Finite Group Databasebeta

← #16944228

Subgroups — #16944228

Order 4352.

322 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 91 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#14537747C211yesmaximal, characteristic
2#14530585C211yesmaximal, characteristic, complemented
3#14530538C211yesmaximal, characteristic, complemented
4#14526767C211yesmaximal, characteristic, complemented
5#14526765C211yesmaximal, characteristic, complemented
6#14526742C211yesmaximal, characteristic, complemented
7C17×#1330C211yesmaximal, characteristic, complemented
8C4×#63254C411yescharacteristic
9C2×#10587469—21no—
10#11762939C2211yescharacteristic
11#11762936C411yescharacteristic
12#11762887C411yescharacteristic
13#11762883—21no—
14#11762878—21no—
15#11762861C411yescharacteristic
16#11762859—21no—
17M16×Dic17—21no—
18C4×C8×D17C2211yescharacteristic
19C4⋊#63214C2211yescharacteristic
20#11762627—21no—
21#11762627—21no—
22#11762588—21no—
23#11762585C2211yescharacteristic
24C17×#436C2211yescharacteristic
25C17×C4⋊C16C2211yescharacteristic
26C17×#346C2211yescharacteristic
27C2×#63254C811yescharacteristic
28C2×M16×C17—21no—
29C4×D4×C17C2×C411yescharacteristic
30D4×Dic17C811yescharacteristic
31C4×C22⋊D17—21no—
32C2×C4×Dic17—21no—
33C2×#63223—21no—
34C2×C8×D17D411yescharacteristic
35C2×C8×D17D411yescharacteristic
36#10587578C811yescharacteristic
37#10587573C811yescharacteristic
38#10587567—21no—
39#10587563—21no—
40C42×D17C2×C411yescharacteristic
41C4×Dic34C2×C411yescharacteristic
42C2×C16×C17—21no—
43C2×C16×C17—21no—
44C17×C4⋊C8C2×C411yescharacteristic
45C17×C22⋊C8—21no—
46C4×C8×C17C2311yescharacteristic
47C22⋊#3622—21no—
48#10587491—21no—
49#10587486—21no—
50#10587486—21no—
51#10587485—21no—
52#10587485—21no—
53C8×Dic17—21no—
54C8×Dic17D411yescharacteristic
55C8×Dic17D411yescharacteristic
56C2×#63214—21no—
57C2×#63214—21no—
58C4⋊#3622C2×C411yescharacteristic
59C4×#3622C2×C411yescharacteristic
60#10587469—42no—
61C2×D4×C17C2×C811yescharacteristic
62C22×C4×C17—21no—
63C2×C22⋊D17—21no—
64C22×Dic17—21no—
65C22×Dic17—21no—
66#63254—42no—
67C2×C4×D17C22⋊C411yescharacteristic
68C2×C4×D17C2×C811yescharacteristic
69C2×C4×D17M1611yescharacteristic
70C2×Dic34C2×C811yescharacteristic
71M16×C17—41no—
72M16×C17—41no—
73C2×C8×C17—21no—
74C2×C8×C17C2×D411yescharacteristic
75C2×C8×C17C2×D411yescharacteristic
76C4⋊C4×C17C2×C811yescharacteristic
77C22⋊C4×C17—21no—
78C42×C17C22×C411yescharacteristic
79C22⋊Dic17—21no—
80#63227—21no—
81C4⋊Dic17C2×C811yescharacteristic
82#63225—21no—
83#63225—21no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17C22⋊C411yescharacteristic
88C4×Dic17C2×C811yescharacteristic
89C4×Dic17M1611yescharacteristic
90#63223—42no—
91C2×#3622—21no—
92C2×#3622C22⋊C411yescharacteristic
93C2×#3622C22⋊C411yescharacteristic
94C8×D17—21no—
95C8×D17—21no—
96C8×D17—41no—
97C16×C17—41no—
98C16×C17—41no—
99#63214—41no—
100#63214—41no—
101#11628—171nomaximal, Sylow
102C23×C17—21no—
103C22×D17C22⋊C811yescharacteristic
104D4×C17—41no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17C2×C22⋊C411yescharacteristic
109C2×C4×C17C22×C811yescharacteristic
110C2×C4×C17C2×M1611yescharacteristic
111C22⋊D17—42no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17C22⋊C811yescharacteristic
117C2×Dic17C22⋊C811yescharacteristic
118C2×Dic17C22⋊C811yescharacteristic
119C4×D17—21no—
120C4×D17—21no—
121C4×D17—22no—
122C4×D17—41no—
123Dic34—41no—
124C8×C17—21no—
125C8×C17—41no—
126C8×C17AGL(1,ℤ/8)11yescharacteristic
127C8×C17#13711yescharacteristic
128#3622—21no—
129#3622—21no—
130#3622—41no—
131#2965—171no—
132#2163—171no—
133#2150—171no—
134#1338—171no—
135#1338—171no—
136#1330—171no—
137#1330D1711yescharacteristic, complemented
138C22×C17—41no—
139C22×C17—41no—
140C22×C17—41no—
