Finite Group Databasebeta

← #17949753

Subgroups — #17949753

Order 4352.

478 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 122 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#14544700C211yesmaximal, characteristic
2#14544499C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5C4×#10587574C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4×#3624—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587574C411yescharacteristic
13C2×C4×Dic34—21no—
14#11762713—21no—
15#11762708C2211yescharacteristic
16#11762706—21no—
17#11762705C2211yescharacteristic
18#11762678C411yescharacteristic
19C4×#63225—21no—
20C4×C4⋊Dic17C411yescharacteristic
21C42×Dic17C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×Dic34—21no—
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—21no—
34C2×#63225—21no—
35C2×#63225—21no—
36C2×#63225—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587574—22no—
45#10587574C814yescomplemented
46C4×Dic34—44no—
47#10587544—42no—
48C4×#3624—24no—
49C17×#95—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17C22⋊C411yescharacteristic
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C2×Dic34—24no—
65C2×Dic34—42no—
66C2×Dic34—42no—
67C2×#3624—24no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17C2×C812yes—
76C42×C17—22no—
77C42×C17—42no—
78C4⋊Dic17—21no—
79C4⋊Dic17—42no—
80C4⋊Dic17—41no—
81C4⋊Dic17C2×C812yes—
82#63225—24no—
83#63225—42no—
84#63225—42no—
85#63225—42no—
86C4×Dic17—22no—
87C4×Dic17—22no—
88C4×Dic17—41no—
89C4×Dic17—41no—
90C4×Dic17—42no—
91C4×Dic17C2×C812yes—
92C4×Dic17M1612yes—
93C4×Dic17SD1612yes—
94C4×Dic17Q1612yes—
95#7591—171nomaximal, Sylow
96C23×C17C2×C22⋊C411yescharacteristic
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17#10112yes—
110C2×C4×C17#10312yes—
111C2×C4×C17C22×C811yescharacteristic
112C2×C4×C17C2×M1611yescharacteristic
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—22no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17C22⋊C812yes—
126C2×Dic17C22⋊C812yes—
127C2×Dic17#10312yes—
128C2×Dic17#10412yes—
129C2×Dic17C2×SD1611yescharacteristic
130C2×Dic17C2×Q1611yescharacteristic
131C2×Dic17AGL(1,ℤ/8)12yes—
132Dic34—48no—
133#3624—44no—
134#3624—82no—
135C4×C4⋊Q8—171no—
136#1831—171no—
137#1744—171no—
138#1271—172no—
139#1271—172no—
140C22×C17C2×C22⋊C811yescharacteristic
141C22×C17#41011yescharacteristic
142C22×C17C2×#10111yescharacteristic
143C22×C17C2×#10311yescharacteristic
144C22×C17#41811yescharacteristic
145C22×C17C2×#10411yescharacteristic
146C22×C17#42111yescharacteristic
147C4×C17—22no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—22no—
151C4×C17—42no—
152C4×C17—81no—
153Dic17—22no—
154Dic17—22no—
155Dic17—21no—
156Dic17—21no—
157Dic17—42no—
158Dic17—81no—
159Dic17Q8⋊C814yes—
160C2×C4⋊Q8—171no—
161C2×C4×Q8—341no—
162C2×C4⋊C8—341no—
163C2×C4×C8—341no—
164#391—341no—
165#389—171no—
166#389—171no—
167#389—341no—
168#384—171no—
169C4×C4⋊C4—171no—
170C4×C4⋊C4—341no—
171C4×C4⋊C4#59511yescharacteristic
172C43—171no—
173#336—172no—
174#336—172no—
175#336—341no—
176#336—341no—
177C2×C17#146111yescharacteristic
178C2×C17C2×Q8⋊C811yescharacteristic
179C2×C17#147811yescharacteristic
180C2×C17#150511yescharacteristic
181C2×C17#151811yescharacteristic
182C2×C17#153111yescharacteristic
183C2×C17#154911yescharacteristic
184C22×Q8—341no—
185C22×C8—342no—
186C22×C8—342no—
187C4⋊Q8—174no—
188C4⋊Q8—342no—
189C4×Q8—684no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4—341no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4C2×#59511yescharacteristic
198C2×C4⋊C4C2×#59511yescharacteristic
199C2×C42—21no—
200C2×C42—171no—
201C2×C42—171no—
202C2×C42—171no—
203C2×C42—171no—
204C2×C42—171no—
205C2×C42—171no—
206C2×C42—341no—
207C2×C42C2×#59511yescharacteristic
208C4⋊C8—682no—
209C4×C8—344no—
210#95—21no—
211#95—341no—
212#95—341no—
213#95—341no—
214C17#759111yescharacteristic, complemented, Sylow
215C2×Q8—344no—
216C2×Q8—682no—
217C2×Q8—682no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—171no—
221C22×C4—171no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22⋊#59511yescharacteristic
228C22×C4C22×#59511yescharacteristic
229C2×C8—344no—
230C2×C8—682no—
231C2×C8—682no—
232C2×C8—682no—
233C2×C8—682no—
234C2×C8—682no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—172no—
238C4⋊C4—344no—
239C4⋊C4—341no—
240C4⋊C4—681no—
241C4⋊C4—682no—
242C4⋊C4—682no—
243C4⋊C4—682no—
244C4⋊C4—682no—
245C4⋊C4#6324212yes—
246C42—22no—
247C42—42no—
248C42—172no—
249C42—172no—
250C42—172no—
251C42—172no—
252C42—342no—
253C42—342no—
254C42—681no—
255C42—681no—
256C42—682no—
257C23C2×C22⋊#59511yescharacteristic
258Q8—688no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—172no—
272C2×C4—172no—
273C2×C4—172no—
274C2×C4—172no—
275C2×C4—171no—
276C2×C4—171no—
277C2×C4—172no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—341no—
282C2×C4—341no—
283C2×C4—341no—
284C2×C4—342no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4#1058754512yes—
291C2×C4#1058754912yes—
292C2×C4C2×#6324211yescharacteristic
293C2×C4D17⋊M1611yescharacteristic
294C8—684no—
295C8—1362no—
296C22#1176377711yescharacteristic
297C22#1176378811yescharacteristic
298C22C2×#1058754511yescharacteristic
299C22C2×#1058754911yescharacteristic
300C22#1176380111yescharacteristic
301C22D17⋊#10411yescharacteristic
302C22#1176380611yescharacteristic
303C4—22no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—81no—
309C4—174no—
310C4—342no—
311C4—341no—
312C4—341no—
313C4—342no—
314C4—682no—
315C4—1361no—
316C2#1454402611yescharacteristic
317C2#1454407311yescharacteristic
318C2#1454408411yescharacteristic
319C2#1454417411yescharacteristic
320C2#1454421711yescharacteristic
321C2#1454425611yescharacteristic
322C2#1454429911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7591
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
45. #10587574C8semidirect
214. C17#7591semidirect

Maximal subgroups

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

subgroupindex
#145447002
#145444992
#145436032
#145436022
C4×#105875742
#759117