Finite Group Databasebeta

← #30595442

Subgroups — #30595442

Order 15616.

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#21461735C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×C4×Dic122—21no—
14#16839666—21no—
15#16839661C2211yescharacteristic
16#16839659—21no—
17#16839658C2211yescharacteristic
18#16839631C411yescharacteristic
19C4×#11758196—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4×#92420—24no—
27C22×Dic122—21no—
28#14519776—22no—
29#14519776C814yescomplemented
30C4×Dic122—44no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×Dic122—24no—
65C2×Dic122—42no—
66C2×Dic122—42no—
67C2×#92420—24no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61C2×C812yes—
76C42×C61—22no—
77C42×C61—42no—
78C4⋊Dic61—21no—
79C4⋊Dic61—42no—
80C4⋊Dic61—41no—
81C4⋊Dic61C2×C812yes—
82#11758196—24no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—42no—
91C4×Dic61C2×C812yes—
92C4×Dic61M1612yes—
93C4×Dic61SD1612yes—
94C4×Dic61Q1612yes—
95C23×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#10112yes—
109C2×C4×C61#10312yes—
110C2×C4×C61C22×C811yescharacteristic
111C2×C4×C61C2×M1611yescharacteristic
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—22no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61C22⋊C812yes—
125C2×Dic61C22⋊C812yes—
126C2×Dic61#10312yes—
127C2×Dic61#10412yes—
128C2×Dic61C2×SD1611yescharacteristic
129C2×Dic61C2×Q1611yescharacteristic
130C2×Dic61AGL(1,ℤ/8)12yes—
131Dic122—48no—
132#92420—44no—
133#92420—82no—
134#7591—611nomaximal, Sylow
135C22×C61C2×C22⋊C811yescharacteristic
136C22×C61#41011yescharacteristic
137C22×C61C2×#10111yescharacteristic
138C22×C61C2×#10311yescharacteristic
139C22×C61#41811yescharacteristic
140C22×C61C2×#10411yescharacteristic
141C22×C61#42111yescharacteristic
142C4×C61—22no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—81no—
148Dic61—22no—
149Dic61—22no—
150Dic61—21no—
151Dic61—21no—
152Dic61—42no—
153Dic61—81no—
154Dic61Q8⋊C814yes—
155C4×C4⋊Q8—611no—
156#1831—611no—
157#1744—611no—
158#1271—612no—
159#1271—612no—
160C2×C61#146111yescharacteristic
161C2×C61C2×Q8⋊C811yescharacteristic
162C2×C61#147811yescharacteristic
163C2×C61#150511yescharacteristic
164C2×C61#151811yescharacteristic
165C2×C61#153111yescharacteristic
166C2×C61#154911yescharacteristic
167C2×C4⋊Q8—611no—
168C2×C4×Q8—1221no—
169C2×C4⋊C8—1221no—
170C2×C4×C8—1221no—
171#391—1221no—
172#389—611no—
173#389—611no—
174#389—1221no—
175#384—611no—
176C4×C4⋊C4—611no—
177C4×C4⋊C4—1221no—
178C4×C4⋊C4#692311yescharacteristic
179C43—611no—
180#336—612no—
181#336—612no—
182#336—1221no—
183#336—1221no—
184C61#759111yescharacteristic, complemented, Sylow
185C22×Q8—1221no—
186C22×C8—1222no—
187C22×C8—1222no—
188C4⋊Q8—614no—
189C4⋊Q8—1222no—
190C4×Q8—2444no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C2×#692311yescharacteristic
199C2×C4⋊C4C2×#692311yescharacteristic
200C2×C42—21no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—1221no—
208C2×C42C2×#692311yescharacteristic
209C4⋊C8—2442no—
210C4×C8—1224no—
211#95—21no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215C2×Q8—1224no—
216C2×Q8—2442no—
217C2×Q8—2442no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22⋊#692311yescharacteristic
228C22×C4C22×#692311yescharacteristic
229C2×C8—1224no—
230C2×C8—2442no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—612no—
238C4⋊C4—1224no—
239C4⋊C4—1221no—
240C4⋊C4—2441no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4D61⋊C812yes—
246C42—22no—
247C42—42no—
248C42—612no—
249C42—612no—
250C42—612no—
251C42—612no—
252C42—1222no—
253C42—1222no—
254C42—2441no—
255C42—2441no—
256C42—2442no—
257C23C2×C22⋊#692311yescharacteristic
258Q8—2448no—
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—612no—
272C2×C4—612no—
273C2×C4—612no—
274C2×C4—612no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1222no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451983812yes—
291C2×C4#1451984012yes—
292C2×C4C2×D61⋊C811yescharacteristic
293C2×C4D61⋊M1611yescharacteristic
294C8—4882no—
295C8—2444no—
296C22D61⋊(C22⋊C8)11yescharacteristic
297C22#1684074111yescharacteristic
298C22C2×#1451983811yescharacteristic
299C22C2×#1451984011yescharacteristic
300C22#1684075411yescharacteristic
301C22D61⋊#10411yescharacteristic
302C22#1684075911yescharacteristic
303C4—22no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—81no—
309C4—614no—
310C4—1221no—
311C4—1221no—
312C4—1222no—
313C4—1222no—
314C4—4881no—
315C4—2442no—
316C2#2146106111yescharacteristic
317C2D61⋊(Q8⋊C8)11yescharacteristic
318C2#2146111911yescharacteristic
319C2#2146120911yescharacteristic
320C2#2146125211yescharacteristic
321C2#2146129111yescharacteristic
322C2#2146133411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7591
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
29. #14519776C8semidirect
184. C61#7591semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615342
#214606382
#214606372
C4×#145197762
#759161