Finite Group Databasebeta

← #14544925

Subgroups — #14544925

Order 2176.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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×#10587539C212yesmaximal, complemented
2C2×#10587551C212yesmaximal, complemented
3#11763751C211yesmaximal, characteristic, complemented
4C4×C22⋊#595C211yesmaximal, characteristic, complemented
5C2×#10587570C211yesmaximal, characteristic
6C22×C22⋊D17C411yescharacteristic, complemented
7C22×C22⋊D17C2211yescharacteristic
8C22×D68C2211yescharacteristic
9C22×C4×D17C2211yescharacteristic
10C2×C22⋊#595C2212yes—
11C2×C22⋊#595C2212yes—
12C2×C4⋊#595—21no—
13C2×C4×#595—21no—
14C2×C22⋊C4×C17C411yescharacteristic, complemented
15C2×#63227C411yescharacteristic, complemented
16C2×#63225C411yescharacteristic, complemented
17#10587570—21no—
18#10587570—21no—
19#10587570—21no—
20#10587570—21no—
21#10587551—24no—
22(C2×#595)⋊C4—21no—
23(C2×#595)⋊C4—21no—
24#10587539—24no—
25C24×C17C2×C411yescharacteristic
26C23×D17C2×C411yescharacteristic
27C23×D17C2311yescharacteristic
28C22×#595—22no—
29C22×#595—22no—
30C22×C4×C17C2×C411yescharacteristic
31C22×C4×C17C2×C411yescharacteristic
32C2×C22⋊D17—22no—
33C2×C22⋊D17—21no—
34C2×C22⋊D17—21no—
35C2×C22⋊D17—22no—
36C2×C22⋊D17—21no—
37C2×C22⋊D17—21no—
38C2×C22⋊D17—42no—
39C22×Dic17C2×C411yescharacteristic
40C22×Dic17C2×C411yescharacteristic
41C2×D68—22no—
42C2×D68—21no—
43C2×D68—21no—
44C2×D68—22no—
45C2×C4×D17—42no—
46C2×C4×D17D411yescharacteristic
47C2×C4×D17D411yescharacteristic
48C2×C4×D17D411yescharacteristic
49C2×C4×D17D411yescharacteristic
50C22⋊#595—22no—
51C22⋊#595—22no—
52C22⋊#595—22no—
53C22⋊#595D414yescomplemented
54C4⋊#595—42no—
55C4×#595—42no—
56C22⋊C4×C17—21no—
57C22⋊C4×C17—21no—
58#63227—21no—
59#63227—21no—
60#63225—21no—
61#63225—21no—
62C23×C17—21no—
63C23×C17—22no—
64C23×C17—41no—
65C23×C17—41no—
66C23×C17C22×C411yescharacteristic
67C22×D17—21no—
68C22×D17—22no—
69C22×D17—41no—
70C22×D17—41no—
71C22×D17—41no—
72C22×D17—41no—
73C22×D17C2×D411yescharacteristic
74C22×D17C2×D411yescharacteristic
75C22×D17C2×D412yes—
76C22×D17#4112yes—
77C2×#595—24no—
78C2×#595—42no—
79C2×#595—42no—
80C2×#595—42no—
81C2×#595—42no—
82C2×#595—42no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—41no—
86C2×C4×C17C22⋊C411yescharacteristic
87C2×C4×C17C22⋊C411yescharacteristic
88C22⋊D17—42no—
89C22⋊D17—42no—
90C22⋊D17—41no—
91C22⋊D17—41no—
92C22⋊D17—42no—
93C2×Dic17—22no—
94C2×Dic17—21no—
95C2×Dic17—22no—
96C2×Dic17C22⋊C411yescharacteristic
97C2×Dic17C22⋊C411yescharacteristic
98D68—42no—
99D68—41no—
100D68—41no—
101C4×D17—22no—
102C4×D17—22no—
103C4×D17—41no—
104C4×D17—41no—
105#1964—171nomaximal, Sylow
106C22×C17—21no—
107C22×C17—21no—
108C22×C17—41no—
109C22×C17—41no—
110C22×C17—41no—
111C22×C17—82no—
112C22×C17C2×C22⋊C411yescharacteristic
113C22×C17C4×D412yes—
114C2×D17—21no—
115C2×D17—21no—
116C2×D17—21no—
117C2×D17—21no—
118C2×D17—42no—
119C2×D17—42no—
120C2×D17—41no—
121C2×D17—41no—
122C2×D17—41no—
123C2×D17—82no—
124C2×D17#12112yes—
125C2×D17#12411yescharacteristic
126C2×D17#12711yescharacteristic
127#595—44no—
128#595—82no—
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—41no—
132Dic17—21no—
133Dic17—41no—
134Dic17#9912yescomplemented
135C2×#121—171no—
136C2×#99—172no—
137C2×#99—172no—
