Finite Group Databasebeta

← #16944919

Subgroups — #16944919

Order 4352.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#10587507C211yesmaximal, characteristic
2#14527128C211yesmaximal, characteristic
3#14526790C214yesmaximal
4C17×#2546C211yesmaximal, characteristic
5#11762866—21no—
6C2×#10587507—21no—
7C4×#63223—21no—
8#11762578C2212yes—
9#11762535—21no—
10#11762535C2212yes—
11C2×C17×C4⋊Q8—21no—
12C2×C17×C4⋊Q8C411yescharacteristic
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#398C412yes—
15C17×#398C2212yes—
16C17×#391—21no—
17C17×#389—21no—
18C17×#389—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Q8×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—44no—
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17C2×C412yes—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17C2311yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2×C411yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C2×#63223—22no—
40C17×#95—22no—
41C17×#95—22no—
42C17×#95C2×C412yes—
43#10587507—24no—
44C22⋊#3622—22no—
45C4⋊#3622—41no—
46#10587474—41no—
47#10587474—41no—
48C4×#3622—41no—
49C2×Q8×C17—22no—
50C2×Q8×C17—22no—
51C2×Q8×C17—41no—
52C2×Q8×C17—42no—
53C2×Q8×C17—42no—
54C2×Q8×C17—42no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C4⋊C4×C17—24no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—42no—
69C4⋊C4×C17—44no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—44no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—42no—
80#63223—24no—
81#63223—42no—
82C2×#3622—42no—
83C2×#3622—42no—
84#11782—171nomaximal, Sylow
85C23×C17C2×C22⋊C411yescharacteristic
86Q8×C17—44no—
87Q8×C17—84no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—22no—
93C2×C4×C17—24no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#10412yes—
111C2×C4×C17AGL(1,ℤ/8)12yes—
112#3622—44no—
113#3622—82no—
114#2546D1711yescharacteristic
115C4×#101—171no—
116#1467—171no—
117#1346—174no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17C2×#9911yescharacteristic
121C22×C17#41811yescharacteristic
122C22×C17C2×#10411yescharacteristic
123C4×C17—21no—
124C4×C17—22no—
125C4×C17—22no—
126C4×C17—44no—
127C4×C17—41no—
128C4×C17—41no—
129C4×C17—41no—
130C4×C17—41no—
131C4×C17—82no—
132C4×C17#35612yes—
133C2×C4⋊Q8—21no—
134C2×C4⋊Q8Dic1711yescharacteristic
135C2×C4×Q8C2×D1711yescharacteristic
136#432—341no—
137C2×#101—341no—
138C4×M16—341no—
139#398Dic1712yes—
140#398C2×D1712yes—
141#391—21no—
142#389—21no—
143#389—21no—
144C4×C4⋊C4Dic1711yescharacteristic
145#343—172no—
146#324—172no—
147#324—341no—
148C2×C17—21no—
149C2×C17—21no—
150C2×C17#150711yescharacteristic
151C2×C17#212311yescharacteristic
152C2×C17C2×#35611yescharacteristic
153C22×Q8—21no—
154C22×Q8C22⋊D1711yescharacteristic
155C2×M16—342no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4⋊Q8—44no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4C2×Dic1712yes—
166C2×C4⋊C4C2×Dic1711yescharacteristic
167C2×C4⋊C4C22⋊D1711yescharacteristic
168C2×C4⋊C4C22×D1711yescharacteristic
169C2×C42—21no—
170C2×C42C2×Dic1711yescharacteristic
171C2×C42C22⋊D1711yescharacteristic
172C2×C42C22⋊D1711yescharacteristic
173C4⋊C8—681no—
174#101—344no—
175C22⋊C8—342no—
176#97—681no—
177#97—681no—
178C4×C8—681no—
179#95—22no—
180#95—22no—
181#95C2×Dic1712yes—
182C17#1178211yescharacteristic, complemented, Sylow
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊Dic1711yescharacteristic
192C22×C4C22⋊Dic1711yescharacteristic
193C22×C4C22⋊Dic1711yescharacteristic
194C22×C4C22⋊Dic1711yescharacteristic
195C22×C4C22×Dic1711yescharacteristic
196C22×C4C2×C22⋊D1711yescharacteristic
197C22×C4C2×C22⋊D1711yescharacteristic
198M16—344no—
199M16—682no—
200C2×C8—682no—
201C2×C8—682no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊Dic1711yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#1058750511yescharacteristic
242C2×C4#1058750511yescharacteristic
243C2×C4#1058750812yes—
244C2×C4#1058761812yes—
245C8—684no—
246C8—1362no—
247C22—21no—
248C22—21no—
249C22C2×#1058750511yescharacteristic
250C22#1176281411yescharacteristic
251C22C2×#1058750811yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#1176260812yes—
262C2—21no—
263C2—21no—
264C2#1452730011yescharacteristic
265C2#1453043811yescharacteristic
266C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2546C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2546D17
hypocenterC17#11782
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
182. C17#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#105875072
#145271282
#145267902
C17×#25462
#1178217