Finite Group Databasebeta

← #14527339

Subgroups — #14527339

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#11763322C211yesmaximal, characteristic
2C22⋊C8×D17C211yesmaximal, characteristic, complemented
3#11762671C211yesmaximal, characteristic, complemented
4#11762546C211yesmaximal, characteristic, complemented
5#11762544C211yesmaximal, characteristic, complemented
6#11762542C211yesmaximal, characteristic, complemented
7C17×#328C211yesmaximal, characteristic, complemented
8C2×#63256C411yescharacteristic, complemented
9C22×C4×D17C2211yescharacteristic
10C17×C22⋊Q8C2211yescharacteristic
11#10587632C411yescharacteristic, complemented
12#10587616C2211yescharacteristic
13C2×#63227—21no—
14C2×C8×D17—21no—
15#10587581C411yescharacteristic, complemented
16#10587580—21no—
17#10587579—21no—
18#10587578C411yescharacteristic, complemented
19#10587568—21no—
20#10587567—21no—
21C17×C22⋊C8C2211yescharacteristic
22C17×#95C2211yescharacteristic
23#10587502—21no—
24#10587502C2211yescharacteristic
25C22⋊#3622C2211yescharacteristic
26#10587491—21no—
27C23×D17D411yescharacteristic
28C2×Q8×C17C2×C411yescharacteristic
29C22×C4×C17—21no—
30C22×C4×C17C2311yescharacteristic
31C2×C22⋊D17—21no—
32C22×Dic17—21no—
33C22×Dic17D411yescharacteristic
34#63256—42no—
35C2×D68—21no—
36C2×D68—21no—
37C2×D68C2×C411yescharacteristic
38C2×C4×D17—21no—
39C2×C4×D17—42no—
40C2×C4×D17C2×C411yescharacteristic
41C2×C4×D17C2×C411yescharacteristic
42C2×C4×D17D411yescharacteristic
43C2×C4×D17D411yescharacteristic
44C2×C8×C17—21no—
45C4⋊C4×C17—21no—
46C4⋊C4×C17C2×C411yescharacteristic
47C22⋊C4×C17—21no—
48#63227—21no—
49#63227—21no—
50#63227—21no—
51#63227—21no—
52#63227—42no—
53C4⋊Dic17C2×C411yescharacteristic
54#63225—21no—
55C4×Dic17—21no—
56C2×#3622—21no—
57C8×D17—42no—
58C23×C17C2×D411yescharacteristic
59C22×D17—21no—
60C22×D17—21no—
61C22×D17—22no—
62C22×D17—21no—
63C22×D17—41no—
64C22×D17C22⋊C411yescharacteristic
65C22×D17C22⋊C411yescharacteristic
66Q8×C17—41no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—41no—
70C2×C4×C17—41no—
71C2×C4×C17—41no—
72C2×C4×C17—41no—
73C2×C4×C17C22×C411yescharacteristic
74C2×C4×C17C2×D411yescharacteristic
75C22⋊D17—41no—
76C22⋊D17—41no—
77C2×Dic17—21no—
78C2×Dic17—41no—
79C2×Dic17—41no—
80C2×Dic17—41no—
81C2×Dic17—41no—
82C2×Dic17C22⋊C411yescharacteristic
83C2×Dic17C22⋊C411yescharacteristic
84D68—41no—
85D68—42no—
86D68—42no—
87C4×D17—22no—
88C4×D17—22no—
89C4×D17—41no—
90C4×D17—41no—
91C4×D17—42no—
92C8×C17—41no—
93#3622—41no—
94#1516—171nomaximal, Sylow
95C22×C17—21no—
96C22×C17—21no—
97C22×C17C2×C22⋊C411yescharacteristic
98C22×C17#13511yescharacteristic
99C22×C17#13511yescharacteristic
100C2×D17—21no—
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—42no—
106C2×D17—42no—
107C2×D17—41no—
108C2×D17—41no—
109C2×D17—41no—
110C2×D17#9912yes—
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—41no—
114C4×C17—41no—
115C4×C17—81no—
116Dic17—21no—
117Dic17—21no—
118Dic17—41no—
119Dic17—81no—
120#525—171no—
121C2×C22⋊C8—171no—
122#381—171no—
123#328—171no—
124#328D1711yescharacteristic, complemented
125#327—171no—
126#327—171no—
127C2×C17—21no—
128C2×C17—21no—
129C2×C17C2×#9911yescharacteristic
130C2×C17#41611yescharacteristic
131C2×C17#42111yescharacteristic
132D17—22no—
133D17—41no—
134D17—81no—
135C2×#41—171no—
136C23×C4—171no—
137C22×C8—341no—
138#123—341no—
139C22⋊Q8—171no—
140C22⋊Q8C2×D1711yescharacteristic
141#121—171no—
142#121—171no—
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×Q8C4×D1711yescharacteristic
158C2×D4—171no—
159C2×D4—341no—
160C2×D4—341no—
161C2×D4—341no—
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—21no—
176C4⋊C4—171no—
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—171no—
187C23—171no—
188C23—342no—
189C23—341no—
190C23—341no—
191C23—341no—
192C23—681no—
193C23D4×D1711yescharacteristic
194Q8—41no—
195D4—681no—
196D4—682no—
197D4—682no—
198D4—681no—
199D4—681no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—171no—
207C2×C4—171no—
208C2×C4—342no—
209C2×C4—342no—
210C2×C4—341no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4—682no—
214C2×C4—681no—
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—172no—
225C22—341no—
226C22—341no—
227C22—341no—
228C22—341no—
229C22—341no—
230C22—682no—
231C22—682no—
232C22—681no—
233C22—681no—
234C22—681no—
235C22C22⋊C4×D1711yescharacteristic
236C22#1058760211yescharacteristic
237C22#1058760511yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—341no—
244C4—341no—
245C4—681no—
246C4—1361no—
247C2—21no—
248C2—21no—
249C2—342no—
250C2—681no—
251C2—1361no—
252C2#99×D1711yescharacteristic
253C2#1176280411yescharacteristic
254C2#1176282411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D17
commutatorC2×C4×C17C22×C4
FrattiniC22×C4C22×D17
FittingC17×#328C2
socleC22×C17C2×C22⋊C4
prime radical#11763322C2
cosocleC22×C4×C17C23
hypercenter#328D17
hypocenterC17#1516
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D17C2semidirect
3. #11762671C2semidirect
4. #11762546C2semidirect
5. #11762544C2semidirect
6. #11762542C2semidirect
7. C17×#328C2semidirect
8. C2×#63256C4semidirect
11. #10587632C4semidirect
15. #10587581C4semidirect
18. #10587578C4semidirect
124. #328D17semidirect
154. C17#1516semidirect

Maximal subgroups

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

subgroupindex
#117633222
C22⋊C8×D172
#117626712
#117625462
#117625442
#117625422
C17×#3282
#151617