Finite Group Databasebeta

← D61×#2982 #30544949

Subgroups — D61×#2982 #30544949

Order 15616.

2234 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2#21454900C211yesmaximal, characteristic, complemented
3#21454899C216yesmaximal, complemented
4#21454898C218yesmaximal, complemented
5C8×Q8×D61C218yesmaximal, complemented
6#431×D61C216yesmaximal
7C61×#2982C211yesmaximal, characteristic, complemented
8C22×Q8×D61C411yescharacteristic
9C2×Q8×Dic61C411yescharacteristic
10C2×C4×Dic122C2213yes—
11C2×#14519742C413yes—
12C4×Q8×D61C414yes—
13C4×Q8×D61C414yes—
14C4×Q8×D61C2214yes—
15C4×Q8×D61C2214yes—
16C2×C4⋊C4×D61C413yes—
17C2×C42×D61C2213yes—
18Q8×#92418C2218yescomplemented
19C8×Dic122C22124yescomplemented
20#16839886C22124yescomplemented
21#16839815C2216yes—
22#16839814C22112yes—
23#16839813C22112yes—
24#16839812C22112yes—
25C4⋊C8×D61C22112yes—
26C22⋊C8×D61C2214yes—
27C4×C8×D61C22112yes—
28C2×C4×Q8×C61C2211yescharacteristic
29C8×Q8×C61C2218yescomplemented
30C61×#431C2216yes—
31C22×Dic122C2×C413yes—
32C2×Q8×D61C8116yescomplemented
33C2×Q8×D61C2×C414yes—
34C2×Q8×D61C2×C414yes—
35C22×C4×D61C2×C413yes—
36C22×C4×D61C2×C413yes—
37C22×C4×D61C2311yescharacteristic
38C2×C8×D61C2318yes—
39Q8×Dic61C2×C414yes—
40Q8×Dic61C2×C414yes—
41C4×Dic122C2×C4112yes—
42C4×Dic122C23112yes—
43#14519742C2×C4112yes—
44#14519742C2×C4112yes—
45C2×C4⋊Dic61C2×C413yes—
46C2×#11758196C2×C416yes—
47C4⋊C4×D61C2×C4112yes—
48C4⋊C4×D61C2×C4112yes—
49C2×C4×Dic61C2×C413yes—
50C2×C4×Dic61C2×C413yes—
51C2×C4×Dic61C2313yes—
52C42×D61C2×C416yes—
53C42×D61C2×C416yes—
54C42×D61C2316yes—
55C42×D61C2316yes—
56C4⋊#92418C23112yes—
57#14519706C23124yes—
58C22⋊#92418C2314yes—
59#14519689C2318yes—
60C4×#92418C23112yes—
61C8×Dic61C23124yes—
62C22×Q8×C61C2×C411yescharacteristic
63C4×Q8×C61C2×C414yes—
64C4×Q8×C61C2314yes—
65C2×C4⋊C4×C61C2×C413yes—
66C2×C42×C61C2313yes—
67C4⋊C8×C61C23112yes—
68C22⋊C8×C61C2314yes—
69C4×C8×C61C23112yes—
70C23×D61C22×C411yescharacteristic
71C2×Q8×C61C2×C818yescomplemented
72C2×Q8×C61C22×C414yes—
73C22×C4×C61C22×C413yes—
74C22×C4×C61C22×C413yes—
75C22×C4×C61C2411yescharacteristic
76C22×Dic61C22×C411yescharacteristic
77C22×Dic61C22×C413yes—
78C22×Dic61C22×C413yes—
79Q8×D61C2×C8132yes—
80Q8×D61C2×C8132yescomplemented
81C2×C4×D61—24no—
82C2×C4×D61—46no—
83C2×C4×D61C2×C8124yes—
84C2×C4×D61C22×C416yes—
85C2×C4×D61C22×C411yescharacteristic
86C2×C4×D61C22×C411yescharacteristic
87C2×C4×D61C22×C416yes—
88C2×C4×D61C22×C416yes—
89C2×C4×D61C22×C416yes—
90C2×C4×D61C2411yescharacteristic
91C2×C4×D61C2411yescharacteristic
92C2×Dic122C2×C8124yescomplemented
93C2×Dic122C22×C4112yes—
94C2×C8×C61C2418yes—
95C4⋊C4×C61C22×C4112yes—
96C42×C61C22×C416yes—
97C42×C61C2416yes—
98C4⋊Dic61C22×C4112yes—
99#11758196C22×C4124yes—
100C4×Dic61C22×C416yes—