141C22×C17C2×C22⋊C811yescharacteristic
142C2×D17—21no—
143C2×D17—21no—
144C2×D17—21no—
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—41no—
148C4×C17#41711yescharacteristic
149C4×C17#42111yescharacteristic
150Dic17—21no—
151Dic17—21no—
152Dic17—41no—
153Dic17—41no—
154Dic17#34912yes—
155C4×#41—171no—
156C2×M32—341no—
157#446—171no—
158#446—171no—
159#436—171no—
160#436C2×D1711yescharacteristic
161#435—341no—
162#435—341no—
163#431—171no—
164#431—341no—
165C4×M16—341no—
166C2×C4×C8—171no—
167C4⋊C16—171no—
168C4⋊C16—341no—
169C4⋊C16—341no—
170C4⋊C16C2×D1711yescharacteristic
171C22⋊C16—341no—
172#346—171no—
173#346C2×D1711yescharacteristic
174C2×C17—81no—
175C2×C17#147711yescharacteristic
176C2×C17C2×#34911yescharacteristic
177C2×C17#211711yescharacteristic
178D17—41no—
179C2×#41—171no—
180C2×M16—21no—
181C2×M16—341no—
182C22×C8—171no—
183C22×C8—171no—
184C4×Q8—171no—
185C4×Q8—171no—
186C4×D4—171no—
187C4×D4—341no—
188C4×D4—341no—
189C4×D4C4×D1711yescharacteristic
190#117—171no—
191#117—341no—
192C2×C42—171no—
193C2×C42—341no—
194M32—682no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—341no—
198C2×C16—341no—
199C4⋊C8—171no—
200C4⋊C8—341no—
201C4⋊C8—341no—
202C4⋊C8C4×D1711yescharacteristic
203C22⋊C8—21no—
204C22⋊C8—341no—
205C22⋊C8—341no—
206#97—341no—
207#97—341no—
208C4×C8—171no—
209C4×C8—171no—
210C4×C8—171no—
211C4×C8—341no—
212C4×C8C22×D1711yescharacteristic
213C17#1162811yescharacteristic, complemented, Sylow
214#41—682no—
215C2×Q8—171no—
216C2×D4—341no—
217C2×D4C8×D1711yescharacteristic
218C22×C4—21no—
219C22×C4—171no—
220C22×C4—171no—
221C22×C4—171no—
222C22×C4—341no—
223C22×C4—341no—
224M16—41no—
225M16—41no—
226M16—682no—
227C2×C8—21no—
228C2×C8—171no—
229C2×C8—171no—
230C2×C8—341no—
231C2×C8—341no—
232C2×C8—341no—
233C2×C8—681no—
234C2×C8D4×D1711yescharacteristic
235C2×C8D4×D1711yescharacteristic
236C4⋊C4—171no—
237C4⋊C4—341no—
238C4⋊C4—341no—
239C4⋊C4C8×D1711yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—341no—
242C22⋊C4—341no—
243C42—171no—
244C42—171no—
245C42—171no—
246C42—341no—
247C42—341no—
248C42—341no—
249C42C2×C4×D1711yescharacteristic
250C16—41no—
251C16—41no—
252C16—681no—
253C16—681no—
254C23—21no—
255C23—171no—
256Q8—681no—
257D4—41no—
258D4—682no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—171no—
263C2×C4—171no—
264C2×C4—171no—
265C2×C4—342no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—681no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4C22⋊C4×D1711yescharacteristic
274C2×C4C2×C8×D1711yescharacteristic
275C2×C4M16×D1711yescharacteristic
276C8—21no—
277C8—41no—
278C8—341no—
279C8—341no—
280C8—681no—
281C8#1058759711yescharacteristic
282C8#1058760111yescharacteristic
283C22—41no—
284C22—41no—
285C22—41no—
286C22—341no—
287C22—341no—
288C22—341no—
289C22C22⋊C8×D1711yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—172no—
294C4—341no—
295C4—341no—
296C4—681no—
297C4—681no—
298C4#1176280711yescharacteristic
299C4#1176282411yescharacteristic
300C2—81no—
301C2—681no—
302C2#1452716811yescharacteristic
303C2D17×#34911yescharacteristic
304C2#1453041011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC2×C4×C17C22×C8
FrattiniC4×C8C22×D17
FittingC17×#1330C2
socleC22×C17C2×C22⋊C8
prime radicalC2×#63254C8
cosocleC4×C8×C17C23
hypercenter#1330D17
hypocenterC17#11628
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #14530585C2semidirect
3. #14530538C2semidirect
4. #14526767C2semidirect
5. #14526765C2semidirect
6. #14526742C2semidirect
7. C17×#1330C2semidirect
137. #1330D17semidirect
213. C17#11628semidirect

Maximal subgroups

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

subgroupindex
#145377472
#145305852
#145305382
#145267672
#145267652
#145267422
C17×#13302
#1162817