Finite Group Databasebeta

← #11771036

Subgroups — #11771036

Order 1152.

463 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 463 conjugacy classes of subgroups — too many to draw. Only its 112 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#10592906C211yesmaximal, characteristic
2C3×#5207C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4#67687—31nomaximal
5#67679—31nomaximal
6C23×C32×C4C2211yescharacteristic
7C2×#3748—21no—
8C2×C3×#208—21no—
9C22×C3×C3⋊C8C412yes—
10#63657—21no—
11#63657C412yes—
12C3×#830—21no—
13C3×#830—21no—
14C3×#830—21no—
15C3×#830C412yes—
16C3×#407—31no—
17C2×C3×C22⋊C8—31no—
18#5207—31no—
19#5207—31no—
20#5207—61no—
21#5207D311yescharacteristic
22C2×#830D311yescharacteristic
23C24×C32Q811yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31#3748—42no—
32C2×C3⋊(C3⋊C8)—22no—
33C3×#208—42no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—42no—
37#1293—91noSylow
38C23×C3×C4—21no—
39C23×C3×C4C2×D311yescharacteristic
40C23×C3×C4C2×D311yescharacteristic
41C2×C3×M16—61no—
42C22×C3×C8—32no—
43C2×#208—21no—
44C2×#208—62no—
45C2×#208—61no—
46C2×#208—61no—
47C22×C3⋊C8Dic312yes—
48C3×C22⋊C8—32no—
49C3×C22⋊C8—61no—
50C3×C22⋊C8—61no—
51C3×C22⋊C8—61no—
52#830—21no—
53#830—21no—
54#830—21no—
55#830—32no—
56#830—32no—
57#830—62no—
58#830—62no—
59#830—61no—
60#830—61no—
61#830Dic312yes—
62C23×C32—22no—
63C23×C32—41no—
64C23×C32—41no—
65C23×C32C4⋊C411yescharacteristic
66C23×C32C4⋊C411yescharacteristic
67C23×C32C4⋊C411yescharacteristic
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C4211yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C3⋊(C3⋊C8)—42no—
79C3×C3⋊C8—42no—
80C3×C3⋊C8—42no—
81#407—31no—
82#407—91no—
83C2×C22⋊C8—31no—
84C24×C3—21no—
85C24×C3Dic611yescharacteristic
86C24×C3Dic611yescharacteristic
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—42no—
94C22×C3×C4—42no—
95C22×C3×C4—44no—
96C22×C3×C4C4×D311yescharacteristic
97C22×C3×C4C4×D311yescharacteristic
98C22×C3×C4C4×D311yescharacteristic
99C22×C3×C4C4×D311yescharacteristic
100C22×C3×C4D1211yescharacteristic
101C22×C3×C4D1211yescharacteristic
102C22×C3×C4C2×Dic311yescharacteristic
103C22×C3×C4C2×Dic311yescharacteristic
104C22×C3×C4#6711yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4#6711yescharacteristic
107C22×C3×C4#6711yescharacteristic
108C3×M16—122no—
109C2×C3×C8—62no—
110C2×C3×C8—62no—
111C2×C3×C8—122no—
112#208—42no—
113#208—124no—
114#208—122no—
115#208—122no—
116C2×C3⋊C8—22no—
117C2×C3⋊C8—22no—
118C2×C3⋊C8—42no—
119C2×C3⋊C8—64no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—44no—
131C22×C32#9511yescharacteristic
132C22×C32#10812yes—
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4#9912yes—
137C23×C4D3211yescharacteristic
138C2×M16—61no—
139C2×M16—181no—
140C22×C8—32no—
141C22⋊C8—32no—
142C22⋊C8—61no—
143C22⋊C8—61no—
144C22⋊C8—61no—
145C22⋊C8—92no—
146C22⋊C8—181no—
147C23×C3—22no—
148C23×C3—22no—
149C23×C3—21no—
150C23×C3—21no—
151C23×C3—21no—
152C23×C3—42no—
153C23×C3—41no—
154C23×C3—41no—
155C23×C3—41no—
156C23×C3—41no—
157C23×C3—42no—
158C23×C3—42no—
159C23×C3Dic3⋊C411yescharacteristic
