Finite Group Databasebeta

← #14529239

Subgroups — #14529239

Order 2176.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10587621C211yesmaximal, characteristic
2C2×#10587563C211yesmaximal, characteristic, complemented
3C2×#10587505C211yesmaximal, characteristic
4#11762670C211yesmaximal, characteristic, complemented
5#11762575C211yesmaximal, characteristic, complemented
6#11762575C211yesmaximal, characteristic, complemented
7C2×C17×#99C211yesmaximal, characteristic
8C22×D4×C17C2211yescharacteristic
9C23×Dic17C2211yescharacteristic
10C2×C22⋊C4×C17C2211yescharacteristic
11C2×C22⋊C4×C17C2211yescharacteristic
12C2×C22⋊Dic17C412yescomplemented
13C2×C22⋊Dic17C2211yescharacteristic
14C2×C22⋊Dic17C2211yescharacteristic
15C2×C22⋊Dic17C2211yescharacteristic
16#10587621—22no—
17#10587621—21no—
18#10587621—21no—
19C2×#63225—21no—
20C2×#63225C412yescomplemented
21C2×C4×Dic17—21no—
22#10587563—22no—
23#10587563—22no—
24C17×#99—22no—
25#10587505—22no—
26#10587502—22no—
27C24×C17C2×C411yescharacteristic
28C24×C17C2311yescharacteristic
29C2×D4×C17—21no—
30C2×D4×C17—21no—
31C2×D4×C17—21no—
32C2×D4×C17—21no—
33C2×D4×C17—21no—
34C2×D4×C17—21no—
35C22×C4×C17—21no—
36C22×C4×C17—21no—
37C22×C4×C17C2×C411yescharacteristic
38C22×Dic17—21no—
39C22×Dic17—21no—
40C22×Dic17—21no—
41C22×Dic17—21no—
42C22×Dic17—21no—
43C22×Dic17—21no—
44C22×Dic17C2×C412yes—
45C22×Dic17C2×C412yes—
46C22×Dic17D412yes—
47C22×Dic17D411yescharacteristic
48C22×Dic17D411yescharacteristic
49C22⋊C4×C17—21no—
50C22⋊C4×C17—21no—
51C22⋊C4×C17—21no—
52C22⋊C4×C17D412yes—
53C22⋊Dic17—21no—
54C22⋊Dic17—21no—
55C22⋊Dic17—21no—
56C22⋊Dic17—22no—
57C22⋊Dic17—22no—
58C22⋊Dic17—21no—
59C22⋊Dic17—21no—
60C22⋊Dic17D412yes—
61#63225—24no—
62#63225—22no—
63#63225—22no—
64C4×Dic17—24no—
65C23×C17—21no—
66C23×C17—21no—
67C23×C17—21no—
68C23×C17—42no—
69C23×C17—42no—
70C23×C17C22×C411yescharacteristic
71C23×C17C2×D411yescharacteristic
72C23×C17C2×D411yescharacteristic
73C23×C17C2×D411yescharacteristic
74C23×C17C2×D411yescharacteristic
75C23×C17#4111yescharacteristic
76C23×C17#4111yescharacteristic
77D4×C17—41no—
78D4×C17—41no—
79D4×C17—41no—
80D4×C17—41no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17—41no—
88C2×Dic17—22no—
89C2×Dic17—22no—
90C2×Dic17—21no—
91C2×Dic17—21no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—41no—
102C2×Dic17C22⋊C412yes—
103C2×Dic17C22⋊C412yes—
104#1899—171nomaximal, Sylow
105C22×C17—22no—
106C22×C17—22no—
107C22×C17—22no—
108C22×C17—41no—
109C22×C17—41no—
110C22×C17—41no—
111C22×C17—41no—
112C22×C17—41no—
113C22×C17—42no—
114C22×C17—81no—
115C22×C17—81no—
116C22×C17C2×C22⋊C411yescharacteristic
117C22×C17C4×D411yescharacteristic
118C22×C17C4×D411yescharacteristic
119C22×C17#12011yescharacteristic
120C22×C17#12111yescharacteristic
121C22×C17#12111yescharacteristic
122C22×C17#12311yescharacteristic
123C4×C17—42no—
124C4×C17—41no—
125C4×C17—81no—
126Dic17—22no—
127Dic17—22no—
128Dic17—42no—
129Dic17—42no—
130Dic17—81no—
131C2×#123—171no—
132C2×#117—171no—
