Finite Group Databasebeta

← C2×#10593754 #11861292

Subgroups — C2×#10593754 #11861292

Order 1152.

698 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 186 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×#64096C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic
4C2×#63777C211yesmaximal, characteristic
5C2×#63777C211yesmaximal, characteristic
6C2×C4⋊#622C211yesmaximal, characteristic
7C2×C4×#622C211yesmaximal, characteristic
8#10593754C218yesmaximal, direct product factor
9C22×#634C411yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C22×#622C2211yescharacteristic
14C2×C32×C4⋊C4C411yescharacteristic
15C2×#3750C411yescharacteristic
16C2×#3750C411yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64096C414yes—
21#64096C2214yes—
22#63779C2214yes—
23#63779C2214yes—
24#63777C2214yes—
25#63777C2214yes—
26C4⋊#622C2214yes—
27C4×#622C2214yes—
28C2×#887—62no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2311yescharacteristic
36C2×#634—24no—
37C2×#634C2×C414yes—
38C2×#622—22no—
39C2×#622—22no—
40C2×#622—22no—
41C2×#622Q814yescomplemented
42C2×#622C2312yes—
43C2×#622C2312yes—
44C2×#622C2312yes—
45C2×#622C2312yes—
46C32×C4⋊C4C2×C414yes—
47#3750C2×C414yes—
48#3750C2×C414yes—
49C4×C3⋊Dic3C2×C412yes—
50C4×C3⋊Dic3C2×C412yes—
51C4×C3⋊Dic3C2×C412yes—
52C4×C3⋊Dic3C2312yes—
53C4×C3⋊Dic3C2312yes—
54C4×C3⋊Dic3C2312yes—
55C2×#446—91nomaximal, Sylow
56C22×Dic6—62no—
57C2×C3×C4⋊C4—22no—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—62no—
61C2×C4×Dic3—62no—
62C2×C4×Dic3—62no—
63#887—68no—
64#887—68no—
65C23×C32C22×C411yescharacteristic
66C2×C32×C4—22no—
67C2×C32×C4—22no—
68C2×C32×C4—22no—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C22×C412yes—
71C2×C32×C4C22×C412yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3M1614yes—
75C2×C3⋊Dic3C22×C412yes—
76C2×C3⋊Dic3C22×C412yes—
77C2×C3⋊Dic3C22×C411yescharacteristic
78C2×C3⋊Dic3C22×C412yes—
79C2×C3⋊Dic3C2×Q812yes—
80C2×C3⋊Dic3#4112yes—
81C2×C3⋊Dic3C2411yescharacteristic
82#634—28no—
83#622—22no—
84#622—22no—
85#622—22no—
86#622C2×Q814yescomplemented
87C2×C4×Q8—91no—
88#446—98no—
89C2×C4⋊C8—91no—
90C2×C4⋊C8—91no—
91C2×C4⋊C8—91no—
92C2×#97—91no—
93C2×#97—91no—
94C2×C4×C8—91no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C22×Dic3—62no—
101C22×Dic3—62no—
102C2×Dic6—68no—
103C2×Dic6—616no—
104C3×C4⋊C4—28no—
105Dic3⋊C4—68no—
106Dic3⋊C4—68no—
107C4×Dic3—64no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C4×Dic3—64no—
111C4×Dic3—64no—
112C4×Dic3—64no—
113C22×C32C4×Q812yes—
114C22×C32C2×M1612yes—
115C22×C32#13112yes—
116C22×C32C23×C411yescharacteristic
117C32×C4—22no—
118C32×C4—22no—
119C32×C4—22no—
120C3⋊Dic3—22no—
121C3⋊Dic3—22no—
122C3⋊Dic3C4×Q812yes—
123C3⋊Dic3C2×M1614yes—
124C3⋊Dic3C22×Q811yescharacteristic
125C3⋊Dic3C2×#4111yescharacteristic
126C22×Q8—91no—
127C22×C8—91no—
128C22×C8—91no—
129C22×C8—91no—
130C22×C8—91no—
131C4×Q8—94no—
132C4×Q8—94no—
133C2×C4⋊C4—91no—
134C2×C4⋊C4—91no—
135C2×C4⋊C4#15711yescharacteristic
136C2×C42—91no—
137C2×C42—91no—
138C2×C42—91no—
139C4⋊C8—94no—
140C4⋊C8—94no—
141C4⋊C8—94no—
142#97—94no—
143#97—94no—
144C4×C8—94no—
145C23×C3—22no—
146C2×C3×C4—28no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—44no—
151C2×C3×C4—44no—
152C2×Dic3—68no—
153C2×Dic3—62no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—62no—
159C2×Dic3—64no—
160C2×Dic3—68no—
161C2×Dic3—124no—
162Dic6—632no—
163C2×C32#44614yescomplemented
164C2×C32C2×C4×Q811yescharacteristic
165C2×C32C22×M1611yescharacteristic
166C2×C32C2×#13111yescharacteristic
167C2×Q8—94no—
168C2×Q8—184no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4C2×#15711yescharacteristic
174C22×C4C2×#15711yescharacteristic
175C22×C4C2×#15711yescharacteristic
176C2×C8—92no—
177C2×C8—94no—
178C2×C8—92no—
179C2×C8—92no—
180C2×C8—92no—
181C2×C8—182no—
182C2×C8—182no—
183C2×C8—182no—
184C4⋊C4—94no—
185C4⋊C4—94no—
186C4⋊C4C2×#15714yes—
187C42—92no—
188C42—92no—
189C42—92no—
190C42—92no—
191C42—92no—
192C42—92no—
193C22×C3—24no—
194C22×C3—24no—
195C22×C3—24no—
196C22×C3—22no—
197C3×C4—28no—
198C3×C4—44no—
199C3×C4—44no—
200Dic3—68no—
201Dic3—64no—
202Dic3—62no—
203Dic3—62no—
204Dic3—68no—
205Dic3—124no—
206C32C2×#44611yescharacteristic, complemented, Sylow
207C23C22×#15711yescharacteristic
208Q8—188no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—94no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—92no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—182no—
221C2×C4—182no—
222C2×C4C22×#15712yes—
223C2×C4C22×#15712yes—
224C2×C4C22×#15712yes—
225C8—94no—
226C8—182no—
227C8—182no—
228C8—182no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—28no—
233C22#6428312yes—
234C22#6428712yes—
235C22Q8×#15712yes—
236C22C23×#15711yescharacteristic
237C4—22no—
238C4—22no—
239C4—22no—
240C4—94no—
241C4—91no—
242C4—91no—
243C4—92no—
244C4—182no—
245C4—182no—
246C3—22no—
247C2#1059375414yesdirect product factor
248C2C2×#6428311yescharacteristic
249C2C2×#6428711yescharacteristic
250C2C2×Q8×#15711yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#446
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #10593754C2direct (N × H)
41. C2×#622Q8semidirect
86. #622C2×Q8semidirect
163. C2×C32#446semidirect
206. C32C2×#446semidirect
247. C2#10593754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#637792
C2×#637772
C2×C4⋊#6222
C2×C4×#6222
#105937542
C2×#4469