Finite Group Databasebeta

← #14544804

Subgroups — #14544804

Order 2176.

358 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 70 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×#10587677C211yesmaximal, characteristic, complemented
2C2×#10587548C212yesmaximal, complemented
3#11763780C211yesmaximal, characteristic, complemented
4#11763679C212yesmaximal, complemented
5#11763319C211yesmaximal, characteristic
6C2×#63254C2211yescharacteristic
7C22×C4×D17C2211yescharacteristic
8C2×C22⋊#595—21no—
9#10587677—24no—
10C2×C4⋊#595—21no—
11C2×C4×#595C2212yes—
12C2×#63243C2212yes—
13C17×#121C411yescharacteristic, complemented
14#10587624C411yescharacteristic, complemented
15#10587623—21no—
16D4×Dic17—21no—
17#10587610C411yescharacteristic, complemented
18#10587583C411yescharacteristic, complemented
19#10587578C2211yescharacteristic
20#10587569—21no—
21#10587567—21no—
22C22⋊#3624—21no—
23#10587548—24no—
24#10587543—21no—
25C23×D17D411yescharacteristic
26C22×#595—22no—
27C2×D4×C17—21no—
28C2×D4×C17C2×C411yescharacteristic
29C22×C4×C17C2×C411yescharacteristic
30C2×C22⋊D17—21no—
31C2×C22⋊D17—21no—
32C22×Dic17—21no—
33C22×Dic17D411yescharacteristic
34#63254—22no—
35#63254—22no—
36C2×C4×D17—22no—
37C2×C4×D17—22no—
38C2×C4×D17C2×C411yescharacteristic
39C2×C4×D17D411yescharacteristic
40C2×C4×D17D411yescharacteristic
41C2×C4×D17C2311yescharacteristic
42C2×Dic34C2×C411yescharacteristic
43C22⋊#595—24no—
44C2×#3624—22no—
45C4⋊#595—24no—
46C4×#595—22no—
47C4×#595D414yescomplemented
48#63243—22no—
49#63243—22no—
50C4⋊C4×C17C2×C411yescharacteristic
51C22⋊C4×C17—21no—
52C22⋊Dic17—21no—
53C22⋊Dic17—21no—
54#63227—21no—
55#63227—21no—
56C4⋊Dic17—21no—
57C4⋊Dic17C2×C411yescharacteristic
58#63225—21no—
59C4×Dic17—21no—
60C23×C17—21no—
61C23×C17C22⋊C411yescharacteristic
62C22×D17—21no—
63C22×D17—21no—
64C22×D17—41no—
65C22×D17—41no—
66C22×D17C22⋊C411yescharacteristic
67C22×D17C2×D411yescharacteristic
68C2×#595—24no—
69C2×#595—42no—
70C2×#595—42no—
71D4×C17—22no—
72D4×C17—42no—
73C2×C4×C17—22no—
74C2×C4×C17—21no—
75C2×C4×C17C22⋊C411yescharacteristic
76C2×C4×C17C22×C411yescharacteristic
77C22⋊D17—42no—
78C22⋊D17—41no—
79C22⋊D17—41no—
80C2×Dic17—22no—
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—42no—
84C2×Dic17C22⋊C411yescharacteristic
85C2×Dic17C2×D411yescharacteristic
86C4×D17—21no—
87C4×D17—21no—
88C4×D17—22no—
89C4×D17—22no—
90C4×D17C2×D412yes—
91C4×D17#4112yes—
92Dic34—22no—
93#3624—42no—
94#1897—171nomaximal, Sylow
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17—41no—
99C22×C17—41no—
100C22×C17—41no—
101C22×C17C2×C22⋊C411yescharacteristic
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—21no—
106C2×D17—21no—
107C2×D17—42no—
108C2×D17—42no—
109C2×D17#12011yescharacteristic
110C2×D17#12311yescharacteristic
111#595—44no—
112C4×C17—21no—
113C4×C17—41no—
114C4×C17C4×D412yes—
115Dic17—21no—
116Dic17—41no—
117Dic17—41no—
118Dic17#12112yes—
119#525—171no—
120C2×#117—171no—
