Finite Group Databasebeta

← #16932196

Subgroups — #16932196

Order 4352.

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

normal subgroups only

This group has 522 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#14537869C211yesmaximal, characteristic, complemented
2#14533689C211yesmaximal, characteristic
3#14527208C212yesmaximal
4#14526644C212yesmaximal, complemented
5C17×#1801C211yesmaximal, characteristic, complemented
6C2×#10587632—21no—
7C2×C4×D68C2211yescharacteristic
8#11762940—24no—
9#11762866—22no—
10#11762862C2212yes—
11#11762739C412yes—
12#11762726C412yes—
13#11762700—22no—
14#11762675C2211yescharacteristic
15#11762666—21no—
16#11762536—24no—
17C2×C4×Q8×C17C2211yescharacteristic
18C17×#423C2212yes—
19C2×C17×#101—21no—
20C17×#343—21no—
21C22×Q8×C17D411yescharacteristic
22C22×D68C2×C411yescharacteristic
23C22×C4×D17—21no—
24C2×M16×C17—22no—
25C4×Q8×C17—22no—
26C4×Q8×C17—22no—
27C2×C4⋊C4×C17C2×C412yes—
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C42×C17D412yes—
30C2×C42×C17C2311yescharacteristic
31#10587632—44no—
32C2×#63227—22no—
33C2×#63227—22no—
34C2×#63227—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—22no—
38C4×D68—22no—
39C4×D68—22no—
40C17×C4⋊C8—22no—
41C17×C4⋊C8—22no—
42C17×#101—42no—
43#10587502—22no—
44#10587502—21no—
45#10587502C2×C412yes—
46C22⋊#3622—22no—
47C4⋊#3622—24no—
48C4⋊#3622—22no—
49#10587474—24no—
50C4×#3622D414yes—
51C23×D17—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—21no—
54C2×Q8×C17—22no—
55C2×Q8×C17—21no—
56C22×C4×C17C22⋊C412yes—
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C22×C411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—22no—
63C2×D68—22no—
64C2×D68—42no—
65C2×C4×D17—42no—
66C2×C4×D17—41no—
67C2×C4×D17—42no—
68C2×C4×D17—41no—
69M16×C17—42no—
70M16×C17—42no—
71C2×C8×C17—42no—
72C4⋊C4×C17—24no—
73C4⋊C4×C17—22no—
74C42×C17—22no—
75C42×C17—22no—
76C42×C17C2×D412yes—
77C42×C17#4112yes—
78#63227—44no—
79#63227—44no—
80#63227—41no—
81#63227—41no—
82C4⋊Dic17—22no—
83C4⋊Dic17—42no—
84#63225—44no—
85C2×#3622—24no—
86#9490—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—22no—
89C22×D17—41no—
90C22×D17—41no—
91C22×D17—41no—
92C22×D17—41no—
93C22×D17—41no—
94C22×D17—41no—
95Q8×C17—42no—
96Q8×C17—42no—
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—42no—
104C2×C4×C17C4×D412yes—
105C2×C4×C17#12011yescharacteristic
106C2×C4×C17#12112yes—
107C2×C4×C17#12311yescharacteristic
108C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C17AGL(1,ℤ/8)12yes—
110C2×C4×C17#13711yescharacteristic
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117D68—24no—
118D68—42no—
119C4×D17—82no—
120C4×D17—82no—
121C8×C17—82no—
122#3622—44no—
123#2983—171no—
124#2536—171no—
125#1801D1711yescharacteristic, complemented
126#1486—172no—
127#1286—172no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17#38611yescharacteristic
131C22×C17#41711yescharacteristic
132C22×C17#41811yescharacteristic
133C2×D17—42no—
134C2×D17—42no—
135C2×D17—42no—
136C2×D17—81no—
137C2×D17—81no—
138C2×D17—81no—
139C2×D17—81no—
140C4×C17—22no—
141C4×C17—21no—
142C4×C17—21no—
143C4×C17—42no—
144C4×C17—42no—
145C4×C17#46812yes—
146C4×C17#46912yes—
147Dic17—82no—
148Dic17—81no—
149C2×C22⋊Q8—341no—
150C2×C4×Q8C2×D1711yescharacteristic
