Finite Group Databasebeta

← #17953708

Subgroups — #17953708

Order 4352.

422 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544650C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543682C212yesmaximal
4#14543637C212yesmaximal
5#14531704C211yesmaximal, characteristic
6#11763826C2212yes—
7#11763812C2212yes—
8C2×#10587545—21no—
9#11763689—21no—
10#11763655—21no—
11#11763654—21no—
12C2×C4×Dic34—21no—
13C2×C4×Dic34C2211yescharacteristic
14#11762707—21no—
15#11762704—21no—
16#11762704—21no—
17#11762675C411yescharacteristic
18#11762673C411yescharacteristic
19#11762673C2211yescharacteristic
20#11762660C411yescharacteristic
21#11762660C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×Dic34D411yescharacteristic
24C2×#63247—22no—
25C2×C4⋊C4×C17—21no—
26C2×C42×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17D411yescharacteristic
30C2×#63225—21no—
31C2×#63225—21no—
32C2×#63225—21no—
33C2×#63225—21no—
34C2×#63225D411yescharacteristic
35C2×#63225D411yescharacteristic
36C2×C4×Dic17—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17C2311yescharacteristic
40C4×Dic34—22no—
41C4×Dic34—22no—
42C4×Dic34—44no—
43C22⋊#3624—22no—
44#10587545—42no—
45#10587544—22no—
46#10587544—22no—
47C4⋊#3624—22no—
48C4×#3624—22no—
49C17×#95C2×C411yescharacteristic
50C17×#95C2×C411yescharacteristic
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502C2×C411yescharacteristic
55#10587502C2×C411yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C2×Dic34—22no—
68C2×Dic34—22no—
69C2×Dic34SD1612yes—
70C2×Dic34Q1612yes—
71#63247—42no—
72#63247—42no—
73C2×#3624—42no—
74C2×#3624—42no—
75C4⋊C4×C17—42no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—42no—
79C4⋊Dic17—22no—
80C4⋊Dic17—42no—
81#63225—22no—
82#63225—22no—
83#63225—42no—
84#63225—42no—
85#63225—42no—
86#63225—42no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—42no—
90C4×Dic17—42no—
91C4×Dic17#4112yes—
92C4×Dic17#4112yes—
93#8767—171nomaximal, Sylow
94C23×C17C2×C22⋊C411yescharacteristic
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17#10312yes—
107C2×C4×C17#11711yescharacteristic
108C2×C4×C17#11711yescharacteristic
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17#10312yes—
121C2×Dic17#12312yes—
122C2×Dic17#12312yes—
123C2×Dic17C2×SD1611yescharacteristic
124C2×Dic17C2×Q1611yescharacteristic
125C2×Dic17AGL(1,ℤ/8)12yes—
126Dic34—24no—
127Dic34—24no—
128#3624—82no—
129#3624—82no—
130#2351—171no—
131#1801—171no—
132#1461—171no—
133#1303—172no—
134#1286—172no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17#38111yescharacteristic
138C22×C17C2×#10311yescharacteristic
139C22×C17#41811yescharacteristic
140C4×C17—22no—
141C4×C17—21no—
142C4×C17—21no—
143C4×C17—42no—
144C4×C17—41no—
145C4×C17—81no—
146Dic17—22no—
147Dic17—22no—
148Dic17—41no—
149Dic17—81no—
150Dic17—81no—
151Dic17#48112yes—
152Dic17#48412yes—
153C2×C4×Q8—171no—
154C2×C4×Q8—341no—
155#431—172no—
156#423—172no—
157C2×#101—341no—
158#389—341no—
159#389—341no—
160#389—341no—
161#382—171no—
162#382—171no—
163#382—171no—
164C4×C4⋊C4—171no—
165C4×C4⋊C4—171no—
166C4×C4⋊C4#59511yescharacteristic
167#343—341no—
168#324—341no—
169#324—341no—
170C2×C17—21no—
171C2×C17—21no—
172C2×C17#182411yescharacteristic
173C2×C17#182711yescharacteristic
174C2×C17#183011yescharacteristic
175C22×Q8—171no—
176C2×M16—342no—
177C4×Q8—342no—
178C4×Q8—342no—
179C4×Q8—684no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4—341no—
186C2×C4⋊C4—341no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C42—21no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42—341no—
193C2×C42—341no—
194C2×C42C2×#59511yescharacteristic
195C4⋊C8—342no—
196C4⋊C8—342no—
197C4⋊C8—342no—
198#101—682no—
199C22⋊C8—342no—
200C4×C8—342no—
201#95—171no—
202#95—171no—
203#95—341no—
204#95—341no—
205#95—341no—
206#95C2×#59511yescharacteristic
207#95C2×#59511yescharacteristic
208C17#876711yescharacteristic, complemented, Sylow
209C2×Q8—172no—
210C2×Q8—172no—
211C2×Q8—342no—
212C2×Q8—342no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4C22⋊#59511yescharacteristic
222C22×C4C22⋊#59511yescharacteristic
223C22×C4C22×#59511yescharacteristic
224M16—682no—
225M16—682no—
226C2×C8—682no—
227C2×C8—682no—
228C4⋊C4—42no—
229C4⋊C4—342no—
230C4⋊C4—342no—
231C4⋊C4—342no—
232C4⋊C4—682no—
233C4⋊C4—682no—
234C4⋊C4—682no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C42—21no—
238C42—21no—
239C42—42no—
240C42—172no—
241C42—172no—
242C42—341no—
243C42—341no—
244C42—682no—
245C42—682no—
246C23C2×C22⋊#59511yescharacteristic
247Q8—344no—
248Q8—344no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—172no—
261C2×C4—171no—
262C2×C4—171no—
263C2×C4—172no—
264C2×C4—172no—
265C2×C4—172no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4#1058754912yes—
278C2×C4#1058767711yescharacteristic
279C2×C4#1058767711yescharacteristic
280C8—1362no—
281C8—1362no—
282C22—21no—
283C22—21no—
284C22#1176375211yescharacteristic
285C22C2×#1058754911yescharacteristic
286C22#1176380111yescharacteristic
287C4—22no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—41no—
292C4—81no—
293C4—172no—
294C4—172no—
295C4—342no—
296C4—342no—
297C4—681no—
298C4—1361no—
299C4—1361no—
300C2—21no—
301C2—21no—
302C2#1454468811yescharacteristic
303C2#1454469311yescharacteristic
304C2#1454469811yescharacteristic
subgroupG/H
centerC22#11763752
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17#381
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#8767
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
208. C17#8767semidirect

Maximal subgroups

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

subgroupindex
#145446502
#145440262
#145436822
#145436372
#145317042
#876717