Finite Group Databasebeta

← #16927634

Subgroups — #16927634

Order 4352.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537759C211yesmaximal, characteristic
2#14527547C211yesmaximal, characteristic, complemented
3#14527307C212yesmaximal
4#14526640C212yesmaximal, complemented
5C4×C17×#107C211yesmaximal, characteristic, complemented
6#11763343C2211yescharacteristic
7#11762939C411yescharacteristic, complemented
8C8×Dic34C411yescharacteristic, complemented
9#11762888C411yescharacteristic, complemented
10#11762880—21no—
11C8×D68C411yescharacteristic, complemented
12C8×C22⋊D17—21no—
13#11762868—21no—
14#11762866C2212yes—
15#11762866C2211yescharacteristic
16#11762763—21no—
17#11762562—21no—
18#11762560—21no—
19#11762545—22no—
20#11762542—22no—
21C2×C17×#107—21no—
22C2×C4×C8×C17C2211yescharacteristic
23C4×C4⋊C4×C17C2212yes—
24C17×#340—21no—
25C22×C8×C17D411yescharacteristic
26C22×C8×C17D411yescharacteristic
27C2×C4⋊C4×C17—22no—
28C2×C42×C17—22no—
29C2×C42×C17C2311yescharacteristic
30#10587616D411yescharacteristic
31#10587615—21no—
32C4×C22⋊D17—21no—
33#10587610D411yescharacteristic
34C2×#63218—21no—
35C2×C8×D17—21no—
36#10587562—21no—
37#10587561Q811yescharacteristic
38C4×D68C2×C411yescharacteristic
39#10587558—21no—
40#10587556Q811yescharacteristic
41C4×Dic34C2×C411yescharacteristic
42C17×#107—24no—
43C4×C8×C17C2×C411yescharacteristic
44C4×C8×C17C2×C411yescharacteristic
45C4×C8×C17D411yescharacteristic
46C4×C8×C17D411yescharacteristic
47C17×#95—22no—
48C22⋊#3622—21no—
49C22⋊#3622—22no—
50#10587491—21no—
51#10587491—21no—
52#10587486—21no—
53#10587485—21no—
54#10587485—21no—
55C8×Dic17—21no—
56C4⋊#3622—22no—
57C4⋊#3622C2×C411yescharacteristic
58C4⋊#3622C2×C411yescharacteristic
59#10587474—21no—
60#10587474—22no—
61C22×C4×C17—42no—
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17#4111yescharacteristic
65C2×C22⋊D17—21no—
66C2×D68C4⋊C411yescharacteristic
67C2×C4×D17—21no—
68C2×Dic34C4⋊C411yescharacteristic
69C2×C8×C17—22no—
70C2×C8×C17—41no—
71C2×C8×C17C22⋊C411yescharacteristic
72C2×C8×C17C22⋊C411yescharacteristic
73C2×C8×C17C22⋊C411yescharacteristic
74C2×C8×C17C22⋊C411yescharacteristic
75C4⋊C4×C17—24no—
76C4⋊C4×C17—42no—
77C42×C17—82no—
78C42×C17C22×C411yescharacteristic
79C42×C17C2×D411yescharacteristic
80C42×C17C2×Q811yescharacteristic
81C42×C17#4111yescharacteristic
82C22⋊Dic17—21no—
83#63227—21no—
84#63227—21no—
85#63227—21no—
86#63227—21no—
87C4⋊Dic17C4⋊C411yescharacteristic
88C4⋊Dic17C4⋊C411yescharacteristic
89#63225—21no—
90#63225—21no—
91#63225—21no—
92#63225—21no—
93C4×Dic17—21no—
94C2×#3622—21no—
95C2×#3622—21no—
96C2×#3622—42no—
97#63218—42no—
98C8×D17—42no—
99#8695—171nomaximal, Sylow
100C23×C17#12111yescharacteristic
101C22×D17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17—44no—
108C2×C4×C17—82no—
109C2×C4×C17—82no—
110C2×C4×C17C2×C22⋊C411yescharacteristic
111C2×C4×C17C2×C4⋊C411yescharacteristic
112C2×C4×C17#11711yescharacteristic
113C2×C4×C17#12111yescharacteristic
114C2×C4×C17C22⋊Q811yescharacteristic
115C2×C4×C17C22⋊Q811yescharacteristic
116C22⋊D17—41no—
117C22⋊D17—41no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121D68—41no—
122C4×D17—41no—
123C4×D17—41no—
124Dic34—41no—
125C8×C17—21no—
126C8×C17—21no—
127C8×C17—21no—
128C8×C17#10412yes—
129#3622—41no—
130#3622—41no—
131#3622—82no—
132#2966—171no—
133C4×#107D1711yescharacteristic, complemented
134#1568—171no—
135#1509—172no—
136#1285—172no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17#38011yescharacteristic
140C22×C17#47211yescharacteristic
141C22×C17#47311yescharacteristic
142C2×D17—41no—
143C2×D17—41no—
144C2×D17—41no—
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—84no—
151C4×C17C2×#10411yescharacteristic
152C4×C17#42111yescharacteristic
