Finite Group Databasebeta

← #104178

Subgroups — #104178

Order 512.

534 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 100 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#29967C211yesmaximal, characteristic
2#27961C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4#9711C211yesmaximal, characteristic
5#8725C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10C2×#384C2211yescharacteristic
11#2100—22no—
12#2099—21no—
13#2088—22no—
14#2058—21no—
15#1990—21no—
16#1853—21no—
17#1834—21no—
18#1824—21no—
19#1824—22no—
20#1797C2211yescharacteristic
21#1797C2211yescharacteristic
22C4×C22⋊C8C2211yescharacteristic
23C2×#328—22no—
24#1442—22no—
25#1441—22no—
26C4⋊#95—21no—
27C4⋊#95—21no—
28C4×#95C2211yescharacteristic
29#1296—22no—
30#1271—22no—
31C2×C4⋊Q8D411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D412yes—
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384D411yescharacteristic
60#380—21no—
61#380—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—24no—
65C2×#95—24no—
66C2×#95D412yes—
67#340—22no—
68#340—22no—
69#340—24no—
70#340—24no—
71#340—22no—
72#336—21no—
73#336—21no—
74#336D412yes—
75#328—44no—
76C22×Q8—21no—
77C23×C4—21no—
78C23×C4—22no—
79C23×C4—22no—
80C23×C4—21no—
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C22×C8—22no—
85C22×C8—22no—
86C22×C8—41no—
87C4⋊Q8—42no—
88C22⋊Q8—42no—
89C22⋊Q8—42no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—44no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—44no—
107C2×C4⋊C4—44no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—82no—
116C2×C4⋊C4Q1612yes—
117C2×C22⋊C4—41no—
118C2×C42—42no—
119C2×C42—42no—
120C2×C42—42no—
121C2×C42—41no—
122C2×C42—41no—
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127#106—82no—
128C4⋊C8—42no—
129C4⋊C8—42no—
130C22⋊C8—42no—
131C22⋊C8—41no—
132C22⋊C8—41no—
133C22⋊C8—42no—
134C4×C8—42no—
135#95—22no—
136#95—42no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—84no—
142#95—84no—
143#95SD1614yes—
144C24#12011yescharacteristic
145C2×Q8—42no—
146C2×Q8—81no—
147C2×Q8—81no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—41no—
164C22×C4—42no—
165C22×C4—41no—
166C22×C4—42no—
167C22×C4—44no—
168C22×C4—44no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—44no—
177C22×C4#12011yescharacteristic
178C22×C4#12011yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12711yescharacteristic
183C22×C4C2×SD1612yes—
184C22×C4C2×Q1611yescharacteristic
185C22×C4#13511yescharacteristic
186C22×C4#13711yescharacteristic
187C22×C4#13711yescharacteristic
188C22×C4#13712yes—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C22⋊C4—82no—
220C42—22no—
221C42—22no—
222C42—41no—
223C42—41no—
224C42—82no—
225C42—82no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23#39211yescharacteristic
231C23#44812yes—
232C23#45111yescharacteristic
233C23#45211yescharacteristic
234C23#45512yes—
235Q8—162no—
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—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—84no—
267C2×C4—88no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#45111yescharacteristic
281C2×C4#45211yescharacteristic
282C2×C4#45412yes—
283C2×C4#45412yes—
284C2×C4#45812yes—
285C2×C4#46112yes—
286C2×C4#46711yescharacteristic
287C2×C4#47011yescharacteristic
288C2×C4#49211yescharacteristic
289C2×C4#49711yescharacteristic
290C8—82no—
291C8—82no—
292C8—161no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22#164312yes—
302C22#164512yes—
303C22#200111yescharacteristic
304C22#200311yescharacteristic
305C22#200311yescharacteristic
306C22#200411yescharacteristic
307C22#200811yescharacteristic
308C22#201311yescharacteristic
309C22#202211yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—22no—
315C4—21no—
316C4—41no—
317C4—84no—
318C4—82no—
319C4—161no—
320C4—161no—
321C4—162no—
322C4—161no—
323C4#161512yes—
324C4#161712yes—
325C2—22no—
326C2—22no—
327C2#992911yescharacteristic
328C2#995111yescharacteristic
329C2#1007311yescharacteristic
330C2#1009711yescharacteristic
331C2#1024911yescharacteristic
332C2#1028511yescharacteristic
333C2#1033211yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#299672
#279612
#151972
#97112
#87252
#75762
#70282