Finite Group Databasebeta

← #14527337

Subgroups — #14527337

Order 2176.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#11763319C211yesmaximal, characteristic
2C22⋊C8×D17C211yesmaximal, characteristic, complemented
3#11762671C211yesmaximal, characteristic, complemented
4#11762547C211yesmaximal, characteristic, complemented
5#11762545C211yesmaximal, characteristic, complemented
6#11762543C211yesmaximal, characteristic, complemented
7C17×#327C211yesmaximal, characteristic, complemented
8C2×#63254C411yescharacteristic, complemented
9C22×C4×D17C2211yescharacteristic
10C17×#121C2211yescharacteristic
11#10587624C411yescharacteristic, complemented
12#10587623—21no—
13D4×Dic17—21no—
14C2×#63227—21no—
15#10587610C2211yescharacteristic
16C2×C8×D17—21no—
17#10587583C411yescharacteristic, complemented
18#10587578C411yescharacteristic, complemented
19#10587569—21no—
20#10587567—21no—
21C17×C22⋊C8C2211yescharacteristic
22C17×#95C2211yescharacteristic
23#10587502—21no—
24#10587502C2211yescharacteristic
25C22⋊#3622C2211yescharacteristic
26#10587491—21no—
27C23×D17D411yescharacteristic
28C2×D4×C17—21no—
29C2×D4×C17C2×C411yescharacteristic
30C22×C4×C17—21no—
31C22×C4×C17C2311yescharacteristic
32C2×C22⋊D17—21no—
33C2×C22⋊D17—21no—
34C22×Dic17—21no—
35C22×Dic17—21no—
36C22×Dic17D411yescharacteristic
37#63254—42no—
38C2×C4×D17—42no—
39C2×C4×D17C2×C411yescharacteristic
40C2×C4×D17C2×C411yescharacteristic
41C2×C4×D17D411yescharacteristic
42C2×C4×D17D411yescharacteristic
43C2×Dic34C2×C411yescharacteristic
44C2×C8×C17—21no—
45C4⋊C4×C17C2×C411yescharacteristic
46C22⋊C4×C17—21no—
47C22⋊Dic17—21no—
48C22⋊Dic17—21no—
49#63227—21no—
50#63227—21no—
51#63227—42no—
52C4⋊Dic17—21no—
53C4⋊Dic17C2×C411yescharacteristic
54#63225—21no—
55C4×Dic17—21no—
56C2×#3622—21no—
57C8×D17—42no—
58C23×C17—21no—
59C23×C17C2×D411yescharacteristic
60C22×D17—21no—
61C22×D17—21no—
62C22×D17—22no—
63C22×D17—41no—
64C22×D17C22⋊C411yescharacteristic
65C22×D17C22⋊C411yescharacteristic
66D4×C17—41no—
67D4×C17—41no—
68D4×C17—41no—
69C2×C4×C17—21no—
70C2×C4×C17—41no—
71C2×C4×C17—41no—
72C2×C4×C17—41no—
73C2×C4×C17—41no—
74C2×C4×C17C22×C411yescharacteristic
75C2×C4×C17C2×D411yescharacteristic
76C22⋊D17—42no—
77C22⋊D17—42no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—41no—
81C2×Dic17—42no—
82C2×Dic17—41no—
83C2×Dic17—41no—
84C2×Dic17—41no—
85C2×Dic17C22⋊C411yescharacteristic
86C2×Dic17C22⋊C411yescharacteristic
87C4×D17—22no—
88C4×D17—22no—
89C4×D17—41no—
90C4×D17—41no—
91Dic34—41no—
92C8×C17—41no—
93#3622—41no—
94#1516—171nomaximal, Sylow
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—41no—
98C22×C17—41no—
99C22×C17—41no—
100C22×C17C2×C22⋊C411yescharacteristic
101C22×C17#13511yescharacteristic
102C22×C17#13511yescharacteristic
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—21no—
106C2×D17—21no—
107C2×D17—21no—
108C2×D17—42no—
109C2×D17—42no—
110C2×D17#9912yes—
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—41no—
114C4×C17—81no—
115Dic17—21no—
116Dic17—21no—
117Dic17—41no—
118Dic17—41no—
119Dic17—81no—
120#525—171no—
121C2×C22⋊C8—171no—
