Finite Group Databasebeta

← #17949798

Subgroups — #17949798

Order 4352.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544712C211yesmaximal, characteristic
2#14544712C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5C4×#10587574C211yesmaximal, characteristic
6#11763675—21no—
7#11763675—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—
47C17×#95—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C22⋊C411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C22×Dic17C2×D411yescharacteristic
62C2×Dic34—24no—
63C2×Dic34—42no—
64C2×Dic34—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17C2×C812yes—
74C42×C17—22no—
75C42×C17—42no—
76C4⋊Dic17—21no—
77C4⋊Dic17—42no—
78C4⋊Dic17—41no—
79C4⋊Dic17C2×C812yes—
80#63225—24no—
81#63225—42no—
82#63225—42no—
83#63225—42no—
84C4×Dic17—22no—
85C4×Dic17—22no—
86C4×Dic17—41no—
87C4×Dic17—41no—
88C4×Dic17—41no—
89C4×Dic17—42no—
90C4×Dic17C2×C812yes—
91C4×Dic17M1612yes—
92#7604—171nomaximal, Sylow
93C23×C17C2×C22⋊C411yescharacteristic
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17#10112yes—
108C2×C4×C17C22×C811yescharacteristic
109C2×C4×C17C2×M1611yescharacteristic
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—22no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17C22⋊C812yes—
125C2×Dic17C22⋊C812yes—
126C2×Dic17AGL(1,ℤ/8)12yes—
127C2×Dic17#13712yes—
128Dic34—48no—
129#3624—82no—
130#3624—82no—
131C4×C4⋊Q8—171no—
132#1839—171no—
133#1839—171no—
134#1271—172no—
135#1271—172no—
136C22×C17C2×C22⋊C811yescharacteristic
137C22×C17#41011yescharacteristic
138C22×C17C2×#10111yescharacteristic
139C22×C17#41811yescharacteristic
140C22×C17#41911yescharacteristic
141C22×C17#42111yescharacteristic
142C22×C17#42111yescharacteristic
143C4×C17—22no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—41no—
147C4×C17—42no—
148C4×C17—81no—
149Dic17—22no—
150Dic17—22no—
151Dic17—22no—
152Dic17—22no—
153Dic17—42no—
154Dic17—81no—
155C2×C4⋊Q8—171no—
156C2×C4×Q8—341no—
157#391—341no—
158#389—171no—
159#389—171no—
160#389—341no—
161#384—171no—
162C4×C4⋊C4—171no—
163C4×C4⋊C4—341no—
164C4×C4⋊C4#59511yescharacteristic
165C43—171no—
166#336—172no—
167#336—172no—
168#336—341no—
169#336—341no—
170#336—341no—
171#336—341no—
172C2×C17#146111yescharacteristic
173C2×C17#147811yescharacteristic
174C2×C17#147911yescharacteristic
175C2×C17#151411yescharacteristic
176C2×C17#151511yescharacteristic
177C2×C17#153711yescharacteristic
178C2×C17#155611yescharacteristic
179C22×Q8—341no—
180C22×C8—342no—
181C22×C8—342no—
182C4⋊Q8—174no—
183C4⋊Q8—342no—
184C4×Q8—684no—
185C2×C4⋊C4—171no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4C2×#59511yescharacteristic
193C2×C4⋊C4C2×#59511yescharacteristic
194C2×C42—21no—
195C2×C42—171no—
196C2×C42—171no—
197C2×C42—171no—
198C2×C42—171no—
199C2×C42—171no—
200C2×C42—171no—
201C2×C42—341no—
202C2×C42C2×#59511yescharacteristic
203#95—21no—
204#95—341no—
205#95—341no—
206#95—341no—
207C17#760411yescharacteristic, complemented, Sylow
208C2×Q8—344no—
209C2×Q8—682no—
210C2×Q8—682no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4C22⋊#59511yescharacteristic
220C22×C4C22⋊#59511yescharacteristic
221C22×C4C22×#59511yescharacteristic
222C2×C8—682no—
223C2×C8—682no—
224C2×C8—682no—
225C2×C8—682no—
226C2×C8—682no—
227C2×C8—682no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—172no—
231C4⋊C4—344no—
232C4⋊C4—341no—
233C4⋊C4—681no—
234C4⋊C4—682no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C4⋊C4—682no—
238C4⋊C4#6324212yes—
239C42—22no—
240C42—42no—
241C42—172no—
242C42—172no—
243C42—342no—
244C42—342no—
245C42—681no—
246C42—681no—
247C42—681no—
248C42—682no—
249C23C2×C22⋊#59511yescharacteristic
250Q8—688no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—172no—
265C2×C4—172no—
266C2×C4—172no—
267C2×C4—172no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—342no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4#1058754512yes—
283C2×C4C2×#6324211yescharacteristic
284C2×C4D17⋊M1611yescharacteristic
285C8—1362no—
286C8—1362no—
287C22#1176377711yescharacteristic
288C22#1176378811yescharacteristic
289C22C2×#1058754511yescharacteristic
290C22#1176380111yescharacteristic
291C22#1176380211yescharacteristic
292C22#1176380611yescharacteristic
293C22#1176380611yescharacteristic
294C4—21no—
295C4—21no—
296C4—22no—
297C4—41no—
298C4—42no—
299C4—81no—
300C4—342no—
301C4—342no—
302C4—342no—
303C4—342no—
304C4—682no—
305C4—1361no—
306C2#1454402611yescharacteristic
307C2#1454408411yescharacteristic
308C2#1454408711yescharacteristic
309C2#1454420311yescharacteristic
310C2#1454420611yescharacteristic
311C2#1454427511yescharacteristic
312C2#1454431311yescharacteristic
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#7604
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
207. C17#7604semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436032
#145436022
C4×#105875742
#760417