Finite Group Databasebeta

← #16944223

Subgroups — #16944223

Order 4352.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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#14537762C211yesmaximal, 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
8#11763341C411yescharacteristic
9C2×#10587469—21no—
10#11762939C2211yescharacteristic
11#11762933C411yescharacteristic
12#11762878—21no—
13D4×#3622C411yescharacteristic
14#11762872—21no—
15#11762867—21no—
16#11762865C411yescharacteristic
17#11762767—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×M16×C17—21no—
28C4×D4×C17C2×C411yescharacteristic
29#10587624C811yescharacteristic
30#10587622C811yescharacteristic
31C4×C22⋊D17—21no—
32#10587612—21no—
33C22×#3622—21no—
34C2×C8×D17D411yescharacteristic
35C2×C8×D17D411yescharacteristic
36#10587583C811yescharacteristic
37#10587576C811yescharacteristic
38#10587569—21no—
39#10587565—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—
64C2×C4×D17C22⋊C411yescharacteristic
65C2×C4×D17C2×C811yescharacteristic
66C2×C4×D17M1611yescharacteristic
67C2×Dic34C2×C811yescharacteristic
68M16×C17—41no—
69M16×C17—41no—
70C2×C8×C17—21no—
71C2×C8×C17C2×D411yescharacteristic
72C2×C8×C17C2×D411yescharacteristic
73C4⋊C4×C17C2×C811yescharacteristic
74C22⋊C4×C17—21no—
75C42×C17C22×C411yescharacteristic
76C22⋊Dic17—21no—
77C22⋊Dic17—21no—
78C22⋊Dic17—21no—
79#63227—21no—
80C4⋊Dic17—21no—
81C4⋊Dic17—21no—
82C4⋊Dic17C2×C811yescharacteristic
83#63225—21no—
84#63225—21no—
85C4×Dic17—21no—
86C4×Dic17C22⋊C411yescharacteristic
87C4×Dic17C2×C811yescharacteristic
88C4×Dic17M1611yescharacteristic
89C2×#3622—21no—
90C2×#3622—42no—
91C2×#3622C22⋊C411yescharacteristic
92C2×#3622C22⋊C411yescharacteristic
93C8×D17—21no—
94C8×D17—21no—
95C8×D17—41no—
96C16×C17—41no—
97C16×C17—41no—
98#63214—41no—
99#63214—41no—
100#11627—171nomaximal, Sylow
101C23×C17—21no—
102C22×D17C22⋊C811yescharacteristic
103D4×C17—41no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17C2×C22⋊C411yescharacteristic
108C2×C4×C17C22×C811yescharacteristic
109C2×C4×C17C2×M1611yescharacteristic
110C22⋊D17—42no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17C22⋊C811yescharacteristic
114C2×Dic17C22⋊C811yescharacteristic
115C2×Dic17C22⋊C811yescharacteristic
116C4×D17—21no—
117C4×D17—21no—
118C4×D17—41no—
119C4×D17—41no—
120Dic34—41no—
121C8×C17—21no—
122C8×C17—41no—
123C8×C17AGL(1,ℤ/8)11yescharacteristic
124C8×C17#13711yescharacteristic
125#3622—21no—
126#3622—21no—
127#3622—41no—
128#2966—171no—
129#2163—171no—
130#2150—171no—
131#1338—171no—
132#1338—171no—
133#1330—171no—
134#1330D1711yescharacteristic, complemented
135C22×C17—41no—
136C22×C17—41no—
137C22×C17—41no—
138C22×C17C2×C22⋊C811yescharacteristic
139C2×D17—21no—
140C2×D17—21no—
141C2×D17—21no—
142C4×C17—21no—
143C4×C17—21no—
144C4×C17—41no—
145C4×C17#41711yescharacteristic
146C4×C17#42111yescharacteristic
147Dic17—21no—
148Dic17—21no—
149Dic17—21no—
150Dic17—41no—
151Dic17—41no—
152#529—171no—
153C2×M32—341no—
154#446—171no—
155C8×Q8—171no—
156#436C2×D1711yescharacteristic
157#435—341no—
158C8×D4—171no—
