Finite Group Databasebeta

← #99699

Subgroups — #99699

Order 512.

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

normal subgroups only

This group has 390 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#23838C211yesmaximal, characteristic
2#23371C211yesmaximal, characteristic
3#9877C211yesmaximal, characteristic
4#9647C211yesmaximal, characteristic
5C4×#330C211yesmaximal, characteristic
6#7030C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2085—21no—
11#2084C411yescharacteristic
12#2083C411yescharacteristic
13#2059—21no—
14#2058C411yescharacteristic
15#2057C411yescharacteristic
16#1940—21no—
17#1939—21no—
18#1917—21no—
19#1917—21no—
20#1916—21no—
21#1916—21no—
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24C4×#107—21no—
25C4×#106—21no—
26#1744C2211yescharacteristic
27C4×#97C2211yescharacteristic
28C4×#97C2211yescharacteristic
29C2×#330—21no—
30C2×Q8⋊C8—21no—
31C2×Q8⋊C8—21no—
32#1295—21no—
33#1279—21no—
34#1279—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×#125D411yescharacteristic
37C2×C4×Q8—21no—
38C2×#107—21no—
39C2×#107—21no—
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×#97—21no—
49C2×#97—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×#97—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57#391—21no—
58#389—21no—
59#389—21no—
60#389C2×C411yescharacteristic
61#389C2×C411yescharacteristic
62#387—21no—
63#387—21no—
64#384C2×C411yescharacteristic
65#382D411yescharacteristic
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4D411yescharacteristic
71C4×C4⋊C4D411yescharacteristic
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—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#330—24no—
89Q8⋊C8—42no—
90Q8⋊C8—42no—
91C22×Q8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—42no—
101#125—22no—
102#125—41no—
103C4×Q8—41no—
104C4×Q8—41no—
105C4×Q8—41no—
106C4×Q8—41no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#107—42no—
132#107—42no—
133#106—42no—
134#106—42no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—81no—
140C4⋊C8—81no—
141#97—22no—
142#97—22no—
143#97—22no—
144#97—22no—
145#97—41no—
146#97—41no—
147#97—41no—
148#97—41no—
149#97—81no—
150C4×C8—22no—
151C4×C8—22no—
152C4×C8—22no—
153C4×C8—22no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—81no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—41no—
164#95—41no—
165C2×Q8—22no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—41no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C2×C22⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12311yescharacteristic
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
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—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C4⋊C4—21no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—42no—
214C4⋊C4—42no—
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—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4#10412yes—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—81no—
250C42—81no—
251C23#38611yescharacteristic
252Q8—42no—
253Q8—42no—
254Q8—81no—
255Q8—81no—
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—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
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—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4C2×#10411yescharacteristic
290C2×C4#42111yescharacteristic
291C2×C4#44311yescharacteristic
292C2×C4#44311yescharacteristic
293C2×C4#44411yescharacteristic
294C2×C4#44411yescharacteristic
295C2×C4#45311yescharacteristic
296C2×C4#45411yescharacteristic
297C2×C4#45511yescharacteristic
298C2×C4#45611yescharacteristic
299C2×C4#45611yescharacteristic
300C2×C4#45611yescharacteristic
301C8—42no—
302C8—42no—
303C8—44no—
304C8—44no—
305C8—81no—
306C8—81no—
307C8—81no—
308C8—81no—
309C22#187111yescharacteristic
310C22#187611yescharacteristic
311C22#187611yescharacteristic
312C22#188211yescharacteristic
313C22#188311yescharacteristic
314C22#188611yescharacteristic
315C22#189111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—42no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—82no—
330C4—161no—
331C4#166011yescharacteristic
332C4#166111yescharacteristic
333C4#166311yescharacteristic
334C4#166411yescharacteristic
335C2#897011yescharacteristic
336C2#897111yescharacteristic
337C2#900011yescharacteristic
338C2#903011yescharacteristic
339C2#905111yescharacteristic
340C2#905211yescharacteristic
341C2#906811yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#238382
#233712
#98772
#96472
C4×#3302
#70302