153Dic17—41no—
154Dic17—41no—
155Dic17—41no—
156#529—171no—
157#446—171no—
158C8×Q8—171no—
159#436—171no—
160#435—341no—
161C8×D4—171no—
162C8×D4—341no—
163#433—341no—
164#432—171no—
165#432—172no—
166C2×#107—21no—
167#405—341no—
168C2×C4×C8C2×D1711yescharacteristic
169C4×C4⋊C4C2×D1712yes—
170#340—21no—
171#335—341no—
172#334—341no—
173#328—342no—
174#327—342no—
175C2×C17—21no—
176C2×C17—21no—
177C2×C17#180611yescharacteristic
178C2×C17#181211yescharacteristic
179C2×C17#181611yescharacteristic
180D17—81no—
181C2×M16—341no—
182C22×C8—341no—
183C22×C8C22⋊D1711yescharacteristic
184C22×C8C22⋊D1711yescharacteristic
185#126—341no—
186#125—171no—
187#124—171no—
188#123—341no—
189C22⋊Q8—171no—
190#121—171no—
191C4×Q8—171no—
192C4×D4—171no—
193C4×D4—341no—
194#117—341no—
195C2×C4⋊C4—22no—
196C2×C42—22no—
197C2×C42C22×D1711yescharacteristic
198#107—24no—
199C4⋊C8—171no—
200C4⋊C8—171no—
201C4⋊C8—341no—
202C4⋊C8—341no—
203C4⋊C8—342no—
204C22⋊C8—341no—
205C22⋊C8—341no—
206C22⋊C8—341no—
207C22⋊C8—342no—
208#97—341no—
209#97—341no—
210#97—342no—
211C4×C8—341no—
212C4×C8C4×D1711yescharacteristic
213C4×C8C4×D1711yescharacteristic
214C4×C8D6811yescharacteristic
215C4×C8D6811yescharacteristic
216#95—22no—
217C17#869511yescharacteristic, complemented, Sylow
218C2×Q8—171no—
219C2×D4—171no—
220C2×D4—341no—
221C22×C4—42no—
222C22×C4—341no—
223C22×C4D4×D1711yescharacteristic
224C22×C4#6325411yescharacteristic
225C22×C4C2×C22⋊D1711yescharacteristic
226M16—682no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—341no—
230C2×C8—341no—
231C2×C8—682no—
232C2×C8—682no—
233C2×C8#6322711yescharacteristic
234C2×C8#6322711yescharacteristic
235C2×C8#6322711yescharacteristic
236C2×C8#6322711yescharacteristic
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—171no—
240C4⋊C4—171no—
241C4⋊C4—341no—
242C4⋊C4—341no—
243C4⋊C4—341no—
244C4⋊C4—341no—
245C22⋊C4—341no—
246C22⋊C4—341no—
247C22⋊C4—341no—
248C22⋊C4—341no—
249C22⋊C4—341no—
250C42—82no—
251C42—341no—
252C42C2×C4×D1711yescharacteristic
253C42C2×D6811yescharacteristic
254C42Q8×D1711yescharacteristic
255C42#6325611yescharacteristic
256C23—341no—
257C23#1058762411yescharacteristic
258Q8—681no—
259D4—681no—
260D4—681no—
261D4—681no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—44no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4C4⋊C4×D1711yescharacteristic
276C2×C4#1058757811yescharacteristic
277C2×C4#1058758111yescharacteristic
278C2×C4#1058758311yescharacteristic
279C2×C4C2×#6322711yescharacteristic
280C2×C4#1058763211yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—681no—
285C8—681no—
286C8—1362no—
287C8#1058747612yes—
288C22—21no—
289C22—21no—
290C22—681no—
291C22—681no—
292C22—681no—
293C22#1176266611yescharacteristic
294C22#1176307611yescharacteristic
295C22#1176308111yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—84no—
302C4—681no—
303C4—681no—
304C4—681no—
305C4C2×#1058747611yescharacteristic
306C4#1176282711yescharacteristic
307C2—21no—
308C2—21no—
309C2—1361no—
310C2#1452880511yescharacteristic
311C2#1452882711yescharacteristic
312C2#1452884911yescharacteristic
subgroupG/H
centerC22#11762666
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC4×C17×#107C2
socleC22×C17#380
prime radical#10587616D4
cosocleC2×C42×C17C23
hypercenterC4×#107D17
hypocenterC17#8695
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #14527547C2semidirect
4. #14526640C2semidirect
5. C4×C17×#107C2semidirect
7. #11762939C4semidirect
8. C8×Dic34C4semidirect
9. #11762888C4semidirect
11. C8×D68C4semidirect
133. C4×#107D17semidirect
217. C17#8695semidirect

Maximal subgroups

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

subgroupindex
#145377592
#145275472
#145273072
#145266402
C4×C17×#1072
#869517