Finite Group Databasebeta

← #17962230

Subgroups — #17962230

Order 4352.

274 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11763735C211yesmaximal, characteristic
2#14544992C211yesmaximal, characteristic
3#14544902C212yesmaximal
4#14543860C212yesmaximal
5D17×#368C211yesmaximal, characteristic
6#11763865C2211yescharacteristic
7#11763820—22no—
8C2×#10587534C2212yes—
9#11763772C2211yescharacteristic
10#11763735—21no—
11#11763735—21no—
12#11763696—21no—
13C16×#595—21no—
14#11763688—22no—
15C2×C16×D17C2211yescharacteristic
16#108×D17C2212yes—
17#11762639C411yescharacteristic, complemented
18#11762638C412yescomplemented
19C17×#368C411yescharacteristic, complemented
20#10587677D411yescharacteristic
21C2×C4⋊#595—22no—
22D17⋊M16D411yescharacteristic
23M16×D17—22no—
24C2×C8×D17C2311yescharacteristic
25#10587538—21no—
26#10587534—22no—
27#10587534—22no—
28#10587534—42no—
29#10587533—42no—
30#10587532—21no—
31C8×#595—21no—
32#10587530Q812yes—
33#10587529—21no—
34C2×C16×C17C2×C411yescharacteristic
35C17×#108C2×C412yes—
36#10587493—22no—
37#10587490C2×C412yes—
38C2×#63214C2×C411yescharacteristic
39C16×D17D411yescharacteristic
40C16×D17D411yescharacteristic
41C16×D17Q811yescharacteristic
42C16×D17Q811yescharacteristic
43C22×#595—42no—
44C2×C4×D17C2×D411yescharacteristic
45C22⋊#595—21no—
46#63247Q1612yes—
47C4⋊#595—42no—
48C4⋊#595—42no—
49C4⋊#595D811yescharacteristic
50C4⋊#595D811yescharacteristic
51C4×#595—21no—
52#63243—21no—
53#63242—21no—
54M16×C17—22no—
55C2×C8×C17C22×C411yescharacteristic
56#63223—22no—
57C2×#3622#4111yescharacteristic
58#63218—42no—
59C8×D17—42no—
60C8×D17C2×D411yescharacteristic
61C8×D17C2×Q811yescharacteristic
62C8×D17C2×Q811yescharacteristic
63C8×D17#4111yescharacteristic
64#63216—22no—
65C16×C17C4⋊C411yescharacteristic
66C16×C17C4⋊C411yescharacteristic
67#63214C4⋊C411yescharacteristic
68#63214C4⋊C411yescharacteristic
69#13171—171nomaximal, Sylow
70C22×D17#13511yescharacteristic
71C2×#595—21no—
72C2×#595—21no—
73C2×#595—82no—
74C2×#595—162no—
75C2×C4×C17C4×D411yescharacteristic
76C2×Dic17C2×Q1611yescharacteristic
77C4×D17#12111yescharacteristic
78C4×D17C4⋊Q811yescharacteristic
79C4×D17C2×D811yescharacteristic
80C4×D17#13511yescharacteristic
81#3624—22no—
82C8×C17—42no—
83C8×C17C2×C4⋊C411yescharacteristic
84C8×C17C4×Q811yescharacteristic
85#3622—42no—
86#3622C22⋊Q811yescharacteristic
87#3622#12511yescharacteristic
88C2×#368—171no—
89C2×#366—171no—
90#2108—171no—
91#1952—172no—
92#1387—172no—
93C22×C17C4×Q1611yescharacteristic
94C2×D17—21no—
95C2×D17—21no—
96C2×D17#46611yescharacteristic
97C2×D17#49911yescharacteristic
98#595—41no—
99#595—41no—
100#595—162no—
101C4×C17#38911yescharacteristic
102C4×C17C4×D811yescharacteristic
103Dic17#46711yescharacteristic
104Dic17#50011yescharacteristic
105C2×M32—171no—
106C22×C16—171no—
107C2×#108—172no—
108#428—342no—
109C2×#107—172no—
110#405—171no—
111#368—171no—
112#368—172no—
113#368#59511yescharacteristic, complemented
114#366—341no—
115#366—341no—
116#346—341no—
117C4×C16—341no—
118#343—342no—
119C2×C17—21no—
120C2×C17#194211yescharacteristic
121D17—21no—
122D17#222111yescharacteristic
123D17#222211yescharacteristic
124C2×M16—171no—
125C2×M16—342no—
126C22×C8—171no—
127#117—171no—
128C2×C4⋊C4—342no—
129M32—172no—
130M32—341no—
131C2×C16—171no—
132C2×C16—171no—
133C2×C16—171no—
134C2×C16—171no—
135C2×C16—171no—
136C2×C16—341no—
137C2×C16C2×#59511yescharacteristic
138#108—172no—
139#108—342no—
140#108C2×#59512yes—
141#107—342no—
142#107—342no—
143#107—682no—
144#106—682no—
145#97—341no—
146C4×C8—341no—
147C17#1317111yescharacteristic, complemented, Sylow
148C22×C4—171no—
149C22×C4—682no—
150M16—22no—
151M16—172no—
152M16—341no—
153M16—342no—
154M16—682no—
155C2×C8—171no—
156C2×C8—171no—
157C2×C8—171no—
158C2×C8—171no—
159C2×C8—171no—
160C2×C8—341no—
161C2×C8—682no—
162C2×C8C22×#59511yescharacteristic
163C4⋊C4—171no—
164C4⋊C4—171no—
165C4⋊C4—682no—
166C4⋊C4—682no—
167C22⋊C4—341no—
168C42—341no—
169C16—171no—
170C16—171no—
171C16—342no—
172C16C4⋊#59511yescharacteristic
173C16C4⋊#59511yescharacteristic
174C23—171no—
175C2×C4—2722no—
176C2×C4—171no—
177C2×C4—171no—
178C2×C4—171no—
179C2×C4—171no—
180C2×C4—171no—
181C2×C4—341no—
182C2×C4—341no—
183C2×C4—1362no—
184C2×C4D4×#59511yescharacteristic
185C8—42no—
186C8—171no—
187C8—171no—
188C8—342no—
189C8—682no—
190C8C2×C4⋊#59511yescharacteristic
191C8Q8×#59511yescharacteristic
192C22—171no—
193C22—171no—
194C22—341no—
195C22—341no—
196C22Q16×#59511yescharacteristic
197C4—2722no—
198C4—171no—
199C4—171no—
200C4—681no—
201C4—681no—
202C4#1176376011yescharacteristic
203C4D8×#59511yescharacteristic
204C2—21no—
205C2—171no—
206C2—171no—
207C2—341no—
208C2#1454488811yescharacteristic
subgroupG/H
centerC2#14544888
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#368C4
socleC2×C17#1942
prime radicalC22×D17#135
cosocleC2×C8×D17C23
hypercenter#368#595
hypocenterC17#13171
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
17. #11762639C4semidirect
18. #11762638C4semidirect
19. C17×#368C4semidirect
113. #368#595semidirect
147. C17#13171semidirect

Maximal subgroups

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

subgroupindex
C2×#117637352
#145449922
#145449022
#145438602
D17×#3682
#1317117