Finite Group Databasebeta

← #16952239

Subgroups — #16952239

Order 4352.

394 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762609C211yesmaximal, characteristic
2C2×#11762609C211yesmaximal, characteristic
3C2×C4×#63214C211yesmaximal, characteristic, complemented
4#14529650C211yesmaximal, characteristic
5#14526875C211yesmaximal, characteristic, complemented
6#14526875C211yesmaximal, characteristic, complemented
7C17×#1942C211yesmaximal, characteristic, complemented
8C22×D136C2211yescharacteristic
9C22×#63214C2211yescharacteristic
10C22×#63214C2211yescharacteristic
11C2×#10587489C2211yescharacteristic
12C2×#10587492—21no—
13#11762711—21no—
14#11762609—22no—
15#11762609C414yescomplemented
16C4×#63214—22no—
17C2×C17×#107C2211yescharacteristic
18C2×C17×#107C2211yescharacteristic
19C2×C4×C8×C17C2211yescharacteristic
20C17×#389—21no—
21C17×#340—21no—
22C22×D68—21no—
23C22×C8×C17D411yescharacteristic
24C22×C8×C17C2311yescharacteristic
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—41no—
28C2×C42×C17D411yescharacteristic
29C2×#63227—41no—
30C2×#63227—41no—
31C2×C4⋊Dic17—21no—
32C2×D136—21no—
33C2×D136—21no—
34C2×D136—21no—
35C2×D136—21no—
36C2×D136—21no—
37C2×D136C2×C412yes—
38C17×#107—21no—
39C17×#107—21no—
40C17×#107—21no—
41C17×#107C2×C412yes—
42C4×C8×C17—21no—
43C4×C8×C17—21no—
44C17×#95—41no—
45#10587492—42no—
46#10587489—21no—
47#10587489—21no—
48C2×#63214—21no—
49C2×#63214—21no—
50C2×#63214—21no—
51C2×#63214—21no—
52C2×#63214C2×C412yes—
53C2×#63214D412yes—
54C23×D17—41no—
55C22×C4×C17—41no—
56C22×C4×C17—41no—
57C22×C4×C17D811yescharacteristic
58C22×C4×C17D811yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×Dic17—41no—
61C2×D68—22no—
62C2×D68—41no—
63C2×D68—41no—
64C2×D68—41no—
65C2×D68—41no—
66C2×D68—41no—
67C2×C8×C17—21no—
68C2×C8×C17—21no—
69C2×C8×C17SD1612yes—
70C2×C8×C17C22×C411yescharacteristic
71C2×C8×C17C2×D411yescharacteristic
72C2×C8×C17#4111yescharacteristic
73C2×C8×C17#4111yescharacteristic
74C2×C8×C17#4111yescharacteristic
75C2×C8×C17#4111yescharacteristic
76C4⋊C4×C17—22no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—82no—
81C42×C17—21no—
82C42×C17—21no—
83#63227—82no—
84#63227—82no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87D136—22no—
88D136—22no—
89D136—41no—
90D136—41no—
91#63214—22no—
92#63214—22no—
93#13147—171nomaximal, Sylow
94C23×C17C2×D811yescharacteristic
95C22×D17—42no—
96C22×D17—81no—
97C22×D17—81no—
98C22×D17—81no—
99C22×D17—81no—
100C22×D17—81no—
101C22×D17—81no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—42no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17D1612yes—
113C2×C4×C17SD3212yes—
114C2×C4×C17C4×D411yescharacteristic
115C2×C4×C17#12111yescharacteristic
116C2×C4×C17#12411yescharacteristic
117C2×C4×C17C2×SD1611yescharacteristic
118C2×C4×C17#13511yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×Dic17—81no—
121C2×Dic17—81no—
122C2×Dic17—81no—
123D68—42no—
124D68—42no—
125D68—81no—
126D68—81no—
127C8×C17—22no—
128C8×C17#11711yescharacteristic
129C8×C17C4×D411yescharacteristic
130C8×C17#12311yescharacteristic
131C8×C17#12611yescharacteristic
132C2×#357—171no—
133C2×#357—171no—
134C2×C4×C16—171no—
135#1970—171no—
136#1942D1711yescharacteristic, complemented
137#1380—171no—
138#1380—171no—
139C22×C17C4×D811yescharacteristic
140C22×C17#46611yescharacteristic
141C22×C17#48611yescharacteristic
142C22×C17C2×D1611yescharacteristic
143C22×C17C2×SD3211yescharacteristic
144C22×C17#50811yescharacteristic
145C22×C17#50811yescharacteristic
146C2×D17—82no—
147C2×D17—82no—
148C2×D17—82no—
149C2×D17—161no—
150C2×D17—161no—
151C2×D17—161no—
152C2×D17—161no—
153C4×C17—22no—
154C4×C17—22no—
155C4×C17—82no—
156C4×C17—161no—
157C4×C17#38811yescharacteristic
158C4×C17C4×SD1611yescharacteristic
159C4×C17#46511yescharacteristic
160C4×C17#48811yescharacteristic
161Dic17—161no—
162C22×D8—171no—
163C22×C16—171no—
164C22×C16—171no—
165C2×#107—171no—
166C2×#107C2×D1711yescharacteristic
