Finite Group Databasebeta

← #17954592

Subgroups — #17954592

Order 4352.

474 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 100 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#14545680C211yesmaximal, characteristic
2#14544086C212yesmaximal
3#14544027C211yesmaximal, characteristic
4#14543608C212yesmaximal
5#14531504C211yesmaximal, characteristic
6#11763860—24no—
7#11763829—22no—
8#11763825C2212yes—
9#11763825C2212yes—
10Q8⋊#3624—24no—
11#11763654—22no—
12C2×Q8×Dic17C2211yescharacteristic
13C2×Q8×Dic17C2211yescharacteristic
14#11762716C411yescharacteristic
15#11762716C411yescharacteristic
16#11762695—22no—
17#11762695—22no—
18#11762675C411yescharacteristic
19#11762655C2211yescharacteristic
20C2×C17×C4⋊Q8C411yescharacteristic
21C22×Q8×C17C2×C411yescharacteristic
22C22×Q8×C17C2×C411yescharacteristic
23C17×C4⋊Q8—22no—
24C17×C4⋊Q8—22no—
25C2×C4⋊C4×C17—22no—
26C2×C42×C17C2×C411yescharacteristic
27Q8×Dic17—22no—
28Q8×Dic17—22no—
29Q8×Dic17—22no—
30Q8×Dic17—22no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17D412yes—
35C2×C4×Dic17—21no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C22⋊#3624—22no—
40C22⋊#3624—22no—
41#10587544—24no—
42#10587542—24no—
43C4⋊#3624—22no—
44C4⋊#3624—22no—
45C4×#3624—22no—
46C4×#3624D414yes—
47#10587502—22no—
48#10587502—22no—
49#10587502—22no—
50#10587502—21no—
51#10587502—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—21no—
54C2×Q8×C17—21no—
55C2×Q8×C17—21no—
56C2×Q8×C17—22no—
57C2×Q8×C17—22no—
58C2×Q8×C17—22no—
59C2×Q8×C17M1612yes—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17C22⋊C412yes—
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17C22⋊C412yes—
67C22×Dic17C2×D411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C2×#3624—24no—
70C2×#3624—42no—
71C4⋊C4×C17—28no—
72C42×C17—21no—
73C42×C17M1612yes—
74C4⋊Dic17—22no—
75C4⋊Dic17—24no—
76C4⋊Dic17—22no—
77C4⋊Dic17—41no—
78C4⋊Dic17—41no—
79C4×Dic17—22no—
80C4×Dic17—22no—
81C4×Dic17—22no—
82C4×Dic17—42no—
83C4×Dic17C2×D412yes—
84C4×Dic17#4112yes—
85#9104—171nomaximal, Sylow
86C23×C17C2×C22⋊C411yescharacteristic
87Q8×C17—24no—
88Q8×C17—42no—
89Q8×C17—42no—
90Q8×C17—42no—
91C2×C4×C17—22no—
92C2×C4×C17—22no—
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17C4×D412yes—
101C2×C4×C17C2×M1611yescharacteristic
102C2×C4×C17C2×M1611yescharacteristic
103C2×C4×C17#13112yes—
104C2×Dic17—22no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17—42no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—42no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17#12011yescharacteristic
114C2×Dic17#12112yes—
115C2×Dic17#12311yescharacteristic
116#3624—44no—
117#3624—82no—
118#2983—171no—
119#2327—171no—
120#1479—172no—
121#1461—171no—
122#1274—172no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17#38611yescharacteristic
126C22×C17#40711yescharacteristic
127C22×C17#40811yescharacteristic
128C4×C17—42no—
129C4×C17—42no—
130C4×C17—42no—
131C4×C17#43512yes—
132C4×C17#43612yes—
133Dic17—22no—
134Dic17—21no—
135Dic17—21no—
136Dic17—42no—
137Dic17—81no—
138Dic17—81no—
139C2×C4⋊Q8#59511yescharacteristic
140C2×C4×Q8—171no—
141C2×C4×Q8—171no—
142#446—344no—
143#432—342no—
144#431—172no—
145#431—172no—
146#391—171no—
147#391—171no—
148#387—342no—
149#387—342no—
150#382—171no—
151#376—171no—
152Q8⋊C8—344no—
153#324—342no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#187011yescharacteristic
157C2×C17#190911yescharacteristic
158C2×C17#191211yescharacteristic
159C22×Q8C2×#59511yescharacteristic
160C22×Q8C2×#59511yescharacteristic
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4×Q8—342no—
164C4×Q8—342no—
165C4×Q8—342no—
166C4×Q8—342no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—172no—
169C2×C4⋊C4—171no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—341no—
172C2×C42—171no—
173C2×C42—172no—
174C2×C42—171no—
175C2×C42—341no—
176C2×C42C2×#59511yescharacteristic
177C4⋊C8—342no—
178C4⋊C8—342no—
179C4⋊C8—344no—
180C22⋊C8—342no—
181C22⋊C8—342no—
182#97—344no—
183C4×C8—174no—
184C4×C8—342no—
185#95—341no—
186#95—341no—
187#95—342no—
188#95—342no—
189#95—342no—
190C17#910411yescharacteristic, complemented, Sylow
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8#6324712yes—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—171no—
202C22×C4—171no—
203C22×C4—172no—
204C22×C4—341no—
205C22×C4—341no—
206C22×C4C22⋊#59512yes—
207C22×C4C22×#59511yescharacteristic
208C2×C8—344no—
209C2×C8—682no—
210C4⋊C4—28no—
211C4⋊C4—344no—
212C4⋊C4—342no—
213C4⋊C4—342no—
214C4⋊C4—681no—
215C4⋊C4—681no—
216C42—21no—
217C42—172no—
218C42—172no—
219C42—342no—
220C42—342no—
221C42—342no—
222C42—682no—
223C42#6324712yes—
224C23C2×C22⋊#59511yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—42no—
228Q8—42no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—171no—
239C2×C4—171no—
240C2×C4—172no—
241C2×C4—342no—
242C2×C4—681no—
243C2×C4—681no—
244C2×C4—682no—
245C2×C4—681no—
246C2×C4—681no—
247C2×C4—682no—
248C2×C4—681no—
249C2×C4—681no—
250C2×C4#1058767812yes—
251C2×C4D4×#59512yes—
252C2×C4C2×#6324711yescharacteristic
253C2×C4C2×#6324711yescharacteristic
254C8—684no—
255C8—1362no—
256C22—21no—
257C22—21no—
258C22#1176375711yescharacteristic
259C22#1176377911yescharacteristic
260C22#1176378211yescharacteristic
261C4—42no—
262C4—42no—
263C4—42no—
264C4—342no—
265C4—341no—
266C4—341no—
267C4—682no—
268C4—1361no—
269C4—1361no—
270C4#1176384012yes—
271C4#1176384412yes—
272C2—21no—
273C2—21no—
274C2#1454476111yescharacteristic
275C2#1454482611yescharacteristic
276C2#1454483111yescharacteristic
subgroupG/H
centerC22#11763757
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#9104
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
190. C17#9104semidirect

Maximal subgroups

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

subgroupindex
#145456802
#145440862
#145440272
#145436082
#145315042
#910417