Finite Group Databasebeta

← #14527797

Subgroups — #14527797

Order 2176.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#11763399C211yesmaximal, characteristic
2#11763122C211yesmaximal, characteristic, complemented
3#11762735C211yesmaximal, characteristic, complemented
4#11762546C211yesmaximal, characteristic, complemented
5#11762544C211yesmaximal, characteristic, complemented
6#11762532C211yesmaximal, characteristic, complemented
7C17×#483C211yesmaximal, characteristic, complemented
8C17×C22⋊Q8C2211yescharacteristic
9C2×C4⋊C4×C17C2211yescharacteristic
10#10587633—21no—
11#10587616C2211yescharacteristic
12C2×#63227—21no—
13C2×#63227C2211yescharacteristic
14#10587584—21no—
15#10587581—21no—
16#10587580—21no—
17#10587568—21no—
18#10587567—21no—
19C17×#106—21no—
20C17×#103—21no—
21C17×C22⋊C8C2211yescharacteristic
22#10587502—21no—
23#10587502C2211yescharacteristic
24C22⋊#3622C2211yescharacteristic
25#10587480—21no—
26#10587478—21no—
27C23×D17D411yescharacteristic
28C2×Q8×C17D411yescharacteristic
29C22×C4×C17—21no—
30C22×C4×C17C2311yescharacteristic
31C2×C22⋊D17—21no—
32C22×Dic17—21no—
33C22×Dic17D411yescharacteristic
34C2×D68—21no—
35C2×D68—21no—
36C2×D68D411yescharacteristic
37C2×C4×D17—21no—
38C2×C8×C17—21no—
39C4⋊C4×C17—21no—
40C4⋊C4×C17—21no—
41C4⋊C4×C17—21no—
42C4⋊C4×C17D411yescharacteristic
43C22⋊C4×C17—21no—
44#63227—21no—
45#63227—21no—
46#63227—21no—
47#63227—21no—
48#63227—21no—
49#63227—21no—
50#63227—42no—
51C4⋊Dic17D411yescharacteristic
52#63225—21no—
53C4×Dic17—21no—
54C2×#3622—21no—
55C23×C17C2×D411yescharacteristic
56C22×D17—21no—
57C22×D17—21no—
58C22×D17—21no—
59C22×D17—21no—
60C22×D17—41no—
61C22×D17—41no—
62Q8×C17—41no—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—41no—
66C2×C4×C17—41no—
67C2×C4×C17—41no—
68C2×C4×C17—41no—
69C2×C4×C17C2×D411yescharacteristic
70C2×C4×C17C2×D411yescharacteristic
71C22⋊D17—41no—
72C22⋊D17—41no—
73C2×Dic17—21no—
74C2×Dic17—21no—
75C2×Dic17—41no—
76C2×Dic17—41no—
77C2×Dic17—41no—
78C2×Dic17—41no—
79D68—41no—
80D68—81no—
81D68—81no—
82C4×D17—81no—
83C8×C17—41no—
84#3622—41no—
85#1612—171nomaximal, Sylow
86C22×C17—21no—
87C22×C17—21no—
88C22×C17#12011yescharacteristic
89C22×C17#13511yescharacteristic
90C22×C17AGL(1,ℤ/8)11yescharacteristic
91C2×D17—42no—
92C2×D17—41no—
93C2×D17—41no—
94C2×D17—41no—
95C2×D17—41no—
96C2×D17—41no—
97C2×D17—41no—
98C2×D17—81no—
99C4×C17—21no—
100C4×C17—21no—
101C4×C17—41no—
102C4×C17—41no—
103C4×C17—81no—
104Dic17—41no—
105Dic17—41no—
106Dic17—81no—
107#538—171no—
108#483D1711yescharacteristic, complemented
109#480—171no—
110#397—171no—
111#328—171no—
112#327—171no—
113#323—171no—
114C2×C17—21no—
115C2×C17—21no—
116C2×C17#44911yescharacteristic
117C2×C17#45511yescharacteristic
118C2×C17#45811yescharacteristic
119D17—81no—
120D17—81no—
121#126—341no—
122#124—341no—
123#123—341no—
124C22⋊Q8C2×D1711yescharacteristic
125#121—171no—
126#121—341no—
127#120—341no—
128C4×D4—341no—
129C2×C4⋊C4C2×D1711yescharacteristic
130C2×C22⋊C4—171no—
131C2×C22⋊C4—341no—
132#107—341no—
133#106—21no—
134#103—21no—
135#102—341no—
136C22⋊C8—171no—
137C22⋊C8C2×D1711yescharacteristic
138#95—171no—
139#95—341no—
140C17#161211yescharacteristic, complemented, Sylow
141C24—171no—
142C2×Q8C22⋊D1711yescharacteristic
143C2×D4—171no—
144C2×D4—341no—
145C2×D4—341no—
146C2×D4—341no—
147C22×C4—21no—
148C22×C4—171no—
149C22×C4—341no—
150C22×C4—341no—
151C22×C4C22×D1711yescharacteristic
152C2×C8—21no—
153C2×C8—341no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—171no—
158C4⋊C4—341no—
159C4⋊C4C22⋊D1711yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—341no—
162C22⋊C4—341no—
163C22⋊C4—341no—
164C22⋊C4—341no—
165C22⋊C4—341no—
166C22⋊C4—341no—
167C22⋊C4—682no—
168C42—341no—
169C23—341no—
170C23—341no—
171C23—341no—
172C23—341no—
173C23—681no—
174C23—681no—
175C23D4×D1711yescharacteristic
176Q8—41no—
177D4—681no—
178D4—681no—
179D4—681no—
180D4—1361no—
181D4—1361no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—341no—
189C2×C4—341no—
190C2×C4—681no—
191C2×C4—681no—
192C2×C4—681no—
193C2×C4—681no—
194C2×C4—1361no—
195C2×C4D4×D1711yescharacteristic
196C2×C4C2×C22⋊D1711yescharacteristic
197C8—41no—
198C8—681no—
199C22—21no—
200C22—21no—
201C22—682no—
202C22—681no—
203C22—681no—
204C22—681no—
205C22—681no—
206C22—681no—
207C22—681no—
208C22—1361no—
209C22#1058760011yescharacteristic
210C22#1058760211yescharacteristic
211C22#1058762311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—681no—
218C4—681no—
219C4—1361no—
220C2—21no—
221C2—21no—
222C2—1361no—
223C2—1361no—
224C2#1176295311yescharacteristic
225C2#1176298511yescharacteristic
226C2#1176299811yescharacteristic
subgroupG/H
centerC22#10587623
commutator, cosocleC22×C4×C17C23
FrattiniC22×C4C22×D17
FittingC17×#483C2
socleC22×C17#120
prime radical#11763399C2
hypercenter#483D17
hypocenterC17#1612
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #11763122C2semidirect
3. #11762735C2semidirect
4. #11762546C2semidirect
5. #11762544C2semidirect
6. #11762532C2semidirect
7. C17×#483C2semidirect
108. #483D17semidirect
140. C17#1612semidirect

Maximal subgroups

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

subgroupindex
#117633992
#117631222
#117627352
#117625462
#117625442
#117625322
C17×#4832
#161217