Finite Group Databasebeta

← #29593487

Subgroups — #29593487

Order 15616.

374 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457539C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic, complemented
4#21445185C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840415—21no—
10C2×#14519723—22no—
11C2×#14519722—21no—
12#16840142C2211yescharacteristic
13#16840043—21no—
14#16840000—21no—
15#16839964—21no—
16#16839923—22no—
17C4×D488C2211yescharacteristic
18C8×D244C2211yescharacteristic
19#16839567—21no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×#11758201—22no—
31C2×D488D411yescharacteristic
32C2×C8×D61—21no—
33#14519777—21no—
34#14519762—42no—
35#14519753—22no—
36#14519752—41no—
37C4×D244—21no—
38C4×D244D411yescharacteristic
39C4⋊C4×D61—41no—
40#14519723—44no—
41#14519722—42no—
42C2×#11758185—21no—
43#14519711—41no—
44#14519711D411yescharacteristic
45C4⋊#92418D411yescharacteristic
46#14519701—22no—
47#14519699—21no—
48#14519699—41no—
49#14519689—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61D412yes—
52C4⋊Q8×C61—21no—
53C2×C16×C61—21no—
54C4⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—22no—
57#11758226—44no—
58#11758226—82no—
59C2×D244—21no—
60C2×D244—42no—
61C2×D244D811yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—42no—
64C2×C4×D61—41no—
65C2×Dic122—41no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61C2×D411yescharacteristic
75#11758201—44no—
76#11758198—21no—
77#11758198—42no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61D811yescharacteristic
83#11758196—42no—
84C2×#92418—21no—
85Dic244—42no—
86Dic244—41no—
87Dic244—41no—
88D488—21no—
89D488D812yes—
90C8×D61—41no—
91C8×D61—41no—
92C16×C61—41no—
93#11758185—22no—
94C22×D61—21no—
95C22×D61—41no—
96Q8×C61—42no—
97Q8×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—81no—
105D244—22no—
106D244—21no—
107D244—21no—
108D244—41no—
109D244—84no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—84no—
113C4×D61—81no—
114C4×D61—81no—
115Dic122—81no—
116Dic122—81no—
117C8×C61—21no—
118C8×C61—81no—
119C8×C61C2×D811yescharacteristic
120C8×C61AGL(1,ℤ/8)11yescharacteristic
121#92418—41no—
122#12323—611nomaximal, Sylow
123C22×C61#44711yescharacteristic
124C2×D61—41no—
125C2×D61—42no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—81no—
129C2×D61—81no—
130C4×C61—21no—
131C4×C61—82no—
132C4×C61#44711yescharacteristic
133C4×C61#45311yescharacteristic
134C4×C61#50811yescharacteristic
135C4×C61#51011yescharacteristic
136Dic61—41no—
137Dic61—81no—
138Dic61—161no—
139#3283—611no—
140#2247—611no—
141#2208—611no—
142#1669—611no—
143#1362D6111yescharacteristic, complemented
144#1331—611no—
145D4⋊C16—611no—
146C2×C61#161911yescharacteristic
147C2×C61#218911yescharacteristic
148C2×C61#219511yescharacteristic
149D61—81no—
150D61—82no—
151C2×#135—1221no—
152#547—1221no—
153C2×Q32—1222no—
154C2×SD32—1221no—
155#494—611no—
156#494C2×D6111yescharacteristic
157#474—1221no—
158#467—1221no—
159#461—1221no—
160#452—1222no—
161C4×D8—611no—
162C8×D4—611no—
163C4⋊C16C2×D6111yescharacteristic
164#358—1221no—
165C4×C16—611no—
166#335C2×D6111yescharacteristic
167#332—1221no—
168C61#1232311yescharacteristic, complemented, Sylow
169C2×#41—1222no—
170#135—2442no—
171#135—2442no—
172C2×Q16—21no—
173C2×Q16—1221no—
174C2×Q16—1221no—
175C2×Q16D24412yes—
176C2×SD16—1222no—
177C2×D8—611no—
178C22×C8—1221no—
179C4⋊Q8—21no—
180C4⋊Q8—1221no—
181#123—2442no—
182C22⋊Q8—1222no—
183#121—2441no—
184C4×D4—611no—
185C4×D4—1221no—
186C2×C4⋊C4—2441no—
187Q32—2444no—
188SD32—2442no—
189C2×C16—21no—
190C2×C16—1221no—
191#107—611no—
192#107—2441no—
193C4⋊C8—21no—
194C4⋊C8—611no—
195#103—1222no—
196#102—1221no—
197#102—2441no—
198C22⋊C8—1221no—
199C4×C8C22×D6111yescharacteristic
200#41—4882no—
201#41—2444no—
202C2×Q8—22no—
203C2×Q8—2441no—
204C2×D4—611no—
205C2×D4—1221no—
206C2×D4—2442no—
207C22×C4—1221no—
208C22×C4—2442no—
209C22×C4—2441no—
210Q16—42no—
211Q16—41no—
212Q16—41no—
213Q16—2442no—
214Q16—2441no—
215Q16—2441no—
216SD16—2444no—
217D8—612no—
218D8—1221no—
219C2×C8—41no—
220C2×C8—1221no—
221C2×C8—2441no—
222C2×C8—2441no—
223C2×C8C2×D24411yescharacteristic
224C2×C8D4×D6111yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—2442no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—1221no—
233C22⋊C4—2442no—
234C22⋊C4—2441no—
235C42D4×D6111yescharacteristic
236C16—41no—
237C16—1222no—
238C23—1221no—
239C23—2441no—
240Q8—42no—
241Q8—42no—
242Q8—4881no—
243Q8—4881no—
244D4—1221no—
245D4—1221no—
246D4—1222no—
247D4—4884no—
248D4—2441no—
249C2×C4—42no—
250C2×C4—1221no—
251C2×C4—4884no—
252C2×C4—4881no—
253C2×C4—4881no—
254C2×C4—4881no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4#1451974711yescharacteristic
259C2×C4D8×D6111yescharacteristic
260C2×C4#1451980411yescharacteristic
261C8—21no—
262C8—81no—
263C8—2441no—
264C8D8×D6111yescharacteristic
265C8#1451980411yescharacteristic
266C22—4881no—
267C22—4881no—
268C22—2442no—
269C22—2441no—
270C22—2441no—
271C22—2441no—
272C22#1683989711yescharacteristic
273C4—21no—
274C4—82no—
275C4—9761no—
276C4—4881no—
277C4—2441no—
278C4#1683989711yescharacteristic
279C4#1683993211yescharacteristic
280C4#1684019311yescharacteristic
281C4#1684020411yescharacteristic
282C2—4882no—
283C2—4881no—
284C2#2144487411yescharacteristic
285C2#2144776211yescharacteristic
286C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radical#21457539C2
hypercenter#1362D61
hypocenterC61#12323
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448071C2semidirect
3. #21447865C2semidirect
4. #21445185C2semidirect
5. #21443779C2semidirect
6. #21443773C2semidirect
7. C61×#1362C2semidirect
143. #1362D61semidirect
168. C61#12323semidirect

Maximal subgroups

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

subgroupindex
#214575392
#214480712
#214478652
#214451852
#214437792
#214437732
C61×#13622
#1232361