138#380—171no—
139C4×C22⋊C4—171no—
140C2×C17—22no—
141C2×C17—81no—
142C2×C17#39011yescharacteristic
143C2×C17C2×#9911yescharacteristic
144C2×C17#41011yescharacteristic
145D17—22no—
146D17—21no—
147D17—21no—
148D17—81no—
149C22×D4—171no—
150C22×D4—171no—
151C22×D4—171no—
152C23×C4—171no—
153#121—341no—
154#121—341no—
155#121—341no—
156#121—341no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—341no—
159C2×C22⋊C4—172no—
160C2×C22⋊C4—171no—
161C2×C22⋊C4—172no—
162C2×C22⋊C4#59511yescharacteristic, complemented
163C2×C42—341no—
164#99—344no—
165#99—344no—
166#95—341no—
167#95—341no—
168C17#196411yescharacteristic, complemented, Sylow
169C24—171no—
170C24—171no—
171C24C2×#59511yescharacteristic
172C2×D4—342no—
173C2×D4—341no—
174C2×D4—341no—
175C2×D4—342no—
176C2×D4—341no—
177C2×D4—341no—
178C2×D4—342no—
179C2×D4—341no—
180C2×D4—341no—
181C2×D4—342no—
182C2×D4—682no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—171no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—342no—
190C22×C4—342no—
191C22×C4—682no—
192C22×C4C2×#59511yescharacteristic
193C22×C4C2×#59511yescharacteristic
194C4⋊C4—341no—
195C4⋊C4—341no—
196C4⋊C4—682no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—174no—
200C22⋊C4—342no—
201C22⋊C4—341no—
202C22⋊C4—341no—
203C22⋊C4—342no—
204C22⋊C4—342no—
205C42—682no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—171no—
211C23—171no—
212C23—172no—
213C23—172no—
214C23—341no—
215C23—342no—
216C23—681no—
217C23—681no—
218C23—681no—
219C23—681no—
220C23C22×#59511yescharacteristic
221D4—682no—
222D4—681no—
223D4—681no—
224D4—682no—
225D4—682no—
226D4—682no—
227D4—681no—
228D4—681no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—171no—
233C2×C4—171no—
234C2×C4—342no—
235C2×C4—342no—
236C2×C4—342no—
237C2×C4—344no—
238C2×C4—342no—
239C2×C4—341no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—682no—
243C2×C4—682no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4C22⋊#59511yescharacteristic
248C2×C4C22⋊#59511yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—172no—
256C22—171no—
257C22—171no—
258C22—341no—
259C22—341no—
260C22—341no—
261C22—341no—
262C22—682no—
263C22—682no—
264C22—681no—
265C22—681no—
266C22—681no—
267C22—1362no—
268C22D4×#59512yes—
269C22C2×C22⋊#59511yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—172no—
274C4—341no—
275C4—684no—
276C4—681no—
277C4—1362no—
278C2—22no—
279C2—81no—
280C2—342no—
281C2—341no—
282C2—341no—
283C2—1361no—
284C2#1176376111yescharacteristic
285C2D17⋊#9911yescharacteristic
286C2#1176378811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C22⋊C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC2×#10587570C2
cosocleC23×D17C23
hypercenterC2×C22⋊C4#595
hypocenterC17#1964
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10587539C2semidirect
2. C2×#10587551C2semidirect
3. #11763751C2semidirect
4. C4×C22⋊#595C2semidirect
6. C22×C22⋊D17C4semidirect
14. C2×C22⋊C4×C17C4semidirect
15. C2×#63227C4semidirect
16. C2×#63225C4semidirect
53. C22⋊#595D4semidirect
134. Dic17#99semidirect
162. C2×C22⋊C4#595semidirect
168. C17#1964semidirect

Maximal subgroups

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

subgroupindex
C2×#105875392
C2×#105875512
#117637512
C4×C22⋊#5952
C2×#105875702
#196417