Finite Group Databasebeta

← #17959483

Subgroups — #17959483

Order 4352.

388 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 66 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#14544685C211yesmaximal, characteristic
2#14544037C211yesmaximal, characteristic
3#14543785C212yesmaximal, complemented
4#14543783C212yesmaximal, complemented
5#14532054C211yesmaximal, characteristic
6#11763829—21no—
7#11763781—21no—
8#11763689—21no—
9#11763689C2212yes—
10#11763655C2212yes—
11#11763653—21no—
12C2×#10587558C2211yescharacteristic
13#11762747C2211yescharacteristic
14#11762744C411yescharacteristic
15#11762742—21no—
16#11762731—21no—
17#11762728C2211yescharacteristic
18#11762720C411yescharacteristic
19C4×#63225—21no—
20C4×C4⋊Dic17C411yescharacteristic
21C4×#63227—21no—
22C2×C4×Q8×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×C4×D17D411yescharacteristic
25C2×#63247—22no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×#63227—21no—
33C2×#63227—21no—
34C2×#63227C2×C411yescharacteristic
35C2×#63227D411yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225D411yescharacteristic
40C2×#63225C2311yescharacteristic
41C2×C4×Dic17—21no—
42C2×C4×Dic17D411yescharacteristic
43#10587558—41no—
44#10587558—41no—
45C22⋊#3624—22no—
46#10587544—41no—
47#10587543—41no—
48#10587543—41no—
49#10587542—41no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502C2×C411yescharacteristic
55#10587502C2×C411yescharacteristic
56C23×D17C22⋊C411yescharacteristic
57C2×Q8×C17—42no—
58C2×Q8×C17—41no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—22no—
72C2×C4×D17—41no—
73#63247—42no—
74#63247—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—42no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—41no—
82C42×C17—41no—
83#63227—41no—
84#63227—41no—
85#63227—42no—
86#63227—42no—
87C4⋊Dic17—42no—
88#63225—41no—
89#63225—41no—
90#63225—42no—
91#63225—42no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—42no—
95#11816—171nomaximal, Sylow
96C23×C17C2×C22⋊C411yescharacteristic
97C22×D17—21no—
98C22×D17—21no—
99C22×D17—21no—
100C22×D17—41no—
101C22×D17—41no—
102Q8×C17—42no—
103Q8×C17—42no—
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#9911yescharacteristic
117C2×C4×C17#9911yescharacteristic
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—22no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17#13712yes—
131C4×D17—42no—
132C4×D17—42no—
133#3624—82no—
134#3624—82no—
135#2396—171no—
136#1822—171no—
137#1464—171no—
138#1354—172no—
139#1353—172no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17C2×#9911yescharacteristic
143C22×C17#41911yescharacteristic
144C22×C17#42111yescharacteristic
145C2×D17—42no—
146C2×D17—41no—
147C2×D17—41no—
148C2×D17—41no—
149C2×D17—81no—
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—42no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—81no—
156Dic17—22no—
157Dic17—42no—
158Dic17—41no—
159Dic17—41no—
160Dic17—81no—
161C2×C4×Q8#59511yescharacteristic
162C2×#117—171no—
163#432—341no—
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#324—172no—
177#323—341no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17#151111yescharacteristic
181C2×C17#212011yescharacteristic
182C2×C17#213211yescharacteristic
183D17—81no—
184C22×Q8C2×#59511yescharacteristic
185C23×C4—171no—
186C2×M16—342no—
187C4×Q8—41no—
188C4×Q8—41no—
189#117—681no—
190#117—681no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—171no—
193C2×C4⋊C4—171no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4—341no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4C2×#59511yescharacteristic
198C2×C22⋊C4—171no—
199C2×C22⋊C4—171no—
200C2×C22⋊C4—341no—
201C2×C22⋊C4—341no—
202C2×C42—21no—
203C2×C42—171no—
204C2×C42—341no—
205C2×C42C2×#59511yescharacteristic
206C4⋊C8—681no—
207C22⋊C8—342no—
208C22⋊C8—681no—
209C22⋊C8—681no—
210#97—681no—
211#95—171no—
212#95—171no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217C17#1181611yescharacteristic, complemented, Sylow
218C24—171no—
219C2×Q8—42no—
220C2×Q8—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—342no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—681no—
232C22×C4C22⋊#59511yescharacteristic
233C22×C4C22⋊#59511yescharacteristic
234C22×C4C22×#59511yescharacteristic
235M16—682no—
236M16—682no—
237C2×C8—682no—
238C2×C8—682no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—681no—
242C4⋊C4—681no—
243C4⋊C4—682no—
244C4⋊C4—682no—
245C4⋊C4—682no—
246C22⋊C4—681no—
247C22⋊C4—681no—
248C22⋊C4—682no—
249C22⋊C4—682no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—41no—
254C42—341no—
255C42—341no—
256C42—682no—
257C23—341no—
258C23—341no—
259C23—341no—
260C23—681no—
261C23—681no—
262C23C2×C22⋊#59511yescharacteristic
263Q8—42no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—172no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—342no—
281C2×C4—341no—
282C2×C4—341no—
283C2×C4—682no—
284C2×C4—682no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4#1058755111yescharacteristic
293C2×C4#1058755111yescharacteristic
294C8—1362no—
295C8—1362no—
296C22—21no—
297C22—21no—
298C22—682no—
299C22—681no—
300C22—681no—
301C22—681no—
302C22—1361no—
303C22C2×#1058755111yescharacteristic
304C22#1176380211yescharacteristic
305C22#1176380811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—342no—
313C4—682no—
314C4—681no—
315C4—681no—
316C4—1361no—
317C2—21no—
318C2—21no—
319C2—1361no—
320C2#1454419411yescharacteristic
321C2#1454503511yescharacteristic
322C2#1454507511yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4×Q8#595
hypocenterC17#11816
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #14543785C2semidirect
4. #14543783C2semidirect
217. C17#11816semidirect

Maximal subgroups

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

subgroupindex
#145446852
#145440372
#145437852
#145437832
#145320542
#1181617