Finite Group Databasebeta

← #97606

Subgroups — #97606

Order 512.

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

normal subgroups only

This group has 758 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×#2506C211yesmaximal, characteristic
2#8706C212yesmaximal
3#8558C211yesmaximal, characteristic
4C4×#324C211yesmaximal, characteristic
5#7573C212yesmaximal
6C22×#125—21no—
7#2506—24no—
8#2506—24no—
9C2×#400—21no—
10C2×#398—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—
27C2×#125—28no—
28C2×#125—44no—
29C2×#125—42no—
30C2×#125—42no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4D411yescharacteristic
42C22×C4⋊C4D411yescharacteristic
43C22×C42—21no—
44C22×C42C2×C411yescharacteristic
45C22×C42C2×C411yescharacteristic
46C22×C42C2311yescharacteristic
47C2×C4⋊C8—22no—
48C2×C22⋊C8—22no—
49C2×C22⋊C8—22no—
50C2×C4×C8—22no—
51#400—28no—
52#398—28no—
53#389—22no—
54#389—22no—
55#389—22no—
56#389—22no—
57#389—22no—
58#389—22no—
59#389—22no—
60#389D414yes—
61#387—28no—
62#384—22no—
63#384—22no—
64C4×C4⋊C4—22no—
65C4×C4⋊C4—22no—
66C4×C4⋊C4—22no—
67C4×C4⋊C4D414yes—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75#336—22no—
76#336—22no—
77#324—24no—
78#324—42no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22×C411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C22×C8—42no—
91C22×C8—42no—
92#125—416no—
93#125—416no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—24no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—24no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4C22⋊C412yes—
129C2×C4⋊C4C22⋊C412yes—
130C2×C4⋊C4C22⋊C412yes—
131C2×C4⋊C4C22⋊C412yes—
132C2×C4⋊C4D812yes—
133C2×C4⋊C4SD1612yes—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—21no—
138C2×C42—24no—
139C2×C42—22no—
140C2×C42—22no—
141C2×C42—42no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—42no—
145C2×C42—42no—
146C2×C42C2×D412yes—
147C2×C42C2×D412yes—
148C4⋊C8—44no—
149C22⋊C8—24no—
150C22⋊C8—42no—
151C22⋊C8—42no—
152C22⋊C8—42no—
153C4×C8—44no—
154#95—24no—
155#95—24no—
156#95—24no—
157#95—24no—
158#95—24no—
159#95—22no—
160#95—22no—
161C24C2×C22⋊C411yescharacteristic
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—24no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—42no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4#10212yes—
214C22×C4#10212yes—
215C22×C4#10412yes—
216C22×C4C2×C22⋊C411yescharacteristic
217C22×C4C2×C22⋊C411yescharacteristic
218C22×C4#12012yes—
219C22×C4#12012yes—
220C22×C4#13112yes—
221C22×C4#13112yes—
222C22×C4C2×D811yescharacteristic
223C22×C4C2×SD1611yescharacteristic
224C22×C4AGL(1,ℤ/8)12yes—
225C2×C8—44no—
226C2×C8—82no—
227C2×C8—82no—
228C2×C8—82no—
229C2×C8—82no—
230C2×C8—82no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—24no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—44no—
238C4⋊C4—42no—
239C4⋊C4—48no—
240C4⋊C4—48no—
241C4⋊C4—48no—
242C4⋊C4—48no—
243C4⋊C4—48no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—44no—
249C4⋊C4#10114yes—
250C42—24no—
251C42—42no—
252C42—42no—
253C42—42no—
254C42—42no—
255C42—42no—
256C42—44no—
257C42—44no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23#37911yescharacteristic
263C23#40811yescharacteristic
264C23#40811yescharacteristic
265C23C2×#10211yescharacteristic
266C23#41811yescharacteristic
267C23C2×#10411yescharacteristic
268C23#42111yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4#40812yes—
330C2×C4#40812yes—
331C2×C4#41012yes—
332C2×C4C2×#10112yes—
333C2×C4#44712yes—
334C2×C4#45012yes—
335C8—84no—
336C8—162no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#148011yescharacteristic
350C22#148411yescharacteristic
351C22#149211yescharacteristic
352C22#149611yescharacteristic
353C22#178011yescharacteristic
354C22#178211yescharacteristic
355C22#178411yescharacteristic
356C22#178611yescharacteristic
357C22#178911yescharacteristic
358C22#179611yescharacteristic
359C22#179611yescharacteristic
360C4—22no—
361C4—22no—
362C4—22no—
363C4—42no—
364C4—42no—
365C4—42no—
366C4—42no—
367C4—44no—
368C4—82no—
369C4—82no—
370C4—81no—
371C4—82no—
372C4#147014yes—
373C2—21no—
374C2—21no—
375C2—21no—
376C2—21no—
377C2#830611yescharacteristic
378C2#831311yescharacteristic
379C2#832711yescharacteristic
380C2#836311yescharacteristic
381C2#837411yescharacteristic
382C2#837611yescharacteristic
383C2#838811yescharacteristic
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×#25062
#87062
#85582
C4×#3242
#75732