Finite Group Databasebeta

← #17959807

Subgroups — #17959807

Order 4352.

372 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544651C211yesmaximal, characteristic
2#14544028C211yesmaximal, characteristic
3#14543783C212yesmaximal
4#14543782C212yesmaximal
5#14533995C211yesmaximal, characteristic
6#11763825—21no—
7#11763812—21no—
8C2×#10587545—21no—
9#11763689C2212yes—
10#11763655—21no—
11#11763655C2212yes—
12C2×#10587574C411yescharacteristic
13C2×#10587573C2211yescharacteristic
14#11762749C2211yescharacteristic
15#11762748C411yescharacteristic
16#11762747C2211yescharacteristic
17#11762713—21no—
18#11762713—21no—
19#11762713—21no—
20#11762673—21no—
21#11762660C411yescharacteristic
22C17×#400C411yescharacteristic
23C22×Dic34—21no—
24C22×Dic34D411yescharacteristic
25C2×#63247—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊Dic17C2×C411yescharacteristic
29C2×#63225—21no—
30C2×#63225—21no—
31C2×#63225D411yescharacteristic
32C2×#63225C2311yescharacteristic
33C2×C4×Dic17—21no—
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37#10587574—41no—
38#10587574—41no—
39#10587573—41no—
40#10587573—41no—
41C22⋊#3624—22no—
42#10587545—42no—
43#10587544—41no—
44C4⋊#3624—41no—
45C4⋊#3624—41no—
46C4×#3624—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502C2×C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×Dic34—41no—
69C2×Dic34—41no—
70C2×Dic34—44no—
71C2×Dic34—41no—
72C2×Dic34—41no—
73C2×Dic34SD1612yes—
74C2×Dic34Q1612yes—
75#63247—42no—
76#63247—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊Dic17—41no—
82#63225—41no—
83#63225—41no—
84#63225—42no—
85#63225—42no—
86C4×Dic17—21no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—21no—
92C4×Dic17—42no—
93#11907—171nomaximal, Sylow
94C23×C17C2×C22⋊C411yescharacteristic
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17#10312yes—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—22no—
112C2×Dic17—21no—
113C2×Dic17—41no—
114C2×Dic17—42no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17#9911yescharacteristic
120C2×Dic17#9911yescharacteristic
121C2×Dic17#10312yes—
122C2×Dic17C2×SD1611yescharacteristic
123C2×Dic17C2×Q1611yescharacteristic
124Dic34—42no—
125Dic34—42no—
126Dic34—82no—
127Dic34—82no—
128#3624—82no—
129#3624—82no—
130#2568—171no—
131#1801—171no—
132#1461—171no—
133#1353—172no—
134#1353—172no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10311yescharacteristic
139C22×C17#42111yescharacteristic
140C4×C17—22no—
141C4×C17—41no—
142C4×C17—41no—
143C4×C17—81no—
144C4×C17—81no—
145Dic17—21no—
146Dic17—21no—
147Dic17—22no—
148Dic17—21no—
149Dic17—41no—
150Dic17—81no—
151Dic17—81no—
152Dic17#35512yes—
153C2×C4⋊Q8—171no—
154C2×C4×Q8—171no—
155#431—341no—
156#423—341no—
157C2×#101—341no—
158#400—171no—
159#400—171no—
160#400—171no—
161#400#59511yescharacteristic
162#391—341no—
163#391—341no—
164#391—341no—
165#382—341no—
166C4×C4⋊C4—171no—
167#343—172no—
168#324—172no—
169#324—341no—
170C2×C17—21no—
171C2×C17—21no—
172C2×C17#152011yescharacteristic
173C2×C17#212311yescharacteristic
174C2×C17C2×#35511yescharacteristic
175C22×Q8—171no—
176C22×Q8—341no—
177C2×M16—342no—
178C4⋊Q8—681no—
179C4⋊Q8—681no—
180C4×Q8—681no—
181C4×Q8—681no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—171no—
185C2×C4⋊C4—341no—
186C2×C4⋊C4—341no—
187C2×C4⋊C4C2×#59511yescharacteristic
188C2×C4⋊C4C2×#59511yescharacteristic
189C2×C42—171no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42—341no—
193C4⋊C8—681no—
194C4⋊C8—681no—
195C4⋊C8—681no—
196#101—682no—
197C22⋊C8—342no—
198C4×C8—681no—
199#95—21no—
200#95—21no—
201#95—171no—
202#95—341no—
203#95—341no—
204#95—341no—
205#95—341no—
206#95—341no—
207#95—341no—
208#95C2×#59511yescharacteristic
209C17#1190711yescharacteristic, complemented, Sylow
210C2×Q8—172no—
211C2×Q8—172no—
212C2×Q8—681no—
213C2×Q8—681no—
214C2×Q8—681no—
215C2×Q8—681no—
216C2×Q8—684no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—171no—
220C22×C4—171no—
221C22×C4—171no—
222C22×C4—171no—
223C22×C4—341no—
224C22×C4—341no—
225C22×C4C22⋊#59511yescharacteristic
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22×#59511yescharacteristic
228M16—682no—
229M16—682no—
230C2×C8—682no—
231C2×C8—682no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—681no—
235C4⋊C4—681no—
236C4⋊C4—681no—
237C4⋊C4—682no—
238C4⋊C4—682no—
239C42—341no—
240C42—341no—
241C42—341no—
242C42—341no—
243C42—341no—
244C42—341no—
245C42—682no—
246C23C2×C22⋊#59511yescharacteristic
247Q8—682no—
248Q8—682no—
249Q8—1362no—
250Q8—1362no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—171no—
263C2×C4—171no—
264C2×C4—171no—
265C2×C4—172no—
266C2×C4—171no—
267C2×C4—342no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—682no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4#1058754912yes—
280C8—1362no—
281C8—1362no—
282C22—21no—
283C22—21no—
284C22D17⋊#9911yescharacteristic
285C22C2×#1058754911yescharacteristic
286C22#1176380611yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—81no—
291C4—81no—
292C4—172no—
293C4—341no—
294C4—342no—
295C4—341no—
296C4—341no—
297C4—681no—
298C4—1361no—
299C4—1361no—
300C2—21no—
301C2—21no—
302C2#1454422211yescharacteristic
303C2#1454504711yescharacteristic
304C2D17⋊#35511yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#400C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenter#400#595
hypocenterC17#11907
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
209. C17#11907semidirect

Maximal subgroups

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

subgroupindex
#145446512
#145440282
#145437832
#145437822
#145339952
#1190717