#46211yescharacteristic
278C2×C4#46311yescharacteristic
279C2×C4#46411yescharacteristic
280C8—42no—
281C8—42no—
282C8—82no—
283C8—81no—
284C8—81no—
285C8—161no—
286C8—161no—
287C22#187711yescharacteristic
288C22#187811yescharacteristic
289C22#188811yescharacteristic
290C22#190111yescharacteristic
291C22#190311yescharacteristic
292C22#190311yescharacteristic
293C22#190911yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—81no—
309C4—162no—
310C4#163511yescharacteristic
311C4#163611yescharacteristic
312C4#163711yescharacteristic
313C4#163811yescharacteristic
314C2#906511yescharacteristic
315C2#924911yescharacteristic
316C2#925011yescharacteristic
317C2#928711yescharacteristic
318C2#928811yescharacteristic
319C2#942411yescharacteristic
320C2#945611yescharacteristic
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
#292182
#231522
#99032
#76522
#70222