Finite Group Databasebeta

← #17981556

Subgroups — #17981556

Order 4352.

440 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 89 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#14545927C212yesmaximal
2#14545785C214yesmaximal
3C4⋊Q8×#595C211yesmaximal, characteristic
4(C2×#3633)⋊C4—22no—
5(C2×#3633)⋊C4—22no—
6(C2×#3633)⋊C4C2214yes—
7C2×Q8×#595C412yes—
8(C2×#595)⋊Q8C2212yes—
9#11763760—22no—
10#11763755C411yescharacteristic
11C4⋊C4×#595—22no—
12C42×#595C2211yescharacteristic
13C4⋊Q8×D17C411yescharacteristic
14C22×#3633—24no—
15C2×Q8×D17C2×C412yes—
16Q8×#595—44no—
17C2×C4⋊#595—22no—
18C2×C4⋊#595—22no—
19C2×C4⋊#595C2×C412yes—
20C2×C4×#595—22no—
21C2×C4×#595C2×C411yescharacteristic
22C2×C4×#595D412yes—
23C2×C4×#595D412yes—
24C2×C4×#595C2311yescharacteristic
25C17×C4⋊Q8C811yescharacteristic, complemented
26#10587630C812yescomplemented
27C4⋊C4×D17—22no—
28#10587574—22no—
29C42×D17C2×C411yescharacteristic
30#10587555C811yescharacteristic, complemented
31(C2×#595)⋊C4—24no—
32C22×#595—22no—
33C22×#595C22⋊C411yescharacteristic
34C22×#595C22⋊C411yescharacteristic
35C22×#595C2×D412yes—
36C2×#3633—44no—
37C2×#3633—44no—
38C2×#3633—44no—
39C2×Q8×C17C2×C812yes—
40Q8×D17—42no—
41Q8×D17—42no—
42C2×C4×D17—22no—
43C2×C4×D17C22⋊C412yes—
44C2×C4×D17C22×C411yescharacteristic
45C2×Dic34—22no—
46C2×Dic34C2×C812yes—
47C4⋊#595—42no—
48C4⋊#595—44no—
49C4⋊#595—44no—
50C4×#595—22no—
51C4×#595—24no—
52C4×#595—42no—
53C4×#595—41no—
54C4×#595—44no—
55C4⋊C4×C17—22no—
56C42×C17C2×C811yescharacteristic
57C4⋊Dic17—22no—
58#63225—24no—
59C4×Dic17C2×C811yescharacteristic
60C4×Dic17M1612yes—
61#7605—171nomaximal, Sylow
62C22×D17C2×C22⋊C411yescharacteristic
63C2×#595—22no—
64C2×#595—22no—
65C2×#595—22no—
66C2×#595—21no—
67C2×#595—22no—
68C2×#595—42no—
69C2×#595—44no—
70C2×#595#10012yes—
71C2×#595#13714yes—
72#3633—84no—
73Q8×C17—42no—
74C2×C4×C17—22no—
75C2×C4×C17C22⋊C812yes—
76C2×C4×C17C22×C811yescharacteristic
77C2×Dic17—22no—
78C2×Dic17C22⋊C812yes—
79C2×Dic17C2×M1611yescharacteristic
80C4×D17—21no—
81C4×D17—21no—
82C4×D17—22no—
83C4×D17—22no—
84C4×D17—42no—
85C4×D17—42no—
86Dic34—44no—
87Dic34—42no—
88C4×C4⋊Q8—171no—
89#1839—172no—
90#1272—174no—
91C22×C17C2×C22⋊C811yescharacteristic
92C2×D17#41011yescharacteristic
93C2×D17C2×#10011yescharacteristic
94C2×D17#41912yes—
95C2×D17#42112yes—
96#595—22no—
97#595—24no—
98#595—41no—
99#595—82no—
100C4×C17—21no—
101C4×C17—22no—
102C4×C17—42no—
103Dic17—21no—
104Dic17—22no—
105Dic17—42no—
106C2×C4⋊Q8—171no—
107C2×C4×Q8—172no—
108#391—172no—
109#389—342no—
110#384—171no—
111C4×C4⋊C4—342no—
112C43—171no—
113#336—174no—
114#336—342no—
115#336—342no—
116C2×C17#146011yescharacteristic
117C2×C17#147912yes—
118D17#151512yes—
119D17#153611yescharacteristic
120D17#155811yescharacteristic
121C22×Q8—172no—
122C22×C8—344no—
123C4⋊Q8—172no—
124C4⋊Q8—171no—
125C4⋊Q8—342no—
126C4⋊Q8#363311yescharacteristic, complemented
127C4×Q8—684no—
128C2×C4⋊C4—172no—
129C2×C4⋊C4—342no—
130C2×C4⋊C4—342no—
131C2×C4⋊C4—342no—
132C2×C42—171no—
133C2×C42—171no—
134C2×C42—172no—
135C2×C42—172no—
136C2×C42—171no—
137C2×C42—342no—
138#95—344no—
139C17#760511yescharacteristic, complemented, Sylow
140C2×Q8—172no—
141C2×Q8—342no—
142C2×Q8—682no—
143C2×Q8—682no—
144C2×Q8C2×#363312yes—
145C22×C4—171no—
146C22×C4—172no—
147C22×C4—172no—
148C22×C4—171no—
149C22×C4—171no—
150C22×C4—342no—
151C22×C4—342no—
152C2×C8—684no—
153C2×C8—684no—
154C2×C8—684no—
155C4⋊C4—22no—
156C4⋊C4—344no—
157C4⋊C4—342no—
158C4⋊C4—682no—
159C4⋊C4—684no—
160C4⋊C4—684no—
161C42—172no—
162C42—171no—
163C42—344no—
164C42—342no—
165C42—684no—
166C42—682no—
167C42—681no—
168C42C2×#363311yescharacteristic
169C23—171no—
170Q8—42no—
171Q8—682no—
172Q8—684no—
173C2×C4—22no—
174C2×C4—172no—
175C2×C4—174no—
176C2×C4—172no—
177C2×C4—171no—
178C2×C4—341no—
179C2×C4—342no—
180C2×C4—342no—
181C2×C4—341no—
182C2×C4—342no—
183C2×C4—342no—
184C2×C4—342no—
185C2×C4—341no—
186C2×C4—342no—
187C2×C4—342no—
188C2×C4—682no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4—684no—
192C2×C4C22⋊#363312yes—
193C2×C4C22×#363311yescharacteristic
194C8—1364no—
195C22—171no—
196C22—171no—
197C22—172no—
198C22—172no—
199C22C2×C22⋊#363311yescharacteristic
200C4—21no—
201C4—22no—
202C4—42no—
203C4—344no—
204C4—342no—
205C4—341no—
206C4—342no—
207C4—681no—
208C4—682no—
209C4—1362no—
210C2—171no—
211C2—172no—
212C2—171no—
213C2#1454589811yescharacteristic
214C2#1454590512yes—
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC2×C4×C17C22×C8
FrattiniC2×C4C22×#3633
FittingC17×C4⋊Q8C8
socleC22×C17C2×C22⋊C8
prime radicalC22×D17C2×C22⋊C4
cosocleC2×C4×#595C23
hypercenterC4⋊Q8#3633
hypocenterC17#7605
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
25. C17×C4⋊Q8C8semidirect
26. #10587630C8semidirect
30. #10587555C8semidirect
126. C4⋊Q8#3633semidirect
139. C17#7605semidirect

Maximal subgroups

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

subgroupindex
#145459272
#145457852
C4⋊Q8×#5952
#760517