Finite Group Databasebeta

← #29593484

Subgroups — #29593484

Order 15616.

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

normal subgroups only

This group has 374 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#21457541C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic, complemented
3#21447861C211yesmaximal, characteristic, complemented
4#21443867C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1669C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840417—21no—
10C2×#14519723—22no—
11C2×#14519720—21no—
12#16840142C2211yescharacteristic
13#16840003—21no—
14#16839968—21no—
15#16839926—22no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19C4×#11758185C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×#474—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#332—21no—
25C2×#11758222—22no—
26#14519799—42no—
27#14519799—42no—
28C2×Dic244—21no—
29C2×Dic244D412yes—
30C2×#11758190—22no—
31C2×D488D411yescharacteristic
32#14519777—21no—
33#14519759—42no—
34#14519756—22no—
35#14519748—41no—
36C4×D244—21no—
37C4⋊C4×D61—41no—
38#14519723—44no—
39#14519720—42no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519702—22no—
44#14519699—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C22×C8×C61—21no—
48C4⋊Q8×C61—21no—
49C4×D4×C61D411yescharacteristic
50#107×C61—41no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61D411yescharacteristic
53#102×C61—41no—
54C22⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—41no—
57C2×D4×C61D811yescharacteristic
58C22×C4×C61—21no—
59C2×C22⋊D61—42no—
60#11758222—44no—
61#11758222—82no—
62C2×D244—21no—
63C2×C4×D61—42no—
64C2×C4×D61—41no—
65C2×Dic122—22no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61D811yescharacteristic
78C22⋊C4×C61—21no—
79C42×C61C2×D411yescharacteristic
80C22⋊Dic61—42no—
81#11758198—41no—
82C4⋊Dic61—21no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85#11758196—42no—
86Dic244—42no—
87Dic244—41no—
88Dic244—41no—
89D488—21no—
90D488D812yes—
91#11758190—44no—
92#11758185—22no—
93#11758185—41no—
94C23×C61—21no—
95C22×D61—41no—
96Q8×C61—81no—
97Q8×C61—81no—
98D4×C61—21no—
99D4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—81no—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61C2×D811yescharacteristic
106C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
107C22⋊D61—84no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110D244—22no—
111D244—41no—
112C4×D61—84no—
113C4×D61—81no—
114C4×D61—81no—
115Dic122—42no—
116Dic122—42no—
117C8×C61—21no—
118C8×C61—41no—
119C8×C61—81no—
120C8×C61C2×D811yescharacteristic
121C8×C61AGL(1,ℤ/8)11yescharacteristic
122#12323—611nomaximal, Sylow
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61#44711yescharacteristic
127C2×D61—42no—
128C2×D61—81no—
129C2×D61—81no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—161no—
133C4×C61#44711yescharacteristic
134C4×C61#45311yescharacteristic
135C4×C61#50811yescharacteristic
136C4×C61#51011yescharacteristic
137Dic61—82no—
138Dic61—81no—
139#3283—611no—
140#2247—611no—
141#2208—611no—
142#1669D6111yescharacteristic, complemented
143#1362—611no—
144#1331—611no—
145D4⋊C16—611no—
146C2×C61—81no—
147C2×C61#161911yescharacteristic
148C2×C61#218911yescharacteristic
149C2×C61#219511yescharacteristic
150D61—82no—
151C2×#135—1221no—
152#547—1221no—
153C2×Q32—1222no—
154C2×SD32—1221no—
155#494—611no—
156#494C2×D6111yescharacteristic
157#474—21no—
158#467—1221no—
159#461—1221no—
160#452—1222no—
161C4×D8—611no—
162C8×D4C2×D6111yescharacteristic
163C4⋊C16—611no—
164#358—1221no—
165C4×C16—611no—
166#335C2×D6111yescharacteristic
167#332—21no—
168C61#1232311yescharacteristic, complemented, Sylow
169C2×#41—1222no—
170#135—2442no—
171#135—2442no—
172C2×Q16—21no—
173C2×Q16—21no—
174C2×Q16—612no—
175C2×Q16—1221no—
176C2×SD16—1222no—
177C2×D8—611no—
178C22×C8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—1221no—
181#123—2442no—
182C22⋊Q8—1222no—
183#121—2441no—
184C4×D4—1221no—
185C4×D4C22⋊D6111yescharacteristic
186C2×C4⋊C4—2441no—
187Q32—2444no—
188SD32—2442no—
189C2×C16—1221no—
190C2×C16—1221no—
191#107—41no—
192#107—611no—
193C4⋊C8—21no—
194C4⋊C8C22⋊D6111yescharacteristic
195#103—1222no—
196#102—41no—
197#102—1221no—
198C22⋊C8—21no—
199C4×C8C22×D6111yescharacteristic
200#41—4882no—
201#41—2444no—
202C2×Q8—41no—
203C2×Q8—1222no—
204C2×D4—1221no—
205C2×D4—2442no—
206C2×D4#1175819911yescharacteristic
207C22×C4—21no—
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—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8D4×D6111yescharacteristic
224C2×C8D4×D6111yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—1221no—
228C4⋊C4—2442no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4#1175819911yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—2442no—
234C22⋊C4—2441no—
235C42C2×C22⋊D6111yescharacteristic
236C16—1222no—
237C16—2441no—
238C23—21no—
239C23—2441no—
240Q8—81no—
241Q8—81no—
242Q8—2442no—
243Q8—2442no—
244D4—21no—
245D4—21no—
246D4—1222no—
247D4—4884no—
248D4—2441no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—4884no—
254C2×C4—4881no—
255C2×C4—4881no—
256C2×C4—2441no—
257C2×C4—2442no—
258C2×C4#1451974511yescharacteristic
259C2×C4C2×#1175819911yescharacteristic
260C2×C4#1451980211yescharacteristic
261C8—21no—
262C8—41no—
263C8—81no—
264C8D8×D6111yescharacteristic
265C8#1451980111yescharacteristic
266C22—41no—
267C22—41no—
268C22—41no—
269C22—4881no—
270C22—4881no—
271C22—2442no—
272C22#1683989511yescharacteristic
273C4—21no—
274C4—41no—
275C4—161no—
276C4—4882no—
277C4—4881no—
278C4#1683989411yescharacteristic
279C4#1683992811yescharacteristic
280C4#1684019211yescharacteristic
281C4#1684020311yescharacteristic
282C2—81no—
283C2—4882no—
284C2#2144487211yescharacteristic
285C2#2144775711yescharacteristic
286C2#2144779511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1669C2
socleC22×C61#447
prime radical#21457541C2
hypercenter#1669D61
hypocenterC61#12323
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1669

Complements

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

NH ≅ G/Ntype
2. #21448071C2semidirect
3. #21447861C2semidirect
4. #21443867C2semidirect
5. #21443779C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1669C2semidirect
142. #1669D61semidirect
168. C61#12323semidirect

Maximal subgroups

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

subgroupindex
#214575412
#214480712
#214478612
#214438672
#214437792
D4⋊#117581852
C61×#16692
#1232361