Finite Group Databasebeta

← #100485

Subgroups — #100485

Order 512.

385 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 94 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#33067C211yesmaximal, characteristic
2#21345C211yesmaximal, characteristic
3#9686C211yesmaximal, characteristic
4#8175C211yesmaximal, characteristic
5#7680C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C42×Q8C2211yescharacteristic
10#1984—21no—
11#1948C411yescharacteristic
12#1948C411yescharacteristic
13#1939—21no—
14#1919—21no—
15#1919—21no—
16#1917—22no—
17#1865—21no—
18#1865—21no—
19#1831C2211yescharacteristic
20#1803C411yescharacteristic
21#1803C411yescharacteristic
22#1767—21no—
23#1767C2211yescharacteristic
24#1767C2211yescharacteristic
25#1745—21no—
26#1744C2211yescharacteristic
27C4×#97C2211yescharacteristic
28C2×#330—21no—
29C2×#330—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1271—22no—
33C2×#125—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×#106—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8C2×C411yescharacteristic
43C2×C4⋊C8C2×C411yescharacteristic
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97D411yescharacteristic
50C2×#97D411yescharacteristic
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#384C2×C411yescharacteristic
58#384C2×C411yescharacteristic
59#382—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4C2×C411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43—21no—
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—22no—
73#336—22no—
74#336—22no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81#330—42no—
82#330—42no—
83Q8⋊C8—24no—
84C22×Q8C22⋊C411yescharacteristic
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—22no—
90C22×C8—41no—
91C22×C8—41no—
92#125—41no—
93#125—41no—
94#125—41no—
95#125—41no—
96C4×Q8—22no—
97C4×Q8—22no—
98C4×Q8—41no—
99C4×Q8—41no—
100C4×Q8—41no—
101C4×Q8—41no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42C22×C411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129#106—42no—
130#106—42no—
131C4⋊C8—22no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—44no—
138#103—42no—
139#103—42no—
140#97—21no—
141#97—21no—
142#97—21no—
143#97—42no—
144#97—41no—
145#97—41no—
146#97—41no—
147#97—41no—
148#97SD1612yes—
149C4×C8—22no—
150C4×C8—41no—
151C4×C8—41no—
152C4×C8—41no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—41no—
157#95—41no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8#10412yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4C2×C22⋊C411yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4C4×D411yescharacteristic
173C22×C4#12011yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12111yescharacteristic
176C22×C4#12311yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4#10112yes—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—42no—
231C42—42no—
232C42—42no—
233C42—42no—
234C42—81no—
235C42—81no—
236C42C2×SD1611yescharacteristic
237C42#13511yescharacteristic
238C42AGL(1,ℤ/8)11yescharacteristic
239C42#13711yescharacteristic
240C23#38611yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—41no—
244Q8—41no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4C2×#10111yescharacteristic
279C2×C4#41311yescharacteristic
280C2×C4C2×#10411yescharacteristic
281C2×C4#42111yescharacteristic
282C2×C4#42111yescharacteristic
283C2×C4#42111yescharacteristic
284C2×C4C4×SD1611yescharacteristic
285C2×C4#44011yescharacteristic
286C2×C4#44811yescharacteristic
287C2×C4#44911yescharacteristic
288C2×C4#46011yescharacteristic
289C2×C4#46411yescharacteristic
290C8—42no—
291C8—42no—
292C8—82no—
293C8—82no—
294C8—82no—
295C8—81no—
296C8—81no—
297C22#187111yescharacteristic
298C22#188011yescharacteristic
299C22#188111yescharacteristic
300C22#189711yescharacteristic
301C22#190111yescharacteristic
302C22#190211yescharacteristic
303C22#190611yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—42no—
313C4—42no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—161no—
318C4—161no—
319C4#152811yescharacteristic
320C4#153211yescharacteristic
321C4#153511yescharacteristic
322C4#153711yescharacteristic
323C2#899211yescharacteristic
324C2#912511yescharacteristic
325C2#916011yescharacteristic
326C2#923811yescharacteristic
327C2#925211yescharacteristic
328C2#931411yescharacteristic
329C2#935111yescharacteristic
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
#330672
#213452
#96862
#81752
#76802
#70492
#70302