Finite Group Databasebeta

← #99692

Subgroups — #99692

Order 512.

381 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 98 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#23777C211yesmaximal, characteristic
2#22824C211yesmaximal, characteristic
3#9868C211yesmaximal, characteristic
4#9643C211yesmaximal, characteristic
5#7562C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2100C411yescharacteristic
11#2095C411yescharacteristic
12#2087—21no—
13#2068—21no—
14#2057C411yescharacteristic
15#2024C411yescharacteristic
16#1985—21no—
17#1917—21no—
18#1916—21no—
19#1842C2211yescharacteristic
20#1832—21no—
21C4×#107—21no—
22#1771—21no—
23#1768—21no—
24#1767C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C4×#103—21no—
28#1744C2211yescharacteristic
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1279—21no—
33#1272—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8D411yescharacteristic
38C2×#107—21no—
39C2×#107—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×#103—21no—
49C2×#103—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391—21no—
57#391C2×C411yescharacteristic
58#391D411yescharacteristic
59#389—21no—
60#389—21no—
61#389C2×C411yescharacteristic
62#389D411yescharacteristic
63#387—21no—
64#387—21no—
65#384C2×C411yescharacteristic
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4D411yescharacteristic
70#376—21no—
71C43C2311yescharacteristic
72#340—21no—
73#340—21no—
74#340—21no—
75#340—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#336—21no—
85#336—21no—
86#336C2×C411yescharacteristic
87#336C2×C411yescharacteristic
88Q8⋊C8—42no—
89Q8⋊C8—42no—
90C22×Q8—21no—
91C22×Q8C22⋊C411yescharacteristic
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—42no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
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—41no—
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#107—42no—
132#107—42no—
133C4⋊C8—22no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—42no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8Q1612yes—
146#103—42no—
147#103—42no—
148#97—41no—
149#97—41no—
150#97—81no—
151C4×C8—22no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—81no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—41no—
166#95—41no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4C2×C22⋊C411yescharacteristic
184C22×C4C4×D411yescharacteristic
185C22×C4C4×D411yescharacteristic
186C22×C4#12011yescharacteristic
187C22×C4#12111yescharacteristic
188C22×C4#12111yescharacteristic
189C22×C4#12311yescharacteristic
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—42no—
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—41no—
210C2×C8—81no—
211C2×C8—81no—
212C2×C8—81no—
213C2×C8—81no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—81no—
246C42—81no—
247C42C2×Q1611yescharacteristic
248C42#13511yescharacteristic
249C42#13511yescharacteristic
250C42#13511yescharacteristic
251C42#13711yescharacteristic
252C42#13711yescharacteristic
253C42#13711yescharacteristic
254C42#13711yescharacteristic
255C23#38611yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—42no—
259Q8—81no—
260Q8—81no—
261Q8—81no—
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—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4#41611yescharacteristic
294C2×C4#41911yescharacteristic
295C2×C4C4×Q1611yescharacteristic
296C2×C4#44111yescharacteristic
297C2×C4#44311yescharacteristic
298C2×C4#44411yescharacteristic
299C2×C4#45111yescharacteristic
300C2×C4#45211yescharacteristic
301C2×C4#45211yescharacteristic
302C2×C4#45211yescharacteristic
303C2×C4#45311yescharacteristic
304C2×C4#45411yescharacteristic
305C2×C4#46211yescharacteristic
306C2×C4#46411yescharacteristic
307C2×C4#48511yescharacteristic
308C2×C4#48511yescharacteristic
309C8—42no—
310C8—42no—
311C8—81no—
312C8—82no—
313C8—82no—
314C8—81no—
315C8—81no—
316C8—81no—
317C22#187311yescharacteristic
318C22#187611yescharacteristic
319C22#187811yescharacteristic
320C22#188111yescharacteristic
321C22#188311yescharacteristic
322C22#188411yescharacteristic
323C22#189111yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—82no—
340C4—161no—
341C4#163011yescharacteristic
342C4#163211yescharacteristic
343C4#163611yescharacteristic
344C4#163811yescharacteristic
345C2#897411yescharacteristic
346C2#899411yescharacteristic
347C2#899711yescharacteristic
348C2#903411yescharacteristic
349C2#904811yescharacteristic
350C2#905211yescharacteristic
351C2#905611yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237772
#228242
#98682
#96432
#75622
#70312
#70272