Finite Group Databasebeta

← #30607411

Subgroups — #30607411

Order 15616.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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
1D61⋊#430C211yesmaximal, characteristic
2D61⋊#365C212yesmaximal, complemented
3#21461697C211yesmaximal, characteristic
4#21460894C212yesmaximal, complemented
5#349×D61C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840777—22no—
8#16840777—22no—
9D61⋊#108—21no—
10D61⋊#108C2212yes—
11C2×#14519846C2211yescharacteristic
12C2×#14519845C2211yescharacteristic
13#16840704—21no—
14#16840687—22no—
15#16840686—22no—
16#16840636—21no—
17C2×M16×D61C2211yescharacteristic
18M32×D61C2212yes—
19#16839544C411yescharacteristic, complemented
20#16839543C412yescomplemented
21C61×#349C411yescharacteristic, complemented
22C2×#11758213—21no—
23C2×#11758213—21no—
24D61⋊M16—22no—
25D61⋊M16—22no—
26D61⋊M16—41no—
27D61⋊M16—41no—
28C2×#11758217—41no—
29C2×D61⋊C8—41no—
30C2×C4⋊#6923—21no—
31C2×C4⋊#6923—21no—
32C2×C22⋊#6923—41no—
33#14519848—22no—
34#14519848—22no—
35#14519847—21no—
36#14519847—21no—
37#14519847D412yes—
38#14519847D412yes—
39#14519846—22no—
40#14519845—22no—
41(C2×#6923)⋊C4—41no—
42C22×C4×D61D411yescharacteristic
43C2×#11758194Q811yescharacteristic
44C2×#11758189C2×C411yescharacteristic
45C2×#11758189Q811yescharacteristic
46M16×D61—22no—
47M16×D61—22no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61C2311yescharacteristic
50#14519717C2×C412yes—
51#14519716—22no—
52C16×D61—22no—
53C2×M16×C61C2×C411yescharacteristic
54M32×C61C2×C412yes—
55C23×D61SD1611yescharacteristic
56C22×#6923—41no—
57C22×#6923—41no—
58C22×C4×C61C4⋊C411yescharacteristic
59C22×Dic61SD1611yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61C4⋊C411yescharacteristic
65C2×C4×D61SD1611yescharacteristic
66C2×C4×D61SD1611yescharacteristic
67C2×C4×D61C2×D411yescharacteristic
68C22⋊#6923—82no—
69#11758217—42no—
70#11758217—42no—
71C2×#92420—41no—
72C2×#92420—41no—
73C4⋊#6923—41no—
74C4⋊#6923—41no—
75C4⋊#6923—41no—
76C4⋊#6923—41no—
77#11758213—22no—
78#11758213—22no—
79#11758213—41no—
80#11758213—41no—
81D61⋊C8—42no—
82D61⋊C8—42no—
83M16×C61—22no—
84C2×C8×C61C4⋊C411yescharacteristic
85C2×C8×C61C22×C411yescharacteristic
86#11758194—22no—
87C2×#92418C4⋊C411yescharacteristic
88C2×#92418C2×Q811yescharacteristic
89#11758189—22no—
90#11758189—22no—
91C8×D61—21no—
92C8×D61—21no—
93C8×D61C2×D412yes—
94C8×D61#4112yes—
95C16×C61—22no—
96#11758185—22no—
97C23×C61#10611yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—41no—
101C22×D61—41no—
102C22×D61#10611yescharacteristic
103C22×D61C2×SD1611yescharacteristic
104C2×#6923—81no—
105C2×#6923—81no—
106C2×#6923—81no—
107C2×#6923—81no—
108C2×#6923—81no—
109C2×#6923—81no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61#10611yescharacteristic
113C2×C4×C61C2×C4⋊C411yescharacteristic
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61#10611yescharacteristic
117C2×Dic61C2×SD1611yescharacteristic
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—21no—
122C4×D61—21no—
123C4×D61—21no—
124C4×D61#12011yescharacteristic
125C4×D61#12311yescharacteristic
126C4×D61AGL(1,ℤ/8)11yescharacteristic
127C4×D61#13711yescharacteristic
128#92420—42no—
129#92420—42no—
130C8×C61—21no—
131C8×C61C4×D412yes—
132#92418—21no—
133#92418C22⋊Q812yes—
134#12931—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—41no—
137C22×C61C2×#10611yescharacteristic
