Finite Group Databasebeta

← #29584836

Subgroups — #29584836

Order 15616.

330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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#21445830C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic
3#21444211C211yesmaximal, characteristic
4#21443716C211yesmaximal, characteristic, complemented
5#21443679C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#1571C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839815C2211yescharacteristic
10#16839786C2211yescharacteristic
11C2×#14519699—21no—
12C2×#14519693—21no—
13#16839628C2211yescharacteristic
14#16839530—21no—
15#16839525—21no—
16#16839491—22no—
17C61×#431C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×#335—22no—
21C22×D244D411yescharacteristic
22C22×C4×D61—21no—
23C2×#11758194—21no—
24C4×D244—21no—
25C4×D244—21no—
26C4×D244—21no—
27C4×D244—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×#11758198—21no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34#14519699—42no—
35#14519693—42no—
36C22⋊#92418—21no—
37C4×#92418—21no—
38#14519684—21no—
39#14519684—21no—
40C2×M16×C61—21no—
41C22×C8×C61—21no—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—21no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C4⋊C8×C61—21no—
48C22⋊C8×C61—21no—
49C4×C8×C61D412yes—
50C23×D61—21no—
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61#4111yescharacteristic
53C22×C4×C61#4111yescharacteristic
54C22×Dic61—21no—
55C22×Dic61—41no—
56C2×D244—21no—
57C2×D244—21no—
58C2×D244—21no—
59C2×D244—21no—
60C2×D244—21no—
61C2×D244D812yes—
62C2×C4×D61—41no—
63C2×C4×D61—41no—
64C2×C4×D61—82no—
65M16×C61—41no—
66M16×C61—41no—
67C2×C8×C61—22no—
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C42×C61C2×D411yescharacteristic
73C42×C61#4111yescharacteristic
74C42×C61#4111yescharacteristic
75C42×C61#4111yescharacteristic
76#11758198—41no—
77#11758198—41no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82#11758194—41no—
83#11758194—41no—
84C2×#92418—41no—
85C2×#92418—41no—
86C23×C61#12311yescharacteristic
87C22×D61—22no—
88C22×D61—41no—
89C22×D61—41no—
90C22×D61—81no—
91C22×D61—81no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#12111yescharacteristic
95C2×C4×C61#12311yescharacteristic
96C2×C4×C61#12311yescharacteristic
97C2×C4×C61#12411yescharacteristic
98C2×C4×C61#12611yescharacteristic
99C2×C4×C61#12611yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61#13511yescharacteristic
102C2×C4×C61#13711yescharacteristic
103C2×C4×C61#13711yescharacteristic
104C2×Dic61—41no—
105C2×Dic61—81no—
106C2×Dic61—81no—
107C2×Dic61—81no—
108C2×Dic61—81no—
109D244—22no—
110D244—22no—
111D244—41no—
112D244—41no—
113C4×D61—82no—
114C4×D61—82no—
115C8×C61—42no—
116C8×C61—81no—
117C8×C61—81no—
118#92418—81no—
119#92418—81no—
120#10637—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#39711yescharacteristic
124C22×C61#48011yescharacteristic
125C22×C61#48511yescharacteristic
126C2×D61—42no—
127C2×D61—82no—
128C2×D61—81no—
129C2×D61—81no—
130C2×D61—82no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61#46611yescharacteristic
136C4×C61#47011yescharacteristic
137C4×C61#48011yescharacteristic
138C4×C61#48511yescharacteristic
139Dic61—81no—
140Dic61—161no—
141#1804—611no—
142#1800—611no—
143#1571D6111yescharacteristic, complemented
144#1478—611no—
145#1301—611no—
146#1286—611no—
147#1286—611no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61#207511yescharacteristic
151C2×C61#208011yescharacteristic
152C2×C61#208111yescharacteristic
153D61—82no—
154C2×C4×D4—611no—
155#431—611no—
156#431C2×D6111yescharacteristic
157#423—611no—
158#423C2×D6111yescharacteristic
159C2×C4⋊C8C2×D6111yescharacteristic
160C2×#102—1221no—
161C2×#100—1221no—
162#382—611no—
163#343—1221no—
164#340—1221no—
165#335—22no—
166D4⋊C8—1222no—
167C61#1063711yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C23×C4—1221no—
170C2×M16—21no—
171C2×M16—1221no—
172C22×C8—21no—
173C4×D4—1221no—
174C4×D4—1221no—
175C4×D4—1221no—
176C4×D4—1221no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C22⋊C4—1221no—
180C2×C42C22×D6111yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189#102—2442no—
190#100—2442no—
191C22⋊C8—21no—
192C22⋊C8—1221no—
193C4×C8—1221no—
194C4×C8C22⋊D6112yes—
195#95—1221no—
196#95—1221no—
197C24—1221no—
198C2×D4—612no—
199C2×D4—1221no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—1221no—
204C22×C4—1221no—
205C22×C4—4882no—
206C22×C4—2441no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4#1175822211yescharacteristic
210C22×C4D4×D6111yescharacteristic
211C22×C4#1175822611yescharacteristic
212M16—41no—
213M16—41no—
214M16—2441no—
215M16—2441no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—2441no—
222C2×C8—2441no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42#1175822211yescharacteristic
230C42#1175822411yescharacteristic
231C42#1175822611yescharacteristic
232C42C2×C22⋊D6111yescharacteristic
233C23—1222no—
234C23—4881no—
235C23—4881no—
236C23—2441no—
237C23—2441no—
238C23#1451976211yescharacteristic
239D4—1222no—
240D4—1222no—
241D4—2441no—
242D4—2441no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—4882no—
246C2×C4—4882no—
247C2×C4—4881no—
248C2×C4—4881no—
249C2×C4—4881no—
250C2×C4—4881no—
251C2×C4—2441no—
252C2×C4#1451974811yescharacteristic
253C2×C4#1451976011yescharacteristic
254C2×C4#1451976211yescharacteristic
255C2×C4#1451976611yescharacteristic
256C2×C4#1451977211yescharacteristic
257C2×C4#1451977211yescharacteristic
258C2×C4D8×D6111yescharacteristic
259C2×C4#1451979611yescharacteristic
260C2×C4#1451980911yescharacteristic
261C2×C4#1451980911yescharacteristic
262C8—42no—
263C8—81no—
264C8—81no—
265C8—4881no—
266C8—4881no—
267C22—21no—
268C22—21no—
269C22—4882no—
270C22—4882no—
271C22—4881no—
272C22—4881no—
273C22—2442no—
274C22#1683968811yescharacteristic
275C22#1684007711yescharacteristic
276C22#1684010511yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—9761no—
282C4—4881no—
283C4#1683999511yescharacteristic
284C4#1684001711yescharacteristic
285C4#1684007711yescharacteristic
286C4#1684010511yescharacteristic
287C2—21no—
288C2—21no—
289C2—4882no—
290C2#2144724311yescharacteristic
291C2#2144727011yescharacteristic
292C2#2144727711yescharacteristic
subgroupG/H
centerC22#16839688
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1571C2
socleC22×C61#397
prime radicalC22×D244D4
hypercenter#1571D61
hypocenterC61#10637
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
4. #21443716C2semidirect
5. #21443679C2semidirect
6. #21443678C2semidirect
7. C61×#1571C2semidirect
143. #1571D61semidirect
167. C61#10637semidirect

Maximal subgroups

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

subgroupindex
#214458302
#214458082
#214442112
#214437162
#214436792
#214436782
C61×#15712
#1063761