Finite Group Databasebeta

← #16930347

Subgroups — #16930347

Order 4352.

524 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534550C211yesmaximal, characteristic
2#14527457C212yesmaximal, complemented
3#14527098C211yesmaximal, characteristic
4#14526644C212yesmaximal, complemented
5C17×#2905C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×#10587610—21no—
8#11762862C2212yes—
9#11762739—21no—
10#11762739C412yes—
11#11762734—21no—
12#11762734C412yes—
13#11762715—21no—
14#11762675C2211yescharacteristic
15#11762556—24no—
16#11762535—21no—
17#11762533—21no—
18C22×M16×C17—21no—
19C2×C17×#117C2211yescharacteristic
20C17×#424—24no—
21C17×#423—21no—
22C17×#423C2212yes—
23C23×C4×C17D411yescharacteristic
24C22×Dic34—21no—
25C2×M16×C17—22no—
26C2×M16×C17—22no—
27C2×M16×C17—42no—
28C2×M16×C17—42no—
29C22×C8×C17—22no—
30C17×#117—22no—
31C17×#117—22no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×C42×C17C2311yescharacteristic
38C2×C22⋊Dic17—22no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17C2×C412yes—
42#10587610—42no—
43#10587610—42no—
44C2×#63225—22no—
45#10587555—22no—
46#10587555—22no—
47C17×C4⋊C8—24no—
48C17×C4⋊C8—22no—
49C17×C4⋊C8D414yes—
50#10587502—22no—
51#10587502—22no—
52#10587502—21no—
53#10587502C2×C412yes—
54C22⋊#3622—22no—
55C4⋊#3622—22no—
56C4×#3622—22no—
57C24×C17C22⋊C411yescharacteristic
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17D812yes—
66C22×C4×C17SD1612yes—
67C22×C4×C17C22×C411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×Dic17—22no—
71C22×Dic17—22no—
72C2×Dic34—41no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34—41no—
76C2×Dic34—41no—
77C2×Dic34—41no—
78M16×C17—44no—
79M16×C17—42no—
80M16×C17—42no—
81C2×C8×C17—24no—
82C2×C8×C17—44no—
83C4⋊C4×C17—22no—
84C4⋊C4×C17—22no—
85C22⋊C4×C17—22no—
86C22⋊C4×C17—22no—
87C42×C17—21no—
88C42×C17—21no—
89C42×C17C2×D412yes—
90C42×C17#4112yes—
91C22⋊Dic17—44no—
92C4⋊Dic17—24no—
93C4⋊Dic17—42no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—44no—
97C2×#3622—42no—
98#9195—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—41no—
102C23×C17—41no—
103C23×C17#10212yes—
104C23×C17C2×C22⋊C411yescharacteristic
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—22no—
108C2×C4×C17—22no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17#10212yes—
118C2×C4×C17C4×D412yes—
119C2×C4×C17#12011yescharacteristic
120C2×C4×C17#12112yes—
121C2×C4×C17#12311yescharacteristic
122C2×C4×C17C2×D811yescharacteristic
123C2×C4×C17C2×SD1611yescharacteristic
124C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C17#13711yescharacteristic
126C2×Dic17—42no—
127C2×Dic17—42no—
128C2×Dic17—42no—
129C2×Dic17—42no—
130C2×Dic17—42no—
131C2×Dic17—42no—
132Dic34—81no—
133Dic34—81no—
134Dic34—81no—
135Dic34—81no—
136C8×C17—44no—
137#3622—82no—
138#2905D1711yescharacteristic
139#2621—171no—
140#1546—172no—
141#1458—171no—
142#1286—172no—
143C22×C17—21no—
144C22×C17—21no—
145C22×C17—22no—
146C22×C17—42no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17—81no—
150C22×C17#38611yescharacteristic
151C22×C17C2×#10211yescharacteristic
152C22×C17#41711yescharacteristic
153C4×C17—22no—
154C4×C17—22no—
155C4×C17—22no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C17#44711yescharacteristic
159C4×C17#44811yescharacteristic
160C4×C17#48011yescharacteristic
161C4×C17#48111yescharacteristic
162Dic17—82no—
163Dic17—82no—
164C22×M16—21no—
165C2×C4⋊Q8—171no—
166C2×C22⋊Q8—341no—
167C2×#117C2×D1711yescharacteristic