167C2×#107C2×D1711yescharacteristic
168C2×#102—341no—
169C2×C4×C8C2×D1711yescharacteristic
170#390—341no—
171#389—21no—
172#357—174no—
173#357—342no—
174C4×C16—342no—
175#340—21no—
176C2×C17#193411yescharacteristic
177C2×C17C4×D1611yescharacteristic
178C2×C17C4×SD3211yescharacteristic
179C2×C17#221511yescharacteristic
180C2×C17#221711yescharacteristic
181C2×C17#224011yescharacteristic
182C2×C17#224211yescharacteristic
183D17—162no—
184C22×D4—341no—
185C2×D8—172no—
186C2×D8—341no—
187C2×D8—341no—
188C2×D8—341no—
189C2×D8—341no—
190C2×D8—341no—
191C22×C8C22⋊D1711yescharacteristic
192C22×C8C22×D1711yescharacteristic
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—341no—
197C2×C22⋊C4—681no—
198C2×C22⋊C4—681no—
199C2×C42C22⋊D1711yescharacteristic
200C2×C16—172no—
201C2×C16—172no—
202C2×C16—341no—
203C2×C16—341no—
204C2×C16—341no—
205C2×C16—341no—
206#107—21no—
207#107—21no—
208#107—21no—
209#107—341no—
210#107—341no—
211#107C4×D1712yes—
212#102—682no—
213C4×C8—21no—
214C4×C8—21no—
215#95—41no—
216C17#1314711yescharacteristic, complemented, Sylow
217C24—681no—
218C2×D4—342no—
219C2×D4—681no—
220C2×D4—681no—
221C2×D4—681no—
222C2×D4—681no—
223C2×D4—681no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—681no—
227C22×C4#6322811yescharacteristic
228C22×C4#6322811yescharacteristic
229C22×C4C2×C22⋊D1711yescharacteristic
230D8—342no—
231D8—342no—
232D8—681no—
233D8—681no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8#6323012yes—
237C2×C8C2×C4×D1711yescharacteristic
238C2×C8#6325211yescharacteristic
239C2×C8D4×D1711yescharacteristic
240C2×C8#6325411yescharacteristic
241C2×C8#6325611yescharacteristic
242C2×C8#6325611yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—82no—
248C4⋊C4—681no—
249C4⋊C4—681no—
250C22⋊C4—1362no—
251C22⋊C4—1362no—
252C42—21no—
253C42—21no—
254C16—342no—
255C16—342no—
256C23—682no—
257C23—1361no—
258C23—1361no—
259C23—1361no—
260C23—1361no—
261C23—1361no—
262C23—1361no—
263C23C2×#6322811yescharacteristic
264D4—682no—
265D4—682no—
266D4—1361no—
267D4—1361no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—1361no—
279C2×C4—1361no—
280C2×C4—1361no—
281C2×C4#1058749712yes—
282C2×C4#1058749912yes—
283C2×C4C4×C22⋊D1711yescharacteristic
284C2×C4#1058762511yescharacteristic
285C2×C4C2×#6323011yescharacteristic
286C2×C4#1058763311yescharacteristic
287C2×C4#1058763611yescharacteristic
288C2×C4#1058763611yescharacteristic
289C8—22no—
290C8#1058757811yescharacteristic
291C8#1058757911yescharacteristic
292C8#1058758011yescharacteristic
293C8#1058758411yescharacteristic
294C22—2721no—
295C22—2721no—
296C22—2721no—
297C22—2721no—
298C22—1362no—
299C22—1362no—
300C22—1362no—
301C22C4×#6322811yescharacteristic
302C22#1176304311yescharacteristic
303C22#1176315711yescharacteristic
304C22C2×#1058749711yescharacteristic
305C22C2×#1058749911yescharacteristic
306C22#1176323911yescharacteristic
307C22#1176323911yescharacteristic
308C4—22no—
309C4—22no—
310C4—82no—
311C4—161no—
312C4—2721no—
313C4#1176269911yescharacteristic
314C4C4×#6323011yescharacteristic
315C4#1176304011yescharacteristic
316C4#1176316611yescharacteristic
317C2—2722no—
318C2#1452946611yescharacteristic
319C2C4×#1058749711yescharacteristic
320C2C4×#1058749911yescharacteristic
321C2#1453086811yescharacteristic
322C2#1453088211yescharacteristic
323C2#1453100911yescharacteristic
324C2#1453101811yescharacteristic
subgroupG/H
centerC23C2×#63228
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1942C2
socleC23×C17C2×D8
prime radicalC22×D136C22
cosocleC22×C8×C17C23
hypercenter#1942D17
hypocenterC17#13147
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
3. C2×C4×#63214C2semidirect
5. #14526875C2semidirect
6. #14526875C2semidirect
7. C17×#1942C2semidirect
15. #11762609C4semidirect
136. #1942D17semidirect
216. C17#13147semidirect

Maximal subgroups

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

subgroupindex
C2×#117626092
C2×C4×#632142
#145296502
#145268752
C17×#19422
#1314717