Finite Group Databasebeta

← #17949445

Subgroups — #17949445

Order 4352.

262 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 46 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×#11763719C211yesmaximal, characteristic
2#14544317C211yesmaximal, characteristic
3#14529177C211yesmaximal, characteristic
4#11763829—21no—
5C2×#10587545—21no—
6#11763719—21no—
7#11763719C412yescomplemented
8#11763669—21no—
9#11763669C412yescomplemented
10C2×#10587630C2211yescharacteristic
11#11762817—21no—
12C2×#10587507C411yescharacteristic
13#11762568—21no—
14C17×#519C411yescharacteristic
15C22×Q8×C17C2×C411yescharacteristic
16C22×Dic34D411yescharacteristic
17C2×#63247—41no—
18C4×Q8×C17—42no—
19C17×#117—21no—
20C17×#117—41no—
21#10587630—41no—
22#10587630C2×C411yescharacteristic
23#10587630C2×C411yescharacteristic
24#10587630D411yescharacteristic
25#10587630Q811yescharacteristic
26C2×#63225—41no—
27C2×C4×Dic17D411yescharacteristic
28C2×#63223—21no—
29C22⋊#3624—41no—
30#10587545—22no—
31#10587545—41no—
32#10587544—22no—
33#10587542—41no—
34#10587507—41no—
35#10587481—42no—
36C2×Q8×C17—21no—
37C2×Q8×C17—41no—
38C2×Q8×C17—41no—
39C2×Q8×C17C4211yescharacteristic
40C2×Q8×C17C4⋊C411yescharacteristic
41C22×C4×C17—21no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×Dic17—21no—
44C22×Dic17—21no—
45C2×Dic34—21no—
46C2×Dic34—41no—
47C2×Dic34—41no—
48C2×Dic34C22⋊C411yescharacteristic
49C2×Dic34C4⋊C411yescharacteristic
50#63247—42no—
51#63247—81no—
52C2×#3624—42no—
53C2×#3624—81no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—42no—
56C22⋊C4×C17—41no—
57C42×C17—41no—
58C42×C17—42no—
59#63225—41no—
60#63225—41no—
61#63225—41no—
62#63225—41no—
63C4×Dic17—21no—
64C4×Dic17C22⋊C411yescharacteristic
65C4×Dic17C4⋊C411yescharacteristic
66#63223—41no—
67#63223—41no—
68C2×#3622—41no—
69#7483—171nomaximal, Sylow
70C23×C17#9911yescharacteristic
71Q8×C17—41no—
72Q8×C17—41no—
73Q8×C17—42no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—41no—
79C2×C4×C17—41no—
80C2×C4×C17—42no—
81C2×C4×C17#9511yescharacteristic
82C2×C4×C17#9911yescharacteristic
83C2×Dic17—21no—
84C2×Dic17—21no—
85C2×Dic17—21no—
86C2×Dic17—21no—
87C2×Dic17—42no—
88C2×Dic17—41no—
89C2×Dic17—41no—
90Dic34—41no—
91Dic34—41no—
92Dic34—81no—
93#3624—82no—
94#3624—82no—
95#3622—81no—
96C2×#356—171no—
97#1886—171no—
98#1558—171no—
99C22×C17—41no—
100C22×C17#34211yescharacteristic
101C22×C17AΣL(1,𝔽16)11yescharacteristic
102C22×C17#35211yescharacteristic
103C4×C17—21no—
104C4×C17—21no—
105C4×C17—41no—
106C4×C17—41no—
107C4×C17—82no—
108Dic17—22no—
109Dic17—41no—
110Dic17—41no—
111Dic17—41no—
112C2×C4⋊Q8—171no—
113#519#59511yescharacteristic
114#432—341no—
115#419—341no—
116C2×#101—171no—
117C2×#101—341no—
118#356—172no—
119#356—341no—
120#339—341no—
121#333—172no—
122#333—341no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17—21no—
126C2×C17#139011yescharacteristic
127C22×Q8—171no—
128C22×Q8C2×#59511yescharacteristic
129C2×M16—341no—
130C2×M16—681no—
131C4⋊Q8—171no—
132C4⋊Q8—171no—
133C4⋊Q8—171no—
134C4⋊Q8—171no—
135C4⋊Q8—681no—
136C4×Q8—42no—
137#117—21no—
138#117—41no—
139C2×C4⋊C4—681no—
140C2×C42—171no—
141C4⋊C8—342no—
142#103—682no—
143#101—342no—
144#101—681no—
145#101—681no—
146C22⋊C8—681no—
147#97—681no—
148C17#748311yescharacteristic, complemented, Sylow
149C2×Q8—21no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—171no—
153C2×Q8—171no—
154C2×Q8—341no—
155C2×Q8—681no—
156C2×Q8—681no—
157C2×Q8C4×#59511yescharacteristic
158C2×Q8C4⋊#59511yescharacteristic
159C22×C4—21no—
160C22×C4—341no—
161C22×C4—341no—
162C22×C4C22⋊#59511yescharacteristic
163M16—681no—
164M16—682no—
165M16—681no—
166M16—1361no—
167C2×C8—681no—
168C2×C8—682no—
169C2×C8—1361no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—681no—
173C4⋊C4—681no—
174C4⋊C4—681no—
175C4⋊C4—681no—
176C22⋊C4—41no—
177C42—41no—
178C42—42no—
179C42—171no—
180C42—171no—
181C42—341no—
182C23#1058755111yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—42no—
186Q8—681no—
187Q8—681no—
188Q8—1361no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—341no—
199C2×C4—341no—
200C2×C4—682no—
201C2×C4—681no—
202C2×C4—681no—
203C2×C4#1058753911yescharacteristic
204C2×C4(C2×#595)⋊C411yescharacteristic
205C8—1361no—
206C8—1362no—
207C8—1362no—
208C22—41no—
209C22#1176368711yescharacteristic
210C22#1176370911yescharacteristic
211C22#1176371111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—82no—
217C4—342no—
218C4—681no—
219C4—681no—
220C4—681no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2#1454386811yescharacteristic
subgroupG/H
centerC2#14543868
commutatorC2×Q8×C17C42
FrattiniC22×Q8C2×#595
FittingC17×#519C4
socleC2×C17#1390
prime radicalC23×C17#99
cosocleC2×#10587630C22
hypercenter#519#595
hypocenterC17#7483
LCSG ▷ C2×Q8×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ #519

Complements

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

NH ≅ G/Ntype
7. #11763719C4semidirect
9. #11763669C4semidirect
148. C17#7483semidirect

Maximal subgroups

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

subgroupindex
C2×#117637192
#145443172
#145291772
#748317