101C4×Dic61C22×C416yes—
102C4×Dic61C22×C416yes—
103C4×Dic61C22×C416yes—
104C4×Dic61C22×C416yes—
105C4×Dic61C2416yes—
106C2×#92418C2418yes—
107C8×D61—216no—
108C23×C61C23×C411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61C22×C814yes—
112C22×D61C23×C411yescharacteristic
113C22×D61C23×C411yescharacteristic
114Q8×C61C22×C8116yes—
115C2×C4×C61—22no—
116C2×C4×C61—43no—
117C2×C4×C61C22×C8112yes—
118C2×C4×C61C23×C411yescharacteristic
119C2×C4×C61C23×C416yes—
120C2×C4×C61C23×C416yes—
121C2×C4×C61C2511yescharacteristic
122C2×Dic61—22no—
123C2×Dic61—43no—
124C2×Dic61C22×C8112yes—
125C2×Dic61C23×C411yescharacteristic
126C2×Dic61C23×C416yes—
127C2×Dic61C23×C411yescharacteristic
128C2×Dic61C23×C416yes—
129C4×D61—22no—
130C4×D61—212no—
131C4×D61—22no—
132C4×D61—22no—
133C4×D61—46no—
134C4×D61C22×C8124yes—
135C4×D61C22×C8124yes—
136C4×D612−1+414yes—
137Dic122C22×C8148yes—
138C8×C61—28no—
139#92418—28no—
140C2×#2982—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61C23×C812yes—
144C22×C61C24×C411yescharacteristic
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—28no—
148C2×D61#51912yes—
149C2×D61C23×C812yes—
150C2×D61C23×C812yes—
151C2×D61#56812yes—
152C4×C61—21no—
153C4×C61—26no—
154C4×C61C23×C8112yes—
155C4×C61C2×2−1+412yes—
156Dic61—21no—
157Dic61—26no—
158Dic61#51912yes—
159Dic61C23×C8112yes—
160C22×C4×Q8—611no—
161#2982—618no—
162#2982—616no—
163#2982—611no—
164#2982D6111yescharacteristic, direct product factor
165C2×C8×Q8—618no—
166C2×#431—616no—
167C2×C61—22no—
168C2×C61C2×#51911yescharacteristic
169C2×C61C24×C811yescharacteristic
170C2×C61C2×#56811yescharacteristic
171D61—22no—
172D61#298214yesdirect product factor
173C23×Q8—611no—
174C2×C4×Q8—611no—
175C2×C4×Q8—614no—
176C2×C4×Q8—614no—
177C2×C4×Q8—614no—
178C2×C4×Q8—614no—
179C2×C4×Q8—613no—
180C2×C4×Q8—613no—
181C2×C4×Q8C2×D6111yescharacteristic
182C22×C4⋊C4—613no—
183C22×C42—613no—
184C8×Q8—618no—
185C8×Q8—6124no—
186C8×Q8—6124no—
187C8×Q8C2×D6118yescomplemented
188#431—616no—
189#431—6112no—
190#431—6112no—
191#431—6112no—
192#431C2×D6116yes—
193C2×C4⋊C8—6112no—
194C2×C22⋊C8—614no—
195C2×C4×C8—6112no—
196C61C2×#298211yescharacteristic, complemented, Sylow
197C22×Q8—6116no—
198C22×Q8—614no—
199C22×Q8—614no—
200C22×Q8—613no—
201C22×Q8C4×D6111yescharacteristic
202C23×C4—613no—
203C23×C4—611no—
204C23×C4—613no—
205C22×C8—618no—
206C4×Q8—614no—
207C4×Q8—614no—
208C4×Q8—6112no—
209C4×Q8—6112no—
210C4×Q8—6112no—
211C4×Q8—6112no—
212C4×Q8C4×D6114yes—
213C4×Q8C22×D6114yes—
214C2×C4⋊C4—616no—
215C2×C4⋊C4—613no—
216C2×C4⋊C4—6112no—
217C2×C4⋊C4—6112no—
218C2×C4⋊C4C4×D6113yes—
219C2×C42—613no—
220C2×C42—613no—
221C2×C42—613no—
222C2×C42—616no—
223C2×C42—616no—
224C2×C42—616no—
225C2×C42—616no—
226C2×C42C22×D6113yes—
227C4⋊C8—6124no—
228C4⋊C8—6112no—