151C2×C4×D4—171no—
152#446—344no—
153#432—342no—
154#431—172no—
155#423C2×D1712yes—
156C2×#101—21no—
157#398—172no—
158#394—172no—
159#388—342no—
160#382—171no—
161#380—341no—
162#343—21no—
163D4⋊C8—344no—
164C2×C17—21no—
165C2×C17—21no—
166C2×C17#189111yescharacteristic
167C2×C17#189511yescharacteristic
168C2×C17#191211yescharacteristic
169D17—82no—
170C22×Q8C22⋊D1711yescharacteristic
171C22×D4—171no—
172C23×C4—341no—
173C2×M16—22no—
174C22⋊Q8—684no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×D4—342no—
178C4×D4—342no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—342no—
182C2×C4⋊C4C4×D1712yes—
183C2×C4⋊C4C22⋊D1711yescharacteristic
184C2×C22⋊C4—341no—
185C2×C22⋊C4—342no—
186C2×C22⋊C4—342no—
187C2×C42D6812yes—
188C2×C42C22×D1711yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8—344no—
192C4⋊C8—342no—
193#101—42no—
194C22⋊C8—342no—
195#97—344no—
196C4×C8—174no—
197#95—172no—
198#95—341no—
199#95—342no—
200C17#949011yescharacteristic, complemented, Sylow
201C24—341no—
202C2×Q8—21no—
203C2×Q8—22no—
204C2×Q8—21no—
205C2×Q8—22no—
206C2×D4—342no—
207C2×D4—682no—
208C22×C4—342no—
209C22×C4—341no—
210C22×C4—681no—
211C22×C4—682no—
212C22×C4—681no—
213C22×C4—682no—
214C22×C4#6322712yes—
215C22×C4#6322712yes—
216C22×C4C2×C4×D1711yescharacteristic
217C22×C4C2×D6811yescharacteristic
218C22×C4C2×C22⋊D1711yescharacteristic
219M16—42no—
220M16—42no—
221C2×C8—42no—
222C2×C8—344no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—342no—
226C4⋊C4—684no—
227C4⋊C4—682no—
228C22⋊C4—684no—
229C22⋊C4—684no—
230C22⋊C4—681no—
231C22⋊C4—681no—
232C42—22no—
233C42—22no—
234C42D4×D1712yes—
235C42#6325412yes—
236C23—342no—
237C23—681no—
238C23—681no—
239C23—681no—
240C23—681no—
241C23—681no—
242C23—681no—
243C23C2×#6322711yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—344no—
247D4—682no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—682no—
256C2×C4—682no—
257C2×C4—681no—
258C2×C4—682no—
259C2×C4—681no—
260C2×C4—681no—
261C2×C4—1362no—
262C2×C4—1362no—
263C2×C4#1058756712yes—
264C2×C4#1058756811yescharacteristic
265C2×C4#1058757211yescharacteristic
266C2×C4#1058761811yescharacteristic
267C2×C4#1058762512yes—
268C2×C4#1058762811yescharacteristic
269C2×C4#1058763512yes—
270C8—82no—
271C8—684no—
272C22—21no—
273C22—21no—
274C22—682no—
275C22—682no—
276C22—682no—
277C22—1361no—
278C22—1361no—
279C22—1361no—
280C22—1361no—
281C22#1176268611yescharacteristic
282C22#1176280811yescharacteristic
283C22#1176281311yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—42no—
288C4—42no—
289C4—1362no—
290C4—1361no—
291C4#1176305712yes—
292C4#1176306012yes—
293C2—21no—
294C2—21no—
295C2—1362no—
296C2#1452920011yescharacteristic
297C2#1452922011yescharacteristic
298C2#1452931911yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1801C2
socleC22×C17#386
prime radicalC22×D68C2×C4
cosocleC2×C42×C17C23
hypercenter#1801D17
hypocenterC17#9490
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #14537869C2semidirect
4. #14526644C2semidirect
5. C17×#1801C2semidirect
125. #1801D17semidirect
200. C17#9490semidirect

Maximal subgroups

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

subgroupindex
#145378692
#145336892
#145272082
#145266442
C17×#18012
#949017