160C23×C3Dic3⋊C411yescharacteristic
161C23×C3Dic3⋊C411yescharacteristic
162C23×C3Dic3⋊C411yescharacteristic
163C23×C3C4⋊Dic311yescharacteristic
164C23×C3C4⋊Dic311yescharacteristic
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4C4×Dic311yescharacteristic
188C2×C3×C4C4×Dic311yescharacteristic
189C2×C3×C4(C2×D3)⋊C411yescharacteristic
190C2×C3×C4(C2×D3)⋊C411yescharacteristic
191C2×C3×C4(C2×D3)⋊C411yescharacteristic
192C2×C3×C4(C2×D3)⋊C411yescharacteristic
193C2×C3×C4#21711yescharacteristic
194C2×C3×C4#21711yescharacteristic
195C3×C8—122no—
196C3×C8—122no—
197C3⋊C8—42no—
198C3⋊C8—42no—
199C3⋊C8—124no—
200C3⋊C8—122no—
201C3⋊C8—122no—
202C2×C32—22no—
203C2×C32—41no—
204C2×C32—41no—
205C2×C32#33811yescharacteristic
206C2×C32#34111yescharacteristic
207C2×C32#34211yescharacteristic
208C24#62711yescharacteristic
209C22×C4—42no—
210C22×C4D3×Dic311yescharacteristic
211C22×C4D3×Dic311yescharacteristic
212C22×C4#62411yescharacteristic
213C22×C4#62511yescharacteristic
214C22×C4#62611yescharacteristic
215C22×C4#62611yescharacteristic
216M16—122no—
217M16—362no—
218C2×C8—62no—
219C2×C8—62no—
220C2×C8—122no—
221C2×C8—182no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—22no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—44no—
249C22×C3—44no—
250C22×C3—48no—
251C22×C3#81912yes—
252C22×C3#82212yes—
253C22×C3C3⋊#9511yescharacteristic
254C22×C3C3⋊#9511yescharacteristic
255C3×C4—22no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—22no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4#80612yes—
266C3×C4#83412yes—
267C32#129311yescharacteristic, complemented, Sylow
268C23—22no—
269C23—41no—
270C23—41no—
271C23Dic3⋊Dic311yescharacteristic
272C23Dic3⋊Dic311yescharacteristic
273C23#372411yescharacteristic
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4Dic3211yescharacteristic
281C2×C4(C2×D3)⋊Dic311yescharacteristic
282C2×C4(C2×D3)⋊Dic311yescharacteristic
283C2×C4#372211yescharacteristic
284C8—122no—
285C8—122no—
286C8—362no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—42no—
293C2×C3—42no—
294C2×C3—42no—
295C2×C3—41no—
296C2×C3—41no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3#452611yescharacteristic
300C2×C3#452711yescharacteristic
301C2×C3#455211yescharacteristic
302C2×C3#455811yescharacteristic
303C2×C3C3⋊#33811yescharacteristic
304C2×C3C3⋊#33811yescharacteristic
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22#6357712yes—
315C22#6357911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4#6358012yes—
320C3—21no—
321C3#6767911yescharacteristic, complemented
322C3#6768711yescharacteristic, complemented
323C2—22no—
324C2—41no—
325C2—41no—
326C2#1058915911yescharacteristic
327C2#1058916611yescharacteristic
328C2#1058918611yescharacteristic
subgroupG/H
centerC22#63579
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32Q8
hypocenterC32#1293
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
267. C32#1293semidirect
321. C3#67679semidirect
322. C3#67687semidirect

Maximal subgroups

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

subgroupindex
#105929062
C3×#52072
C2×C3×#8302
#676873
#676793