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—81no—
145C2×D61#44811yescharacteristic
146C2×D61#48111yescharacteristic
147#6923—161no—
148#6923—161no—
149C4×C61—21no—
150C4×C61#38511yescharacteristic
151C4×C61#42811yescharacteristic
152Dic61—21no—
153Dic61#45011yescharacteristic
154Dic61#48311yescharacteristic
155C2×#430—611no—
156C2×#365—612no—
157C2×#349—611no—
158#1809—611no—
159#1387—612no—
160C2×C61—21no—
161C2×C61—41no—
162C2×C61#185311yescharacteristic
163D61—21no—
164D61—41no—
165D61#223811yescharacteristic
166D61#223911yescharacteristic
167C22×M16—611no—
168C22×M16—1221no—
169C2×M32—612no—
170#430—1222no—
171#430—1222no—
172C2×#108—612no—
173C2×#108—1221no—
174C2×#107—611no—
175C2×#106—611no—
176#380—1221no—
177#365—1222no—
178#365—1222no—
179#349—611no—
180#349—612no—
181#349#692311yescharacteristic, complemented
182#340—1221no—
183C61#1293111yescharacteristic, complemented, Sylow
184C23×C4—611no—
185C2×M16—611no—
186C2×M16—611no—
187C2×M16—611no—
188C2×M16—1222no—
189C2×M16—1222no—
190C2×M16—1222no—
191C2×M16—1222no—
192C2×M16—1221no—
193C2×M16—1221no—
194C2×M16—2441no—
195C2×M16—2441no—
196C2×M16—2441no—
197C2×M16C2×#692311yescharacteristic
198C22×C8—611no—
199C22×C8—611no—
200C22×C8—2441no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C22⋊C4—2441no—
204M32—612no—
205M32—1222no—
206M32C2×#692312yes—
207C2×C16—1222no—
208#108—612no—
209#108—612no—
210#108—1222no—
211#108—1221no—
212#108—1221no—
213#108—1222no—
214#107—1222no—
215#106—1222no—
216#95—2441no—
217C24—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4C4⋊#692311yescharacteristic
230M16—22no—
231M16—1222no—
232M16—1222no—
233M16—1222no—
234M16—1222no—
235M16—1222no—
236M16—2442no—
237M16—2441no—
238M16—2441no—
239M16—2442no—
240C2×C8—611no—
241C2×C8—612no—
242C2×C8—612no—
243C2×C8—611no—
244C2×C8—1221no—
245C2×C8—1221no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8C4⋊#692311yescharacteristic
251C2×C8C22×#692311yescharacteristic
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C22⋊C4—4882no—
257C16—22no—
258C16—1222no—
259C23—611no—
260C23—611no—
261C23—1221no—
262C23—1221no—
263C23—2441no—
264C23—2441no—
265C23#1451984511yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—4881no—
286C2×C4—4881no—
287C2×C4—4881no—
288C2×C4#1451984511yescharacteristic
289C2×C4C2×C4⋊#692311yescharacteristic
290C8—21no—
291C8—612no—
292C8—1221no—
293C8—2442no—
294C8—2442no—
295C8D4×#692312yes—
296C22—21no—
297C22—41no—
298C22—611no—
299C22—611no—
300C22—1221no—
301C22—1221no—
302C22—1221no—
303C22—4881no—
304C22—2441no—
305C22—2441no—
306C22—2441no—
307C22C2×#1451984511yescharacteristic
308C4—21no—
309C4—611no—
310C4—611no—
311C4—1221no—
312C4—9761no—
313C4—9761no—
314C4#1684070911yescharacteristic
315C4#1684077311yescharacteristic
316C2—21no—
317C2—41no—
318C2—611no—
319C2—611no—
320C2—1221no—
321C2—2441no—
322C2#2146176911yescharacteristic
subgroupG/H
centerC2#21461769
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#349C4
socleC2×C61#1853
prime radicalC23×D61SD16
cosocleC2×C8×D61C23
hypercenter#349#6923
hypocenterC61#12931
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. D61⋊#365C2semidirect
4. #21460894C2semidirect
19. #16839544C4semidirect
20. #16839543C4semidirect
21. C61×#349C4semidirect
181. #349#6923semidirect
183. C61#12931semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4302
D61⋊#3652
#214616972
#214608942
#349×D612
#1293161