Finite Group Databasebeta

← #30605353

Subgroups — #30605353

Order 15616.

344 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462183C211yesmaximal, characteristic, complemented
2#21461743C211yesmaximal, characteristic, complemented
3#21460810C212yesmaximal, complemented
4#21460809C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6#16840766—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840651—21no—
10#16840638—21no—
11#16840638C2212yes—
12#16840309—21no—
13#16840166C411yescharacteristic
14#16840137C411yescharacteristic
15#16840107—21no—
16#16839999C2211yescharacteristic
17#16839997—21no—
18#16839995C2211yescharacteristic
19C4×D488C411yescharacteristic
20C4×#11758199—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27C2×#11758222—41no—
28C2×D488C2×C411yescharacteristic
29C2×#11758199—21no—
30C2×C8×D61D411yescharacteristic
31C2×C8×D61C2311yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519752—21no—
36#14519750—41no—
37#14519748—21no—
38C4×D244—21no—
39C4×C22⋊D61—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59#11758222—84no—
60C2×D244—21no—
61C2×D244—41no—
62C2×C4×D61—41no—
63C2×C4×D61SD1611yescharacteristic
64C2×C4×D61SD1611yescharacteristic
65C2×C4×D61C2×D411yescharacteristic
66C2×Dic122—41no—
67C2×#92420—42no—
68#11758213—42no—
69#11758213—42no—
70D8×C61—41no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22×C411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C42×C61C22⋊C411yescharacteristic
76C22⋊Dic61—41no—
77#11758199—42no—
78#11758198—41no—
79#11758198—41no—
80C4⋊Dic61—21no—
81#11758196—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61D811yescharacteristic
84C4×Dic61D811yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87D488—41no—
88C8×D61—41no—
89C8×D61—41no—
90#11758187—42no—
91C23×C61—41no—
92C22×D61—41no—
93C22×D61C2×SD1611yescharacteristic
94D4×C61—41no—
95D4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—82no—
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61#10211yescharacteristic
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C22⋊D61—82no—
102C22⋊D61—82no—
103C22⋊D61—82no—
104C2×Dic61—41no—
105C2×Dic61#10211yescharacteristic
106C2×Dic61#10211yescharacteristic
107C2×Dic61C2×D811yescharacteristic
108D244—41no—
109D244—41no—
110D244—82no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—41no—
115C4×D61—82no—
116Dic122—82no—
117#92420—82no—
118C8×C61—21no—
119C8×C61—21no—
120#92418—21no—
121#92418—21no—
122#11864—611nomaximal, Sylow
123C22×C61—81no—
124C22×C61—81no—
125C22×C61—81no—
126C22×C61C2×#10211yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—81no—
133C4×C61—21no—
134C4×C61—81no—
135C4×C61#36112yes—
136C4×C61#41011yescharacteristic
137C4×C61#42111yescharacteristic
138Dic61—21no—
139Dic61—21no—
140Dic61—21no—
141Dic61—81no—
142#3169—611no—
143#2163—611no—
144#1837—611no—
145#1349—612no—
146#1349—612no—
147C2×C61—161no—
148C2×C61#151711yescharacteristic
149C2×C61#214311yescharacteristic
150C2×C61C2×#36111yescharacteristic
151D61—41no—
152D61—161no—
153#532—1221no—
154#500—611no—
155#493—611no—
156#486—1221no—
157#466—611no—
158#466—611no—
159#466—1221no—
160C4×D8—611no—
161C4×D8—1221no—
162C4×D8#692311yescharacteristic
163#423—1221no—
164C2×C4×C8—611no—
165C4⋊C16—1221no—
166C22⋊C16—612no—
167#346—1221no—
168#341—612no—
169#341—1221no—
170C61#1186411yescharacteristic, complemented, Sylow
171C2×#41—2441no—
172C2×D8—611no—
173C2×D8—1221no—
174C2×D8C2×#692311yescharacteristic
175C2×M16—1222no—
176C22×C8—611no—
177C22×C8—611no—
178C4⋊Q8—1221no—
179#127—1221no—
180#124—2441no—
181#121—1221no—
182#121—1221no—
183#121—2441no—
184C4×D4—21no—
185C4×D4—1221no—
186C4×D4—2441no—
187C2×C42—611no—
188C2×C16—1222no—
189#107—611no—
190#107—1221no—
191#107C2×#692311yescharacteristic
192C4⋊C8—2441no—
193C4⋊C8—2441no—
194#102—21no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198C4×C8—611no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8C2×#692311yescharacteristic
202#41—4884no—
203C2×Q8—2441no—
204C2×D4—21no—
205C2×D4—1221no—
206C2×D4—2441no—
207C2×D4—2441no—
208C2×D4—2441no—
209C2×D4—2441no—
210C22×C4—41no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—2441no—
215D8—41no—
216D8—2441no—
217D8—2442no—
218M16—2442no—
219M16—2442no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—2441no—
223C2×C8—2441no—
224C2×C8—2442no—
225C2×C8C22⋊#692311yescharacteristic
226C2×C8C22×#692311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—1221no—
229C4⋊C4—2441no—
230C22⋊C4—41no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42C22⋊#692311yescharacteristic
238C16—2442no—
239C23—41no—
240C23—611no—
241C23—2441no—
242Q8—4882no—
243D4—41no—
244D4—41no—
245D4—4882no—
246D4—4882no—
247D4—4882no—
248D4—4882no—
249D4—2441no—
250D4—2441no—
251C2×C4—41no—
252C2×C4—82no—
253C2×C4—611no—
254C2×C4—611no—
255C2×C4—611no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—4882no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451983911yescharacteristic
263C2×C4#1451983911yescharacteristic
264C2×C4C2×C22⋊#692311yescharacteristic
265C8—21no—
266C8—21no—
267C8—1221no—
268C8—1221no—
269C8—4882no—
270C22—81no—
271C22—81no—
272C22—81no—
273C22—1221no—
274C22—1221no—
275C22—1221no—
276C22—4881no—
277C22—4881no—
278C22—4881no—
279C22C2×#1451983911yescharacteristic
280C4—21no—
281C4—81no—
282C4—1221no—
283C4—1221no—
284C4—1221no—
285C4—4881no—
286C4#1684068012yes—
287C4#1684074111yescharacteristic
288C4#1684075911yescharacteristic
289C2—161no—
290C2—9761no—
291C2—2441no—
292C2#2146124911yescharacteristic
293C2#2146213311yescharacteristic
294C2C2×#1684068011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#21456395C2
cosocleC2×C8×D61C23
hypercenterC4×D8#6923
hypocenterC61#11864
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462183C2semidirect
2. #21461743C2semidirect
3. #21460810C2semidirect
4. #21460809C2semidirect
170. C61#11864semidirect

Maximal subgroups

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

subgroupindex
#214621832
#214617432
#214608102
#214608092
#214563952
#1186461