133C2×#99—171no—
134C2×#99D1711yescharacteristic
135#381—171no—
136#342—171no—
137#342—171no—
138C2×C17—21no—
139C2×C17—21no—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17—21no—
144C2×C17—81no—
145C2×C17#38611yescharacteristic
146C2×C17#41012yes—
147C22×D4C2×D1711yescharacteristic
148C23×C4—171no—
149#123—342no—
150#123—341no—
151#123—341no—
152#117—342no—
153#117—342no—
154C2×C4⋊C4—172no—
155C2×C4⋊C4—341no—
156C2×C22⋊C4—171no—
157C2×C22⋊C4—172no—
158C2×C22⋊C4—171no—
159C2×C22⋊C4—171no—
160C2×C22⋊C4C2×D1711yescharacteristic
161C2×C22⋊C4C2×D1711yescharacteristic
162C2×C42—341no—
163#99—22no—
164#99—342no—
165#95—342no—
166C17#189911yescharacteristic, complemented, Sylow
167C24C4×D1711yescharacteristic
168C24C22×D1711yescharacteristic
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—172no—
178C22×C4—172no—
179C22×C4—171no—
180C22×C4—171no—
181C22×C4—172no—
182C22×C4—341no—
183C22×C4—341no—
184C22×C4—341no—
185C22×C4—341no—
186C22×C4—341no—
187C22×C4—341no—
188C22×C4C4×D1711yescharacteristic
189C4⋊C4—342no—
190C4⋊C4—342no—
191C4⋊C4—344no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—172no—
196C22⋊C4—342no—
197C22⋊C4—342no—
198C22⋊C4—341no—
199C22⋊C4—341no—
200C22⋊C4—341no—
201C22⋊C4—341no—
202C22⋊C4—341no—
203C22⋊C4C22⋊D1712yes—
204C42—344no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23—42no—
210C23C2×C4×D1711yescharacteristic
211C23#6325211yescharacteristic
212C23D4×D1711yescharacteristic
213C23D4×D1711yescharacteristic
214C23D4×D1711yescharacteristic
215C23#6325411yescharacteristic
216C23C2×C22⋊D1711yescharacteristic
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—172no—
229C2×C4—172no—
230C2×C4—342no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—342no—
234C2×C4—342no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—342no—
238C2×C4—342no—
239C2×C4—342no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4—682no—
243C2×C4—681no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—81no—
254C22—81no—
255C22C22⋊C4×D1711yescharacteristic
256C22#1058756711yescharacteristic
257C22#1058756911yescharacteristic
258C22#1058757011yescharacteristic
259C22C4×C22⋊D1711yescharacteristic
260C22#1058762311yescharacteristic
261C22#1058762411yescharacteristic
262C4—42no—
263C4—41no—
264C4—81no—
265C4—342no—
266C4—342no—
267C4—682no—
268C4—682no—
269C4—1361no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—81no—
277C2#1176268511yescharacteristic
278C2#1176278112yes—
subgroupG/H
centerC22C22⋊C4×D17
commutatorC23×C17C22×C4
FrattiniC24C22×D17
FittingC2×C17×#99C2
socleC22×C17C2×C22⋊C4
prime radicalC22×D4×C17C22
cosocleC24×C17C23
hypercenterC2×#99D17
hypocenterC17#1899
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10587563C2semidirect
4. #11762670C2semidirect
5. #11762575C2semidirect
6. #11762575C2semidirect
12. C2×C22⋊Dic17C4semidirect
20. C2×#63225C4semidirect
166. C17#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#105876212
C2×#105875632
C2×#105875052
#117626702
#117625752
C2×C17×#992
#189917