159C8×D4—341no—
160#433—341no—
161#432—171no—
162#405—341no—
163C2×C4×C8—171no—
164C4⋊C16—171no—
165C4⋊C16—341no—
166C4⋊C16—341no—
167C4⋊C16C2×D1711yescharacteristic
168C22⋊C16—341no—
169#346—171no—
170#346C2×D1711yescharacteristic
171C2×C17—81no—
172C2×C17#147711yescharacteristic
173C2×C17#211511yescharacteristic
174C2×C17#211711yescharacteristic
175D17—41no—
176C2×M16—21no—
177C22×C8—171no—
178C22×C8—171no—
179C22×C8—341no—
180#126—341no—
181#125—171no—
182#124—171no—
183#123—341no—
184C22⋊Q8—171no—
185#121—171no—
186C4×Q8—171no—
187C4×D4—341no—
188C4×D4C4×D1711yescharacteristic
189#117—341no—
190C2×C42—171no—
191M32—682no—
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—341no—
195C2×C16—341no—
196C4⋊C8—171no—
197C4⋊C8—341no—
198C4⋊C8—341no—
199C4⋊C8C4×D1711yescharacteristic
200C22⋊C8—21no—
201C22⋊C8—341no—
202C22⋊C8—341no—
203#97—341no—
204#97—341no—
205C4×C8—171no—
206C4×C8—171no—
207C4×C8—171no—
208C4×C8—341no—
209C4×C8C22×D1711yescharacteristic
210C17#1162711yescharacteristic, complemented, Sylow
211C2×Q8—171no—
212C2×D4—341no—
213C2×D4C8×D1711yescharacteristic
214C22×C4—21no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—171no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—171no—
222C2×C8—171no—
223C2×C8—341no—
224C2×C8—341no—
225C2×C8—341no—
226C2×C8—681no—
227C2×C8—682no—
228C2×C8D4×D1711yescharacteristic
229C2×C8D4×D1711yescharacteristic
230C4⋊C4—171no—
231C4⋊C4—341no—
232C4⋊C4—341no—
233C4⋊C4—341no—
234C4⋊C4—341no—
235C4⋊C4C8×D1711yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—341no—
238C22⋊C4—341no—
239C22⋊C4—341no—
240C22⋊C4—341no—
241C42—171no—
242C42—171no—
243C42—171no—
244C42—341no—
245C42C2×C4×D1711yescharacteristic
246C16—41no—
247C16—41no—
248C16—681no—
249C16—681no—
250C23—21no—
251C23—171no—
252Q8—681no—
253D4—41no—
254D4—682no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—171no—
259C2×C4—171no—
260C2×C4—171no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4C22⋊C4×D1711yescharacteristic
268C2×C4C2×C8×D1711yescharacteristic
269C2×C4M16×D1711yescharacteristic
270C8—21no—
271C8—41no—
272C8—341no—
273C8—341no—
274C8—681no—
275C8#1058759711yescharacteristic
276C8#1058760111yescharacteristic
277C22—41no—
278C22—41no—
279C22—41no—
280C22—341no—
281C22—341no—
282C22—341no—
283C22C22⋊C8×D1711yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—341no—
288C4—341no—
289C4—341no—
290C4—681no—
291C4—681no—
292C4#1176280711yescharacteristic
293C4#1176282411yescharacteristic
294C2—81no—
295C2—681no—
296C2#1452716811yescharacteristic
297C2#1453040311yescharacteristic
298C2#1453041011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC2×C4×C17C22×C8
FrattiniC4×C8C22×D17
FittingC17×#1330C2
socleC22×C17C2×C22⋊C8
prime radical#10587624C8
cosocleC4×C8×C17C23
hypercenter#1330D17
hypocenterC17#11627
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
134. #1330D17semidirect
210. C17#11627semidirect

Maximal subgroups

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

subgroupindex
#145377622
#145305852
#145305382
#145267672
#145267652
#145267422
C17×#13302
#1162717