Finite Group Databasebeta

← #103524

Subgroups — #103524

Order 512.

432 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 82 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#29966C211yesmaximal, characteristic
2#29939C211yesmaximal, characteristic
3#23747C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#8710C211yesmaximal, characteristic
6#7687C211yesmaximal, characteristic
7#7045C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10#2285C2211yescharacteristic
11#2101—22no—
12#2100—21no—
13#2100—21no—
14#2099—21no—
15#2099—21no—
16#2086—22no—
17#2083—21no—
18#2076—22no—
19#2057—21no—
20#1987—21no—
21#1947—21no—
22#1852—21no—
23#1823—21no—
24#1797C2211yescharacteristic
25#1797C2211yescharacteristic
26C4×C22⋊C8C2211yescharacteristic
27#1736—21no—
28#1736—21no—
29#1728C2211yescharacteristic
30#1280—22no—
31#1279—22no—
32#1272—22no—
33C22×M16—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C22⋊Q8—21no—
36C2×#117—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42C2311yescharacteristic
41C2×#107—22no—
42C2×#107—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D412yes—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8D412yes—
48C2×C4×C8—21no—
49#391—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384D411yescharacteristic
57#384D411yescharacteristic
58#384D411yescharacteristic
59#382—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C2×#95—21no—
67#340—22no—
68#340—22no—
69#340—22no—
70#340—22no—
71#340—22no—
72#340—22no—
73#340—22no—
74#340—22no—
75#340—22no—
76#340—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336D412yes—
82C22×Q8—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4#4111yescharacteristic
88C2×M16—42no—
89C2×M16—42no—
90C2×M16—41no—
91C2×M16—41no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—41no—
96C4⋊Q8—42no—
97C22⋊Q8—82no—
98#117—44no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
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—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4Q1612yes—
123C2×C22⋊C4—41no—
124C2×C22⋊C4—41no—
125C2×C42—42no—
126C2×C42—41no—
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131#107—82no—
132#107—82no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135C22⋊C8—22no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—42no—
140C4×C8—42no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C24#12111yescharacteristic
148C2×Q8—42no—
149C2×Q8—81no—
150C2×Q8—81no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—42no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4#12011yescharacteristic
174C22×C4#12011yescharacteristic
175C22×C4#12011yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12711yescharacteristic
179C22×C4C2×Q1611yescharacteristic
180C22×C4#13511yescharacteristic
181C22×C4#13711yescharacteristic
182C22×C4#13711yescharacteristic
183M16—82no—
184M16—82no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—81no—
196C2×C8—81no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—81no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C22⋊C4—82no—
220C22⋊C4—82no—
221C42—22no—
222C42—22no—
223C42—41no—
224C42—41no—
225C42—82no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23#39211yescharacteristic
233C23#46711yescharacteristic
234C23#47011yescharacteristic
235Q8—162no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—162no—
276C2×C4#45111yescharacteristic
277C2×C4#45111yescharacteristic
278C2×C4#45211yescharacteristic
279C2×C4#45211yescharacteristic
280C2×C4#45412yes—
281C2×C4#45511yescharacteristic
282C2×C4#45611yescharacteristic
283C2×C4#45812yes—
284C2×C4#47212yes—
285C8—82no—
286C8—82no—
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22#200111yescharacteristic
300C22#200311yescharacteristic
301C22#200711yescharacteristic
302C22#200911yescharacteristic
303C22#201711yescharacteristic
304C22#201811yescharacteristic
305C22#202211yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—22no—
311C4—41no—
312C4—41no—
313C4—82no—
314C4—161no—
315C4—161no—
316C4—161no—
317C4—161no—
318C4—161no—
319C4#161512yes—
320C4#161712yes—
321C2—41no—
322C2—41no—
323C2#992911yescharacteristic
324C2#993711yescharacteristic
325C2#997711yescharacteristic
326C2#1011011yescharacteristic
327C2#1012311yescharacteristic
328C2#1019011yescharacteristic
329C2#1025911yescharacteristic
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
#299662
#299392
#237472
#98792
#87102
#76872
#70452