Finite Group Databasebeta

← #11774277

Subgroups — #11774277

Order 1152.

574 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593726C211yesmaximal, characteristic, complemented
3#10593725C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×#3832C411yescharacteristic
7C2×#3787—21no—
8C32×C4×Q8C411yescharacteristic
9Q8×C3⋊Dic3C2211yescharacteristic
10#64102—21no—
11#64102C2211yescharacteristic
12#64101—21no—
13#64101C411yescharacteristic
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C411yescharacteristic
16C42×C3⋊D3—21no—
17C42×C3⋊D3C2211yescharacteristic
18#63779—21no—
19#63779—21no—
20#63778—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×#239—62no—
24C2×C32×Q8C2×C411yescharacteristic
25#3832—22no—
26#3832C814yescomplemented
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#3787—42no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C42—21no—
41C32×C42C2×C411yescharacteristic
42#3752—21no—
43#3752—21no—
44#3752—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52#1477—91nomaximal, Sylow
53C2×#239—62no—
54C3×C4×Q8—22no—
55Q8×Dic3—62no—
56#893—62no—
57#893—64no—
58#892—62no—
59#892—64no—
60C4×D12—62no—
61C4×D12—64no—
62C42×D3—62no—
63C42×D3—64no—
64C22×C3⋊D3—21no—
65C22×C3⋊D3C22⋊C411yescharacteristic
66C32×Q8—21no—
67C32×Q8C2×C812yescomplemented
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4⋊(C3⋊D3)—24no—
78C4⋊(C3⋊D3)—21no—
79C4⋊(C3⋊D3)C2×C812yescomplemented
80C4×C3⋊D3—24no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—42no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3C2×C812yes—
88C4×C3⋊D3M1612yes—
89#622—42no—
90#622—42no—
91C4×#41—91no—
92#431—91no—
93C2×C4⋊C8—91no—
94Q8⋊C8—92no—
95D4⋊C8—92no—
96C2×C3×Q8—22no—
97#239—68no—
98#239—68no—
99C2×D12—62no—
100C2×D12—64no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C3×C4⋊C4—24no—
108C3×C4⋊C4—22no—
109C3×C42—24no—
110C3×C42—22no—
111(C2×D3)⋊C4—64no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—64no—
114C4⋊Dic3—62no—
115C4⋊Dic3—64no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—22no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—41no—
126C2×C3⋊D3—41no—
127C2×C3⋊D3C22⋊C812yes—
128C32×C4—22no—
129C32×C4—21no—
130C32×C4—21no—
131C32×C4—41no—
132C32×C4C22×C811yescharacteristic
133C32×C4C2×M1611yescharacteristic
134C3⋊Dic3—21no—
135C3⋊Dic3—41no—
136C3⋊Dic3C22⋊C812yes—
137C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
138C3⋊Dic3#13711yescharacteristic
139C2×#41—91no—
140C22×C8—181no—
141C4×Q8—91no—
142C4×Q8#15711yescharacteristic
143C4×D4—91no—
144C4×D4—91no—
145C4×D4—181no—
146C4×D4—181no—
147#117—91no—
148#117—181no—
149C2×C42—91no—
150C2×C42—181no—
151C4⋊C8—92no—
152C4⋊C8—181no—
153C4⋊C8—181no—
154C22⋊C8—181no—
155C4×C8—92no—
156C22×D3—62no—
157C22×D3—64no—
158C3×Q8—24no—
159C3×Q8—24no—
160C2×C3×C4—24no—
161C2×C3×C4—24no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—64no—
169D12—64no—
170D12—616no—
171D12—64no—
172C4×D3—64no—
173C4×D3—64no—
174C4×D3—616no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—124no—
178C4×D3—124no—
179C4×D3—124no—
180C4×D3—128no—
181C2×C32C2×C22⋊C811yescharacteristic
182C2×C32#41711yescharacteristic
183C2×C32#42111yescharacteristic
184C3⋊D3—22no—
185C3⋊D3—42no—
186#41—94no—
187#41—182no—
188C2×Q8C2×#15711yescharacteristic
189C2×D4—91no—
190C2×D4—181no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—181no—
195C22×C4—181no—
196C22×C4—181no—
197C2×C8—182no—
198C2×C8—182no—
199C2×C8—362no—
200C4⋊C4—21no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4C2×#15711yescharacteristic
204C22⋊C4—181no—
205C22⋊C4—181no—
206C22⋊C4—181no—
207C42—21no—
208C42—91no—
209C42—91no—
210C42—91no—
211C42—181no—
212C42—181no—
213C42C2×#15711yescharacteristic
214C22×C3—22no—
215C2×D3—64no—
216C2×D3—68no—
217C2×D3—122no—
218C2×D3—122no—
219C2×D3—124no—
220C2×D3—124no—
221C3×C4—28no—
222C3×C4—24no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—42no—
226C3×C4—44no—
227Dic3—64no—
228Dic3—62no—
229Dic3—62no—
230Dic3—122no—
231Dic3—124no—
232C32#147711yescharacteristic, complemented, Sylow
233C23—91no—
234C23—181no—
235Q8—21no—
236Q8#378712yescomplemented
237D4—92no—
238D4—184no—
239D4—181no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—91no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—184no—
250C2×C4—181no—
251C2×C4—361no—
252C2×C4—362no—
253C2×C4—361no—
254C2×C4—361no—
255C2×C4C22⋊#15711yescharacteristic
256C2×C4C22⋊#15711yescharacteristic
257C2×C4C22×#15711yescharacteristic
258C8—362no—
259C8—362no—
260C2×C3—22no—
261C2×C3—22no—
262C2×C3—22no—
263D3—124no—
264D3—128no—
265C22—92no—
266C22—181no—
267C22—181no—
268C22—182no—
269C22—361no—
270C22—361no—
271C22C2×C22⋊#15711yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—92no—
277C4—91no—
278C4—91no—
279C4—181no—
280C4—361no—
281C4C2×#378711yescharacteristic
282C4#6428311yescharacteristic
283C3—22no—
284C2—182no—
285C2—362no—
286C2#1059380011yescharacteristic
287C2#1059383111yescharacteristic
288C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×Q8#157
hypocenterC32#1477
LCSG ▷ 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. #10593726C2semidirect
3. #10593725C2semidirect
4. Q8⋊#622C2semidirect
5. #10590160C2semidirect
26. #3832C8semidirect
67. C32×Q8C2×C8semidirect
79. C4⋊(C3⋊D3)C2×C8semidirect
232. C32#1477semidirect
236. Q8#3787semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105937262
#105937252
Q8⋊#6222
#105901602
#14779