Finite Group Databasebeta

← #11774652

Subgroups — #11774652

Order 1152.

576 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#3832C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic, complemented
3C4×#3788C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×#3832C411yescharacteristic
7C2×#3788—21no—
8C2×#3788—21no—
9C32×C4×Q8C411yescharacteristic
10Q8×C3⋊Dic3C2211yescharacteristic
11#64102—21no—
12#64102C2211yescharacteristic
13#64101—21no—
14#64101C411yescharacteristic
15C4×C4⋊(C3⋊D3)—21no—
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C42×C3⋊D3—21no—
18C42×C3⋊D3C2211yescharacteristic
19#63777—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×#239—62no—
24C2×C32×Q8C2×C411yescharacteristic
25#3832—22no—
26#3832—22no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×#622—22no—
36C2×#622—22no—
37#3788—24no—
38#3788—42no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C42—21no—
42C32×C42C2×C411yescharacteristic
43#3752—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3—21no—
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53#1489—91nomaximal, Sylow
54C2×#239—62no—
55C3×C4×Q8—22no—
56Q8×Dic3—62no—
57#893—62no—
58#893—64no—
59#892—62no—
60#892—64no—
61C4×D12—62no—
62C4×D12—64no—
63C42×D3—62no—
64C42×D3—64no—
65C22×C3⋊D3—21no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C32×Q8—21no—
68C32×Q8M1612yescomplemented
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C4⋊(C3⋊D3)—24no—
79C4⋊(C3⋊D3)—21no—
80C4⋊(C3⋊D3)M1612yescomplemented
81C4×C3⋊D3—24no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—21no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—41no—
89C4×C3⋊D3—41no—
90#622—24no—
91#622—42no—
92C4×#41—91no—
93#423—91no—
94C4×M16—91no—
95Q8⋊C8—92no—
96D4⋊C8—92no—
97C2×C3×Q8—22no—
98#239—68no—
99#239—68no—
100C2×D12—62no—
101C2×D12—64no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—64no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4—22no—
110C3×C42—24no—
111C3×C42—22no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—64no—
114(C2×D3)⋊C4—64no—
115C4⋊Dic3—62no—
116C4⋊Dic3—64no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—22no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3—41no—
128C2×C3⋊D3—41no—
129C32×C4—22no—
130C32×C4—21no—
131C32×C4—41no—
132C32×C4#10412yes—
133C32×C4C2×M1611yescharacteristic
134C32×C4C2×M1611yescharacteristic
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3—41no—
138C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
139C3⋊Dic3#13711yescharacteristic
140C2×#41—91no—
141C2×M16—181no—
142C2×M16—181no—
143C4×Q8—91no—
144C4×Q8#15711yescharacteristic
145C4×D4—91no—
146C4×D4—91no—
147C4×D4—181no—
148C4×D4—181no—
149#117—91no—
150#117—181no—
151C2×C42—91no—
152C2×C42—181no—
153C4⋊C8—92no—
154C4⋊C8—181no—
155#97—181no—
156C4×C8—92no—
157C22×D3—62no—
158C22×D3—64no—
159C3×Q8—24no—
160C3×Q8—24no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170D12—64no—
171D12—616no—
172D12—64no—
173C4×D3—616no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—124no—
179C4×D3—124no—
180C4×D3—124no—
181C4×D3—128no—
182C2×C32#40711yescharacteristic
183C2×C32#41711yescharacteristic
184C2×C32C2×#10411yescharacteristic
185C3⋊D3—41no—
186C3⋊D3—42no—
187#41—182no—
188#41—182no—
189C2×Q8C2×#15711yescharacteristic
190C2×D4—91no—
191C2×D4—181no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4—181no—
198M16—184no—
199M16—362no—
200C2×C8—182no—
201C2×C8—182no—
202C4⋊C4—21no—
203C4⋊C4—91no—
204C4⋊C4—181no—
205C4⋊C4C2×#15711yescharacteristic
206C22⋊C4—181no—
207C22⋊C4—181no—
208C22⋊C4—181no—
209C42—21no—
210C42—91no—
211C42—91no—
212C42—91no—
213C42—181no—
214C42—181no—
215C42C2×#15711yescharacteristic
216C22×C3—22no—
217C2×D3—68no—
218C2×D3—64no—
219C2×D3—122no—
220C2×D3—122no—
221C2×D3—124no—
222C2×D3—124no—
223C3×C4—28no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—24no—
227C3×C4—42no—
228C3×C4—44no—
229Dic3—62no—
230Dic3—62no—
231Dic3—64no—
232Dic3—122no—
233Dic3—124no—
234C32#148911yescharacteristic, complemented, Sylow
235C23—91no—
236C23—181no—
237Q8—21no—
238Q8#378812yescomplemented
239D4—92no—
240D4—184no—
241D4—181no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—184no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—182no—
253C2×C4—181no—
254C2×C4—361no—
255C2×C4—361no—
256C2×C4—362no—
257C2×C4C22⋊#15711yescharacteristic
258C2×C4C22⋊#15711yescharacteristic
259C2×C4C22×#15711yescharacteristic
260C8—184no—
261C8—362no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—22no—
265D3—124no—
266D3—128no—
267C22—182no—
268C22—181no—
269C22—181no—
270C22—181no—
271C22—361no—
272C22—361no—
273C22C2×C22⋊#15711yescharacteristic
274C4—22no—
275C4—21no—
276C4—41no—
277C4—91no—
278C4—91no—
279C4—181no—
280C4—181no—
281C4—361no—
282C4#6378512yes—
283C4C2×#378811yescharacteristic
284C4#6428311yescharacteristic
285C3—22no—
286C2—361no—
287C2—362no—
288C2#1059380311yescharacteristic
289C2C2×#6378511yescharacteristic
290C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×Q8#157
hypocenterC32#1489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10593728C2semidirect
3. C4×#3788C2semidirect
4. Q8⋊#622C2semidirect
5. #10590160C2semidirect
68. C32×Q8M16semidirect
80. C4⋊(C3⋊D3)M16semidirect
234. C32#1489semidirect
238. Q8#3788semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105937282
C4×#37882
Q8⋊#6222
#105901602
#14899