Finite Group Databasebeta

← #17955937

Subgroups — #17955937

Order 4352.

546 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 142 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#14544716C211yesmaximal, characteristic
2#14544499C211yesmaximal, characteristic
3C2×#11763659C212yesmaximal
4C2×Q8⋊#3624C212yesmaximal
5#14531353C211yesmaximal, characteristic
6C2×C4⋊#3624—22no—
7C2×C4⋊#3624C2212yes—
8C2×C4×#3624C2212yes—
9#11763675—22no—
10#11763659—24no—
11Q8⋊#3624—24no—
12C2×#10587630C411yescharacteristic
13C2×Q8×Dic17C2211yescharacteristic
14C2×#10587573C2211yescharacteristic
15#11762715C411yescharacteristic
16#11762706—22no—
17#11762678C411yescharacteristic
18#11762660—22no—
19C42×Dic17C2211yescharacteristic
20C17×#391C411yescharacteristic
21C22×Q8×C17C2×C411yescharacteristic
22C22×Dic34C2×C411yescharacteristic
23C22×#3624—22no—
24C22×#3624—22no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C42×C17C2×C411yescharacteristic
27Q8×Dic17—22no—
28Q8×Dic17—22no—
29#10587630—22no—
30#10587630—22no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—22no—
34C2×#63225—22no—
35C2×#63225—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D412yes—
40C2×C4×Dic17D412yes—
41C2×C4×Dic17C2311yescharacteristic
42#10587573—22no—
43#10587573—22no—
44C4⋊#3624—22no—
45C4⋊#3624—22no—
46C4⋊#3624—44no—
47C4×#3624—22no—
48C4×#3624D414yes—
49C17×#95—22no—
50#10587502—22no—
51C2×Q8×C17—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—22no—
54C2×Q8×C17M1612yes—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17C22⋊C412yes—
62C22×Dic17C2×D411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C2×Dic34—22no—
65C2×Dic34—22no—
66C2×Dic34—21no—
67C2×Dic34M1612yes—
68C2×#3624—24no—
69C2×#3624—44no—
70C2×#3624—42no—
71C2×#3624—44no—
72C4⋊C4×C17—22no—
73C42×C17—22no—
74C4⋊Dic17—22no—
75C4⋊Dic17—42no—
76#63225—28no—
77#63225—44no—
78#63225—42no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—42no—
82C4×Dic17—41no—
83C4×Dic17—41no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86C4×Dic17SD1614yes—
87C4×Dic17Q1614yes—
88C4×Dic17C2×D412yes—
89C4×Dic17#4112yes—
90#9643—171nomaximal, Sylow
91C23×C17C2×C22⋊C411yescharacteristic
92Q8×C17—24no—
93Q8×C17—42no—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17#10314yes—
102C2×C4×C17C4×D412yes—
103C2×C4×C17C2×M1611yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C2×C4×C17#13112yes—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—42no—
114C2×Dic17#10314yes—
115C2×Dic17#12112yes—
116C2×Dic17#12411yescharacteristic
117C2×Dic17#12711yescharacteristic
118C2×Dic17C2×SD1612yes—
119C2×Dic17C2×Q1612yes—
120Dic34—24no—
121Dic34—42no—
122#3624—44no—
123#3624—82no—
124C4×C4⋊Q8—171no—
125#1842—171no—
126#1744—171no—
127C2×Q8⋊C8—172no—
128C2×Q8⋊C8—172no—
129C22×C17#39011yescharacteristic
130C22×C17#40711yescharacteristic
131C22×C17#40811yescharacteristic
132C22×C17C2×#10312yes—
133C22×C17#42112yes—
134C4×C17—24no—
135C4×C17—42no—
136C4×C17—81no—
137C4×C17#43512yes—
138C4×C17#43512yes—
139Dic17—22no—
140Dic17—24no—
141Dic17—42no—
142Dic17—81no—
