Finite Group Databasebeta

← #17949261

Subgroups — #17949261

Order 4352.

252 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543881C211yesmaximal, characteristic
2#14543715C211yesmaximal, characteristic
3#14529884C211yesmaximal, characteristic
4C2×#10587545—21no—
5#11763654—21no—
6C22×#63231—21no—
7C2×#10587506—21no—
8#11762715C2211yescharacteristic
9#11762564C411yescharacteristic
10C2×C17×C4⋊Q8C411yescharacteristic
11C22×Q8×C17—21no—
12C22×Dic34D411yescharacteristic
13C2×#63247—41no—
14C17×C4⋊Q8—42no—
15C2×C4⋊C4×C17—41no—
16C2×C42×C17C2×C411yescharacteristic
17C2×#63231—42no—
18C2×#63231—42no—
19C2×#63231—41no—
20C2×#63231—41no—
21C2×C4⋊Dic17D411yescharacteristic
22C22×#3622—21no—
23C22⋊#3624—41no—
24#10587545—22no—
25#10587545—41no—
26#10587506—42no—
27#10587502—41no—
28C2×Q8×C17—22no—
29C2×Q8×C17—41no—
30C2×Q8×C17—41no—
31C2×Q8×C17—41no—
32C2×Q8×C17—41no—
33C2×Q8×C17—41no—
34C22×C4×C17—21no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17—21no—
38C22×Dic17—21no—
39C2×Dic34—21no—
40C2×Dic34—41no—
41C2×Dic34—41no—
42C2×Dic34D811yescharacteristic
43C2×Dic34SD1611yescharacteristic
44#63247—42no—
45#63247—81no—
46C2×#3624—81no—
47C2×#3624—81no—
48C4⋊C4×C17—42no—
49C4⋊C4×C17—42no—
50C42×C17—41no—
51#63231—44no—
52#63231—44no—
53C4⋊Dic17—41no—
54C2×#3622—22no—
55C2×#3622—41no—
56C2×#3622—41no—
57#7405—171nomaximal, Sylow
58C23×C17#9911yescharacteristic
59Q8×C17—42no—
60Q8×C17—42no—
61Q8×C17—81no—
62Q8×C17—81no—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—22no—
66C2×C4×C17—41no—
67C2×C4×C17—41no—
68C2×C4×C17—42no—
69C2×C4×C17—81no—
70C2×C4×C17—81no—
71C2×C4×C17#10211yescharacteristic
72C2×C4×C17#10411yescharacteristic
73C2×Dic17—21no—
74C2×Dic17—21no—
75C2×Dic17—41no—
76C2×Dic17—41no—
77C2×Dic17—41no—
78C2×Dic17—81no—
79Dic34—41no—
80Dic34—41no—
81Dic34—81no—
82#3624—82no—
83#3624—161no—
84#3622—42no—
85#2016—171no—
86#1394—171no—
87#1319—171no—
88C22×C17—21no—
89C22×C17—21no—
90C22×C17#32711yescharacteristic
91C22×C17AΣL(1,𝔽16)11yescharacteristic
92C22×C17#35311yescharacteristic
93C4×C17—21no—
94C4×C17—21no—
95C4×C17—42no—
96C4×C17—82no—
97Dic17—41no—
98Dic17—41no—
99Dic17—81no—
100C22×Q16—341no—
101C2×C4⋊Q8#59511yescharacteristic
102C2×#103—341no—
103C2×#101—341no—
104#391—171no—
105#336—171no—
106#324—341no—
107C2×C17—21no—
108C2×C17—21no—
109C2×C17#134311yescharacteristic
110C2×C17#140711yescharacteristic
111C2×C17#141111yescharacteristic
112C22×Q8—21no—
113C22×Q8—171no—
114C2×Q16—682no—
115C2×Q16—682no—
116C2×Q16—681no—
117C2×Q16—681no—
118C2×M16—681no—
119C22×C8—341no—
120C4⋊Q8—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—171no—
123C2×C42C2×#59511yescharacteristic
124#103—682no—
125#101—342no—
126#101—681no—
127C22⋊C8—681no—
128#95—681no—
129C17#740511yescharacteristic, complemented, Sylow
130C2×Q8—22no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—171no—
137C2×Q8—171no—
138C2×Q8—341no—
139C2×Q8—681no—
140C2×Q8—681no—
141C22×C4—21no—
142C22×C4—41no—
143C22×C4—341no—
144C22×C4—341no—
145C22×C4C22⋊#59511yescharacteristic
146Q16—684no—
147Q16—684no—
148M16—682no—
149M16—1361no—
150C2×C8—342no—
151C2×C8—681no—
152C2×C8—681no—
153C2×C8—1361no—
154C2×C8—1361no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—681no—
158C42—41no—
159C23#1058755111yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—81no—
163Q8—81no—
164Q8—681no—
165Q8—681no—
166Q8—1361no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—341no—
176C2×C4—341no—
177C2×C4—681no—
178C2×C4—681no—
179C2×C4—681no—
180C2×C4—1361no—
181C2×C4#1058754711yescharacteristic
182C2×C4#1058754811yescharacteristic
183C8—2721no—
184C8—682no—
185C8—1362no—
186C22—21no—
187C22—21no—
188C22#1176366011yescharacteristic
189C22#1176370911yescharacteristic
190C22#1176371311yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—82no—
195C4—681no—
196C4—681no—
197C4—1361no—
198C2—21no—
199C2—21no—
200C2#1454376211yescharacteristic
201C2#1454391311yescharacteristic
202C2#1454392111yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17#353
prime radicalC23×C17#99
cosocle#11762715C22
hypercenterC2×C4⋊Q8#595
hypocenterC17#7405
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
129. C17#7405semidirect

Maximal subgroups

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

subgroupindex
#145438812
#145437152
#145298842
#740517