229C4⋊C8C22×D61112yes—
230C22⋊C8—614no—
231C22⋊C8—618no—
232C22⋊C8C22×D6114yes—
233C4×C8—6124no—
234C4×C8—6112no—
235C4×C8C22×D61112yes—
236C24—611no—
237C2×Q8—6132no—
238C2×Q8—6132no—
239C2×Q8—6112no—
240C2×Q8—6124no—
241C2×Q8C8×D6118yescomplemented
242C2×Q8C2×C4×D6114yes—
243C22×C4—613no—
244C22×C4—616no—
245C22×C4—616no—
246C22×C4—611no—
247C22×C4—6124no—
248C22×C4—611no—
249C22×C4—613no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—616no—
253C22×C4—611no—
254C22×C4—616no—
255C22×C4—1224no—
256C22×C4—2446no—
257C22×C4C2×C4×D6113yes—
258C22×C4C2×C4×D6113yes—
259C22×C4C23×D6111yescharacteristic
260C2×C8—618no—
261C2×C8—12216no—
262C2×C8C23×D6118yes—
263C4⋊C4—6124no—
264C4⋊C4—6112no—
265C4⋊C4C2×C4×D61112yes—
266C42—616no—
267C42—616no—
268C42—616no—
269C42—616no—
270C42—616no—
271C42—616no—
272C42C2×C4×D6116yes—
273C42C23×D6116yes—
274C23—611no—
275C23—614no—
276C23—611no—
277C23—1222no—
278C23—1222no—
279C23C22×C4×D6111yescharacteristic
280Q8—6148no—
281Q8C2×C8×D61116yes—
282C2×C4—22no—
283C2×C4—43no—
284C2×C4—6112no—
285C2×C4—611no—
286C2×C4—616no—
287C2×C4—6124no—
288C2×C4—6124no—
289C2×C4—614no—
290C2×C4—611no—
291C2×C4—616no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—12212no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—2446no—
298C2×C4—2443no—
299C2×C4C2×C8×D61112yes—
300C2×C4C22×C4×D6111yescharacteristic
301C2×C4C22×C4×D6116yes—
302C2×C4C22×C4×D6116yes—
303C2×C4C24×D6111yescharacteristic
304C8—28no—
305C8—1228no—
306C22—21no—
307C22—21no—
308C22—612no—
309C22—612no—
310C22—612no—
311C22—612no—
312C22—1228no—
313C22—1221no—
314C22—1221no—
315C22C22×C8×D6112yes—
316C22C23×C4×D6111yescharacteristic
317C4—26no—
318C4—21no—
319C4—6112no—
320C4—612no—
321C4—1226no—
322C4—1221no—
323C4C22×C8×D61112yes—
324C42−1+4×D6112yes—
325C2—22no—
326C2—614no—
327C2—1222no—
328C2#519×D6111yescharacteristic
329C2C23×C8×D6111yescharacteristic
330C2#568×D6111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutatorC2×C61C24×C8
FittingC61×#2982C2
socleC22×C61C24×C4
prime radicalC23×D61C22×C4
cosocleC2×C4×C61C25
hypercenter#2982D61
hypocenterC61C2×#2982
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #21454900C2semidirect
3. #21454899C2semidirect
4. #21454898C2semidirect
5. C8×Q8×D61C2semidirect
7. C61×#2982C2semidirect
18. Q8×#92418C22semidirect
19. C8×Dic122C22semidirect
20. #16839886C22semidirect
29. C8×Q8×C61C22semidirect
32. C2×Q8×D61C8semidirect
71. C2×Q8×C61C2×C8semidirect
80. Q8×D61C2×C8semidirect
92. C2×Dic122C2×C8semidirect
164. #2982D61direct (N × H)
172. D61#2982direct (N × H)
187. C8×Q8C2×D61semidirect
196. C61C2×#2982semidirect
241. C2×Q8C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
#214549002
#214548992
#214548982
C8×Q8×D612
#431×D612
C61×#29822
C2×#298261