Finite Group Databasebeta

← #16945485

Subgroups — #16945485

Order 4352.

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

normal subgroups only

This group has 372 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#14533995C211yesmaximal, characteristic
2#14528779C211yesmaximal, characteristic
3#14527106C211yesmaximal, characteristic
4#14526812C211yesmaximal, characteristic
5#14526811C211yesmaximal, characteristic
6#14526810C211yesmaximal, characteristic
7C17×#1353C211yesmaximal, characteristic
8C2×#10587574C411yescharacteristic
9C2×#10587573C2211yescharacteristic
10#11762859—21no—
11#11762832—21no—
12C2×#10587495—21no—
13#11762749C411yescharacteristic
14#11762748C2211yescharacteristic
15#11762747C411yescharacteristic
16#11762713—21no—
17#11762713—21no—
18#11762713—21no—
19#11762673—21no—
20#11762660C411yescharacteristic
21#11762578C2211yescharacteristic
22#11762535C2211yescharacteristic
23#11762534—21no—
24C17×#400C2211yescharacteristic
25C17×#343C2211yescharacteristic
26C17×#324C2211yescharacteristic
27C22×Dic34—21no—
28C22×Dic34D411yescharacteristic
29C2×M16×C17—21no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—21no—
34C2×#63225—21no—
35C2×#63225C2×C411yescharacteristic
36C2×#63225D411yescharacteristic
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×#63223—21no—
42#10587574—41no—
43#10587574—41no—
44#10587573—41no—
45#10587573—41no—
46C17×C22⋊C8—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502C2×C411yescharacteristic
57C22⋊#3622—21no—
58#10587495—42no—
59#10587485—41no—
60#10587485—41no—
61#10587485—41no—
62C8×Dic17—41no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17C22×C411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17C22⋊C411yescharacteristic
73C22×Dic17C22⋊C411yescharacteristic
74C2×Dic34—41no—
75C2×Dic34—41no—
76C2×Dic34—44no—
77C2×Dic34—41no—
78C2×Dic34—41no—
79C2×Dic34SD1612yes—
80C2×Dic34Q1612yes—
81M16×C17—41no—
82M16×C17—41no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—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—42no—
99#63223—41no—
100#63223—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103#11907—171nomaximal, Sylow
104C23×C17C2×C22⋊C411yescharacteristic
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—42no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17C2×SD1611yescharacteristic
117C2×C4×C17C2×Q1611yescharacteristic
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—22no—
123C2×Dic17—21no—
124C2×Dic17—41no—
125C2×Dic17—42no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17#9911yescharacteristic
131C2×Dic17#9911yescharacteristic
132C2×Dic17#10312yes—
133C2×Dic17#10312yes—
134Dic34—42no—
135Dic34—42no—
136Dic34—82no—
137Dic34—82no—
138C8×C17—81no—
139C8×C17—81no—
140#3622—81no—
141#3622—81no—
142#2568—171no—
143#1801—171no—
144#1461—171no—
145#1353—171no—
146#1353—171no—
147#1353—171no—
148#1353D1711yescharacteristic
149C22×C17—21no—
150C22×C17—21no—
151C22×C17C2×#9911yescharacteristic
152C22×C17C2×#10311yescharacteristic
153C22×C17#42111yescharacteristic
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C17—81no—
159C4×C17—81no—
160Dic17—21no—
161Dic17—22no—
162Dic17—22no—
163Dic17—41no—
164Dic17—81no—
165Dic17—81no—
166Dic17#35512yes—
167C2×C4⋊Q8—171no—
168C2×C4×Q8—171no—
169#431—341no—
170#423—341no—
171C2×#101—341no—
172#400—171no—
173#400—171no—
174#400—171no—
175#400C2×D1711yescharacteristic
176#391—341no—
177#391—341no—
178#391—341no—
179#382—341no—
180C4×C4⋊C4—171no—
181#343—171no—
182#343C2×D1711yescharacteristic
183#324—171no—
184#324—341no—
185#324C2×D1711yescharacteristic
186C2×C17—21no—
187C2×C17—21no—
188C2×C17#152011yescharacteristic
189C2×C17#212311yescharacteristic
190C2×C17C2×#35511yescharacteristic
191C22×Q8—171no—
192C22×Q8—341no—
193C2×M16—21no—
194C2×M16—341no—
195C4⋊Q8—681no—
196C4⋊Q8—681no—
197C4×Q8—681no—
198C4×Q8—681no—
199C2×C4⋊C4—171no—
200C2×C4⋊C4—171no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4C4×D1711yescharacteristic
205C2×C4⋊C4C22×D1711yescharacteristic
206C2×C42—171no—
207C2×C42—171no—
208C2×C42—171no—
209C2×C42—341no—
210C4⋊C8—681no—
211C4⋊C8—681no—
212C4⋊C8—681no—
213#101—682no—
214C22⋊C8—21no—
215C22⋊C8—341no—
216C4×C8—681no—
217#95—21no—
218#95—21no—
219#95—171no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224#95—341no—
225#95—341no—
226#95C4×D1711yescharacteristic
227C17#1190711yescharacteristic, complemented, Sylow
228C2×Q8—172no—
229C2×Q8—172no—
230C2×Q8—681no—
231C2×Q8—681no—
232C2×Q8—681no—
233C2×Q8—681no—
234C2×Q8—684no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4—171no—
240C22×C4—171no—
241C22×C4—341no—
242C22×C4—341no—
243C22×C4C2×C4×D1711yescharacteristic
244C22×C4D4×D1711yescharacteristic
245C22×C4D4×D1711yescharacteristic
246M16—41no—
247M16—41no—
248M16—681no—
249M16—681no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—681no—
253C2×C8—681no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—682no—
260C4⋊C4—682no—
261C42—341no—
262C42—341no—
263C42—341no—
264C42—341no—
265C42—341no—
266C42—341no—
267C42—682no—
268C23C22⋊C4×D1711yescharacteristic
269Q8—682no—
270Q8—682no—
271Q8—1362no—
272Q8—1362no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—171no—
285C2×C4—171no—
286C2×C4—172no—
287C2×C4—172no—
288C2×C4—342no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—682no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4SD16×D1711yescharacteristic
301C2×C4Q16×D1711yescharacteristic
302C8—81no—
303C8—81no—
304C8—1361no—
305C8—1361no—
306C22—21no—
307C22—21no—
308C22#99×D1711yescharacteristic
309C22#103×D1711yescharacteristic
310C22#1176282411yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—172no—
318C4—342no—
319C4—342no—
320C4—341no—
321C4—681no—
322C4—1361no—
323C4—1361no—
324C2—21no—
325C2—21no—
326C2#1452735411yescharacteristic
327C2#1453043611yescharacteristic
328C2D17×#35511yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1353C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1353D17
hypocenterC17#11907
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
227. C17#11907semidirect

Maximal subgroups

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

subgroupindex
#145339952
#145287792
#145271062
#145268122
#145268112
#145268102
C17×#13532
#1190717