Finite Group Databasebeta

← #17949910

Subgroups — #17949910

Order 4352.

520 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 110 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#14544570C212yesmaximal, complemented
2#14543604C212yesmaximal, complemented
3#14543601C212yesmaximal
4C4×#10587633C211yesmaximal, characteristic
5C2×C4⋊#3624—22no—
6C2×#10587542—22no—
7#11763675C2214yes—
8C2×#10587633C411yescharacteristic
9C2×C4×D68C411yescharacteristic
10#11762716C2211yescharacteristic
11#11762710C2211yescharacteristic
12#11762699—22no—
13#11762674C411yescharacteristic
14C4×#63227—22no—
15C42×Dic17C2211yescharacteristic
16C2×C4×Q8×C17C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C22×#3624—24no—
21C4×Q8×C17—42no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26#10587633—22no—
27#10587633—22no—
28C2×#63227—21no—
29C2×#63227—22no—
30C2×#63227—22no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C4×D68—42no—
37#10587542—44no—
38C4⋊#3624—28no—
39#10587502—22no—
40#10587502—22no—
41C23×D17—21no—
42C2×Q8×C17—21no—
43C2×Q8×C17—41no—
44C2×Q8×C17—41no—
45C2×Q8×C17M1612yes—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17C22⋊C412yes—
53C22×Dic17C2×D412yes—
54C2×D68—21no—
55C2×D68—41no—
56C2×D68—41no—
57C2×D68M1612yes—
58C2×C4×D17—42no—
59C2×C4×D17—44no—
60C2×#3624—28no—
61C2×#3624—44no—
62C2×#3624—44no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—42no—
65C42×C17—22no—
66C42×C17—42no—
67#63227—28no—
68#63227—42no—
69#63227—42no—
70#63227—42no—
71C4⋊Dic17—41no—
72C4×Dic17—24no—
73C4×Dic17—21no—
74C4×Dic17—21no—
75C4×Dic17—22no—
76C4×Dic17—22no—
77C4×Dic17—41no—
78#7635—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80C22×D17—22no—
81C22×D17—41no—
82C22×D17—41no—
83C22×D17—42no—
84C22×D17—42no—
85Q8×C17—42no—
86Q8×C17—42no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17#10012yes—
97C2×C4×C17#10414yes—
98C2×C4×C17C2×M1611yescharacteristic
99C2×C4×C17C2×M1611yescharacteristic
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—41no—
106C2×Dic17—42no—
107C2×Dic17AGL(1,ℤ/8)12yes—
108C2×Dic17#13712yes—
109D68—42no—
110D68—42no—
111C4×D17—84no—
112#3624—48no—
113C4×#124—171no—
114#1767—172no—
115#1272—172no—
116#1270—172no—
117C22×C17#40711yescharacteristic
118C22×C17#41011yescharacteristic
119C22×C17C2×#10011yescharacteristic
120C22×C17#41712yes—
121C22×C17C2×#10412yes—
122C2×D17—42no—
123C2×D17—44no—
124C2×D17—81no—
125C2×D17—82no—
126C2×D17—81no—
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—41no—
130C4×C17—42no—
131C4×C17—81no—
132C4×C17#32914yes—
133Dic17—22no—
134Dic17—22no—
135Dic17—42no—
136Dic17—81no—
137C2×#124—171no—
138C2×C4×Q8#59511yescharacteristic
139C2×C4×D4—171no—
140C2×C4⋊C8—342no—
141C2×#97—342no—
142#391—171no—
143#390—171no—
144#388—342no—
145#382—171no—
146C4×C22⋊C4—342no—
147C43—171no—
148#336—174no—
149C2×C17#146611yescharacteristic
150C2×C17#148912yes—
151C2×C17#150912yes—
152C2×C17C2×#32911yescharacteristic
153C2×C17#156011yescharacteristic
154D17—82no—
155C22×Q8C2×#59511yescharacteristic
156C22×D4—171no—
157C23×C4—341no—
158C22×C8—344no—
159#124—342no—
160#124—342no—
161C4×Q8—42no—
162C4×D4—682no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4C2×#59511yescharacteristic
166C2×C22⋊C4—342no—
167C2×C22⋊C4—342no—
168C2×C22⋊C4—341no—
169C2×C42—21no—
170C2×C42—172no—
171C2×C42—172no—
172C2×C42—171no—
173C2×C42—171no—
174C2×C42C2×#59511yescharacteristic
175C4⋊C8—348no—
176#97—684no—
177#95—342no—
178#95—342no—
179C17#763511yescharacteristic, complemented, Sylow
180C24—341no—
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8#6324312yes—
185C2×D4—172no—
186C2×D4—341no—
187C2×D4—681no—
188C2×D4—681no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—172no—
192C22×C4—172no—
193C22×C4—341no—
194C22×C4—684no—
195C22×C4—682no—
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22×#59511yescharacteristic
199C2×C8—348no—
200C2×C8—684no—
201C2×C8—684no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—681no—
205C22⋊C4—348no—
206C22⋊C4—682no—
207C22⋊C4—682no—
208C22⋊C4—682no—
209C42—22no—
210C42—42no—
211C42—342no—
212C42—342no—
213C42—341no—
214C42—341no—
215C42—344no—
216C42—681no—
217C23—342no—
218C23—681no—
219C23—681no—
220C23—682no—
221C23—682no—
222C23C2×C22⋊#59511yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—682no—
226D4—682no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—172no—
237C2×C4—172no—
238C2×C4—342no—
239C2×C4—342no—
240C2×C4—342no—
241C2×C4—342no—
242C2×C4—342no—
243C2×C4—681no—
244C2×C4—682no—
245C2×C4—1364no—
246C2×C4#1058755014yes—
247C2×C4#1058755312yes—
248C2×C4C2×#6324311yescharacteristic
249C2×C4D17⋊M1611yescharacteristic
250C8—688no—
251C22—682no—
252C22—684no—
253C22—1362no—
254C22—1361no—
255C22—1361no—
256C22#1176378011yescharacteristic
257C22#1176378811yescharacteristic
258C22C2×#1058755311yescharacteristic
259C22#1176380012yes—
260C22C2×#1058755012yes—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—81no—
266C4—342no—
267C4—342no—
268C4—682no—
269C4—1361no—
270C4#1176366514yes—
271C2—1362no—
272C2#1454404311yescharacteristic
273C2#1454412212yes—
274C2#1454418812yes—
275C2C2×#1176366511yescharacteristic
276C2#1454432111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7635
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14544570C2semidirect
2. #14543604C2semidirect
179. C17#7635semidirect

Maximal subgroups

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

subgroupindex
#145445702
#145436042
#145436012
C4×#105876332
#763517