Finite Group Databasebeta

← #103627

Subgroups — #103627

Order 512.

540 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 96 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#29951C211yesmaximal, characteristic
2#27972C211yesmaximal, characteristic
3C2×#2095C211yesmaximal, characteristic
4#9878C211yesmaximal, characteristic
5#8725C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C22×#107—21no—
9C22×#103—21no—
10#2857C2211yescharacteristic
11C2×#391C2211yescharacteristic
12C2×#384C2211yescharacteristic
13#2096—21no—
14#2095—22no—
15#2095—22no—
16#2072—22no—
17#2066—22no—
18#2024—21no—
19#1956—21no—
20#1872—22no—
21#1853—21no—
22#1834—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1787—21no—
26C4×C22⋊C8C2211yescharacteristic
27C2×#336C2211yescharacteristic
28#1296—22no—
29#1280—22no—
30#1271—22no—
31C23×Q8D411yescharacteristic
32C23×C8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C22⋊Q8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C42C2311yescharacteristic
40C2×#107—24no—
41C2×#107—44no—
42C2×#106—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D412yes—
45C2×#103—24no—
46C2×#103—22no—
47C2×#103—22no—
48C2×#103—24no—
49C2×#103—44no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8D412yes—
53C2×C4×C8—21no—
54#391—21no—
55#391—21no—
56#391—21no—
57#391—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#384—21no—
62#384—21no—
63#384—21no—
64#384D412yes—
65#384D411yescharacteristic
66#380—21no—
67#380—21no—
68C2×#95—21no—
69C2×#95—21no—
70#340—22no—
71#340—24no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336D412yes—
77C22×Q8—21no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—42no—
84C22×Q8—42no—
85C22×Q8Q1612yes—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—41no—
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4#4111yescharacteristic
92C22×C8—24no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—22no—
96C22×C8—42no—
97C22×C8—41no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—42no—
101C22⋊Q8—42no—
102C22⋊Q8—42no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
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—22no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—82no—
121C2×C4⋊C4—82no—
122C2×C22⋊C4—41no—
123C2×C42—42no—
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128#107—48no—
129#106—82no—
130C4⋊C8—42no—
131C4⋊C8—42no—
132#103—48no—
133#103—84no—
134#103—82no—
135#103—82no—
136C22⋊C8—22no—
137C22⋊C8—22no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—42no—
141C4×C8—42no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148C24#12111yescharacteristic
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—44no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—44no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8—82no—
163C2×Q8—82no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—82no—
182C22×C4—82no—
183C22×C4—82no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4#12011yescharacteristic
187C22×C4#12011yescharacteristic
188C22×C4#12011yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12711yescharacteristic
192C22×C4C2×Q1611yescharacteristic
193C22×C4#13511yescharacteristic
194C22×C4#13512yes—
195C22×C4#13711yescharacteristic
196C22×C4#13711yescharacteristic
197C22×C4#13712yes—
198C2×C8—24no—
199C2×C8—42no—
200C2×C8—44no—
201C2×C8—44no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—81no—
210C2×C8—81no—
211C2×C8—81no—
212C4⋊C4—42no—
213C4⋊C4—44no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C4⋊C4—81no—
223C4⋊C4—82no—
224C4⋊C4—82no—
225C4⋊C4—82no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C22⋊C4—82no—
229C42—22no—
230C42—22no—
231C42—41no—
232C42—41no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23#39211yescharacteristic
238C23#46412yes—
239C23#46711yescharacteristic
240C23#47011yescharacteristic
241C23#47112yes—
242Q8—44no—
243Q8—44no—
244Q8—82no—
245Q8—84no—
246Q8—82no—
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—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—82no—
270C2×C4—81no—
271C2×C4—82no—
272C2×C4—81no—
273C2×C4—82no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—82no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—164no—
283C2×C4—162no—
284C2×C4#45111yescharacteristic
285C2×C4#45111yescharacteristic
286C2×C4#45211yescharacteristic
287C2×C4#45212yes—
288C2×C4#45211yescharacteristic
289C2×C4#45312yes—
290C2×C4#45812yes—
291C2×C4#47312yes—
292C2×C4#49511yescharacteristic
293C2×C4#49711yescharacteristic
294C8—44no—
295C8—82no—
296C8—82no—
297C8—161no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—22no—
306C22#168412yes—
307C22#170412yes—
308C22#200111yescharacteristic
309C22#200211yescharacteristic
310C22#200811yescharacteristic
311C22#201511yescharacteristic
312C22#201911yescharacteristic
313C22#202011yescharacteristic
314C22#202211yescharacteristic
315C4—22no—
316C4—21no—
317C4—21no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—82no—
323C4—161no—
324C4—162no—
325C4—161no—
326C4—161no—
327C4#161412yes—
328C4#161812yes—
329C2—22no—
330C2—22no—
331C2#992811yescharacteristic
332C2#995811yescharacteristic
333C2#999511yescharacteristic
334C2#1012911yescharacteristic
335C2#1015411yescharacteristic
336C2#1018311yescharacteristic
337C2#1027711yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
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
#299512
#279722
C2×#20952
#98782
#87252
#76652
#70292