Finite Group Databasebeta

← #11774276

Subgroups — #11774276

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×#3830C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic, complemented
3#10593725C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590161C212yesmaximal, complemented
6C2×#3830C411yescharacteristic
7C2×#3787—21no—
8C32×C4×D4C411yescharacteristic
9D4×C3⋊Dic3C2211yescharacteristic
10C4×#638—21no—
11C2×C4×C3⋊Dic3—21no—
12#64101C411yescharacteristic
13#64096C2211yescharacteristic
14#64090—21no—
15#64086—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634C411yescharacteristic
18#63779—21no—
19#63779—21no—
20#63778—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×#237—62no—
24C2×C32×D4C2×C411yescharacteristic
25C22×C32×C4—21no—
26C2×#638—21no—
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29#3830—22no—
30#3830C814yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#634C2×C411yescharacteristic
35C2×#622—22no—
36C2×#622—22no—
37#3787—42no—
38C32×C4⋊C4C2×C411yescharacteristic
39C32×C22⋊C4—21no—
40C32×C42C2×C411yescharacteristic
41#3757—21no—
42#3752—21no—
43C4⋊(C3⋊Dic3)C2×C411yescharacteristic
44#3750—21no—
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52#1477—91nomaximal, Sylow
53C2×#237—62no—
54C3×C4×D4—22no—
55D4×Dic3—62no—
56C4×#67—64no—
57C2×C4×Dic3—64no—
58#892—62no—
59#887—62no—
60#67⋊C4—64no—
61#877—64no—
62C42×D3—62no—
63C4×Dic6—62no—
64C23×C32—21no—
65C22×C3⋊D3C22⋊C411yescharacteristic
66C32×D4—21no—
67C32×D4C2×C812yescomplemented
68C2×C32×C4—21no—
69C2×C32×C4—42no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73#638—24no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C2×D411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3C2×C812yes—
86C4×C3⋊D3M1612yes—
87#634—21no—
88#634C2×C812yescomplemented
89#622—42no—
90#622—42no—
91C4×#41—91no—
92#431—91no—
93C2×C4⋊C8—91no—
94Q8⋊C8—92no—
95D4⋊C8—92no—
96C2×C3×D4—22no—
97C22×C3×C4—24no—
98C2×#67—64no—
99C22×Dic3—64no—
100C22×Dic3—64no—
101#237—68no—
102#237—68no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×Dic6—62no—
107C3×C4⋊C4—22no—
108C3×C22⋊C4—24no—
109C3×C42—22no—
110#217—64no—
111(C2×D3)⋊C4—64no—
112C4⋊Dic3—62no—
113Dic3⋊C4—64no—
114Dic3⋊C4—64no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C22×C32—22no—
122C22×C32—41no—
123C22×C32—41no—
124C22×C32C2×C22⋊C411yescharacteristic
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3C22⋊C812yes—
128C32×C4—21no—
129C32×C4—21no—
130C32×C4—41no—
131C32×C4C22×C811yescharacteristic
132C32×C4C2×M1611yescharacteristic
133C3⋊Dic3—22no—
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—91no—
143C4×D4—91no—
144C4×D4—181no—
145C4×D4—181no—
146C4×D4#15711yescharacteristic
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—
156C23×C3—24no—
157C22×D3—62no—
158C3×D4—24no—
159C3×D4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—48no—
165#67—616no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170C2×Dic3—616no—
171C2×Dic3—64no—
172C2×Dic3—124no—
173C2×Dic3—124no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—124no—
179Dic6—64no—
180Dic6—64no—
181C2×C32—42no—
182C2×C32C2×C22⋊C811yescharacteristic
183C2×C32#41711yescharacteristic
184C2×C32#42111yescharacteristic
185C3⋊D3—22no—
186#41—94no—
187#41—182no—
188C2×Q8—91no—
189C2×D4—181no—
190C2×D4C2×#15711yescharacteristic
191C22×C4—21no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—181no—
196C22×C4—181no—
197C2×C8—182no—
198C2×C8—182no—
199C2×C8—362no—
200C4⋊C4—91no—
201C4⋊C4—181no—
202C4⋊C4—181no—
203C4⋊C4C2×#15711yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—181no—
206C22⋊C4—181no—
207C42—91no—
208C42—91no—
209C42—91no—
210C42—181no—
211C42—181no—
212C42—181no—
213C42C2×#15711yescharacteristic
214C22×C3—28no—
215C22×C3—22no—
216C22×C3—44no—
217C22×C3—44no—
218C2×D3—64no—
219C2×D3—122no—
220C2×D3—122no—
221C3×C4—24no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—42no—
225C3×C4—44no—
226Dic3—64no—
227Dic3—62no—
228Dic3—62no—
229Dic3—68no—
230Dic3—122no—
231Dic3—124no—
232C32#147711yescharacteristic, complemented, Sylow
233C23—21no—
234C23—91no—
235Q8—92no—
236Q8—181no—
237D4—21no—
238D4—184no—
239D4#378712yescomplemented
240C2×C4—21no—
241C2×C4—42no—
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—181no—
252C2×C4—361no—
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—
263C2×C3—48no—
264D3—124no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—92no—
269C22—181no—
270C22—181no—
271C22C2×C22⋊#15711yescharacteristic
272C4—21no—
273C4—21no—
274C4—41no—
275C4—92no—
276C4—91no—
277C4—91no—
278C4—182no—
279C4—181no—
280C4—361no—
281C4C2×#378711yescharacteristic
282C4#6428311yescharacteristic
283C3—22no—
284C2—42no—
285C2—182no—
286C2#1059380011yescharacteristic
287C2#1059381611yescharacteristic
288C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×D4#157
hypocenterC32#1477
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593726C2semidirect
3. #10593725C2semidirect
4. D4⋊#622C2semidirect
5. #10590161C2semidirect
30. #3830C8semidirect
67. C32×D4C2×C8semidirect
88. #634C2×C8semidirect
232. C32#1477semidirect
239. D4#3787semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105937262
#105937252
D4⋊#6222
#105901612
#14779