122#381—171no—
123#328—171no—
124#328—171no—
125#327—171no—
126#327D1711yescharacteristic, complemented
127C2×C17—21no—
128C2×C17—21no—
129C2×C17—81no—
130C2×C17C2×#9911yescharacteristic
131C2×C17#41611yescharacteristic
132C2×C17#42111yescharacteristic
133D17—22no—
134D17—41no—
135C2×#41—171no—
136C23×C4—171no—
137C22×C8—341no—
138#123—341no—
139C22⋊Q8—171no—
140C22⋊Q8—171no—
141#121—171no—
142#121C2×D1711yescharacteristic
143#120—341no—
144C4×D4—341no—
145C4×D4—341no—
146#117—171no—
147C2×C22⋊C4—341no—
148C22⋊C8—171no—
149C22⋊C8—341no—
150C22⋊C8C2×D1711yescharacteristic
151#95—171no—
152#95—341no—
153#95C2×D1711yescharacteristic
154C17#151611yescharacteristic, complemented, Sylow
155C24—171no—
156#41—682no—
157C2×Q8—171no—
158C2×D4—21no—
159C2×D4—341no—
160C2×D4—341no—
161C2×D4C4×D1711yescharacteristic
162C22×C4—21no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—171no—
168C22×C4—341no—
169C22×C4—341no—
170C22×C4—682no—
171C22×C4C22×D1711yescharacteristic
172C2×C8—21no—
173C2×C8—341no—
174C2×C8—682no—
175C4⋊C4—171no—
176C4⋊C4—341no—
177C4⋊C4—341no—
178C4⋊C4C4×D1711yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—341no—
181C22⋊C4—341no—
182C22⋊C4—341no—
183C22⋊C4—341no—
184C22⋊C4—682no—
185C42—341no—
186C23—21no—
187C23—171no—
188C23—171no—
189C23—342no—
190C23—341no—
191C23—341no—
192C23—681no—
193C23D4×D1711yescharacteristic
194Q8—681no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—682no—
199D4—682no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—171no—
206C2×C4—171no—
207C2×C4—342no—
208C2×C4—342no—
209C2×C4—341no—
210C2×C4—341no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4—681no—
214C2×C4—682no—
215C2×C4—681no—
216C2×C4—681no—
217C2×C4—681no—
218C2×C4C2×C4×D1711yescharacteristic
219C2×C4D4×D1711yescharacteristic
220C8—41no—
221C8—681no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—172no—
228C22—341no—
229C22—341no—
230C22—341no—
231C22—341no—
232C22—341no—
233C22—682no—
234C22—682no—
235C22C22⋊C4×D1711yescharacteristic
236C22#1058759811yescharacteristic
237C22#1058760211yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—341no—
243C4—341no—
244C4—681no—
245C4—681no—
246C4—1361no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—342no—
251C2—681no—
252C2#99×D1711yescharacteristic
253C2#1176280211yescharacteristic
254C2#1176282411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D17
commutatorC2×C4×C17C22×C4
FrattiniC22×C4C22×D17
FittingC17×#327C2
socleC22×C17C2×C22⋊C4
prime radical#11763319C2
cosocleC22×C4×C17C23
hypercenter#327D17
hypocenterC17#1516
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D17C2semidirect
3. #11762671C2semidirect
4. #11762547C2semidirect
5. #11762545C2semidirect
6. #11762543C2semidirect
7. C17×#327C2semidirect
8. C2×#63254C4semidirect
11. #10587624C4semidirect
17. #10587583C4semidirect
18. #10587578C4semidirect
126. #327D17semidirect
154. C17#1516semidirect

Maximal subgroups

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

subgroupindex
#117633192
C22⋊C8×D172
#117626712
#117625472
#117625452
#117625432
C17×#3272
#151617