Finite Group Databasebeta

← #11772621

Subgroups — #11772621

Order 1152.

338 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#63780C211yesmaximal, characteristic
2#10591273C211yesmaximal, characteristic
3C2×#63561C211yesmaximal, characteristic
4C22×#634C2211yescharacteristic
5C2×#3792—21no—
6C2×C3×#208—21no—
7C2×#3724C411yescharacteristic
8C2×Dic32C411yescharacteristic
9#63780—21no—
10#63780C412yescomplemented
11C3×C3⋊#95—21no—
12#63579—21no—
13#63561—21no—
14#63561C412yescomplemented
15C2×#824—61no—
16#4646—61no—
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20C2×#634—41no—
21C2×#634—41no—
22C2×#634C2×C411yescharacteristic
23C2×#634C2×C411yescharacteristic
24C2×#634D411yescharacteristic
25C2×#634Q811yescharacteristic
26C22×C3×Dic3—21no—
27C22×C3×Dic3—21no—
28#3792—22no—
29#3792—41no—
30C2×#622—41no—
31C3×#208—22no—
32C3×#208—41no—
33C2×C3×C3⋊C8—41no—
34#3724—41no—
35Dic32—41no—
36#1394—91nomaximal, Sylow
37C22×Dic6—61no—
38C22×Dic6—61no—
39C2×C3×M16—61no—
40C2×Dic3⋊C4—61no—
41C2×C4×Dic3—61no—
42C2×#208—21no—
43C3×#95—61no—
44C3⋊#95—21no—
45C3⋊#95—61no—
46C3⋊#95—61no—
47#824—62no—
48#824—62no—
49C23×C32C22⋊C411yescharacteristic
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C32×C4C4⋊C411yescharacteristic
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3C4211yescharacteristic
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C4⋊C411yescharacteristic
62#634—41no—
63#634—41no—
64#634—41no—
65#634—41no—
66C2×C3×Dic3—22no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—41no—
72#622—42no—
73C3×C3⋊C8—42no—
74C2×#101—91no—
75C2×#101—91no—
76#391—91no—
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—61no—
80C22×C3×C4—61no—
81C22×Dic3—21no—
82C22×Dic3—21no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C2×Dic6—61no—
90C2×Dic6—61no—
91C2×Dic6—61no—
92C2×Dic6—61no—
93C2×Dic6—61no—
94C2×Dic6—61no—
95C2×Dic6—122no—
96C2×Dic6—122no—
97C2×Dic6—121no—
98C2×Dic6—121no—
99C2×Dic6—121no—
100C2×Dic6—121no—
101C3×M16—62no—
102C3×M16—121no—
103C2×C3×C8—121no—
104Dic3⋊C4—122no—
105C4×Dic3—122no—
106#208—22no—
107#208—41no—
108C2×C3⋊C8—41no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32#9511yescharacteristic
112C22×C32#9911yescharacteristic
113C22×C32#9911yescharacteristic
114C32×C4—21no—
115C32×C4—21no—
116C3⋊Dic3—21no—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3×Dic3—42no—
121C3×Dic3—81no—
122C22×Q8—91no—
123C2×M16—61no—
124C2×M16—181no—
125C2×C4⋊C4—91no—
126C2×C42—91no—
127#101—92no—
128#101—92no—
129#101—181no—
130#101—181no—
131#95—61no—
132#95—181no—
133C23×C3—21no—
134C23×C3—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—62no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4—121no—
149C2×C3×C4—121no—
150C2×C3×C4—121no—
151C2×Dic3—22no—
152C2×Dic3—41no—
153C2×Dic3—41no—
154C2×Dic3—41no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173Dic6—122no—
174Dic6—122no—
175Dic6—122no—
176Dic6—122no—
177Dic6—121no—
178Dic6—121no—
179Dic6—121no—
180Dic6—121no—
181Dic6—121no—
182Dic6—121no—
183Dic6—121no—
184Dic6—121no—
185C3×C8—122no—
186C3⋊C8—42no—
187C2×C32—21no—
188C2×C32—21no—
189C2×C32#34211yescharacteristic
190C2×C32#35511yescharacteristic
191C2×C32#35611yescharacteristic
192C2×Q8—91no—
193C2×Q8—91no—
194C2×Q8—91no—
195C2×Q8—91no—
196C2×Q8—361no—
197C2×Q8—361no—
198C22×C4—61no—
199C22×C4—61no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4GO+(4,𝔽2)11yescharacteristic
203M16—62no—
204M16—121no—
205M16—182no—
206M16—361no—
207C2×C8—121no—
208C2×C8—361no—
209C4⋊C4—361no—
210C42—361no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—41no—
222C22×C3—41no—
223C3×C4—21no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—41no—
228C3×C4—41no—
229C3×C4—122no—
230C3×C4—241no—
231Dic3—42no—
232Dic3—62no—
233Dic3—62no—
234Dic3—81no—
235Dic3—121no—
236Dic3—121no—
237Dic3—121no—
238Dic3—121no—
239Dic3—121no—
240Dic3—121no—
241C32#139411yescharacteristic, complemented, Sylow
242C23D32⋊C411yescharacteristic
243Q8—361no—
244Q8—361no—
245Q8—361no—
246Q8—361no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—62no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—121no—
255C2×C4—121no—
256C2×C4—121no—
257C2×C4—121no—
258C2×C4—121no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—181no—
263C2×C4D32⋊C411yescharacteristic
264C2×C4#377311yescharacteristic
265C8—122no—
266C8—362no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—41no—
278C2×C3—41no—
279C22—21no—
280C22—21no—
281C22#6373711yescharacteristic
282C22#6373811yescharacteristic
283C22#6373811yescharacteristic
284C4—21no—
285C4—21no—
286C4—122no—
287C4—181no—
288C4—181no—
289C4—181no—
290C4—181no—
291C4—241no—
292C3—21no—
293C3—21no—
294C2—21no—
295C2—21no—
296C2#1059005911yescharacteristic
297C2#1059006011yescharacteristic
298C2#1059007611yescharacteristic
subgroupG/H
centerC22#63738
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC22×#634C22
hypocenterC32#1394
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. #63780C4semidirect
14. #63561C4semidirect
241. C32#1394semidirect

Maximal subgroups

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

subgroupindex
C2×#637802
#105912732
C2×#635612
#13949