168#431—172no—
169#424—24no—
170#423—21no—
171#423C2×D1712yes—
172#398—172no—
173#398—341no—
174#397—172no—
175#397—341no—
176#391—341no—
177#382—171no—
178#332—344no—
179#324—341no—
180#323—341no—
181C2×C17—21no—
182C2×C17—21no—
183C2×C17—42no—
184C2×C17#187411yescharacteristic
185C2×C17#190911yescharacteristic
186C2×C17#191511yescharacteristic
187C22×Q8—341no—
188C23×C4C22⋊D1711yescharacteristic
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—42no—
192C2×M16—42no—
193C22×C8—22no—
194C4⋊Q8—342no—
195C4⋊Q8—342no—
196C22⋊Q8—682no—
197C22⋊Q8—682no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—172no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—342no—
204C2×C4⋊C4C4×D1711yescharacteristic
205C2×C4⋊C4D6811yescharacteristic
206C2×C22⋊C4—342no—
207C2×C22⋊C4C4×D1711yescharacteristic
208C2×C22⋊C4D6811yescharacteristic
209C2×C42C22⋊D1711yescharacteristic
210C2×C42C22×D1711yescharacteristic
211C4⋊C8—24no—
212C4⋊C8—22no—
213C4⋊C8—342no—
214C4⋊C8C22⋊D1714yes—
215C22⋊C8—342no—
216C4×C8—342no—
217#95—172no—
218#95—341no—
219#95—342no—
220#95—342no—
221C17#919511yescharacteristic, complemented, Sylow
222C24#6322711yescharacteristic
223C2×Q8—681no—
224C2×Q8—681no—
225C2×Q8—681no—
226C2×Q8—681no—
227C2×Q8—681no—
228C2×Q8—681no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—342no—
234C22×C4—342no—
235C22×C4#6322711yescharacteristic
236C22×C4#6322711yescharacteristic
237C22×C4#6322711yescharacteristic
238C22×C4#6322812yes—
239C22×C4#6323012yes—
240C22×C4C2×C4×D1711yescharacteristic
241C22×C4C2×D6811yescharacteristic
242C22×C4C2×C22⋊D1711yescharacteristic
243M16—44no—
244M16—42no—
245M16—42no—
246C2×C8—24no—
247C2×C8—44no—
248C2×C8—682no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—344no—
252C4⋊C4—684no—
253C4⋊C4—682no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—684no—
259C42—21no—
260C42—21no—
261C42#6325212yes—
262C42C2×C22⋊D1712yes—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23#1058748012yes—
268C23C2×#6322711yescharacteristic
269Q8—1361no—
270Q8—1361no—
271Q8—1361no—
272Q8—1361no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—682no—
286C2×C4—682no—
287C2×C4—682no—
288C2×C4—682no—
289C2×C4—682no—
290C2×C4—682no—
291C2×C4#1058748012yes—
292C2×C4C4×C22⋊D1712yes—
293C2×C4#1058761511yescharacteristic
294C2×C4#1058761612yes—
295C2×C4C2×#6322811yescharacteristic
296C2×C4#1058761811yescharacteristic
297C2×C4C2×#6323011yescharacteristic
298C2×C4#1058762811yescharacteristic
299C2×C4#1058763911yescharacteristic
300C8—44no—
301C8—1362no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—81no—
309C22#1176268811yescharacteristic
310C22C2×#1058748011yescharacteristic
311C22#1176280811yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—1362no—
318C4—1362no—
319C4#1176294311yescharacteristic
320C4#1176294811yescharacteristic
321C4#1176312211yescharacteristic
322C4#1176312711yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1452910111yescharacteristic
327C2#1452930611yescharacteristic
328C2#1452933611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2905C2
socleC22×C17#386
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2905D17
hypocenterC17#9195
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #14527457C2semidirect
4. #14526644C2semidirect
221. C17#9195semidirect

Maximal subgroups

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

subgroupindex
#145345502
#145274572
#145270982
#145266442
C17×#29052
#919517