Finite Group Databasebeta

← #17958784

Subgroups — #17958784

Order 4352.

326 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#14545144C211yesmaximal, characteristic, complemented
2C4×#10587530C211yesmaximal, characteristic, complemented
3#14543751C212yesmaximal, complemented
4D4⋊#63216C212yesmaximal, complemented
5#14537762C211yesmaximal, characteristic
6C2×#10587530—21no—
7C4⋊#63216C2212yes—
8#11763704—21no—
9#11763698—21no—
10#11763695—21no—
11C4×#63216C2212yes—
12#11763341C411yescharacteristic
13#11762939C411yescharacteristic
14#11762933C2211yescharacteristic
15#11762878—21no—
16D4×#3622C2211yescharacteristic
17#11762872—21no—
18#11762867—21no—
19#11762865C411yescharacteristic
20#11762767—21no—
21C4×C8×D17C2211yescharacteristic
22C17×#436C411yescharacteristic
23C2×M16×C17—21no—
24C4×D4×C17C2×C411yescharacteristic
25#10587624C811yescharacteristic
26#10587622C811yescharacteristic
27C4×C22⋊D17—21no—
28#10587612—21no—
29C22×#3622—21no—
30C2×C8×D17D411yescharacteristic
31C2×C8×D17D411yescharacteristic
32#10587583C811yescharacteristic
33#10587576C811yescharacteristic
34#10587569—21no—
35#10587565—21no—
36C42×D17C2×C411yescharacteristic
37C4×Dic34C2×C411yescharacteristic
38C2×#63216—22no—
39C2×#63216—22no—
40#10587530—24no—
41C17×C4⋊C8C2×C411yescharacteristic
42C17×C22⋊C8—21no—
43C4×C8×C17C2×C411yescharacteristic
44C22⋊#3622—21no—
45#10587491—21no—
46#10587486—21no—
47#10587486—21no—
48#10587485—21no—
49#10587485—21no—
50C8×Dic17—21no—
51C8×Dic17D411yescharacteristic
52C8×Dic17D411yescharacteristic
53C4⋊#3622C2×C411yescharacteristic
54C4×#3622C2311yescharacteristic
55C2×D4×C17C2×C811yescharacteristic
56C22×C4×C17—21no—
57C2×C22⋊D17—21no—
58C2×C4×D17C22⋊C411yescharacteristic
59C2×C4×D17C2×C811yescharacteristic
60C2×C4×D17M1611yescharacteristic
61C2×Dic34C2×C811yescharacteristic
62M16×C17—42no—
63C2×C8×C17—21no—
64C2×C8×C17C22⋊C411yescharacteristic
65C2×C8×C17C22⋊C411yescharacteristic
66C4⋊C4×C17C2×C811yescharacteristic
67C22⋊C4×C17—21no—
68C42×C17C22×C411yescharacteristic
69C22⋊Dic17—21no—
70C22⋊Dic17—21no—
71C22⋊Dic17—21no—
72#63227—21no—
73C4⋊Dic17—21no—
74C4⋊Dic17—21no—
75C4⋊Dic17C2×C811yescharacteristic
76#63225—21no—
77#63225—21no—
78C4×Dic17—21no—
79C4×Dic17C22⋊C411yescharacteristic
80C4×Dic17C2×C811yescharacteristic
81C4×Dic17M1611yescharacteristic
82C2×#3622—21no—
83C2×#3622—42no—
84C2×#3622C2×D411yescharacteristic
85C2×#3622C2×D411yescharacteristic
86C8×D17—22no—
87C8×D17—22no—
88#63216—24no—
89#63216—42no—
90#11614—171nomaximal, Sylow
91C23×C17—21no—
92C22×D17C22⋊C811yescharacteristic
93D4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17C2×C22⋊C411yescharacteristic
98C2×C4×C17C22×C811yescharacteristic
99C2×C4×C17C2×M1611yescharacteristic
100C22⋊D17—42no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17C22⋊C811yescharacteristic
104C2×Dic17C22⋊C811yescharacteristic
105C2×Dic17C22⋊C811yescharacteristic
106C4×D17—21no—
107C4×D17—21no—
108C4×D17—22no—
109C4×D17—41no—
110Dic34—22no—
111C8×C17—21no—
112C8×C17—41no—
113C8×C17#10412yes—
114#3622—21no—
115#3622—41no—
116#3622#13512yes—
117#2966—171no—
118#2162—171no—
119C4×M32—171no—
120Q8⋊C16—172no—
121D4⋊C16—172no—
122C22×C17—41no—
123C22×C17—41no—
124C22×C17—41no—
125C22×C17C2×C22⋊C811yescharacteristic
126C2×D17—21no—
127C2×D17—21no—
128C2×D17—21no—
