Finite Group Databasebeta

← #14545039

Subgroups — #14545039

Order 2176.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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×#10587553C211yesmaximal, characteristic, complemented
2C2×#10587551C211yesmaximal, characteristic, complemented
3#11763711C212yesmaximal, complemented
4#11763709C212yesmaximal, complemented
5#11763368C211yesmaximal, characteristic
6C22×D4×C17C411yescharacteristic, complemented
7C22×C22⋊D17C2211yescharacteristic
8C2×C22⋊#595—21no—
9C2×#63247—21no—
10#10587639C411yescharacteristic, complemented
11#10587639C2211yescharacteristic
12C2×C22⋊Dic17C411yescharacteristic, complemented
13#10587625—21no—
14#10587625—21no—
15#10587623—21no—
16#10587621—21no—
17#10587615C411yescharacteristic, complemented
18#10587615C2211yescharacteristic
19#10587553—21no—
20#10587553C2212yes—
21#10587551—21no—
22#10587551C2212yes—
23C24×C17C2×C411yescharacteristic
24C24×C17C2×C411yescharacteristic, complemented
25C23×D17D411yescharacteristic
26C22×#595—41no—
27C2×D4×C17—21no—
28C2×D4×C17—21no—
29C2×D4×C17—41no—
30C2×D4×C17—41no—
31C22×C4×C17C2×C411yescharacteristic, complemented
32C2×C22⋊D17—21no—
33C2×C22⋊D17—21no—
34C2×C22⋊D17—41no—
35C2×C22⋊D17—41no—
36C2×C22⋊D17C2×C411yescharacteristic
37C2×C22⋊D17D411yescharacteristic
38C2×C22⋊D17D411yescharacteristic
39C2×C22⋊D17C2311yescharacteristic
40C22×Dic17—21no—
41C22×Dic17D411yescharacteristic
42C22⋊#595—22no—
43C22⋊#595—41no—
44#63247—22no—
45#63247—41no—
46C2×#3624—41no—
47C22⋊Dic17—21no—
48C22⋊Dic17—21no—
49C22⋊Dic17—21no—
50C22⋊Dic17C2×C411yescharacteristic, complemented
51C22⋊Dic17C2×C411yescharacteristic, complemented
52#63227—21no—
53#63227—21no—
54#63225—21no—
55#63225—21no—
56C23×C17—21no—
57C23×C17—21no—
58C23×C17—21no—
59C23×C17—41no—
60C23×C17—81no—
61C23×C17—81no—
62C23×C17C22⋊C411yescharacteristic
63C23×C17C22⋊C411yescharacteristic
64C23×C17C22×C411yescharacteristic
65C22×D17—21no—
66C22×D17—21no—
67C22×D17—81no—
68C22×D17C22⋊C411yescharacteristic
69C22×D17C2×D411yescharacteristic
70C2×#595—42no—
71C2×#595—82no—
72D4×C17—42no—
73D4×C17—41no—
74D4×C17—41no—
75C2×C4×C17—21no—
76C2×C4×C17—41no—
77C22⋊D17—41no—
78C22⋊D17—41no—
79C22⋊D17—41no—
80C22⋊D17—41no—
81C22⋊D17—81no—
82C22⋊D17—81no—
83C2×Dic17—21no—
84C2×Dic17—21no—
85C2×Dic17—21no—
86C2×Dic17—21no—
87C2×Dic17—81no—
88C2×Dic17C22⋊C411yescharacteristic
89C2×Dic17C2×D411yescharacteristic
90#3624—42no—
91#2121—171nomaximal, Sylow
92C22×C17—21no—
93C22×C17—21no—
94C22×C17—41no—
95C22×C17—41no—
96C22×C17—41no—
97C22×C17—41no—
98C22×C17—41no—
99C22×C17—41no—
100C22×C17—81no—
101C22×C17—81no—
102C22×C17—82no—
103C22×C17#9911yescharacteristic
104C22×C17#9911yescharacteristic
105C22×C17C2×C22⋊C411yescharacteristic
106C2×D17—21no—
107C2×D17—21no—
108C2×D17—42no—
109C2×D17—41no—
110C2×D17—41no—
111C2×D17—81no—
112#595—82no—
113C4×C17—41no—
114Dic17—21no—
115Dic17—21no—
116Dic17—41no—
117Dic17—41no—
118#534—171no—
119C2×#100—171no—
