Finite Group Databasebeta

← #100762

Subgroups — #100762

Order 512.

373 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 373 conjugacy classes of subgroups — too many to draw. Only its 88 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#28694C211yesmaximal, characteristic
2#23372C211yesmaximal, characteristic
3#9905C211yesmaximal, characteristic
4#9705C211yesmaximal, characteristic
5#8580C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7049C211yesmaximal, characteristic
8C2×#501—21no—
9#2868C2211yescharacteristic
10C4×#125C2211yescharacteristic
11#2084C412yes—
12#2083C412yes—
13#1993—21no—
14#1948—21no—
15#1947—21no—
16#1940—21no—
17#1940—21no—
18#1917—21no—
19#1917—21no—
20#1917—21no—
21#1917—21no—
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26#1767C2211yescharacteristic
27C2×#332—21no—
28C2×#332—21no—
29C2×#330—21no—
30#1296—21no—
31#1296—21no—
32#1295—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×#125D411yescharacteristic
37#501—42no—
38#501—42no—
39C2×#107—22no—
40C2×#106—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×#97—21no—
51C2×#97—21no—
52C2×#97—21no—
53C2×#97—21no—
54C2×#97—21no—
55#389C2×C411yescharacteristic
56#389C2×C411yescharacteristic
57#387—21no—
58#387—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384C2×C412yes—
63#382D411yescharacteristic
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4D411yescharacteristic
67C4×C4⋊C4D411yescharacteristic
68C43C2311yescharacteristic
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#336C2×C412yes—
82#332—42no—
83#332—42no—
84#330—42no—
85C22×Q8—41no—
86C22×C8—22no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—41no—
92C22×C8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—82no—
102#125—21no—
103#125—21no—
104#125—21no—
105#125—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
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#107—44no—
130#106—44no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—81no—
142C4⋊C8—81no—
143#97—41no—
144#97—41no—
145#97—41no—
146#97—41no—
147#97—41no—
148#97—41no—
149#97—81no—
150#97—81no—
151#95—21no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—21no—
157C2×Q8—81no—
158C2×Q8—81no—
159C2×Q8—81no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8—81no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—42no—
168C22×C4C2×C22⋊C411yescharacteristic
169C22×C4C4×D411yescharacteristic
170C22×C4C4×D411yescharacteristic
171C22×C4#12011yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4#12311yescharacteristic
175C2×C8—24no—
176C2×C8—42no—
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—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—41no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42AGL(1,ℤ/8)11yescharacteristic
232C42AGL(1,ℤ/8)11yescharacteristic
233C42AGL(1,ℤ/8)11yescharacteristic
234C42#13711yescharacteristic
235C23#38611yescharacteristic
236Q8—161no—
237Q8—161no—
238Q8—161no—
239Q8—161no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4#41711yescharacteristic
271C2×C4#41811yescharacteristic
272C2×C4#45311yescharacteristic
273C2×C4#45411yescharacteristic
274C2×C4#45511yescharacteristic
275C2×C4#45611yescharacteristic
276C2×C4#45611yescharacteristic
277C2×C4#45611yescharacteristic
278C2×C4#46811yescharacteristic
279C2×C4#46811yescharacteristic
280C2×C4#46911yescharacteristic
281C2×C4#46911yescharacteristic
282C8—44no—
283C8—82no—
284C8—82no—
285C8—81no—
286C8—81no—
287C8—81no—
288C8—81no—
289C22#188211yescharacteristic
290C22#188311yescharacteristic
291C22#188611yescharacteristic
292C22#189511yescharacteristic
293C22#190211yescharacteristic
294C22#190311yescharacteristic
295C22#191511yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—81no—
309C4—162no—
310C4#166011yescharacteristic
311C4#166111yescharacteristic
312C4#166311yescharacteristic
313C4#166411yescharacteristic
314C2#900011yescharacteristic
315C2#932011yescharacteristic
316C2#932211yescharacteristic
317C2#933811yescharacteristic
318C2#933911yescharacteristic
319C2#940211yescharacteristic
320C2#942011yescharacteristic
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
#286942
#233722
#99052
#97052
#85802
#70492