121C2×#104—172no—
122#407—171no—
123#339—172no—
124C2×C17—41no—
125C2×C17—81no—
126C2×C17#38611yescharacteristic
127C2×C17#42111yescharacteristic
128C2×C17#42111yescharacteristic
129D17—21no—
130D17—21no—
131D17—41no—
132C2×#41—171no—
133C23×C4—171no—
134C2×M16—172no—
135#123—341no—
136C22⋊Q8—171no—
137C22⋊Q8—171no—
138#121—171no—
139#121#59511yescharacteristic, complemented
140#120—341no—
141C4×D4—341no—
142C4×D4—341no—
143#117—171no—
144#117—344no—
145C2×C4⋊C4—341no—
146C2×C22⋊C4—341no—
147C2×C42—172no—
148#104—344no—
149C22⋊C8—341no—
150C22⋊C8—341no—
151C17#189711yescharacteristic, complemented, Sylow
152C24—171no—
153#41—342no—
154#41—342no—
155C2×Q8—171no—
156C2×D4—21no—
157C2×D4—341no—
158C2×D4—341no—
159C2×D4C2×#59511yescharacteristic
160C22×C4—171no—
161C22×C4—171no—
162C22×C4—171no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—342no—
166C22×C4—342no—
167C22×C4—341no—
168C22×C4—342no—
169C22×C4C2×#59511yescharacteristic
170M16—342no—
171M16—342no—
172C2×C8—342no—
173C4⋊C4—171no—
174C4⋊C4—341no—
175C4⋊C4—344no—
176C4⋊C4—341no—
177C4⋊C4C2×#59511yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—341no—
180C22⋊C4—341no—
181C22⋊C4—341no—
182C22⋊C4—344no—
183C22⋊C4—341no—
184C42—174no—
185C42—341no—
186C42—342no—
187C23—21no—
188C23—171no—
189C23—171no—
190C23—341no—
191C23—341no—
192C23—681no—
193C23—681no—
194C23C22⋊#59511yescharacteristic
195Q8—342no—
196D4—22no—
197D4—42no—
198D4—681no—
199D4—681no—
200D4—682no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—171no—
204C2×C4—172no—
205C2×C4—172no—
206C2×C4—171no—
207C2×C4—342no—
208C2×C4—341no—
209C2×C4—341no—
210C2×C4—342no—
211C2×C4—342no—
212C2×C4—344no—
213C2×C4—341no—
214C2×C4—341no—
215C2×C4—682no—
216C2×C4—682no—
217C2×C4—682no—
218C2×C4C22⋊#59511yescharacteristic
219C2×C4C22×#59511yescharacteristic
220C8—682no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—171no—
228C22—171no—
229C22—341no—
230C22—341no—
231C22—341no—
232C22—341no—
233C22—341no—
234C22—682no—
235C22—682no—
236C22C2×C22⋊#59511yescharacteristic
237C4—21no—
238C4—41no—
239C4—172no—
240C4—341no—
241C4—684no—
242C4—681no—
243C4—681no—
244C4D4×#59512yes—
245C2—41no—
246C2—81no—
247C2—341no—
248C2—341no—
249C2—681no—
250C2#1176375711yescharacteristic
251C2#1176380611yescharacteristic
252C2#1176380711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#121C4
socleC22×C17C2×C22⋊C4
prime radical#11763319C2
cosocleC2×C4×D17C23
hypercenter#121#595
hypocenterC17#1897
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10587677C2semidirect
2. C2×#10587548C2semidirect
3. #11763780C2semidirect
4. #11763679C2semidirect
13. C17×#121C4semidirect
14. #10587624C4semidirect
17. #10587610C4semidirect
18. #10587583C4semidirect
47. C4×#595D4semidirect
139. #121#595semidirect
151. C17#1897semidirect

Maximal subgroups

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

subgroupindex
C2×#105876772
C2×#105875482
#117637802
#117636792
#117633192
#189717