Finite Group Databasebeta

← #30595672

Subgroups — #30595672

Order 15616.

432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461747C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460636C212yesmaximal
5#21454192C211yesmaximal, characteristic
6C2×C4×#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519765C411yescharacteristic
13#16839667C411yescharacteristic
14#16839667C2211yescharacteristic
15#16839663C411yescharacteristic
16#16839663C2211yescharacteristic
17#16839652—21no—
18#16839652—21no—
19#16839652—21no—
20#16839652—21no—
21C42×Dic61C2211yescharacteristic
22C2×#125×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4×#92420—24no—
26C22×Dic122C2×C411yescharacteristic
27C22×D244C2×C411yescharacteristic
28#14519765—42no—
29C2×#11758198—21no—
30C2×#11758198—21no—
31C2×#11758198—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#125×C61—42no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51C23×D61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×D244—22no—
63C2×D244—41no—
64C2×D244—41no—
65C2×Dic122—22no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×#92420—24no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—42no—
78C42×C61—22no—
79#11758198—42no—
80#11758198—42no—
81#11758198—42no—
82#11758198—42no—
83#11758198—42no—
84#11758198—42no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C23×C61C2×C22⋊C411yescharacteristic
92C22×D61—41no—
93C22×D61—41no—
94C22×D61—41no—
95C22×D61—41no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61—41no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#10012yes—
113C2×C4×C61#13112yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61#10412yes—
127C2×Dic61#13512yes—
128C2×Dic61#13512yes—
129D244—82no—
130Dic122—82no—
131#92420—44no—
132#92420—82no—
133#7656—611nomaximal, Sylow
134C22×C61#40811yescharacteristic
135C22×C61#41011yescharacteristic
136C22×C61C2×#10011yescharacteristic
137C22×C61#41611yescharacteristic
138C22×C61#41611yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C22×C61#42111yescharacteristic
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—81no—
145C2×D61—81no—
146C2×D61—81no—
147C2×D61—81no—
148C4×C61—22no—
149C4×C61—22no—
150C4×C61—41no—
151C4×C61—81no—
152C4×C61—81no—
153Dic61—22no—
154Dic61—22no—
155Dic61—22no—
156Dic61—41no—
157Dic61—81no—
158#2861—611no—
159#1839—611no—
160#1744—611no—
161#1272—612no—
162#1270—612no—
163C2×C61#146911yescharacteristic
164C2×C61#148211yescharacteristic
165C2×C61#149411yescharacteristic
166C2×C61#150011yescharacteristic
167C2×C61#152111yescharacteristic
168C2×C61#153011yescharacteristic
169C2×C61#154311yescharacteristic
170D61—161no—
171C2×#125#692311yescharacteristic
172C2×#124—611no—
173C2×C4×C8—1221no—
174#391—611no—
175#391—611no—
176#390—611no—
177#390—611no—
178#388—1221no—
179#388—1221no—
180#388—1221no—
181#388—1221no—
182C43—611no—
183#336—612no—
184#336—612no—
185#336—1221no—
186#336—1221no—
187#336—1221no—
188C61#765611yescharacteristic, complemented, Sylow
189C22×Q8—611no—
190C22×D4—611no—
191C22×C8—1222no—
192C22×C8—1222no—
193#125—42no—
194#124—2442no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C4⋊C4C2×#692311yescharacteristic
199C2×C22⋊C4—1221no—
200C2×C22⋊C4—1221no—
201C2×C22⋊C4—1221no—
202C2×C22⋊C4—1221no—
203C2×C22⋊C4—1221no—
204C2×C22⋊C4—1221no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42C2×#692311yescharacteristic
212C4×C8—1224no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C24—1221no—
218C2×Q8—1222no—
219C2×Q8—2441no—
220C2×Q8—2441no—
221C2×D4—1222no—
222C2×D4—2441no—
223C2×D4—2441no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1221no—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22⋊#692311yescharacteristic
233C22×C4C22×#692311yescharacteristic
234C2×C8—1224no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—2442no—
245C22⋊C4—2442no—
246C22⋊C4—2442no—
247C22⋊C4—2442no—
248C22⋊C4—2442no—
249C22⋊C4—2442no—
250C42—22no—
251C42—1222no—
252C42—1222no—
253C42—1222no—
254C42—1222no—
255C42—2441no—
256C42—2441no—
257C23—2441no—
258C23—2441no—
259C23—2441no—
260C23—2441no—
261C23—2441no—
262C23—2441no—
263C23—2441no—
264C23C2×C22⋊#692311yescharacteristic
265Q8—4882no—
266D4—4882no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—612no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4#1451983712yes—
296C2×C4#1451986512yes—
297C8—4882no—
298C8—2444no—
299C22—4881no—
300C22—4881no—
301C22—4881no—
302C22—4881no—
303C22—4881no—
304C22—4881no—
305C22—4881no—
306C22#1684073711yescharacteristic
307C22#1684074311yescharacteristic
308C22C2×#1451983711yescharacteristic
309C22#1684075211yescharacteristic
310C22#1684075211yescharacteristic
311C22D61⋊#10411yescharacteristic
312C22#1684075911yescharacteristic
313C4—22no—
314C4—22no—
315C4—41no—
316C4—81no—
317C4—81no—
318C4—1222no—
319C4—1222no—
320C4—1222no—
321C4—4881no—
322C4—2441no—
323C2—9761no—
324C2#2146109011yescharacteristic
325C2#2146113311yescharacteristic
326C2#2146117311yescharacteristic
327C2#2146119311yescharacteristic
328C2#2146126211yescharacteristic
329C2#2146128811yescharacteristic
330C2#2146132211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#7656
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21461534C2semidirect
3. #21460640C2semidirect
188. C61#7656semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214615342
#214606402
#214606362
#214541922
#765661