Finite Group Databasebeta

← #30595655

Subgroups — #30595655

Order 15616.

456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 456 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#21461736C211yesmaximal, characteristic
2#21461736C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×C4⋊#92420—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—
25C4⋊#92420—42no—
26C4⋊#92420—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—42no—
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—41no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—42no—
95C4×Dic61D812yes—
96C4×Dic61SD1612yes—
97C4×Dic61SD1612yes—
98C4×Dic61Q1612yes—
99C23×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
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#10112yes—
112C2×C4×C61#10212yes—
113C2×C4×C61#10312yes—
114C2×C4×C61C2×M1611yescharacteristic
115C2×C4×C61C2×M1611yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—22no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#10212yes—
131C2×Dic61#10312yes—
132C2×Dic61C2×D811yescharacteristic
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61C2×SD1611yescharacteristic
135C2×Dic61C2×Q1611yescharacteristic
136Dic122—48no—
137#92420—82no—
138#92420—82no—
139#7652—611nomaximal, Sylow
140C22×C61#40711yescharacteristic
141C22×C61#41011yescharacteristic
142C22×C61C2×#10111yescharacteristic
143C22×C61C2×#10211yescharacteristic
144C22×C61C2×#10311yescharacteristic
145C22×C61#42111yescharacteristic
146C22×C61#42111yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—42no—
151C4×C61—81no—
152C4×C61#33214yes—
153Dic61—22no—
154Dic61—22no—
155Dic61—21no—
156Dic61—21no—
157Dic61—21no—
158Dic61—21no—
159Dic61—42no—
160Dic61—81no—
161C4×C4⋊Q8—611no—
162#1831—611no—
163#1831—611no—
164#1271—612no—
165#1271—612no—
166C2×C61#146711yescharacteristic
167C2×C61#148611yescharacteristic
168C2×C61#148711yescharacteristic
169C2×C61#151711yescharacteristic
170C2×C61#151811yescharacteristic
171C2×C61#153711yescharacteristic
172C2×C61C2×#33211yescharacteristic
173C2×C4⋊Q8—611no—
174C2×C4×Q8—1221no—
175C2×C4⋊C8—1221no—
176C2×C4⋊C8—1221no—
177#391—1221no—
178#389—611no—
179#389—611no—
180#389—1221no—
181#384—611no—
182C4×C4⋊C4—611no—
183C4×C4⋊C4—1221no—
184C4×C4⋊C4#692311yescharacteristic
185C43—611no—
186#336—612no—
187#336—612no—
188#336—1221no—
189#336—1221no—
190C61#765211yescharacteristic, complemented, Sylow
191C22×Q8—1221no—
192C22×C8—1222no—
193C22×C8—1222no—
194C4⋊Q8—1222no—
195C4⋊Q8—1222no—
196C4×Q8—2442no—
197C4×Q8—2442no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C4⋊C4C2×#692311yescharacteristic
207C2×C42—21no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—1221no—
215C2×C42C2×#692311yescharacteristic
216C4⋊C8—2442no—
217C4⋊C8—2442no—
218#95—21no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222C2×Q8—1224no—
223C2×Q8—2442no—
224C2×Q8—2442no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22⋊#692311yescharacteristic
235C22×C4C22×#692311yescharacteristic
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2442no—
241C2×C8—2442no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—612no—
245C4⋊C4—1224no—
246C4⋊C4—1221no—
247C4⋊C4—2441no—
248C4⋊C4—2442no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2442no—
254C4⋊C4#1175821312yes—
255C42—22no—
256C42—42no—
257C42—612no—
258C42—612no—
259C42—612no—
260C42—612no—
261C42—1221no—
262C42—1221no—
263C42—2441no—
264C42—2441no—
265C42—2441no—
266C42—2442no—
267C23C2×C22⋊#692311yescharacteristic
268Q8—2448no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—612no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1222no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451983812yes—
301C2×C4#1451983912yes—
302C2×C4#1451984012yes—
303C2×C4D61⋊M1611yescharacteristic
304C2×C4C2×#1175821311yescharacteristic
305C8—4882no—
306C8—4882no—
307C22#1684073311yescharacteristic
308C22#1684074111yescharacteristic
309C22C2×#1451983811yescharacteristic
310C22C2×#1451983911yescharacteristic
311C22C2×#1451984011yescharacteristic
312C22#1684075911yescharacteristic
313C22#1684075911yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—42no—
318C4—81no—
319C4—1221no—
320C4—1221no—
321C4—1221no—
322C4—1221no—
323C4—1222no—
324C4—1222no—
325C4—4881no—
326C4—2442no—
327C4#1684062114yes—
328C2#2146108111yescharacteristic
329C2#2146114511yescharacteristic
330C2#2146114811yescharacteristic
331C2#2146124911yescharacteristic
332C2#2146125211yescharacteristic
333C2#2146131011yescharacteristic
334C2C2×#1684062111yescharacteristic
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#7652
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
190. C61#7652semidirect

Maximal subgroups

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

subgroupindex
#214617362
#214606382
#214606372
C4×#145197762
#765261