143Dic17#48712yes—
144Dic17#49211yescharacteristic
145Dic17#49411yescharacteristic
146C2×C4⋊Q8—171no—
147C2×C4×Q8—171no—
148C2×C4×Q8—171no—
149C2×C4⋊C8—172no—
150C2×C4⋊C8—342no—
151C2×C4×C8—172no—
152#391—171no—
153#391#59511yescharacteristic
154#389—342no—
155#384—171no—
156C4×C4⋊C4—342no—
157C43—171no—
158#336—342no—
159Q8⋊C8—344no—
160Q8⋊C8—344no—
161C2×C17#148112yes—
162C2×C17#148712yes—
163C2×C17#195511yescharacteristic
164C2×C17#195611yescharacteristic
165C2×C17#196311yescharacteristic
166C22×Q8—171no—
167C22×Q8C2×#59511yescharacteristic
168C22×C8—342no—
169C22×C8—342no—
170C4⋊Q8—342no—
171C4⋊Q8—342no—
172C4×Q8—342no—
173C4×Q8—342no—
174C4×Q8—342no—
175C4×Q8—342no—
176C2×C4⋊C4—171no—
177C2×C4⋊C4—342no—
178C2×C4⋊C4—341no—
179C2×C4⋊C4—341no—
180C2×C4⋊C4—342no—
181C2×C4⋊C4C2×#59511yescharacteristic
182C2×C42—172no—
183C2×C42—171no—
184C2×C42—171no—
185C2×C42—172no—
186C2×C42—341no—
187C2×C42—341no—
188C2×C42C2×#59511yescharacteristic
189C4⋊C8—342no—
190C4⋊C8—342no—
191C4⋊C8—684no—
192C4×C8—174no—
193C4×C8—342no—
194#95—22no—
195#95—342no—
196C17#964311yescharacteristic, complemented, Sylow
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—172no—
201C2×Q8—341no—
202C2×Q8—342no—
203C2×Q8—342no—
204C2×Q8#6324312yes—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—171no—
208C22×C4—172no—
209C22×C4—171no—
210C22×C4—341no—
211C22×C4—341no—
212C22×C4C22⋊#59512yes—
213C22×C4C22×#59511yescharacteristic
214C2×C8—344no—
215C2×C8—684no—
216C2×C8—682no—
217C2×C8—684no—
218C4⋊C4—22no—
219C4⋊C4—348no—
220C4⋊C4—342no—
221C4⋊C4—682no—
222C4⋊C4—682no—
223C4⋊C4—684no—
224C42—22no—
225C42—172no—
226C42—172no—
227C42—174no—
228C42—174no—
229C42—341no—
230C42—341no—
231C42—682no—
232C42—681no—
233C42—681no—
234C42—681no—
235C42—681no—
236C23C2×C22⋊#59511yescharacteristic
237Q8—24no—
238Q8—42no—
239Q8—344no—
240Q8—682no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—171no—
249C2×C4—171no—
250C2×C4—172no—
251C2×C4—172no—
252C2×C4—172no—
253C2×C4—174no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—342no—
257C2×C4—342no—
258C2×C4—681no—
259C2×C4—681no—
260C2×C4—681no—
261C2×C4—682no—
262C2×C4#1058754914yes—
263C2×C4C2×#6324311yescharacteristic
264C2×C4D17⋊M1611yescharacteristic
265C2×C4#1058767812yes—
266C2×C4D4×#59512yes—
267C8—684no—
268C8—1362no—
269C22#1176376111yescharacteristic
270C22#1176378011yescharacteristic
271C22#1176378211yescharacteristic
272C22C2×#1058754912yes—
273C22#1176380612yes—
274C4—24no—
275C4—42no—
276C4—81no—
277C4—171no—
278C4—172no—
279C4—171no—
280C4—342no—
281C4—344no—
282C4—682no—
283C4—1361no—
284C4#1176383812yes—
285C4#1176384112yes—
286C2#1454409212yes—
287C2#1454411312yes—
288C2#1454490911yescharacteristic
289C2#1454491111yescharacteristic
290C2#1454492111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#391#595
hypocenterC17#9643
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
196. C17#9643semidirect

Maximal subgroups

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

subgroupindex
#145447162
#145444992
C2×#117636592
C2×Q8⋊#36242
#145313532
#964317