Finite Group Databasebeta

← #16944914

Subgroups — #16944914

Order 4352.

482 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 87 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#14533783C211yesmaximal, characteristic
2#14527128C211yesmaximal, characteristic, complemented
3#14526786C214yesmaximal, complemented
4C4×C17×#101C211yesmaximal, characteristic, complemented
5C2×#10587560C411yescharacteristic
6C2×#10587633—21no—
7#11762866—21no—
8#11762726C412yes—
9#11762726C2212yes—
10#11762711—21no—
11#11762711—21no—
12#11762710—21no—
13C4×C4⋊Dic17C411yescharacteristic
14#11762535—21no—
15#11762535C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C2×C17×#101—21no—
18C4×M16×C17—21no—
19C17×#343C2212yes—
20C22×Q8×C17D411yescharacteristic
21C22×D68—21no—
22C22×D68—21no—
23C22×D68C2×C412yes—
24C2×M16×C17—22no—
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17C2311yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17D411yescharacteristic
33#10587633—44no—
34C2×#63227—22no—
35C2×#63227—22no—
36C2×#63227—22no—
37C2×#63227—22no—
38C2×C4⋊Dic17—21no—
39C2×C4×Dic17—21no—
40#10587560—41no—
41#10587560—41no—
42C17×#101—24no—
43C17×#97—41no—
44C4×C8×C17—41no—
45#10587502C2×C412yes—
46C22⋊#3622—22no—
47C4⋊#3622—41no—
48#10587474—41no—
49C23×D17—22no—
50C2×Q8×C17—22no—
51C2×Q8×C17—22no—
52C2×Q8×C17—41no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×Dic17—22no—
61C2×D68—42no—
62C2×D68—42no—
63C2×D68—42no—
64C2×D68—42no—
65C2×D68—42no—
66C2×D68—41no—
67C2×D68—41no—
68C2×D68—42no—
69C2×D68—82no—
70M16×C17—24no—
71M16×C17—42no—
72C2×C8×C17—42no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82#63227—44no—
83#63227—44no—
84#63227—82no—
85#63227—82no—
86C4⋊Dic17—42no—
87C4×Dic17—42no—
88C2×#3622—42no—
89#11781—171nomaximal, Sylow
90C23×C17C2×C22⋊C411yescharacteristic
91C22×D17—42no—
92C22×D17—42no—
93C22×D17—42no—
94C22×D17—42no—
95C22×D17—42no—
96C22×D17—42no—
97C22×D17—42no—
98Q8×C17—44no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17#9911yescharacteristic
114C2×C4×C17#9911yescharacteristic
115C2×C4×C17#10412yes—
116C2×C4×C17AGL(1,ℤ/8)12yes—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120D68—82no—
121D68—84no—
122D68—84no—
123D68—82no—
124C8×C17—44no—
125#3622—82no—
126#2548—171no—
127C4×#101D1711yescharacteristic, complemented
128#1467—171no—
129#1345—174no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17C2×#9911yescharacteristic
133C22×C17#41811yescharacteristic
134C22×C17C2×#10411yescharacteristic
135C2×D17—82no—
136C2×D17—82no—
137C2×D17—82no—
138C2×D17—82no—
139C2×D17—82no—
140C2×D17—82no—
141C2×D17—82no—
142C4×C17—21no—
143C4×C17—22no—
144C4×C17—22no—
145C4×C17—41no—
146C4×C17—41no—
147C4×C17—41no—
148C4×C17—41no—
149C4×C17#35512yes—
150Dic17—82no—
151C2×#127—171no—
152C2×#124—341no—
153C2×C4×Q8C2×D1711yescharacteristic
154#432—341no—
155C2×#101—21no—
156C4×M16—21no—
157#394—172no—
158#394—172no—
159#390—341no—
160#390—341no—
161#390—341no—
162C4×C4⋊C4—171no—
163#343C2×D1712yes—
164#324—172no—
165#324—341no—
166C2×C17—21no—
167C2×C17—21no—
168C2×C17#150711yescharacteristic
169C2×C17#212211yescharacteristic
170C2×C17C2×#35511yescharacteristic
171D17—162no—
172C22×Q8C22⋊D1711yescharacteristic
173C22×D4—172no—
174C22×D4—341no—
175C22×D4—341no—
176C2×M16—22no—
177#127—681no—
178#127—681no—
179#124—684no—
180C4×Q8—41no—
181C4×Q8—41no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C4×D1711yescharacteristic
184C2×C4⋊C4D6811yescharacteristic
185C2×C4⋊C4C22×D1711yescharacteristic
186C2×C22⋊C4—342no—
187C2×C22⋊C4—342no—
188C2×C22⋊C4—342no—
189C2×C22⋊C4—342no—
190C2×C42—341no—
191C2×C42C4×D1711yescharacteristic
192C2×C42D6811yescharacteristic
193C2×C42C22⋊D1711yescharacteristic
194C4⋊C8—681no—
195#101—24no—
196C22⋊C8—342no—
197#97—41no—
198#97—681no—
199C4×C8—41no—
200#95—172no—
201C17#1178111yescharacteristic, complemented, Sylow
202C24—342no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×D4—682no—
207C2×D4—682no—
208C2×D4—682no—
209C2×D4—682no—
210C2×D4—682no—
211C2×D4—682no—
212C2×D4—681no—
213C2×D4—681no—
214C2×D4—1362no—
215C22×C4—342no—
216C22×C4#6322711yescharacteristic
217C22×C4#6322711yescharacteristic
218C22×C4#6322711yescharacteristic
219C22×C4#6322711yescharacteristic
220C22×C4C2×C4×D1711yescharacteristic
221C22×C4C2×D6811yescharacteristic
222C22×C4C2×C22⋊D1711yescharacteristic
223M16—24no—
224M16—42no—
225C2×C8—42no—
226C2×C8—682no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—682no—
231C22⋊C4—684no—
232C22⋊C4—684no—
233C22⋊C4—1362no—
234C22⋊C4—1362no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—682no—
242C23—682no—
243C23—682no—
244C23—682no—
245C23—682no—
246C23—682no—
247C23—682no—
248C23—682no—
249C23C2×#6322711yescharacteristic
250Q8—44no—
251D4—1364no—
252D4—1362no—
253D4—1364no—
254D4—1362no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—682no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4#1058747612yes—
273C2×C4#1058747711yescharacteristic
274C2×C4#1058747711yescharacteristic
275C2×C4#1058763512yes—
276C8—44no—
277C8—1362no—
278C22—21no—
279C22—21no—
280C22—1362no—
281C22—1362no—
282C22—1362no—
283C22—1362no—
284C22—1362no—
285C22—1362no—
286C22—1362no—
287C22C2×#1058747711yescharacteristic
288C22#1176281311yescharacteristic
289C22C2×#1058747611yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—1362no—
298C4#1176260512yes—
299C2—21no—
300C2—21no—
301C2—2722no—
302C2#1452729911yescharacteristic
303C2#1453043511yescharacteristic
304C2C2×#1176260511yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC4×C17×#101C2
socleC22×C17C2×#99
prime radicalC2×#10587560C4
cosocleC2×C4⋊C4×C17C23
hypercenterC4×#101D17
hypocenterC17#11781
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #14527128C2semidirect
3. #14526786C2semidirect
4. C4×C17×#101C2semidirect
127. C4×#101D17semidirect
201. C17#11781semidirect

Maximal subgroups

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

subgroupindex
#145337832
#145271282
#145267862
C4×C17×#1012
#1178117