Finite Group Databasebeta

← #101280

Subgroups — #101280

Order 512.

415 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 90 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#23658C211yesmaximal, characteristic
2#21921C211yesmaximal, characteristic
3#8724C211yesmaximal, characteristic
4#8723C211yesmaximal, characteristic
5#7598C211yesmaximal, characteristic
6#7045C211yesmaximal, characteristic
7#7045C211yesmaximal, characteristic
8C2×#428—21no—
9#2296C2211yescharacteristic
10C2×#384C2211yescharacteristic
11#2084—21no—
12#2084C412yes—
13#2083—21no—
14#2083C412yes—
15#1917—21no—
16#1917—21no—
17#1916—21no—
18#1916—21no—
19#1818—21no—
20#1797C2211yescharacteristic
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24#1750—21no—
25#1736—21no—
26#1728C2211yescharacteristic
27#1296—21no—
28#1296—21no—
29#1296—21no—
30#1296—21no—
31#1271—21no—
32#1271—21no—
33C22×M16—21no—
34C2×#117D411yescharacteristic
35C2×#117D411yescharacteristic
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C42C2311yescharacteristic
40#428—42no—
41#428—42no—
42C2×#107—22no—
43C2×#106—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×#97—21no—
55C2×C4×C8—21no—
56#389C2×C411yescharacteristic
57#389C2×C411yescharacteristic
58#389D411yescharacteristic
59#389D411yescharacteristic
60#385—21no—
61#385—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384C2×C412yes—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68#340—22no—
69#340—22no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336C2×C412yes—
82C23×C4—41no—
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C23×C4#4111yescharacteristic
86C2×M16—22no—
87C2×M16—22no—
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C2×M16—41no—
92C22×C8—22no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—41no—
98C22×C8—41no—
99#117—21no—
100#117—21no—
101#117—21no—
102#117—21no—
103#117—41no—
104#117—41no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—82no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4—81no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C22⋊C4—21no—
127C2×C22⋊C4—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42C22×C411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136#107—44no—
137#106—44no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—81no—
151C22⋊C8—81no—
152#97—81no—
153C4×C8—81no—
154#95—21no—
155#95—21no—
156#95—21no—
157#95—21no—
158C24#12311yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4—82no—
177C22×C4—82no—
178C22×C4—81no—
179C22×C4—81no—
180C22×C4C2×C22⋊C411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4#12011yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#13511yescharacteristic
187C22×C4#13511yescharacteristic
188C22×C4AGL(1,ℤ/8)11yescharacteristic
189C22×C4AGL(1,ℤ/8)11yescharacteristic
190M16—42no—
191M16—42no—
192M16—42no—
193M16—42no—
194C2×C8—24no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—81no—
210C2×C8—81no—
211C2×C8—81no—
212C2×C8—81no—
213C2×C8—81no—
214C2×C8—81no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—81no—
228C4⋊C4—81no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—81no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23#38611yescharacteristic
256C23#48211yescharacteristic
257C23#48211yescharacteristic
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—162no—
298C2×C4—162no—
299C2×C4#41611yescharacteristic
300C2×C4#41811yescharacteristic
301C2×C4#44911yescharacteristic
302C2×C4#44911yescharacteristic
303C2×C4#45611yescharacteristic
304C2×C4#45611yescharacteristic
305C2×C4#45811yescharacteristic
306C2×C4#45811yescharacteristic
307C2×C4#47111yescharacteristic
308C2×C4#47111yescharacteristic
309C2×C4#47211yescharacteristic
310C2×C4#47311yescharacteristic
311C8—44no—
312C8—81no—
313C8—81no—
314C8—81no—
315C8—81no—
316C8—161no—
317C8—161no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22#187511yescharacteristic
329C22#188611yescharacteristic
330C22#189011yescharacteristic
331C22#190211yescharacteristic
332C22#190311yescharacteristic
333C22#190711yescharacteristic
334C22#190811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—162no—
348C4#160911yescharacteristic
349C4#160911yescharacteristic
350C4#160911yescharacteristic
351C4#160911yescharacteristic
352C2—41no—
353C2—41no—
354C2#902611yescharacteristic
355C2#917211yescharacteristic
356C2#917411yescharacteristic
357C2#942011yescharacteristic
358C2#943411yescharacteristic
359C2#952111yescharacteristic
360C2#952211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×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
#236582
#219212
#87242
#87232
#75982
#70452