Finite Group Databasebeta

← #16932183

Subgroups — #16932183

Order 4352.

518 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 115 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#14534138C211yesmaximal, characteristic
2#14528776C211yesmaximal, characteristic
3#14527214C212yesmaximal, complemented
4#14526643C212yesmaximal, complemented
5C17×#2975C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7#11762833C2212yes—
8C2×#10587504—21no—
9#11762745C412yes—
10#11762721C412yes—
11#11762712—21no—
12#11762705—21no—
13#11762682—22no—
14#11762675C2211yescharacteristic
15#11762578—21no—
16#11762541—24no—
17C2×C4×D4×C17C2211yescharacteristic
18C17×#436—24no—
19C17×#431C2212yes—
20C17×#407—22no—
21C22×D4×C17D411yescharacteristic
22C23×C4×C17D412yes—
23C22×Dic34C2×C411yescharacteristic
24C2×M16×C17—24no—
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—
37C2×#63223—22no—
38C4×Dic34—22no—
39C4×Dic34—22no—
40C17×C4⋊C8—22no—
41C17×C22⋊C8—24no—
42C17×C22⋊C8—22no—
43C4×C8×C17D414yes—
44#10587504—42no—
45#10587502—22no—
46#10587502—21no—
47#10587502C2×C412yes—
48C4⋊#3622—22no—
49C4⋊#3622—22no—
50C24×C17C22⋊C412yes—
51C2×D4×C17—22no—
52C2×D4×C17—21no—
53C2×D4×C17—22no—
54C2×D4×C17—21no—
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—84no—
68C2×C8×C17—24no—
69C4⋊C4×C17—22no—
70C22⋊C4×C17—24no—
71C42×C17C2×D412yes—
72C42×C17#4112yes—
73C22⋊Dic17—44no—
74C22⋊Dic17—82no—
75C4⋊Dic17—22no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78#63225—41no—
79#63225—41no—
80#63225—82no—
81C4×Dic17—42no—
82#63223—42no—
83#63223—42no—
84C2×#3622—42no—
85#9487—171nomaximal, Sylow
86C23×C17—22no—
87C23×C17—22no—
88C23×C17—22no—
89C23×C17—42no—
90C23×C17—42no—
91C23×C17C2×C22⋊C411yescharacteristic
92D4×C17—42no—
93D4×C17—42no—
94C2×C4×C17—22no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—44no—
98C2×C4×C17—42no—
99C2×C4×C17—82no—
100C2×C4×C17C4×D412yes—
101C2×C4×C17#12011yescharacteristic
102C2×C4×C17#12112yes—
103C2×C4×C17#12311yescharacteristic
104C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
105C2×C4×C17#13712yes—
106C2×C4×C17#13711yescharacteristic
107C2×Dic17—22no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—42no—
111C2×Dic17—41no—
112C2×Dic17—42no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—42no—
116Dic34—24no—
117Dic34—42no—
118C8×C17—44no—
119#3622—82no—
120#2975D1711yescharacteristic
121#2580—171no—
122#1800—171no—
123#1487—172no—
124#1286—172no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—44no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—42no—
131C22×C17—82no—
132C22×C17#38611yescharacteristic
133C22×C17#41711yescharacteristic
134C22×C17#41911yescharacteristic
135C4×C17—22no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—42no—
139C4×C17#46812yes—
140C4×C17#47012yes—
141Dic17—42no—
142Dic17—82no—
143Dic17—81no—
144C2×C4×Q8—171no—
145C2×C4×D4C2×D1711yescharacteristic
146#436—24no—
147#431C2×D1712yes—
148#423—172no—
149C2×#100—341no—
150#407—22no—
151#399—172no—
152#393—172no—
153#390—341no—
154#389—341no—
155#385—342no—
156#382—171no—
157#343—341no—
158Q8⋊C8—344no—
159C2×C17—21no—
160C2×C17—21no—
161C2×C17—82no—
162C2×C17#189111yescharacteristic
163C2×C17#189411yescharacteristic
164C2×C17#191111yescharacteristic
165C22×Q8—171no—
166C22×D4D6811yescharacteristic
167C23×C4C22⋊D1712yes—
168C2×M16—24no—
169C2×M16—342no—
170C4×Q8—342no—
171C4×Q8—342no—
172C4×D4—22no—
173C4×D4—22no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—341no—
176C2×C4⋊C4—341no—
177C2×C4⋊C4—342no—
178C2×C4⋊C4D6811yescharacteristic
179C2×C22⋊C4—342no—
180C2×C22⋊C4—342no—
181C2×C22⋊C4C4×D1712yes—
182C2×C42—341no—
183C2×C42C22×D1711yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—342no—
186C4⋊C8—342no—
187#100—682no—
188C22⋊C8—24no—
189C22⋊C8—22no—
190C4×C8C22⋊D1714yes—
191#95—172no—
192#95—341no—
193#95—342no—
194C17#948711yescharacteristic, complemented, Sylow
195C24#6322712yes—
196C2×Q8—342no—
197C2×Q8—682no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—82no—
205C22×C4—341no—
206C22×C4—342no—
207C22×C4—341no—
208C22×C4#6322712yes—
209C22×C4C2×C4×D1711yescharacteristic
210C22×C4C2×D6811yescharacteristic
211C22×C4C2×C22⋊D1711yescharacteristic
212M16—84no—
213M16—682no—
214M16—682no—
215C2×C8—24no—
216C2×C8—682no—
217C4⋊C4—22no—
218C4⋊C4—342no—
219C4⋊C4—681no—
220C4⋊C4—681no—
221C4⋊C4—681no—
222C4⋊C4—681no—
223C4⋊C4—1362no—
224C22⋊C4—24no—
225C22⋊C4—684no—
226C22⋊C4—1362no—
227C42—682no—
228C42#6325212yes—
229C42C2×C22⋊D1712yes—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×#6322711yescharacteristic
236Q8—344no—
237Q8—682no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—342no—
247C2×C4—681no—
248C2×C4—681no—
249C2×C4—682no—
250C2×C4—681no—
251C2×C4—682no—
252C2×C4—681no—
253C2×C4—681no—
254C2×C4—682no—
255C2×C4#1058759411yescharacteristic
256C2×C4#1058759512yes—
257C2×C4#1058759511yescharacteristic
258C2×C4C4×C22⋊D1712yes—
259C2×C4#1058761511yescharacteristic
260C2×C4#1058761612yes—
261C2×C4#1058763911yescharacteristic
262C8—44no—
263C8—1362no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#1176268811yescharacteristic
272C22#1176281111yescharacteristic
273C22#1176281911yescharacteristic
274C4—21no—
275C4—21no—
276C4—22no—
277C4—42no—
278C4—682no—
279C4—1362no—
280C4—1361no—
281C4#1176305512yes—
282C4#1176306712yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#1452920211yescharacteristic
287C2#1452921711yescharacteristic
288C2#1452931611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2975C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#2975D17
hypocenterC17#9487
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #14527214C2semidirect
4. #14526643C2semidirect
194. C17#9487semidirect

Maximal subgroups

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

subgroupindex
#145341382
#145287762
#145272142
#145266432
C17×#29752
#948717