Finite Group Databasebeta

← #16932161

Subgroups — #16932161

Order 4352.

542 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 127 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#14537808C211yesmaximal, characteristic
2#14534138C211yesmaximal, characteristic
3#14527212C212yesmaximal, complemented
4#14526644C212yesmaximal, complemented
5C17×#1800C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7D4×#3622—24no—
8#11762862C2212yes—
9C2×C22⋊#3622—22no—
10#11762745C412yes—
11#11762721C412yes—
12#11762712—21no—
13#11762705—21no—
14#11762682—22no—
15#11762675C2211yescharacteristic
16#11762539—24no—
17C2×C4×D4×C17C2211yescharacteristic
18C17×#423C2212yes—
19C2×C17×#100—21no—
20C17×#343—21no—
21C22×D4×C17D411yescharacteristic
22C23×C4×C17D412yes—
23C22×Dic34C2×C411yescharacteristic
24C2×M16×C17—22no—
25C4×D4×C17—22no—
26C4×D4×C17—22no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C22⋊C4×C17C2×C412yes—
29C2×C42×C17C2311yescharacteristic
30C2×C22⋊Dic17—22no—
31C2×C22⋊Dic17—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—22no—
35C2×#63225—21no—
36C2×C4×Dic17—21no—
37C22×#3622—24no—
38C4×Dic34—22no—
39C4×Dic34—22no—
40C17×C4⋊C8—22no—
41C17×C4⋊C8—22no—
42C17×#100—42no—
43#10587502—22no—
44#10587502—21no—
45#10587502C2×C412yes—
46C22⋊#3622—24no—
47C22⋊#3622—22no—
48C4⋊#3622—22no—
49C4×#3622D414yes—
50C24×C17C22⋊C412yes—
51C2×D4×C17—22no—
52C2×D4×C17—22no—
53C2×D4×C17SD1612yes—
54C2×D4×C17Q1612yes—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—82no—
58C22×C4×C17C22⋊C412yes—
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—22no—
64C22×Dic17—21no—
65C2×Dic34—22no—
66C2×Dic34—42no—
67M16×C17—42no—
68M16×C17—42no—
69C2×C8×C17—42no—
70C4⋊C4×C17—22no—
71C22⋊C4×C17—24no—
72C42×C17C2×D412yes—
73C42×C17#4112yes—
74C22⋊Dic17—44no—
75C22⋊Dic17—82no—
76C4⋊Dic17—22no—
77C4⋊Dic17—42no—
78#63225—41no—
79#63225—41no—
80#63225—82no—
81C4×Dic17—42no—
82C2×#3622—24no—
83C2×#3622—84no—
84#9483—171nomaximal, Sylow
85C23×C17—22no—
86C23×C17—22no—
87C23×C17—42no—
88C23×C17—42no—
89C23×C17#10314yes—
90C23×C17C2×C22⋊C411yescharacteristic
91D4×C17—24no—
92D4×C17—24no—
93C2×C4×C17—22no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—44no—
97C2×C4×C17—42no—
98C2×C4×C17—82no—
99C2×C4×C17C4×D412yes—
100C2×C4×C17#12011yescharacteristic
101C2×C4×C17#12112yes—
102C2×C4×C17#12311yescharacteristic
103C2×C4×C17C2×SD1611yescharacteristic
104C2×C4×C17C2×Q1611yescharacteristic
105C2×C4×C17#13512yes—
106C2×Dic17—22no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—42no—
110C2×Dic17—41no—
111C2×Dic17—42no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—42no—
115Dic34—24no—
116Dic34—42no—
117C8×C17—82no—
118#3622—44no—
119#2972—171no—
120#2580—171no—
121#1800D1711yescharacteristic
122#1487—172no—
123#1286—172no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—24no—
127C22×C17—44no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—82no—
131C22×C17#38611yescharacteristic
132C22×C17C2×#10311yescharacteristic
133C22×C17#41611yescharacteristic
134C4×C17—22no—
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—42no—
138C4×C17#46512yes—
139C4×C17#46712yes—
