Finite Group Databasebeta

← #16943979

Subgroups — #16943979

Order 4352.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#14533972C211yesmaximal, characteristic
2#14527126C211yesmaximal, characteristic
3#14527106C211yesmaximal, characteristic
4#14526730C211yesmaximal, characteristic
5#14526727C211yesmaximal, characteristic
6#14526727C211yesmaximal, characteristic
7C17×#1325C211yesmaximal, characteristic
8C2×#10587576C411yescharacteristic
9C2×#10587573C2211yescharacteristic
10#11762863—21no—
11#11762859—21no—
12#11762740—21no—
13#11762740—21no—
14#11762715C411yescharacteristic
15#11762714C411yescharacteristic
16#11762695—21no—
17#11762695—21no—
18#11762674C2211yescharacteristic
19C4×#63225C411yescharacteristic
20#11762535C2211yescharacteristic
21#11762535C2211yescharacteristic
22#11762534—21no—
23#11762534—21no—
24C17×#384C2211yescharacteristic
25C17×#324C2211yescharacteristic
26C17×#324C2211yescharacteristic
27C22×Dic34C2×C411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×#63225—21no—
36C2×#63225—21no—
37C2×#63225D411yescharacteristic
38C2×#63225D411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17C2×C411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43#10587576—41no—
44#10587576—41no—
45#10587573—41no—
46#10587573—41no—
47C17×C22⋊C8—21no—
48C17×C22⋊C8—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C22⋊#3622—21no—
57C22⋊#3622—21no—
58#10587486—41no—
59#10587485—41no—
60#10587485—41no—
61C8×Dic17—41no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17C22×C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17C22⋊C411yescharacteristic
73C2×Dic34—21no—
74C2×Dic34—21no—
75C2×Dic34—22no—
76C2×Dic34—41no—
77C2×C8×C17—41no—
78C2×C8×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C42×C17—21no—
84C42×C17—21no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88#63225—41no—
89#63225—41no—
90#63225—42no—
91#63225—42no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—21no—
95C4×Dic17—21no—
96C4×Dic17—21no—
97C4×Dic17—21no—
98C4×Dic17—21no—
99C4×Dic17—21no—
100C2×#3622—41no—
101C2×#3622—41no—
102#11571—171nomaximal, Sylow
103C23×C17C2×C22⋊C411yescharacteristic
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—22no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17#13111yescharacteristic
117C2×C4×C17#13111yescharacteristic
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—42no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17#9911yescharacteristic
132C2×Dic17#9911yescharacteristic
133C2×Dic17#10112yes—
134Dic34—42no—
135Dic34—42no—
136C8×C17—81no—
137C8×C17—81no—
138#3622—81no—
139#3622—81no—
140#2565—171no—
141#1467—171no—
142#1461—171no—
143#1325—171no—
144#1325D1711yescharacteristic
145#1324—171no—
146#1324—171no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17#40811yescharacteristic
150C22×C17C2×#9911yescharacteristic
151C22×C17C2×#10111yescharacteristic
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—42no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—81no—
158Dic17—21no—
159Dic17—21no—
160Dic17—22no—
161Dic17—41no—
162Dic17—41no—
163Dic17—81no—
164Dic17—81no—
165C2×#125—171no—
166C2×C4×Q8—171no—
167#432—341no—
168#431—341no—
169#398—341no—
170#398—341no—
171#391—171no—
172#391—171no—
173#387—341no—
174#387—341no—
175#384C2×D1711yescharacteristic
176#382—171no—
177C4×C4⋊C4—171no—
178#324—171no—
179#324—171no—
180#324—341no—
181#324—341no—
182#324C2×D1711yescharacteristic
183#324C2×D1711yescharacteristic
184C2×C17—21no—
185C2×C17—21no—
186C2×C17#147211yescharacteristic
187C2×C17#212611yescharacteristic
188C2×C17#213311yescharacteristic
189C22×Q8—171no—
190#125—681no—
191#125—681no—
192C4×Q8—681no—
193C4×Q8—681no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—171no—
197C2×C4⋊C4—171no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4C4×D1711yescharacteristic
203C2×C4⋊C4C22×D1711yescharacteristic
204C2×C42—171no—
205C2×C42—171no—
206C2×C42—171no—
207C2×C42—171no—
208C2×C42C4×D1711yescharacteristic
209C4⋊C8—681no—
210C4⋊C8—681no—
211C22⋊C8—21no—
212C22⋊C8—21no—
213C22⋊C8—341no—
214C22⋊C8—341no—
215#97—681no—
216C4×C8—681no—
217#95—341no—
218#95—341no—
219#95—341no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224C17#1157111yescharacteristic, complemented, Sylow
225C2×Q8—342no—
226C2×Q8—341no—
227C2×Q8—341no—
228C2×Q8—681no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—171no—
232C22×C4—171no—
233C22×C4—171no—
234C22×C4—171no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4C2×C4×D1711yescharacteristic
238C22×C4D4×D1711yescharacteristic
239C22×C4D4×D1711yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—681no—
243C2×C8—681no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—681no—
249C4⋊C4—681no—
250C4⋊C4—681no—
251C4⋊C4—682no—
252C4⋊C4—681no—
253C4⋊C4—681no—
254C4⋊C4—682no—
255C42—21no—
256C42—21no—
257C42—341no—
258C42—341no—
259C42—341no—
260C42—341no—
261C42—341no—
262C42—341no—
263C42—341no—
264C42—341no—
265C23C22⋊C4×D1711yescharacteristic
266Q8—682no—
267Q8—682no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—171no—
281C2×C4—171no—
282C2×C4—172no—
283C2×C4—341no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—682no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4#1058758711yescharacteristic
297C2×C4#1058759311yescharacteristic
298C8—81no—
299C8—81no—
300C8—1361no—
301C8—1361no—
302C22—21no—
303C22—21no—
304C22#1176277411yescharacteristic
305C22#99×D1711yescharacteristic
306C22#101×D1711yescharacteristic
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—341no—
314C4—341no—
315C4—342no—
316C4—681no—
317C4—681no—
318C4—1361no—
319C4—1361no—
320C2—21no—
321C2—21no—
322C2#1452714611yescharacteristic
323C2#1453044611yescharacteristic
324C2#1453047211yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1325C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1325D17
hypocenterC17#11571
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
224. C17#11571semidirect

Maximal subgroups

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

subgroupindex
#145339722
#145271262
#145271062
#145267302
#145267272
C17×#13252
#1157117