Finite Group Databasebeta

← #11796289

Subgroups — #11796289

Order 1152.

702 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 157 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#10596296C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic
3#10592936C211yesmaximal, characteristic
4#10589338C214yesmaximal, complemented
5#70058—34nomaximal
6C2×C32×#41C2211yescharacteristic
7C22×#634C411yescharacteristic, complemented
8C32×#117—21no—
9#64153—21no—
10#64145—21no—
11#64144C412yescomplemented
12#64144C2212yes—
13#64135C411yescharacteristic, complemented
14#64133—21no—
15#64133—21no—
16C2×#3748—21no—
17C32×#99—21no—
18C32×#99C2212yes—
19#63663—21no—
20#63660C2212yes—
21#5825—34no—
22C3×#410D314yes—
23#5237—34no—
24#4472—316no—
25C32×#41—41no—
26C32×#41—41no—
27C2×C32×Q8D411yescharacteristic
28C2×C32×D4C2×C411yescharacteristic
29C2×C32×D4D411yescharacteristic
30C2×C32×D4C2311yescharacteristic
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C3⋊Dic3C2×C412yes—
35C2×#634—21no—
36C2×#634—21no—
37C2×#634—41no—
38C2×#634—41no—
39C32×C4⋊C4—41no—
40C32×C22⋊C4—22no—
41C32×C42—41no—
42#3757—22no—
43#3757—22no—
44#3757C2×C412yes—
45C4⋊(C3⋊Dic3)—21no—
46#3750—22no—
47#3750—22no—
48C4×C3⋊Dic3—21no—
49#3748—22no—
50#3748—41no—
51C2×C3⋊(C3⋊C8)—41no—
52#2123—91noSylow
53C2×C3×#41C2×D314yes—
54C22×Dic6—34no—
55C3×#117—24no—
56#944—64no—
57#936—64no—
58#935—38no—
59#935—38no—
60#926—34no—
61#924—64no—
62#924—64no—
63C2×#208—64no—
64C3×#99—24no—
65C3×#99C2×D318yes—
66#836—64no—
67#833—38no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22×C411yescharacteristic
70C23×C32C2×D411yescharacteristic
71C32×Q8—41no—
72C32×D4—41no—
73C32×D4—41no—
74C32×D4—41no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—42no—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—42no—
89#634—42no—
90#634—41no—
91#634—41no—
92C3⋊(C3⋊C8)—42no—
93#536—91no—
94#413—91no—
95#410C3⋊D311yescharacteristic
96#352—94no—
97C3×#41—44no—
98C3×#41—44no—
99C2×C3×Q8D1214yes—
100C2×C3×D4C4×D314yes—
101C2×C3×D4#6714yes—
102C2×C3×D4C22×D314yes—
103C22×C3×C4C4×D314yes—
104C22×C3×C4D1214yes—
105C22×C3×C4#6714yes—
106C22×Dic3—38no—
107C2×Dic6—64no—
108C2×Dic6—64no—
109C2×Dic6—124no—
110C2×Dic6—124no—
111C3×C4⋊C4—44no—
112C3×C22⋊C4—28no—
113C3×C42—44no—
114#217—38no—
115#217—68no—
116#217—68no—
117C4⋊Dic3—64no—
118Dic3⋊C4—68no—
119Dic3⋊C4—68no—
120C4×Dic3—64no—
121#208—68no—
122#208—124no—
123C2×C3⋊C8—124no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32—41no—
130C22×C32C2×C22⋊C411yescharacteristic
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—21no—
134C32×C4—82no—
135C32×C4#9911yescharacteristic
136C32×C4#9911yescharacteristic
137C3⋊Dic3—42no—
138C3⋊Dic3—42no—
139C2×#41C2×C3⋊D311yescharacteristic
140C22×Q8—91no—
141C2×M16—181no—
142C4⋊Q8—181no—
143#124—181no—
144#123—92no—
145#123—92no—
146C22⋊Q8—181no—
147C22⋊Q8—181no—
148#117—21no—