140Dic17—42no—
141Dic17—82no—
142Dic17—81no—
143C2×C4×Q8—171no—
144C2×C4×D4C2×D1711yescharacteristic
145C8×D4—344no—
146#431—172no—
147#423C2×D1712yes—
148C2×#100—21no—
149C2×C22⋊C8—342no—
150#399—172no—
151#393—172no—
152#390—341no—
153#389—341no—
154#385—342no—
155#382—171no—
156#343—21no—
157Q8⋊C8—344no—
158C2×C17—21no—
159C2×C17—21no—
160C2×C17—44no—
161C2×C17#189111yescharacteristic
162C2×C17#189211yescharacteristic
163C2×C17#191111yescharacteristic
164C22×Q8—171no—
165C22×D4C22⋊D1711yescharacteristic
166C23×C4D6812yes—
167C2×M16—22no—
168C22×C8—344no—
169C4×Q8—342no—
170C4×Q8—342no—
171C4×D4—22no—
172C4×D4—22no—
173C2×C4⋊C4—171no—
174C2×C4⋊C4—341no—
175C2×C4⋊C4—341no—
176C2×C4⋊C4—342no—
177C2×C4⋊C4C22⋊D1711yescharacteristic
178C2×C22⋊C4—342no—
179C2×C22⋊C4—342no—
180C2×C22⋊C4C4×D1712yes—
181C2×C42—341no—
182C2×C42C22×D1711yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—342no—
186#100—42no—
187C22⋊C8—344no—
188C22⋊C8—342no—
189C4×C8—174no—
190#95—172no—
191#95—341no—
192#95—342no—
193C17#948311yescharacteristic, complemented, Sylow
194C24#6322712yes—
195C2×Q8—342no—
196C2×Q8—682no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4#6322912yes—
200C2×D4#6323112yes—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—82no—
204C22×C4—341no—
205C22×C4—342no—
206C22×C4—341no—
207C22×C4#6322712yes—
208C22×C4C2×C4×D1711yescharacteristic
209C22×C4C2×D6811yescharacteristic
210C22×C4C2×C22⋊D1711yescharacteristic
211M16—42no—
212M16—42no—
213C2×C8—42no—
214C2×C8—344no—
215C2×C8—1364no—
216C4⋊C4—22no—
217C4⋊C4—342no—
218C4⋊C4—681no—
219C4⋊C4—681no—
220C4⋊C4—682no—
221C4⋊C4—1362no—
222C22⋊C4—24no—
223C22⋊C4—684no—
224C22⋊C4—1362no—
225C42—682no—
226C42D4×D1712yes—
227C42#6325412yes—
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23#1058748114yes—
233C23C2×#6322711yescharacteristic
234Q8—344no—
235Q8—682no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—342no—
245C2×C4—681no—
246C2×C4—681no—
247C2×C4—682no—
248C2×C4—681no—
249C2×C4—682no—
250C2×C4—681no—
251C2×C4—682no—
252C2×C4—681no—
253C2×C4#1058756712yes—
254C2×C4#1058756811yescharacteristic
255C2×C4#1058757211yescharacteristic
256C2×C4C2×#6322911yescharacteristic
257C2×C4#1058762512yes—
258C2×C4C2×#6323111yescharacteristic
259C2×C4#1058763612yes—
260C8—82no—
261C8—684no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22#1176268611yescharacteristic
270C22C2×#1058748111yescharacteristic
271C22#1176280311yescharacteristic
272C4—21no—
273C4—21no—
274C4—22no—
275C4—42no—
276C4—682no—
277C4—1362no—
278C4—1361no—
279C4#1176303612yes—
280C4#1176304812yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2#1452920011yescharacteristic
285C2#1452920511yescharacteristic
286C2#1452931411yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1800C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#1800D17
hypocenterC17#9483
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #14527212C2semidirect
4. #14526644C2semidirect
193. C17#9483semidirect

Maximal subgroups

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

subgroupindex
#145378082
#145341382
#145272122
#145266442
C17×#18002
#948317