Finite Group Databasebeta

← #16943890

Subgroups — #16943890

Order 4352.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#14527114C211yesmaximal, characteristic
2C2×#11762535C211yesmaximal, characteristic
3#14526728C212yesmaximal, complemented
4#14526718C212yesmaximal, complemented
5C17×#2503C211yesmaximal, characteristic
6#11762773—21no—
7C2×C22⋊#3622—21no—
8#11762535—21no—
9#11762535—21no—
10#11762535C2212yes—
11#11762535C2212yes—
12C2×C17×C22⋊Q8C411yescharacteristic
13C22×C4⋊C4×C17C2211yescharacteristic
14C17×#400—21no—
15C17×#400—21no—
16C17×#391C411yescharacteristic
17C17×#391C2211yescharacteristic
18C17×#382C411yescharacteristic
19C17×#382C2211yescharacteristic
20C17×#381—21no—
21C17×#381—21no—
22C4×C22⋊C4×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C17×C22⋊Q8—41no—
28C17×C22⋊Q8—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17C2311yescharacteristic
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C42×C17C2×C411yescharacteristic
40C2×C42×C17C2×C411yescharacteristic
41C2×#63223—41no—
42C22×#3622—41no—
43C17×#95—21no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C22⋊#3622—22no—
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—41no—
72C22×C4×C17—42no—
73C22×C4×C17—42no—
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22×C411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—42no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C42×C17—22no—
90C42×C17—41no—
91#63223—82no—
92C2×#3622—42no—
93C2×#3622—42no—
94C2×#3622—82no—
95#11551—171nomaximal, Sylow
96C23×C17—22no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—41no—
100C23×C17#9911yescharacteristic
101C23×C17#9911yescharacteristic
102C23×C17C2×C22⋊C411yescharacteristic
103Q8×C17—82no—
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—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—42no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—42no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—81no—
133C2×C4×C17—81no—
134C2×C4×C17#13112yes—
135#3622—82no—
136#3622—82no—
137#2503D1711yescharacteristic
138#1463—171no—
139C2×#324—171no—
140#1324—172no—
141#1319—172no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—21no—
145C22×C17—21no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—42no—
150C22×C17—42no—
151C22×C17#35412yes—
152C22×C17#40811yescharacteristic
153C22×C17C2×#9911yescharacteristic
154C22×C17#41311yescharacteristic
155C4×C17—22no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C17—41no—
159C4×C17—41no—
160C4×C17—41no—
161C4×C17—81no—
162C4×C17—81no—
163C4×C17—81no—
164C4×C17—81no—
165C2×C22⋊Q8Dic1711yescharacteristic
166C22×C4⋊C4C2×D1711yescharacteristic
167#407—341no—
168C2×C22⋊C8—341no—
169#400—21no—
170#400—21no—
171#391Dic1711yescharacteristic
172#391C2×D1711yescharacteristic
173#382Dic1711yescharacteristic
174#382C2×D1711yescharacteristic
175#381—21no—
176#381—21no—
177C4×C22⋊C4Dic1711yescharacteristic
178#324—172no—
179#324—172no—
180#324—341no—
181#324—341no—
182C2×C17—21no—
183C2×C17—21no—
184C2×C17—22no—
185C2×C17—41no—
186C2×C17#146811yescharacteristic
187C2×C17C2×#35411yescharacteristic
188C2×C17#213311yescharacteristic
189C22×Q8C2×Dic1711yescharacteristic
190C23×C4C2×Dic1711yescharacteristic
191C23×C4C22⋊D1711yescharacteristic
192C23×C4C22⋊D1711yescharacteristic
193C2×M16—681no—
194C22×C8—681no—
195C22⋊Q8—41no—
196C22⋊Q8—41no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4C2×Dic1711yescharacteristic
201C2×C4⋊C4C2×Dic1711yescharacteristic
202C2×C4⋊C4C22⋊D1711yescharacteristic
203C2×C4⋊C4C22⋊D1711yescharacteristic
204C2×C4⋊C4C22×D1711yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42C2×Dic1711yescharacteristic
208C2×C42C2×Dic1711yescharacteristic
209C22⋊C8—342no—
210C22⋊C8—342no—
211C22⋊C8—681no—
212C22⋊C8—681no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C17#1155111yescharacteristic, complemented, Sylow
223C24C22⋊Dic1711yescharacteristic
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊Dic1711yescharacteristic
242C22×C4C22⋊Dic1711yescharacteristic
243C22×C4C22⋊Dic1711yescharacteristic
244C22×C4C22×Dic1711yescharacteristic
245C22×C4C2×C22⋊D1711yescharacteristic
246C22×C4C2×C22⋊D1711yescharacteristic
247M16—1362no—
248C2×C8—682no—
249C2×C8—682no—
250C2×C8—1362no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—22no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—22no—
265C23—41no—
266C23#1058750511yescharacteristic
267C23#1058750511yescharacteristic
268C23C2×C22⋊Dic1711yescharacteristic
269Q8—82no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#1058763412yes—
301C8—1362no—
302C8—1362no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22#1176260412yes—
313C22#1176277611yescharacteristic
314C22C2×#1058750511yescharacteristic
315C22#1176279311yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4—81no—
326C2—21no—
327C2—21no—
328C2—22no—
329C2—41no—
330C2#1452713211yescharacteristic
331C2C2×#1176260411yescharacteristic
332C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2503C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2503D17
hypocenterC17#11551
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
3. #14526728C2semidirect
4. #14526718C2semidirect
222. C17#11551semidirect

Maximal subgroups

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

subgroupindex
#145271142
C2×#117625352
#145267282
#145267182
C17×#25032
#1155117