Finite Group Databasebeta

← #30595562

Subgroups — #30595562

Order 15616.

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

normal subgroups only

This group has 462 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#21461747C211yesmaximal, characteristic
2#21461605C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519832—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—
25C4⋊#92420—24no—
26#14519832—42no—
27C22×Dic122—21no—
28#14519776—22no—
29#14519776—22no—
30C4×Dic122—42no—
31C4×Dic122—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×Dic122—24no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×#92420—24no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61M1612yes—
77C42×C61—22no—
78C42×C61—42no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61M1612yes—
84#11758196—24no—
85#11758196—42no—
86#11758196—42no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—42no—
96C4×Dic61D812yes—
97C4×Dic61SD1612yes—
98C23×C61C2×C22⋊C411yescharacteristic
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—22no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61#10112yes—
112C2×C4×C61#10212yes—
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61C2×M1611yescharacteristic
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—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#10212yes—
130C2×Dic61#10412yes—
131C2×Dic61C2×D811yescharacteristic
132C2×Dic61C2×SD1611yescharacteristic
133C2×Dic61#13712yes—
134Dic122—48no—
135#92420—44no—
136#92420—82no—
137#7625—611nomaximal, Sylow
138C22×C61#40711yescharacteristic
139C22×C61#41011yescharacteristic
140C22×C61C2×#10111yescharacteristic
141C22×C61C2×#10211yescharacteristic
142C22×C61#41911yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—22no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—22no—
149C4×C61—42no—
150C4×C61—81no—
151Dic61—22no—
152Dic61—22no—
153Dic61—21no—
154Dic61—21no—
155Dic61—22no—
156Dic61—42no—
157Dic61—81no—
158C4×C4⋊Q8—611no—
159#1839—611no—
160#1767—611no—
161#1271—612no—
162#1271—612no—
163C2×C61#146711yescharacteristic
164C2×C61#148611yescharacteristic
165C2×C61#149111yescharacteristic
166C2×C61#150211yescharacteristic
167C2×C61#151511yescharacteristic
168C2×C61#153111yescharacteristic
169C2×C61#154611yescharacteristic
170C2×C4⋊Q8—611no—
171C2×C4×Q8—1221no—
172C2×C4⋊C8—1221no—
173C2×#97—1221no—
174#391—1221no—
175#389—611no—
176#389—611no—
177#389—1221no—
178#384—611no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4—1221no—
181C4×C4⋊C4#692311yescharacteristic
182C43—611no—
183#336—612no—
184#336—612no—
185#336—1221no—
186#336—1221no—
187C61#762511yescharacteristic, complemented, Sylow
188C22×Q8—1221no—
189C22×C8—1222no—
190C22×C8—1222no—
191C4⋊Q8—1222no—
192C4⋊Q8—1222no—
193C4×Q8—2442no—
194C4×Q8—2442no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C2×#692311yescharacteristic
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C42—21no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—1221no—
212C2×C42C2×#692311yescharacteristic
213C4⋊C8—1224no—
214#97—2442no—
215#95—21no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219C2×Q8—1224no—
220C2×Q8—2442no—
221C2×Q8—2442no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233C2×C8—1224no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—612no—
242C4⋊C4—1224no—
243C4⋊C4—1221no—
244C4⋊C4—2441no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4#1175821312yes—
252C42—22no—
253C42—42no—
254C42—612no—
255C42—612no—
256C42—1222no—
257C42—1222no—
258C42—1221no—
259C42—1221no—
260C42—2441no—
261C42—2441no—
262C42—2442no—
263C23C2×C22⋊#692311yescharacteristic
264Q8—2448no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1222no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4#1451983812yes—
297C2×C4#1451983912yes—
298C2×C4D61⋊M1611yescharacteristic
299C2×C4C2×#1175821311yescharacteristic
300C8—4882no—
301C8—2444no—
302C22#1684073311yescharacteristic
303C22#1684074111yescharacteristic
304C22C2×#1451983811yescharacteristic
305C22C2×#1451983911yescharacteristic
306C22#1684075511yescharacteristic
307C22D61⋊#10411yescharacteristic
308C22#1684075911yescharacteristic
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—1222no—
316C4—1222no—
317C4—1221no—
318C4—1221no—
319C4—1222no—
320C4—4881no—
321C4—2442no—
322C2#2146108111yescharacteristic
323C2#2146114511yescharacteristic
324C2#2146116211yescharacteristic
325C2#2146119811yescharacteristic
326C2#2146124111yescharacteristic
327C2#2146129111yescharacteristic
328C2#2146132811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7625
LCSG ▷ C22×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
187. C61#7625semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214616052
#214606382
#214606372
C4×#145197762
#762561