Finite Group Databasebeta

← #17950159

Subgroups — #17950159

Order 4352.

426 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 88 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#14544699C211yesmaximal, characteristic, complemented
2#14544501C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543600C212yesmaximal
5#14537148C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×#10587542—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587565—21no—
13#11762712C411yescharacteristic
14#11762712C2211yescharacteristic
15#11762708C411yescharacteristic
16#11762707C411yescharacteristic
17#11762705C2211yescharacteristic
18#11762703—21no—
19#11762702—21no—
20#11762697—21no—
21C42×Dic17C2211yescharacteristic
22C17×#390C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C22⋊C4×C17—21no—
28C2×C22⋊C4×C17—21no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17—21no—
32C2×C22⋊Dic17—21no—
33C2×C22⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45#10587565—44no—
46#10587542—24no—
47C4⋊#3624—42no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51C24×C17—21no—
52C2×D4×C17—22no—
53C2×D4×C17—41no—
54C2×D4×C17—41no—
55C22×C4×C17—21no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×#3624—24no—
66C2×#3624—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C4⋊C4×C17—41no—
72C22⋊C4×C17—42no—
73C22⋊C4×C17—42no—
74C42×C17—22no—
75C22⋊Dic17—42no—
76C22⋊Dic17—42no—
77C22⋊Dic17—42no—
78C22⋊Dic17—41no—
79C22⋊Dic17—41no—
80C4⋊Dic17—22no—
81C4⋊Dic17—42no—
82C4⋊Dic17—41no—
83#63225—42no—
84#63225—42no—
85C4×Dic17—22no—
86C4×Dic17—21no—
87C4×Dic17—22no—
88C4×Dic17—21no—
89C4×Dic17—41no—
90C4×Dic17—41no—
91C4×Dic17—41no—
92#7706—171nomaximal, Sylow
93C23×C17—41no—
94C23×C17—41no—
95C23×C17—41no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17—41no—
100C23×C17C2×C22⋊C411yescharacteristic
101D4×C17—82no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
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—41no—
112C2×C4×C17#10412yes—
113C2×C4×C17#13112yes—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
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—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17AGL(1,ℤ/8)11yescharacteristic
131C2×Dic17AGL(1,ℤ/8)12yes—
132C2×Dic17#13711yescharacteristic
133#3624—44no—
134#3624—82no—
135#2860—171no—
136#1831—171no—
137#1745—171no—
138#1271—172no—
139#1270—172no—
140C22×C17—81no—
141C22×C17—81no—
142C22×C17—81no—
143C22×C17—81no—
144C22×C17—81no—
145C22×C17—81no—
146C22×C17—81no—
147C22×C17#40811yescharacteristic
148C22×C17#41011yescharacteristic
149C22×C17#41311yescharacteristic
150C22×C17#41711yescharacteristic
151C22×C17#41811yescharacteristic
152C22×C17C2×#10411yescharacteristic
153C22×C17#42111yescharacteristic
154C4×C17—22no—
155C4×C17—22no—
156C4×C17—41no—
157C4×C17—81no—
158Dic17—22no—
159Dic17—21no—
160Dic17—21no—
161Dic17—41no—
162Dic17—41no—
163Dic17—81no—
164Dic17—81no—
165C2×#126—341no—
166C2×C4⋊C8—341no—
167C2×#97—341no—
168#390—171no—
169#390—171no—
170#390#59511yescharacteristic
171#389—171no—
172#389—171no—
173#389—171no—
174#388—341no—
175#388—341no—
176#388—341no—
177C43—171no—
178#336—172no—
179#336—172no—
180#336—341no—
181#336—341no—
182C2×C17—161no—
183C2×C17#147311yescharacteristic
184C2×C17#148311yescharacteristic
185C2×C17#149611yescharacteristic
186C2×C17#150511yescharacteristic
187C2×C17#151211yescharacteristic
188C2×C17#152911yescharacteristic
189C2×C17#155711yescharacteristic
190C22×D4C2×#59511yescharacteristic
191C22×C8—342no—
192C22×C8—342no—
193#126—684no—
194C2×C4⋊C4—171no—
195C2×C4⋊C4—171no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4—341no—
198C2×C4⋊C4—341no—
199C2×C4⋊C4C2×#59511yescharacteristic
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—341no—
203C2×C22⋊C4—341no—
204C2×C22⋊C4—341no—
205C2×C22⋊C4—341no—
206C2×C42—171no—
207C2×C42—171no—
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—171no—
211C2×C42—171no—
212C2×C42C2×#59511yescharacteristic
213C4⋊C8—682no—
214#97—344no—
215#95—341no—
216#95—341no—
217#95—341no—
218C17#770611yescharacteristic, complemented, Sylow
219C24—21no—
220C2×D4—22no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22⋊#59511yescharacteristic
232C22×C4C22×#59511yescharacteristic
233C2×C8—344no—
234C2×C8—682no—
235C2×C8—682no—
236C2×C8—682no—
237C2×C8—682no—
238C2×C8—682no—
239C4⋊C4—41no—
240C4⋊C4—342no—
241C4⋊C4—681no—
242C4⋊C4—682no—
243C4⋊C4—682no—
244C4⋊C4—682no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—681no—
248C22⋊C4—681no—
249C22⋊C4—682no—
250C22⋊C4—682no—
251C22⋊C4—682no—
252C42—22no—
253C42—341no—
254C42—342no—
255C42—341no—
256C42—342no—
257C42—681no—
258C42—681no—
259C42—681no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C22⋊#59511yescharacteristic
268D4—82no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—171no—
280C2×C4—171no—
281C2×C4—172no—
282C2×C4—341no—
283C2×C4—341no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4#1058754812yes—
299C2×C4#1058767812yes—
300C8—684no—
301C8—1362no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1176378211yescharacteristic
310C22#1176378911yescharacteristic
311C22#1176379511yescharacteristic
312C22#1176380011yescharacteristic
313C22#1176380111yescharacteristic
314C22C2×#1058754811yescharacteristic
315C22#1176380611yescharacteristic
316C4—22no—
317C4—22no—
318C4—41no—
319C4—81no—
320C4—342no—
321C4—341no—
322C4—341no—
323C4—681no—
324C4—681no—
325C4—1361no—
326C4—1361no—
327C2—161no—
328C2#1454406611yescharacteristic
329C2#1454409911yescharacteristic
330C2#1454414311yescharacteristic
331C2#1454417311yescharacteristic
332C2#1454419611yescharacteristic
333C2#1454424911yescharacteristic
334C2#1454431511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#390C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC2×C4×Dic17C23
hypercenter#390#595
hypocenterC17#7706
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14544699C2semidirect
2. #14544501C2semidirect
3. #14543603C2semidirect
218. C17#7706semidirect

Maximal subgroups

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

subgroupindex
#145446992
#145445012
#145436032
#145436002
#145371482
#770617