Finite Group Databasebeta

← #97622

Subgroups — #97622

Order 512.

682 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C2×#2507C211yesmaximal, characteristic
2#8707C212yesmaximal
3#8558C211yesmaximal, characteristic
4C4×#324C211yesmaximal, characteristic
5#7576C212yesmaximal
6#2507—24no—
7#2507—24no—
8C2×#398—21no—
9C2×#398—21no—
10C2×#389—21no—
11C2×#389C411yescharacteristic
12C2×#389C411yescharacteristic
13C2×#389C411yescharacteristic
14C2×#389C2211yescharacteristic
15C2×#387—21no—
16C2×#384C411yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19#1797C2212yes—
20C4×C22⋊C8C2212yes—
21C2×#324—21no—
22C2×#324—21no—
23#1280—21no—
24#1280—21no—
25#1279—24no—
26#1271—24no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2×C411yescharacteristic
41C22×C42C2×C411yescharacteristic
42C22×C42C2311yescharacteristic
43C2×C4⋊C8—22no—
44C2×C22⋊C8—22no—
45C2×C22⋊C8—22no—
46C2×C4×C8—22no—
47#398—28no—
48#398—28no—
49#389—28no—
50#389—22no—
51#389—22no—
52#389—22no—
53#389—22no—
54#389—22no—
55#389—22no—
56#389—22no—
57#389D414yes—
58#387—28no—
59#384—22no—
60#384—22no—
61C4×C4⋊C4—22no—
62C4×C4⋊C4—22no—
63C4×C4⋊C4—22no—
64C4×C4⋊C4D414yes—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95D411yescharacteristic
71C2×#95D411yescharacteristic
72#336—22no—
73#336—22no—
74#324—24no—
75#324—42no—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4C22⋊C411yescharacteristic
81C23×C4C22⋊C411yescharacteristic
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22×C411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C22×C8—42no—
88C22×C8—42no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—22no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—24no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—82no—
113C2×C4⋊C4—82no—
114C2×C4⋊C4—82no—
115C2×C4⋊C4—82no—
116C2×C4⋊C4—82no—
117C2×C4⋊C4C22⋊C412yes—
118C2×C4⋊C4C22⋊C412yes—
119C2×C4⋊C4C22⋊C412yes—
120C2×C4⋊C4C22⋊C412yes—
121C2×C4⋊C4SD1612yes—
122C2×C4⋊C4Q1612yes—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—22no—
128C2×C42—22no—
129C2×C42—24no—
130C2×C42—42no—
131C2×C42—42no—
132C2×C42—82no—
133C2×C42C2×D412yes—
134C2×C42C2×D412yes—
135C4⋊C8—44no—
136C22⋊C8—24no—
137C22⋊C8—42no—
138C22⋊C8—42no—
139C22⋊C8—42no—
140C4×C8—44no—
141#95—24no—
142#95—24no—
143#95—24no—
144#95—24no—
145#95—24no—
146#95—22no—
147#95—22no—
148C24C2×C22⋊C411yescharacteristic
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—24no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—22no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4#10312yes—
197C22×C4#10312yes—
198C22×C4#10412yes—
199C22×C4C2×C22⋊C411yescharacteristic
200C22×C4C2×C22⋊C411yescharacteristic
201C22×C4#12012yes—
202C22×C4#12012yes—
203C22×C4#13112yes—
204C22×C4#13112yes—
205C22×C4C2×SD1611yescharacteristic
206C22×C4C2×Q1611yescharacteristic
207C22×C4#13712yes—
208C2×C8—44no—
209C2×C8—82no—
210C2×C8—82no—
211C2×C8—82no—
212C2×C8—82no—
213C2×C8—82no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C4⋊C4—44no—
221C4⋊C4—42no—
222C4⋊C4—48no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—84no—
227C4⋊C4—84no—
228C4⋊C4—84no—
229C4⋊C4—84no—
230C4⋊C4—84no—
231C4⋊C4#10114yes—
232C42—24no—
233C42—42no—
234C42—42no—
235C42—42no—
236C42—42no—
237C42—42no—
238C42—84no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23#37911yescharacteristic
244C23#40811yescharacteristic
245C23#40811yescharacteristic
246C23C2×#10311yescharacteristic
247C23#41911yescharacteristic
248C23C2×#10411yescharacteristic
249C23#42111yescharacteristic
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—42no—
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—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#40812yes—
307C2×C4#40812yes—
308C2×C4#41012yes—
309C2×C4C2×#10112yes—
310C2×C4#44812yes—
311C2×C4#45112yes—
312C8—84no—
313C8—162no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22#148111yescharacteristic
327C22#148511yescharacteristic
328C22#149311yescharacteristic
329C22#149711yescharacteristic
330C22#178011yescharacteristic
331C22#178211yescharacteristic
332C22#178411yescharacteristic
333C22#178711yescharacteristic
334C22#178911yescharacteristic
335C22#179511yescharacteristic
336C22#179511yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—44no—
344C4—42no—
345C4—81no—
346C4—82no—
347C4—82no—
348C4—82no—
349C4#147014yes—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2#830611yescharacteristic
355C2#831411yescharacteristic
356C2#832611yescharacteristic
357C2#836211yescharacteristic
358C2#837211yescharacteristic
359C2#838011yescharacteristic
360C2#839611yescharacteristic
subgroupG/H
center, socleC23#379
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ 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
C2×#25072
#87072
#85582
C4×#3242
#75762