Finite Group Databasebeta

← #29593549

Subgroups — #29593549

Order 15616.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448074C211yesmaximal, characteristic, complemented
2#21447864C211yesmaximal, characteristic, complemented
3#21445189C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic, complemented
7C61×#3391C211yesmaximal, characteristic
8C2×#14519721—22no—
9C2×#14519721—21no—
10#16840142C2211yescharacteristic
11#16840047—21no—
12C4⋊#11758185C2211yescharacteristic
13#16839565—21no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17C61×#550—21no—
18C61×#493—21no—
19C61×#493C2211yescharacteristic
20C61×#459—22no—
21C61×#459—21no—
22C8×Q8×C61C2211yescharacteristic
23C4×D8×C61—21no—
24C4×D8×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27#14519777—21no—
28#14519721—44no—
29#14519721—42no—
30C2×#11758185—21no—
31C2×#11758185—21no—
32#14519708—41no—
33C4⋊#92418—21no—
34#14519701—41no—
35C2×#41×C61—41no—
36C2×D8×C61—22no—
37C2×D8×C61—21no—
38C2×D8×C61D411yescharacteristic
39C2×D8×C61D412yes—
40#127×C61—22no—
41#127×C61—21no—
42#121×C61—42no—
43#121×C61—41no—
44C4×Q8×C61D411yescharacteristic
45C4×D4×C61—22no—
46C4×D4×C61—21no—
47#107×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#102×C61—22no—
51#102×C61—21no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54#41×C61—82no—
55#41×C61—82no—
56C2×Q8×C61D811yescharacteristic
57C2×D4×C61—21no—
58C2×D4×C61—22no—
59C2×D4×C61—42no—
60C2×D4×C61—42no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—42no—
64C22×C4×C61—41no—
65C2×Dic122—41no—
66D8×C61—21no—
67D8×C61—21no—
68D8×C61—42no—
69D8×C61—41no—
70D8×C61—41no—
71D8×C61—82no—
72C2×C8×C61—21no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61D811yescharacteristic
78C22⋊C4×C61—42no—
79C22⋊C4×C61—41no—
80C42×C61—21no—
81C42×C61C2×D411yescharacteristic
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C2×#92418—41no—
85Dic244—42no—
86Dic244—41no—
87Dic244—41no—
88#11758185—22no—
89#11758185—41no—
90C23×C61—42no—
91C23×C61—41no—
92Q8×C61—21no—
93Q8×C61SD3212yescomplemented
94D4×C61—41no—
95D4×C61—42no—
96D4×C61—42no—
97D4×C61—41no—
98D4×C61—84no—
99D4×C61—81no—
100D4×C61—81no—
101D4×C61—161no—
102D4×C61—162no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—84no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61C2×D811yescharacteristic
111C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
112C2×Dic61—81no—
113Dic122—81no—
114Dic122—81no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61#13511yescharacteristic
118C8×C61AGL(1,ℤ/8)11yescharacteristic
119#92418—81no—
120#12332—611nomaximal, Sylow
121C22×C61—81no—
122C22×C61—82no—
123C22×C61—82no—
124C22×C61—81no—
125C22×C61—82no—
126C22×C61—81no—
127C22×C61#44711yescharacteristic
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61—81no—
132C4×C61#44911yescharacteristic
133C4×C61#45311yescharacteristic
134C4×C61C2×SD3211yescharacteristic
135C4×C61#50911yescharacteristic
136Dic61—161no—
137#3391D6111yescharacteristic
138#2248—611no—
139#2208—611no—
140#1670—611no—
141#1361—611no—
142Q8⋊C16—611no—
143#1331—611no—
144C2×C61—161no—
145C2×C61—162no—
146C2×C61#162111yescharacteristic
147C2×C61#218711yescharacteristic
148C2×C61#219411yescharacteristic
149#550—21no—
150C2×SD32—1221no—
151C2×SD32—1222no—
152#494—611no—
153#493—21no—
154#493C2×D6111yescharacteristic
155#475—1221no—
156#459—22no—
157#459—21no—
158C8×Q8C2×D6111yescharacteristic
159C4×D8—21no—
160C4×D8C2×D6111yescharacteristic
161C4⋊C16—611no—
162#358—1221no—
163C4×C16—611no—
164#335—611no—
165#332—1221no—
166C61#1233211yescharacteristic, complemented, Sylow
167C2×#41—41no—
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×D8—22no—
171C2×D8—21no—
172C2×D8C22⋊D6111yescharacteristic
173C2×D8C22⋊D6112yes—
174C4⋊Q8—1221no—
175#127—22no—
176#127—21no—
177#121—42no—
178#121—41no—
179C4×Q8C22⋊D6111yescharacteristic
180C4×D4—22no—
181C4×D4—21no—
182SD32—2444no—
183SD32—2442no—
184C2×C16—1221no—
185C2×C16—1221no—
186#107C22⋊D6111yescharacteristic
187#106—2441no—
188C4⋊C8—21no—
189C4⋊C8—1221no—
190C4⋊C8C22⋊D6111yescharacteristic
191#103—2441no—
192#102—22no—
193#102—21no—
194C4×C8—21no—
195C4×C8C22×D6111yescharacteristic
196#41—82no—
197#41—82no—
198C2×Q8—2441no—
199C2×Q8#1175819911yescharacteristic
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—42no—
207C22×C4—41no—
208Q16—2442no—
209Q16—2441no—
210Q16—2441no—
211D8—21no—
212D8—21no—
213D8—42no—
214D8—41no—
215D8—41no—
216D8—82no—
217C2×C8—21no—
218C2×C8—2441no—
219C2×C8C2×C22⋊D6111yescharacteristic
220C2×C8C2×C22⋊D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4#1175819911yescharacteristic
226C22⋊C4—42no—
227C22⋊C4—41no—
228C42—21no—
229C42C2×C22⋊D6111yescharacteristic
230C16—1222no—
231C16—2441no—
232C23—42no—
233C23—41no—
234Q8—21no—
235Q8—4881no—
236Q8—4881no—
237Q8#1451972112yescomplemented
238D4—41no—
239D4—42no—
240D4—42no—
241D4—41no—
242D4—84no—
243D4—81no—
244D4—81no—
245D4—161no—
246D4—162no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—4881no—
254C2×C4#1451974611yescharacteristic
255C2×C4C2×#1175819911yescharacteristic
256C2×C4#1451980311yescharacteristic
257C8—21no—
258C8—41no—
259C8—4881no—
260C8#1451979711yescharacteristic
261C8#1451980211yescharacteristic
262C22—81no—
263C22—82no—
264C22—82no—
265C22—81no—
266C22—82no—
267C22—81no—
268C22#1683989611yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—81no—
273C4—9761no—
274C4#1683990711yescharacteristic
275C4#1683993011yescharacteristic
276C4C2×#1451972111yescharacteristic
277C4#1684019811yescharacteristic
278C2—161no—
279C2—162no—
280C2#2144488411yescharacteristic
281C2#2144774811yescharacteristic
282C2#2144779011yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#3391C2
socleC22×C61#447
hypercenter#3391D61
hypocenterC61#12332
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. #21448074C2semidirect
2. #21447864C2semidirect
3. #21445189C2semidirect
4. #21443865C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443780C2semidirect
93. Q8×C61SD32semidirect
166. C61#12332semidirect
237. Q8#14519721semidirect

Maximal subgroups

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

subgroupindex
#214480742
#214478642
#214451892
#214438652
Q8⋊#117581852
#214437802
C61×#33912
#1233261