Finite Group Databasebeta

← #16930380

Subgroups — #16930380

Order 4352.

516 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 111 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#14534597C211yesmaximal, characteristic
2#14531387C211yesmaximal, characteristic
3#14527357C212yesmaximal
4#14526652C212yesmaximal
5C2×C17×#324C211yesmaximal, characteristic
6C2×#10587610C2211yescharacteristic
7#11762748C412yescomplemented
8#11762742—22no—
9#11762729C412yescomplemented
10#11762695—24no—
11#11762682—21no—
12#11762672—21no—
13#11762672—21no—
14#11762669C2211yescharacteristic
15#11762669C2212yes—
16C4×C22⋊Dic17—21no—
17#11762547—24no—
18C22×C4⋊C4×C17C2211yescharacteristic
19C2×C17×C22⋊C8C2212yes—
20C17×#324—22no—
21C23×C4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C23×C4×C17C2311yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C22×C8×C17—22no—
26C2×C4⋊C4×C17—22no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17C2×C412yes—
29C2×C4⋊C4×C17D412yes—
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17—22no—
32C2×C22⋊Dic17—21no—
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36#10587610—22no—
37#10587610—22no—
38C2×#63225—22no—
39C2×#63225—21no—
40C2×C4×Dic17—22no—
41C17×C22⋊C8—22no—
42C17×C22⋊C8—22no—
43#10587502—22no—
44#10587502—24no—
45#10587502—22no—
46#10587502—22no—
47#10587502—22no—
48#10587502C2×C412yes—
49#10587502D414yes—
50C24×C17C2×D411yescharacteristic
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—21no—
57C22×C4×C17—81no—
58C22×C4×C17—81no—
59C22×C4×C17C22⋊C412yes—
60C22×C4×C17C22⋊C412yes—
61C22×C4×C17C22×C411yescharacteristic
62C22×C4×C17C2×D412yes—
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17#4112yes—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—22no—
68C22×Dic17—24no—
69C2×Dic34—22no—
70C2×Dic34—81no—
71C2×C8×C17—42no—
72C2×C8×C17—82no—
73C4⋊C4×C17—24no—
74C4⋊C4×C17—24no—
75C22⋊Dic17—41no—
76C22⋊Dic17—41no—
77C22⋊Dic17—42no—
78C22⋊Dic17—42no—
79C22⋊Dic17—42no—
80C4⋊Dic17—22no—
81C4⋊Dic17—82no—
82C4⋊Dic17—81no—
83#63225—42no—
84#63225—82no—
85C4×Dic17—82no—
86#9202—171nomaximal, Sylow
87C23×C17—41no—
88C23×C17—41no—
89C23×C17C2×C22⋊C411yescharacteristic
90C23×C17#12011yescharacteristic
91C23×C17#12311yescharacteristic
92C23×C17#13512yes—
93C23×C17#13712yes—
94C2×C4×C17—22no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—42no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—81no—
107C2×C4×C17C4×D412yes—
108C2×C4×C17#12112yes—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—44no—
112C2×Dic17—42no—
113C2×Dic17—44no—
114C2×Dic17—42no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17—44no—
119Dic34—82no—
120C8×C17—82no—
121#2627—171no—
122#2313—171no—
123#1520—172no—
124C2×#324D1711yescharacteristic
125#1289—172no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—42no—
133C22×C17—42no—
134C22×C17#38611yescharacteristic
135C22×C17#41611yescharacteristic
136C22×C17#41911yescharacteristic
137C22×C17#45212yes—
138C22×C17#48512yes—
139C4×C17—22no—
140C4×C17—22no—
141C4×C17—42no—
142C4×C17—42no—
143Dic17—82no—
144Dic17—84no—
145Dic17—81no—
146Dic17—81no—
147C2×C22⋊Q8—171no—
148C22×C4⋊C4C2×D1711yescharacteristic
149C2×C22⋊C8C2×D1712yes—
150#400—172no—
151#398—342no—
152#395—172no—
153#387—344no—
154#385—341no—
155#381—341no—
156#381—341no—
157#380—171no—
158#380—172no—
159C4×C22⋊C4—341no—
160#328—344no—
161#324—22no—
162C2×C17—21no—
163C2×C17—22no—
164C2×C17—21no—
165C2×C17—22no—
166C2×C17#187311yescharacteristic
167C2×C17#191211yescharacteristic
168C2×C17#191311yescharacteristic
169C22×Q8—171no—
170C23×C4D6811yescharacteristic
171C23×C4D6811yescharacteristic
172C23×C4C22×D1711yescharacteristic
173C22×C8—22no—
174C22⋊Q8—342no—
175C22⋊Q8—342no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—341no—
180C2×C4⋊C4—342no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—342no—
183C2×C4⋊C4C4×D1712yes—
184C2×C4⋊C4C22⋊D1712yes—
185C2×C22⋊C4—341no—
186C2×C22⋊C4—342no—
187C2×C22⋊C4—341no—
188C2×C42—342no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#95—172no—
192#95—174no—
193#95—342no—
194#95—344no—
195#95—342no—
196#95—342no—
197#95—342no—
198C17#920211yescharacteristic, complemented, Sylow
199C24C2×D6811yescharacteristic
200C2×Q8—342no—
201C2×Q8—1361no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—344no—
211C22×C4—342no—
212C22×C4—341no—
213C22×C4—341no—
214C22×C4#6322712yes—
215C22×C4#6322712yes—
216C22×C4C2×C4×D1711yescharacteristic
217C22×C4D4×D1712yes—
218C22×C4#6325412yes—
219C22×C4C2×C22⋊D1711yescharacteristic
220C2×C8—42no—
221C2×C8—82no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—342no—
225C4⋊C4—682no—
226C4⋊C4—1362no—
227C4⋊C4—1362no—
228C4⋊C4—1361no—
229C22⋊C4—681no—
230C22⋊C4—681no—
231C22⋊C4—682no—
232C22⋊C4—682no—
233C22⋊C4—682no—
234C42—1362no—
235C23—41no—
236C23—41no—
237C23#1058756811yescharacteristic
238C23#1058757211yescharacteristic
239C23#1058759012yes—
240C23#1058759512yes—
241C23C2×#6322711yescharacteristic
242Q8—1362no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—81no—
256C2×C4—684no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—684no—
260C2×C4—682no—
261C2×C4—682no—
262C2×C4—684no—
263C2×C4—682no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4#1058756712yes—
267C2×C4#1058762512yes—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1176268611yescharacteristic
278C22#1176280611yescharacteristic
279C22#1176281911yescharacteristic
280C22#1176297312yes—
281C22#1176315112yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—1364no—
287C4—1362no—
288C4—1361no—
289C4—1361no—
290C2—22no—
291C2—21no—
292C2—21no—
293C2—22no—
294C2#1452909411yescharacteristic
295C2#1452931911yescharacteristic
296C2#1452932411yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#324C2
socleC22×C17#386
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#324D17
hypocenterC17#9202
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
7. #11762748C4semidirect
9. #11762729C4semidirect
198. C17#9202semidirect

Maximal subgroups

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

subgroupindex
#145345972
#145313872
#145273572
#145266522
C2×C17×#3242
#920217