Finite Group Databasebeta

← #29593476

Subgroups — #29593476

Order 15616.

368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457569C211yesmaximal, characteristic
2#21447866C211yesmaximal, characteristic, complemented
3#21445181C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic
7C61×#2247C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9#16840427—21no—
10C2×#14519723—21no—
11#16840039—21no—
12#16840000—21no—
13#16839969—21no—
14#16839916—22no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C2×Q32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#494C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244D411yescharacteristic
27C2×#11758202—22no—
28Q16×D61—42no—
29Q16×D61—42no—
30C2×C8×D61—21no—
31#14519776—41no—
32#14519755—42no—
33#14519753—22no—
34C4×Dic122—21no—
35C4×D244D411yescharacteristic
36#14519739—41no—
37#14519723—42no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40#14519710—41no—
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519702—21no—
44#14519701—22no—
45#14519697—41no—
46#14519689—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61—21no—
50C2×Q16×C61D412yes—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53Q32×C61—44no—
54C2×C16×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—22no—
57C2×Q8×C61—41no—
58Q8×D61—44no—
59Q8×D61—82no—
60C2×D244D811yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—42no—
63C2×Dic122—21no—
64C2×Dic122—42no—
65Q16×C61—42no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69Q16×C61—41no—
70Q16×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758202—44no—
79#11758198—21no—
80#11758198—42no—
81C4⋊Dic61—21no—
82C4⋊Dic61D811yescharacteristic
83#11758196—42no—
84#11758196—41no—
85C4×Dic61—41no—
86C2×#92418—21no—
87C2×#92418—41no—
88Dic244—21no—
89Dic244D812yes—
90C8×D61—41no—
91C8×D61—41no—
92C16×C61—22no—
93#11758185—41no—
94C22×D61—21no—
95Q8×C61—42no—
96Q8×C61—42no—
97Q8×C61—81no—
98Q8×C61—81no—
99C2×C4×C61—42no—
100C2×C4×C61—81no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107D244—21no—
108D244Q3212yescomplemented
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—84no—
112Dic122—22no—
113Dic122—41no—
114Dic122—84no—
115C8×C61—21no—
116C8×C61C2×D811yescharacteristic
117C8×C61AGL(1,ℤ/8)11yescharacteristic
118#92418—41no—
119#92418—81no—
120#12322—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—22no—
123C2×D61—41no—
124C2×D61—41no—
125C4×C61—21no—
126C4×C61—82no—
127C4×C61—161no—
128C4×C61#44711yescharacteristic
129C4×C61#45311yescharacteristic
130C4×C61C2×Q3211yescharacteristic
131C4×C61#51011yescharacteristic
132Dic61—42no—
133Dic61—41no—
134Dic61—81no—
135D4×Q16—611no—
136#2247D6111yescharacteristic, complemented
137#2209—611no—
138#1669—611no—
139#1362—611no—
140#1332—611no—
141D4⋊C16—611no—
142C2×C61#161911yescharacteristic
143C2×C61#218811yescharacteristic
144C2×C61#219511yescharacteristic
145D61—42no—
146C22×Q16—1221no—
147D4×Q8—1221no—
148C2×Q32—22no—
149C2×Q32—1221no—
150#494C2×D6111yescharacteristic
151#494C2×D6111yescharacteristic
152#474—1221no—
153#467—1221no—
154#462—1221no—
155#451—1222no—
156C4×Q16—611no—
157C8×D4—611no—
158C4⋊C16—611no—
159#358—1221no—
160C4×C16C2×D6111yescharacteristic
161#335—611no—
162#332—1221no—
163C61#1232211yescharacteristic, complemented, Sylow
164C22×Q8—1222no—
165C2×Q16—21no—
166C2×Q16—21no—
167C2×Q16—21no—
168C2×Q16—611no—
169C2×Q16—1222no—
170C2×Q16—2442no—
171C2×Q16—2442no—
172C2×Q16C22⋊D6112yes—
173C22×C8—1221no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—2441no—
177C22⋊Q8—1222no—
178C22⋊Q8—2442no—
179C4×Q8—1221no—
180C4×D4—611no—
181C4×D4—2441no—
182Q32—44no—
183Q32—2442no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—611no—
187#107—2441no—
188C4⋊C8—611no—
189C4⋊C8—1221no—
190#103—1222no—
191#103—1221no—
192#102—2441no—
193C22⋊C8—1221no—
194C4×C8C22×D6111yescharacteristic
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—1221no—
198C2×Q8—4882no—
199C2×Q8—2442no—
200C2×Q8—2444no—
201C2×D4—611no—
202C22×C4—1221no—
203C22×C4—2442no—
204Q16—42no—
205Q16—42no—
206Q16—41no—
207Q16—41no—
208Q16—41no—
209Q16—41no—
210Q16—612no—
211Q16—1221no—
212Q16—2444no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8D4×D6111yescharacteristic
218C2×C8C2×C22⋊D6111yescharacteristic
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4—2442no—
226C4⋊C4—2441no—
227C22⋊C4—1221no—
228C22⋊C4—2442no—
229C42—2441no—
230C42D4×D6111yescharacteristic
231C16—22no—
232C16—2441no—
233C23—1221no—
234Q8—42no—
235Q8—42no—
236Q8—81no—
237Q8—81no—
238Q8—1222no—
239Q8—4884no—
240Q8—2441no—
241D4—612no—
242D4—1221no—
243C2×C4—42no—
244C2×C4—81no—
245C2×C4—1221no—
246C2×C4—4884no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4#1451974511yescharacteristic
252C2×C4D8×D6111yescharacteristic
253C2×C4#1451980111yescharacteristic
254C8—21no—
255C8—4881no—
256C8—2441no—
257C8D8×D6111yescharacteristic
258C8#1451980111yescharacteristic
259C22—1222no—
260C22—2441no—
261C22—2441no—
262C22#1683989411yescharacteristic
263C4—21no—
264C4—82no—
265C4—161no—
266C4—4881no—
267C4—2441no—
268C4—2442no—
269C4#1683989411yescharacteristic
270C4#1683992911yescharacteristic
271C4Q32×D6111yescharacteristic
272C4#1684020411yescharacteristic
273C2—2442no—
274C2#2144487111yescharacteristic
275C2#2144775111yescharacteristic
276C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2247C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#2247D61
hypocenterC61#12322
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

Complements

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

NH ≅ G/Ntype
2. #21447866C2semidirect
4. #21443868C2semidirect
5. #21443784C2semidirect
7. C61×#2247C2semidirect
108. D244Q32semidirect
136. #2247D61semidirect
163. C61#12322semidirect

Maximal subgroups

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

subgroupindex
#214575692
#214478662
#214451812
#214438682
#214437842
#214437752
C61×#22472
#1232261