Finite Group Databasebeta

← #11785295

Subgroups — #11785295

Order 1152.

454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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×Q8×#157C211yesmaximal, characteristic
2#10593344C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic
4#10591552C212yesmaximal
5#10590049C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7Q8×#157—22no—
8Q8×#157C414yescomplemented
9C2×C4⋊#157—21no—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×C4×#157C2211yescharacteristic
13#63900C2212yes—
14C2×#3710C2212yes—
15#63737—21no—
16#63737—21no—
17#63732—22no—
18C3×#835—22no—
19#63567—22no—
20D3×#103—62no—
21C22×#157—21no—
22C22×#157D411yescharacteristic
23C22×#157D411yescharacteristic
24C2×C32×Q8D411yescharacteristic
25Q8×C3⋊D3—21no—
26Q8×C3⋊D3—21no—
27Q8×C3⋊D3C2×C412yes—
28Q8×C3⋊D3Q812yes—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#634—21no—
32C2×#634D411yescharacteristic
33C2×#624—22no—
34C4⋊#157—24no—
35C4⋊#157—21no—
36C4⋊#157C2×C412yes—
37C4×#157—24no—
38C4×#157C2×C412yes—
39C4×#157D412yes—
40C3×C4⋊Dic3—22no—
41C2×C3×C3⋊C8—22no—
42#3724—22no—
43#3710—22no—
44#3710—22no—
45#1805—91nomaximal, Sylow
46C2×D3×Q8—62no—
47C2×D3×C8—62no—
48D3×C4⋊C4—62no—
49C3×#103—62no—
50#835—22no—
51#816—62no—
52#810—62no—
53C22×C3⋊D3C2×D411yescharacteristic
54C2×#157—22no—
55C2×#157—22no—
56C2×#157—22no—
57C2×#157—42no—
58C2×#157C22⋊C412yes—
59C2×#157C22⋊C412yes—
60C32×Q8—21no—
61C32×Q8C4⋊C412yes—
62C2×C32×C4—21no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3#4111yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3C22×C411yescharacteristic
69C4×C3⋊D3C2×D411yescharacteristic
70C4×C3⋊D3C2×Q811yescharacteristic
71C4×C3⋊D3#4111yescharacteristic
72#634—21no—
73#634—22no—
74#634—22no—
75#634C4⋊C412yes—
76C2×C3×Dic3—42no—
77#624—42no—
78#624—42no—
79C3×C3⋊C8—42no—
80C2×C4×Q8—91no—
81C2×C4⋊C8—91no—
82C2×#103—92no—
83#382—91no—
84#340—92no—
85C2×C3×Q8—22no—
86D3×Q8—64no—
87D3×Q8—64no—
88D3×Q8—122no—
89D3×Q8—122no—
90C2×C4×D3—62no—
91C2×C4×D3—122no—
92C2×C4×D3—122no—
93C2×Dic6—62no—
94C2×Dic6—122no—
95C2×C3×C8—62no—
96C3×C4⋊C4—62no—
97C4⋊Dic3—22no—
98Dic3⋊C4—122no—
99C2×C3⋊C8—22no—
100D3×C8—122no—
101D3×C8—122no—
102C22×C32#12111yescharacteristic
103C2×C3⋊D3C2×C22⋊C411yescharacteristic
104C2×C3⋊D3C22⋊Q811yescharacteristic
105C2×C3⋊D3#13512yes—
106C2×C3⋊D3#13712yes—
107#157—22no—
108#157—22no—
109#157—42no—
110C32×C4—22no—
111C32×C4C2×C4⋊C411yescharacteristic
112C32×C4#12111yescharacteristic
113C3⋊Dic3—22no—
114C3⋊Dic3#11711yescharacteristic
115C3⋊Dic3C22⋊Q811yescharacteristic
116C3×Dic3—82no—
117C22×Q8—91no—
118C22×C8—92no—
119C4×Q8—94no—
120C4×Q8—182no—
121C2×C4⋊C4—92no—
122C2×C4⋊C4—91no—
123C2×C4⋊C4—181no—
124C2×C42—91no—
125C2×C42—181no—
126C4⋊C8—182no—
127#103—62no—
128#103—182no—
129#95—181no—
130#95—181no—
131C22×D3—62no—
132C3×Q8—24no—
133C3×Q8—42no—
134C2×C3×C4—22no—
135C2×C3×C4—42no—
136C2×C3×C4—122no—
137C2×Dic3—42no—
138C2×Dic3—62no—
139C2×Dic3—122no—
140C4×D3—62no—
141C4×D3—62no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—124no—
145C4×D3—124no—
146C4×D3—242no—
147C4×D3—242no—
148Dic6—64no—
149Dic6—124no—
150Dic6—124no—
151Dic6—122no—
152C3×C8—122no—
153C3⋊C8—42no—
154C2×C32#38011yescharacteristic
155C2×C32#46412yes—
156C3⋊D3#41611yescharacteristic
157C3⋊D3#41911yescharacteristic
158C3⋊D3#47912yes—
159C2×Q8—92no—
160C2×Q8—92no—
161C2×Q8—91no—
162C2×Q8—181no—
163C2×Q8—181no—
164C2×Q8—181no—
165C2×Q8GO+(4,𝔽2)11yescharacteristic
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—181no—
170C22×C4—182no—
171C22×C4—181no—
172C2×C8—62no—
173C2×C8—182no—
174C2×C8—182no—
175C4⋊C4—62no—
176C4⋊C4—92no—
177C4⋊C4—182no—
178C4⋊C4—181no—
179C4⋊C4—184no—
180C42—92no—
181C42—92no—
182C42—184no—
183C22×C3—22no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—62no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—62no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—44no—
193C3×C4—242no—
194Dic3—62no—
195Dic3—62no—
196Dic3—82no—
197Dic3—124no—
198C32#180511yescharacteristic, complemented, Sylow
199C23—91no—
200Q8—21no—
201Q8—92no—
202Q8—182no—
203Q8—182no—
204Q8—181no—
205Q8#377312yes—
206C2×C4—21no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—122no—
215C2×C4—182no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4—182no—
219C2×C4—181no—
220C2×C4—182no—
221C2×C4—362no—
222C2×C4—362no—
223C2×C4—362no—
224C2×C4C2×GO+(4,𝔽2)11yescharacteristic
225C8—122no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229D3—62no—
230D3—62no—
231D3—62no—
232D3—62no—
233C22—92no—
234C22—92no—
235C22—91no—
236C22—91no—
237C22#6424211yescharacteristic
238C4—22no—
239C4—91no—
240C4—91no—
241C4—182no—
242C4—182no—
243C4—182no—
244C4—242no—
245C4—362no—
246C4C2×#377311yescharacteristic
247C4#6424211yescharacteristic
248C3—22no—
249C2—91no—
250C2—91no—
251C2—92no—
252C2#1059347412yes—
253C2#1059351611yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1805
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
8. Q8×#157C4semidirect
198. C32#1805semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
#105933442
C2×#637322
#105915522
#105900492
#18059