120C2×#99—171no—
121#352—172no—
122AΣL(1,𝔽16)—172no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17—21no—
126C2×C17—41no—
127C2×C17—41no—
128C2×C17—81no—
129C2×C17C2×#9911yescharacteristic
130D17—41no—
131D17—41no—
132C22×D4—171no—
133C22×D4#59511yescharacteristic, complemented
134C2×M16—341no—
135#123—171no—
136#123—171no—
137#123—341no—
138#121—341no—
139#121—341no—
140#120—171no—
141#120—171no—
142#120—341no—
143C2×C22⋊C4—171no—
144C2×C22⋊C4—341no—
145#100—172no—
146#100—341no—
147#99—172no—
148#99—341no—
149C17#212111yescharacteristic, complemented, Sylow
150C24—171no—
151C24C2×#59511yescharacteristic
152C24C2×#59511yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—171no—
158C2×D4—171no—
159C2×D4—171no—
160C2×D4—171no—
161C2×D4—341no—
162C2×D4—341no—
163C2×D4—681no—
164C2×D4—681no—
165C22×C4—171no—
166C22×C4—341no—
167C22×C4—681no—
168C22×C4C2×#59511yescharacteristic, complemented
169M16—342no—
170M16—681no—
171C2×C8—681no—
172C4⋊C4—341no—
173C4⋊C4—341no—
174C22⋊C4—171no—
175C22⋊C4—171no—
176C22⋊C4—341no—
177C22⋊C4—341no—
178C22⋊C4—341no—
179C22⋊C4—341no—
180C22⋊C4—341no—
181C22⋊C4—342no—
182C22⋊C4—681no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—81no—
188C23—81no—
189C23—171no—
190C23—171no—
191C23—341no—
192C23—341no—
193C23—1361no—
194C23C22⋊#59511yescharacteristic
195C23C22⋊#59511yescharacteristic
196C23C22×#59511yescharacteristic
197D4—42no—
198D4—41no—
199D4—41no—
200D4—681no—
201D4—681no—
202D4—681no—
203D4—681no—
204D4—1361no—
205D4—1361no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—171no—
209C2×C4—171no—
210C2×C4—341no—
211C2×C4—341no—
212C2×C4—341no—
213C2×C4—341no—
214C2×C4—682no—
215C2×C4—1361no—
216C2×C4—1362no—
217C8—682no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—81no—
227C22—81no—
228C22—82no—
229C22—341no—
230C22—341no—
231C22—681no—
232C22—681no—
233C22—682no—
234C22—1361no—
235C22#1058755111yescharacteristic
236C22#1058755111yescharacteristic
237C22C2×C22⋊#59511yescharacteristic
238C4—41no—
239C4—341no—
240C4—341no—
241C4—681no—
242C4—681no—
243C4—1362no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2—681no—
251C2—681no—
252C2C2×#1058755111yescharacteristic
subgroupG/H
centerC2C2×#10587551
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC22×D4×C17C4
socleC2×C17C2×#99
prime radical#11763368C2
cosocleC2×C22⋊D17C23
hypercenterC22×D4#595
hypocenterC17#2121
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10587553C2semidirect
2. C2×#10587551C2semidirect
3. #11763711C2semidirect
4. #11763709C2semidirect
6. C22×D4×C17C4semidirect
10. #10587639C4semidirect
12. C2×C22⋊Dic17C4semidirect
17. #10587615C4semidirect
24. C24×C17C2×C4semidirect
31. C22×C4×C17C2×C4semidirect
50. C22⋊Dic17C2×C4semidirect
51. C22⋊Dic17C2×C4semidirect
133. C22×D4#595semidirect
149. C17#2121semidirect
152. C24C2×#595semidirect
168. C22×C4C2×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#105875532
C2×#105875512
#117637112
#117637092
#117633682
#212117