Finite Group Databasebeta

← #17961438

Subgroups — #17961438

Order 4352.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11763719C212yesmaximal
2#14544650C212yesmaximal
3#14543882C212yesmaximal
4#14531500C211yesmaximal, characteristic
5#11763812—22no—
6C2×#10587545C2214yes—
7#11763719—24no—
8#11763689—22no—
9C2×#10587630C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762716C411yescharacteristic
12#11762714C2211yescharacteristic
13#11762693—22no—
14#11762690—22no—
15#11762674C411yescharacteristic
16#11762655C411yescharacteristic
17C2×C4×Q8×C17C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C22×Dic34C2311yescharacteristic
20C2×#63247—24no—
21C4×Q8×C17—42no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26#10587630—22no—
27#10587630D412yes—
28#10587630Q812yes—
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×#63225—22no—
31C2×#63225D412yes—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D412yes—
35C4×Dic34—42no—
36#10587545—24no—
37#10587545—24no—
38#10587544—42no—
39C4⋊#3624—42no—
40#10587502—21no—
41#10587502—21no—
42#10587502—22no—
43#10587502—22no—
44#10587502—22no—
45C2×Q8×C17—21no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17C4⋊C412yes—
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—21no—
55C22×Dic17—21no—
56C22×Dic17C22⋊C412yes—
57C22×Dic17C2×D412yes—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34C2×D411yescharacteristic
61C2×Dic34C2×Q811yescharacteristic
62C2×Dic34#4112yes—
63#63247—44no—
64#63247—44no—
65C2×#3624—44no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C42×C17—22no—
69C42×C17—42no—
70C4⋊Dic17—41no—
71#63225—24no—
72#63225—24no—
73#63225—42no—
74C4×Dic17—22no—
75C4×Dic17—22no—
76C4×Dic17—21no—
77C4×Dic17—41no—
78C4×Dic17C4⋊C412yes—
79#12804—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81Q8×C17—42no—
82Q8×C17—42no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—21no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—42no—
92C2×C4×C17—41no—
93C2×C4×C17#9912yes—
94C2×C4×C17C2×C4⋊C411yescharacteristic
95C2×C4×C17#11711yescharacteristic
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—22no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—42no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—41no—
106C2×Dic17#12112yes—
107C2×Dic17C22⋊Q812yes—
108Dic34—41no—
109Dic34—41no—
110Dic34—42no—
111#3624—84no—
112#2327—171no—
113C2×#356—172no—
114#1801—172no—
115#1394—172no—
116C22×C17—21no—
117C22×C17—21no—
118C22×C17#38011yescharacteristic
119C22×C17C2×#9911yescharacteristic
120C22×C17#41011yescharacteristic
121C4×C17—21no—
122C4×C17—21no—
123C4×C17—22no—
124C4×C17—42no—
125C4×C17—41no—
126C4×C17—81no—
127Dic17—22no—
128Dic17—22no—
129Dic17—42no—
130Dic17—42no—
131Dic17—81no—
132C2×C4⋊Q8—171no—
133C2×C4×Q8—171no—
134C2×C4×Q8#59511yescharacteristic
135#423—342no—
136C2×#101—174no—
137#391—171no—
138#391—171no—
139#387—342no—
140#387—342no—
141#382—171no—
142#376—171no—
143#356—344no—
144#343—342no—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17#179911yescharacteristic
148C2×C17#213311yescharacteristic
149C2×C17#213511yescharacteristic
150C22×Q8—171no—
151C22×Q8C2×#59511yescharacteristic
152C2×M16—344no—
153C4⋊Q8—172no—
154C4⋊Q8—172no—
155C4⋊Q8—342no—
156C4×Q8—42no—
157C4×Q8—682no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—172no—
160C2×C4⋊C4—171no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4C2×#59511yescharacteristic
163C2×C42—21no—
164C2×C42—171no—
165C2×C42—172no—
166C2×C42—171no—
167C2×C42C2×#59511yescharacteristic
168C4⋊C8—682no—
169C4⋊C8—682no—
170#101—344no—
171#101—344no—
172#95—342no—
173#95—342no—
174#95—342no—
175#95—341no—
176#95—341no—
177C17#1280411yescharacteristic, complemented, Sylow
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—171no—
182C2×Q8—171no—
183C2×Q8—172no—
184C2×Q8—681no—
185C2×Q8—681no—
186C2×Q8C4⋊#59512yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—172no—
190C22×C4—172no—
191C22×C4—341no—
192C22×C4—341no—
193C22×C4C22⋊#59511yescharacteristic
194C22×C4C22⋊#59511yescharacteristic
195C22×C4C22×#59511yescharacteristic
196M16—684no—
197M16—684no—
198C2×C8—684no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—344no—
202C4⋊C4—344no—
203C4⋊C4—682no—
204C4⋊C4—681no—
205C42—22no—
206C42—42no—
207C42—172no—
208C42—341no—
209C42—342no—
210C42—342no—
211C42—681no—
212C23C2×C22⋊#59511yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—681no—
216Q8—681no—
217Q8—682no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—172no—
229C2×C4—172no—
230C2×C4—342no—
231C2×C4—342no—
232C2×C4—342no—
233C2×C4—342no—
234C2×C4—681no—
235C2×C4—681no—
236C2×C4—682no—
237C2×C4—681no—
238C2×C4—681no—
239C2×C4—681no—
240C2×C4#1058755112yes—
241C2×C4C2×C4⋊#59511yescharacteristic
242C2×C4#1058767711yescharacteristic
243C8—1364no—
244C22—21no—
245C22—21no—
246C22#1176375111yescharacteristic
247C22C2×#1058755111yescharacteristic
248C22#1176378811yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—81no—
255C4—342no—
256C4—342no—
257C4—682no—
258C4—682no—
259C4—1361no—
260C2—21no—
261C2—21no—
262C2#1454464411yescharacteristic
263C2#1454507911yescharacteristic
264C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenterC2×C4×Q8#595
hypocenterC17#12804
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
177. C17#12804semidirect

Maximal subgroups

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

subgroupindex
C2×#117637192
#145446502
#145438822
#145315002
#1280417