Finite Group Databasebeta

← #100694

Subgroups — #100694

Order 512.

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

normal subgroups only

This group has 383 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#29759C211yesmaximal, characteristic
2#21919C211yesmaximal, characteristic
3#7728C211yesmaximal, characteristic
4#7665C211yesmaximal, characteristic
5#7579C211yesmaximal, characteristic
6#7044C211yesmaximal, characteristic
7#7020C211yesmaximal, characteristic
8C2×#485—21no—
9#2857C2211yescharacteristic
10#2296C2211yescharacteristic
11#2084C411yescharacteristic
12#2083C411yescharacteristic
13#2068—21no—
14#2066—21no—
15#2043C411yescharacteristic
16#2043C411yescharacteristic
17#1917—21no—
18#1917—21no—
19#1916—21no—
20#1916—21no—
21#1873—21no—
22#1818—21no—
23#1817C2211yescharacteristic
24#1797C2211yescharacteristic
25#1797C2211yescharacteristic
26#1797C2211yescharacteristic
27#1750—21no—
28C2×#336C2211yescharacteristic
29#1271—21no—
30#1271—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C23×C8—21no—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×#117D411yescharacteristic
39C2×#117D411yescharacteristic
40C22×C42C2311yescharacteristic
41#485—42no—
42#485—42no—
43C2×#107—21no—
44C2×#106—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×#103—21no—
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×#97—21no—
57C2×C4×C8—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389C2×C411yescharacteristic
62#389C2×C411yescharacteristic
63#389D411yescharacteristic
64#389D411yescharacteristic
65#385—21no—
66#385—21no—
67#384C2×C411yescharacteristic
68#380—21no—
69#380—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72#340—21no—
73#340—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#336D411yescharacteristic
89#336D411yescharacteristic
90C22×Q8—21no—
91C23×C4C2×D411yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—22no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—81no—
105C22×C8—81no—
106C4⋊Q8—81no—
107C22⋊Q8—41no—
108C22⋊Q8—41no—
109C22⋊Q8—41no—
110C22⋊Q8—41no—
111#117—21no—
112#117—21no—
113#117—21no—
114#117—21no—
115#117—81no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C22⋊C4—41no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—81no—
136C2×C42C22×C411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140#107—42no—
141#106—42no—
142C4⋊C8—81no—
143C4⋊C8—81no—
144C4⋊C8—81no—
145#103—42no—
146#103—42no—
147#103—81no—
148#103—81no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—81no—
156#97—81no—
157C4×C8—81no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162#95—41no—
163#95—41no—
164C24#12311yescharacteristic
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—41no—
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—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4C2×C22⋊C411yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4C4×D411yescharacteristic
190C22×C4#12011yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12111yescharacteristic
193C22×C4#13511yescharacteristic
194C22×C4#13511yescharacteristic
195C22×C4AGL(1,ℤ/8)11yescharacteristic
196C22×C4AGL(1,ℤ/8)11yescharacteristic
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—42no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—81no—
217C2×C8—82no—
218C2×C8—81no—
219C2×C8—82no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8—81no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—81no—
247C22⋊C4—81no—
248C22⋊C4—81no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23#38611yescharacteristic
264C23#48211yescharacteristic
265C23#48211yescharacteristic
266Q8—81no—
267Q8—81no—
268Q8—81no—
269Q8—81no—
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
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—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4#41611yescharacteristic
312C2×C4#41811yescharacteristic
313C2×C4#44311yescharacteristic
314C2×C4#44411yescharacteristic
315C2×C4#44911yescharacteristic
316C2×C4#44911yescharacteristic
317C2×C4#47111yescharacteristic
318C2×C4#47311yescharacteristic
319C8—81no—
320C8—81no—
321C8—81no—
322C8—81no—
323C8—81no—
324C8—81no—
325C8—82no—
326C8—161no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22#187511yescharacteristic
338C22#187611yescharacteristic
339C22#188111yescharacteristic
340C22#190211yescharacteristic
341C22#190811yescharacteristic
342C22#191211yescharacteristic
343C22#191311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—161no—
359C4—161no—
360C2—41no—
361C2—41no—
362C2#899611yescharacteristic
363C2#917211yescharacteristic
364C2#920611yescharacteristic
365C2#926311yescharacteristic
366C2#928611yescharacteristic
367C2#933111yescharacteristic
368C2#937411yescharacteristic
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
#297592
#219192
#77282
#76652
#75792
#70442
#70202