Finite Group Databasebeta

← #100477

Subgroups — #100477

Order 512.

403 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 403 conjugacy classes of subgroups — too many to draw. Only its 94 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#33027C211yesmaximal, characteristic
2#21345C211yesmaximal, characteristic
3#9890C211yesmaximal, characteristic
4#8175C211yesmaximal, characteristic
5#7682C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C2×#477C411yescharacteristic
9C2×#462C411yescharacteristic
10#2862C2211yescharacteristic
11C42×Q8C2211yescharacteristic
12#1987C411yescharacteristic
13#1984—21no—
14#1981C411yescharacteristic
15#1939—21no—
16#1928—21no—
17#1928—21no—
18#1917—22no—
19#1878—21no—
20#1878—21no—
21#1831C2211yescharacteristic
22#1767—21no—
23#1767C2211yescharacteristic
24#1767C2211yescharacteristic
25#1745—21no—
26#1744C2211yescharacteristic
27C4×#97C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1295—21no—
30#1295—21no—
31#1279—21no—
32#1272—22no—
33C22×Q16—21no—
34C2×C4⋊Q8C2×C411yescharacteristic
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4×Q8C2×C411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38C2×C4×Q8D411yescharacteristic
39#477—42no—
40#462—42no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8C2×C411yescharacteristic
46C2×C4⋊C8C2×C411yescharacteristic
47C2×#103—21no—
48C2×#103—21no—
49C2×#103—21no—
50C2×#103—21no—
51C2×#97—21no—
52C2×#97—21no—
53C2×#97—21no—
54C2×#97D411yescharacteristic
55C2×#97D411yescharacteristic
56C2×C4×C8—21no—
57C2×C4×C8—21no—
58#391—21no—
59#391—21no—
60#391—21no—
61#391—21no—
62#382—21no—
63#382—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4C2×C411yescharacteristic
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C43—21no—
71C43C2311yescharacteristic
72#340—21no—
73#340—21no—
74#336—22no—
75#336—22no—
76#336—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D412yes—
83Q8⋊C8—24no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8C22⋊C411yescharacteristic
87C2×Q16—42no—
88C2×Q16—42no—
89C2×Q16—42no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—22no—
95C22×C8—41no—
96C22×C8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4×Q8—22no—
102C4×Q8—22no—
103C4×Q8—41no—
104C4×Q8—41no—
105C4×Q8—41no—
106C4×Q8—41no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42C22×C411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129C2×C42#4111yescharacteristic
130#107—42no—
131C4⋊C8—22no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—44no—
138#103—42no—
139#103—42no—
140#103—42no—
141#103—42no—
142#97—21no—
143#97—21no—
144#97—21no—
145#97—42no—
146#97—41no—
147#97—41no—
148#97—41no—
149#97—41no—
150#97Q1612yescomplemented
151C4×C8—22no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—41no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—42no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—81no—
175C2×Q8—81no—
176C2×Q8#10412yes—
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
190Q16—84no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—81no—
209C2×C8—81no—
210C2×C8—81no—
211C2×C8—81no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4#10012yes—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—42no—
236C42—42no—
237C42—42no—
238C42—42no—
239C42—81no—
240C42—81no—
241C42C2×Q1611yescharacteristic
242C42#13511yescharacteristic
243C42#13711yescharacteristic
244C42#13711yescharacteristic
245C23#38611yescharacteristic
246Q8—22no—
247Q8—22no—
248Q8—41no—
249Q8—41no—
250Q8—81no—
251Q8—81no—
252Q8—81no—
253Q8—81no—
254Q8—162no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
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—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4C2×#10011yescharacteristic
289C2×C4#41311yescharacteristic
290C2×C4C2×#10411yescharacteristic
291C2×C4#42111yescharacteristic
292C2×C4#42111yescharacteristic
293C2×C4#42111yescharacteristic
294C2×C4C4×Q1611yescharacteristic
295C2×C4#44111yescharacteristic
296C2×C4#45111yescharacteristic
297C2×C4#45211yescharacteristic
298C2×C4#46211yescharacteristic
299C2×C4#46411yescharacteristic
300C8—42no—
301C8—42no—
302C8—82no—
303C8—82no—
304C8—82no—
305C8—81no—
306C8—81no—
307C22#187111yescharacteristic
308C22#187811yescharacteristic
309C22#188111yescharacteristic
310C22#189711yescharacteristic
311C22#190011yescharacteristic
312C22#190211yescharacteristic
313C22#190611yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—42no—
323C4—42no—
324C4—41no—
325C4—81no—
326C4—81no—
327C4—161no—
328C4—161no—
329C4#152711yescharacteristic
330C4#153211yescharacteristic
331C4#153511yescharacteristic
332C4#153611yescharacteristic
333C2#899011yescharacteristic
334C2#912311yescharacteristic
335C2#916011yescharacteristic
336C2#923611yescharacteristic
337C2#924811yescharacteristic
338C2#931411yescharacteristic
339C2#934911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
150. #97Q16semidirect

Maximal subgroups

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

subgroupindex
#330272
#213452
#98902
#81752
#76822
#70492
#70302