129C4×C17—21no—
130C4×C17—41no—
131C4×C17#41611yescharacteristic
132C4×C17C2×#10411yescharacteristic
133C4×C17#50412yes—
134Dic17—21no—
135Dic17—21no—
136Dic17—21no—
137Dic17—41no—
138Dic17—41no—
139#529—171no—
140C2×M32—341no—
141#446—171no—
142C8×Q8—171no—
143#436#59511yescharacteristic
144#435—341no—
145C8×D4—171no—
146C8×D4—341no—
147#433—341no—
148#432—171no—
149#405—341no—
150C2×C4×C8—171no—
151C4⋊C16—172no—
152C22⋊C16—341no—
153#346—341no—
154C4×C16—172no—
155C4×C16—341no—
156C2×C17—81no—
157C2×C17#147611yescharacteristic
158C2×C17#211311yescharacteristic
159C2×C17#211711yescharacteristic
160D17—41no—
161C2×M16—21no—
162C22×C8—171no—
163C22×C8—171no—
164C22×C8—341no—
165#126—341no—
166#125—171no—
167#124—171no—
168#123—341no—
169C22⋊Q8—171no—
170#121—171no—
171C4×Q8—171no—
172C4×D4—341no—
173C4×D4C2×#59511yescharacteristic
174#117—341no—
175C2×C42—171no—
176M32—344no—
177C2×C16—342no—
178C2×C16—342no—
179C4⋊C8—171no—
180C4⋊C8—341no—
181C4⋊C8—341no—
182C4⋊C8C2×#59511yescharacteristic
183C22⋊C8—21no—
184C22⋊C8—341no—
185C22⋊C8—341no—
186#97—341no—
187#97—341no—
188C4×C8—171no—
189C4×C8—171no—
190C4×C8—171no—
191C4×C8—341no—
192C4×C8C2×#59511yescharacteristic
193C17#1161411yescharacteristic, complemented, Sylow
194C2×Q8—171no—
195C2×D4—341no—
196C2×D4#6324211yescharacteristic
197C22×C4—21no—
198C22×C4—171no—
199C22×C4—171no—
200C22×C4—171no—
201M16—42no—
202C2×C8—21no—
203C2×C8—171no—
204C2×C8—171no—
205C2×C8—342no—
206C2×C8—342no—
207C2×C8—341no—
208C2×C8—682no—
209C2×C8C22⋊#59511yescharacteristic
210C2×C8C22⋊#59511yescharacteristic
211C4⋊C4—171no—
212C4⋊C4—341no—
213C4⋊C4—341no—
214C4⋊C4—341no—
215C4⋊C4—341no—
216C4⋊C4#6324211yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—341no—
219C22⋊C4—341no—
220C22⋊C4—341no—
221C22⋊C4—341no—
222C42—171no—
223C42—171no—
224C42—171no—
225C42—341no—
226C42C22×#59511yescharacteristic
227C16—344no—
228C16—682no—
229C23—21no—
230C23—171no—
231Q8—342no—
232D4—22no—
233D4—682no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—171no—
238C2×C4—171no—
239C2×C4—171no—
240C2×C4—341no—
241C2×C4—341no—
242C2×C4—342no—
243C2×C4—341no—
244C2×C4—341no—
245C2×C4—681no—
246C2×C4C2×#6324211yescharacteristic
247C2×C4D17⋊M1611yescharacteristic
248C2×C4C2×C22⋊#59511yescharacteristic
249C8—21no—
250C8—41no—
251C8—172no—
252C8—341no—
253C8—681no—
254C8#1058754812yes—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—341no—
259C22—341no—
260C22—341no—
261C22#1176377711yescharacteristic
262C4—21no—
263C4—41no—
264C4—341no—
265C4—341no—
266C4—341no—
267C4—681no—
268C4—681no—
269C4#1176379911yescharacteristic
270C4C2×#1058754811yescharacteristic
271C4#1176386812yes—
272C2—81no—
273C2—681no—
274C2#1454407611yescharacteristic
275C2#1454501511yescharacteristic
276C2#1454502711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC42C22×#595
FittingC17×#436C4
socleC22×C17C2×C22⋊C8
prime radical#10587624C8
cosocleC4×#3622C23
hypercenter#436#595
hypocenterC17#11614
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #14545144C2semidirect
2. C4×#10587530C2semidirect
3. #14543751C2semidirect
4. D4⋊#63216C2semidirect
193. C17#11614semidirect

Maximal subgroups

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

subgroupindex
#145451442
C4×#105875302
#145437512
D4⋊#632162
#145377622
#1161417