Finite Group Databasebeta

← #17958314

Subgroups — #17958314

Order 4352.

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

normal subgroups only

This group has 428 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#14544027C212yesmaximal
2#14543727C212yesmaximal
3#14543715C212yesmaximal
4#14531353C211yesmaximal, characteristic
5#11763825—22no—
6#11763654—22no—
7#11763654C2214yes—
8C2×#10587630C411yescharacteristic
9C2×Q8×Dic17C2211yescharacteristic
10C2×#10587573C411yescharacteristic
11#11762715C2211yescharacteristic
12#11762706—22no—
13#11762678C2211yescharacteristic
14#11762660—22no—
15C42×Dic17C411yescharacteristic
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C2×C4⋊C4×C17C2×C411yescharacteristic
20C2×C42×C17C2×C411yescharacteristic
21Q8×Dic17—41no—
22Q8×Dic17—41no—
23#10587630—22no—
24#10587630C814yescomplemented
25C2×C4⋊Dic17D412yes—
26C2×C4⋊Dic17C2311yescharacteristic
27C2×#63225—22no—
28C2×#63225—21no—
29C2×#63225—22no—
30C2×C4×Dic17—21no—
31C2×C4×Dic17—21no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D412yes—
36#10587573—41no—
37#10587573—41no—
38C22⋊#3624—24no—
39C4⋊#3624—42no—
40C4×#3624—42no—
41C17×#95—22no—
42#10587502—22no—
43C2×Q8×C17—41no—
44C2×Q8×C17—41no—
45C2×Q8×C17C2×C812yes—
46C2×Q8×C17M1612yes—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C412yes—
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17—21no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D412yes—
56C2×Dic34—21no—
57C2×Dic34—41no—
58C2×Dic34—41no—
59C2×Dic34C2×C812yes—
60C2×#3624—44no—
61C4⋊C4×C17—41no—
62C42×C17—41no—
63C4⋊Dic17—42no—
64C4⋊Dic17—41no—
65#63225—28no—
66#63225—42no—
67#63225—44no—
68C4×Dic17—24no—
69C4×Dic17—21no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—21no—
73C4×Dic17—21no—
74C4×Dic17—42no—
75C4×Dic17—41no—
76C4×Dic17—41no—
77C4×Dic17C2×C812yes—
78#11478—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80Q8×C17—42no—
81Q8×C17—42no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17—41no—
91C2×C4×C17C22⋊C814yes—
92C2×C4×C17C22×C811yescharacteristic
93C2×C4×C17C2×M1611yescharacteristic
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—22no—
100C2×Dic17—21no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17#9911yescharacteristic
106C2×Dic17#9911yescharacteristic
107Dic34—42no—
108Dic34—42no—
109#3624—84no—
110C4×C4⋊Q8—171no—
111#1461—172no—
112#1325—172no—
113#1319—172no—
114C22×C17—21no—
115C22×C17—21no—
116C22×C17C2×C22⋊C811yescharacteristic
117C22×C17C2×#9911yescharacteristic
118C22×C17#41311yescharacteristic
119C4×C17—21no—
120C4×C17—21no—
121C4×C17—24no—
122C4×C17—42no—
123C4×C17—81no—
124Dic17—24no—
125Dic17—21no—
126Dic17—42no—
127Dic17—41no—
128Dic17—42no—
129Dic17#35612yes—
130C2×C4⋊Q8—171no—
131C2×C4×Q8—171no—
132C2×C4×Q8—171no—
133#431—342no—
134#391—171no—
135#391#59511yescharacteristic
136#389—342no—
137#384—171no—
138C4×C4⋊C4—342no—
139C43—171no—
140#324—174no—
141#324—342no—
142C2×C17—21no—
143C2×C17—21no—
144C2×C17#145911yescharacteristic
145C2×C17#212611yescharacteristic
146C2×C17C2×#35611yescharacteristic
147C22×Q8—171no—
148C22×Q8C2×#59511yescharacteristic
149C4⋊Q8—174no—
150C4⋊Q8—342no—
151C4×Q8—681no—
152C4×Q8—681no—
153C4×Q8—681no—
154C4×Q8—681no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—171no—
157C2×C4⋊C4—342no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4C2×#59511yescharacteristic
161C2×C42—171no—
162C2×C42—172no—
163C2×C42—171no—
164C2×C42—341no—
165C2×C42—341no—
166C2×C42—341no—
167C2×C42C2×#59511yescharacteristic
168C4⋊C8—682no—
169C22⋊C8—344no—
170C4×C8—682no—
171#95—22no—
172#95—342no—
173C17#1147811yescharacteristic, complemented, Sylow
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—172no—
177C2×Q8—341no—
178C2×Q8—681no—
179C2×Q8—681no—
180C2×Q8#6324212yes—
181C2×Q8#6324312yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—172no—
187C22×C4—341no—
188C22×C4—341no—
189C22×C4C22⋊#59512yes—
190C22×C4C22×#59511yescharacteristic
191C2×C8—684no—
192C4⋊C4—41no—
193C4⋊C4—348no—
194C4⋊C4—681no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C4⋊C4—684no—
198C42—41no—
199C42—172no—
200C42—342no—
201C42—342no—
202C42—341no—
203C42—341no—
204C42—344no—
205C42—341no—
206C42—681no—
207C42—681no—
208C42—682no—
209C23C2×C22⋊#59511yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—682no—
213Q8—682no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—171no—
224C2×C4—171no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—342no—
228C2×C4—342no—
229C2×C4—342no—
230C2×C4—341no—
231C2×C4—342no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—682no—
236C2×C4#1058754314yes—
237C2×C4C2×#6324211yescharacteristic
238C2×C4C2×#6324311yescharacteristic
239C8—1364no—
240C22—21no—
241C22—21no—
242C22C2×#1058754311yescharacteristic
243C22D17⋊#9911yescharacteristic
244C22#1176379611yescharacteristic
245C4—21no—
246C4—21no—
247C4—24no—
248C4—42no—
249C4—81no—
250C4—172no—
251C4—344no—
252C4—341no—
253C4—682no—
254C4—682no—
255C4—681no—
256C2—21no—
257C2—21no—
258C2#1454402211yescharacteristic
259C2#1454505611yescharacteristic
260C2D17⋊#35611yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#391#595
hypocenterC17#11478
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
24. #10587630C8semidirect
173. C17#11478semidirect

Maximal subgroups

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

subgroupindex
#145440272
#145437272
#145437152
#145313532
#1147817