149#117—91no—
150#101—181no—
151#100—92no—
152#99—21no—
153#99C2×C3⋊D312yes—
154C23×C3(C2×D3)⋊C414yes—
155C23×C3C2×C4×D314yes—
156C23×C3C2×#6714yes—
157C3×Q8—44no—
158C3×D4—44no—
159C3×D4—44no—
160C3×D4—44no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—24no—
167C2×C3×C4—48no—
168C2×C3×C4(C2×D3)⋊C414yes—
169C2×C3×C4(C2×D3)⋊C414yes—
170C2×C3×C4(C2×D3)⋊C414yes—
171C2×C3×C4C2×D1214yes—
172C2×Dic3—68no—
173C2×Dic3—68no—
174C2×Dic3—128no—
175Dic6—128no—
176Dic6—124no—
177Dic6—124no—
178C3⋊C8—128no—
179C2×C32—21no—
180C2×C32—41no—
181C2×C32—41no—
182C2×C32—41no—
183C2×C32C2×#9911yescharacteristic
184#41—41no—
185#41—41no—
186C2×Q8—181no—
187C2×Q8—181no—
188C2×Q8—361no—
189C2×Q8—361no—
190C2×Q8C4⋊(C3⋊D3)11yescharacteristic
191C2×D4C4×C3⋊D311yescharacteristic
192C2×D4#63811yescharacteristic
193C2×D4C22×C3⋊D311yescharacteristic
194C22×C4—92no—
195C22×C4C4×C3⋊D311yescharacteristic
196C22×C4C4⋊(C3⋊D3)11yescharacteristic
197C22×C4#63811yescharacteristic
198M16—182no—
199M16—361no—
200C2×C8—361no—
201C4⋊C4—41no—
202C4⋊C4—182no—
203C4⋊C4—181no—
204C4⋊C4—182no—
205C22⋊C4—22no—
206C22⋊C4—92no—
207C22⋊C4—182no—
208C22⋊C4—182no—
209C42—41no—
210C42—181no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3—44no—
217C22×C3C2×(C2×D3)⋊C414yes—
218C3×C4—24no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—88no—
222C3×C4#80614yes—
223C3×C4#80614yes—
224Dic3—128no—
225Dic3—128no—
226C32#212311yescharacteristic, complemented, Sylow
227C23#375211yescharacteristic
228C23C2×C4×C3⋊D311yescharacteristic
229C23C2×#63811yescharacteristic
230Q8—41no—
231Q8—362no—
232Q8—361no—
233Q8—361no—
234D4—41no—
235D4—41no—
236D4—41no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—182no—
245C2×C4—182no—
246C2×C4—362no—
247C2×C4#375211yescharacteristic
248C2×C4#375211yescharacteristic
249C2×C4#375211yescharacteristic
250C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
251C8—362no—
252C2×C3—24no—
253C2×C3—44no—
254C2×C3—44no—
255C2×C3—44no—
256C2×C3C2×#80614yes—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22C2×#375211yescharacteristic
264C4—21no—
265C4—21no—
266C4—21no—
267C4—82no—
268C4—362no—
269C4—362no—
270C4#6363311yescharacteristic
271C4#6363311yescharacteristic
272C3#7005814yescomplemented
273C2—21no—
274C2—41no—
275C2—41no—
276C2—41no—
277C2C2×#6363311yescharacteristic
subgroupG/H
centerC2C2×#63633
commutatorC23×C32C22×C4
FrattiniC2×D4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32C2×#99
prime radicalC2×C32×#41C22
cosocleC2×C32×D4C23
hypercenter#410C3⋊D3
hypocenterC32#2123
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
4. #10589338C2semidirect
7. C22×#634C4semidirect
11. #64144C4semidirect
13. #64135C4semidirect
226. C32#2123semidirect
272. C3#70058semidirect

Maximal subgroups

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

subgroupindex
#105962962
C32×#4102
#105929362
#105893382
#700583