Finite Group Databasebeta

← #16945068

Subgroups — #16945068

Order 4352.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#14532052C211yesmaximal, characteristic
2#14528867C211yesmaximal, characteristic
3#14526815C212yesmaximal, complemented
4#14526812C212yesmaximal, complemented
5C17×#1464C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic
7#11762773—21no—
8#11762748C2211yescharacteristic
9#11762745C411yescharacteristic
10#11762742—21no—
11#11762732—21no—
12#11762729C2211yescharacteristic
13#11762721C411yescharacteristic
14C4×#63225—21no—
15C4×C4⋊Dic17C411yescharacteristic
16C4×C22⋊Dic17—21no—
17#11762578—21no—
18#11762578C2212yes—
19C2×C17×#117C2211yescharacteristic
20C17×#432—21no—
21C17×#324C2212yes—
22C17×#323—21no—
23C23×C4×C17D411yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C17×#117—41no—
26C17×#117—41no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C4⋊C4×C17C2311yescharacteristic
29C2×C22⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17—21no—
42C2×#63223—22no—
43C4×Dic34—41no—
44C4×Dic34—41no—
45C17×C4⋊C8—41no—
46C17×C22⋊C8—22no—
47C17×#97—41no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—22no—
60C22×C4×C17—41no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C2×Dic34—41no—
72C2×Dic34—42no—
73C2×C8×C17—42no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C22⋊Dic17—42no—
83C22⋊Dic17—42no—
84C4⋊Dic17—42no—
85C4⋊Dic17—41no—
86#63225—42no—
87#63225—42no—
88#63225—42no—
89C4×Dic17—42no—
90C4×Dic17—41no—
91C4×Dic17—41no—
92#63223—42no—
93#63223—42no—
94C2×#3622—42no—
95#11816—171nomaximal, Sylow
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17C2×C22⋊C411yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
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—42no—
111C2×C4×C17—42no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17#9911yescharacteristic
117C2×C4×C17#9911yescharacteristic
118C2×C4×C17#13712yes—
119C2×Dic17—22no—
120C2×Dic17—22no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131Dic34—42no—
132Dic34—42no—
133C8×C17—82no—
134#3622—82no—
135#2396—171no—
136#1822—171no—
137#1464D1711yescharacteristic
138#1354—172no—
139#1353—172no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17—42no—
143C22×C17—41no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17—81no—
147C22×C17C2×#9911yescharacteristic
148C22×C17#41911yescharacteristic
149C22×C17#42111yescharacteristic
150C4×C17—22no—
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17—41no—
157Dic17—42no—
158Dic17—42no—
159Dic17—81no—
160Dic17—81no—
161C2×C4×Q8—171no—
162C2×#117C2×D1711yescharacteristic
163#432—21no—
164#407—341no—
165#400—171no—
166#399—171no—
167#398—341no—
168#396—341no—
169#395—171no—
170#393—171no—
171C4×C4⋊C4—171no—
172C4×C4⋊C4—341no—
173C4×C22⋊C4—341no—
174#343—172no—
175#343—341no—
176#324C2×D1712yes—
177#323—21no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17—81no—
181C2×C17#151111yescharacteristic
182C2×C17#212011yescharacteristic
183C2×C17#213211yescharacteristic
184C22×Q8—171no—
185C23×C4D6811yescharacteristic
186C2×M16—342no—
187C4×Q8—681no—
188C4×Q8—681no—
189#117—41no—
190#117—41no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4—341no—
196C2×C4⋊C4D6811yescharacteristic
197C2×C4⋊C4C22×D1711yescharacteristic
198C2×C22⋊C4—341no—
199C2×C22⋊C4—341no—
200C2×C22⋊C4C4×D1711yescharacteristic
201C2×C22⋊C4C22⋊D1711yescharacteristic
202C2×C42—341no—
203C2×C42—341no—
204C2×C42C4×D1711yescharacteristic
205C2×C42C22⋊D1711yescharacteristic
206C4⋊C8—41no—
207C22⋊C8—22no—
208C22⋊C8—681no—
209C22⋊C8—681no—
210#97—41no—
211#95—171no—
212#95—171no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217C17#1181611yescharacteristic, complemented, Sylow
218C24#6322711yescharacteristic
219C2×Q8—681no—
220C2×Q8—682no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4#6322711yescharacteristic
230C22×C4#6322711yescharacteristic
231C22×C4#6322711yescharacteristic
232C22×C4C2×C4×D1711yescharacteristic
233C22×C4C2×D6811yescharacteristic
234C22×C4C2×C22⋊D1711yescharacteristic
235M16—682no—
236M16—682no—
237C2×C8—42no—
238C2×C8—682no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—681no—
242C4⋊C4—682no—
243C4⋊C4—682no—
244C4⋊C4—682no—
245C4⋊C4—682no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—682no—
249C22⋊C4—682no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—682no—
255C42—681no—
256C42—681no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×#6322711yescharacteristic
263Q8—682no—
264Q8—682no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—342no—
280C2×C4—342no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4#1058747711yescharacteristic
292C2×C4#1058747711yescharacteristic
293C2×C4#1058759512yes—
294C8—82no—
295C8—1362no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#1058747711yescharacteristic
304C22#1176281911yescharacteristic
305C22#1176282511yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—682no—
314C4—682no—
315C4—1361no—
316C4—1361no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1452731811yescharacteristic
321C2#1453042311yescharacteristic
322C2#1453046711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1464C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1464D17
hypocenterC17#11816
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #14526815C2semidirect
4. #14526812C2semidirect
217. C17#11816semidirect

Maximal subgroups

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

subgroupindex
#145320522
#145288672
#145268152
#145268122
C17×#14642
#1181617