Finite Group Databasebeta

← #30604696

Subgroups — #30604696

Order 15616.

368 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462025C211yesmaximal, characteristic, complemented
2#21461373C211yesmaximal, characteristic, complemented
3#21460778C212yesmaximal, complemented
4#21460777C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840765—21no—
8#16840651C2212yes—
9#16840648—21no—
10#16840624—21no—
11#16840623C2212yes—
12#16840307—21no—
13#16840166C411yescharacteristic
14#16840137C411yescharacteristic
15#16840107—21no—
16#16839998C411yescharacteristic
17#16839996—21no—
18D8×Dic61C2211yescharacteristic
19#16839844C2211yescharacteristic
20#16839842—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758217—41no—
24#14519851—24no—
25C2×#11758187—22no—
26#14519844—41no—
27C4⋊#92420—22no—
28C2×#11758224—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C22×#92418D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519751—21no—
36#14519749—41no—
37D4×Dic61—21no—
38#14519739—21no—
39#14519737—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62C22×Dic61D811yescharacteristic
63C22×Dic61SD1611yescharacteristic
64#11758224—84no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68#11758217—82no—
69C2×#92420—42no—
70D8×C61—22no—
71C2×C8×C61—22no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22×C411yescharacteristic
74C4⋊C4×C61—21no—
75C22⋊C4×C61—41no—
76C22⋊Dic61—41no—
77#11758199—42no—
78#11758198—41no—
79#11758198—41no—
80C4⋊Dic61—21no—
81#11758196—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61D811yescharacteristic
84C4×Dic61SD1611yescharacteristic
85C4×Dic61C2×D411yescharacteristic
86C2×#92418—22no—
87C2×#92418C22⋊C411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89D488—22no—
90#11758187—24no—
91C23×C61—41no—
92C23×C61#10211yescharacteristic
93C22×D61—41no—
94D4×C61—41no—
95D4×C61—41no—
96D4×C61—82no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61#10211yescharacteristic
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C22⋊D61—82no—
103C22⋊D61—82no—
104C22⋊D61—82no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—41no—
108C2×Dic61—82no—
109C2×Dic61#10211yescharacteristic
110C2×Dic61#10211yescharacteristic
111C2×Dic61C2×D811yescharacteristic
112C2×Dic61C2×SD1611yescharacteristic
113D244—41no—
114D244—41no—
115C4×D61—82no—
116Dic122—82no—
117#92420—82no—
118C8×C61—21no—
119C8×C61#13112yes—
120#92418—21no—
121#92418#10412yes—
122#11680—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61C2×#10211yescharacteristic
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—81no—
133C4×C61—21no—
134C4×C61—81no—
135C4×C61#40811yescharacteristic
136C4×C61C2×#10411yescharacteristic
137Dic61—21no—
138Dic61—21no—
139Dic61—81no—
140Dic61#36012yes—
141Dic61#36112yes—
142#3169—611no—
143C4×M32—611no—
144#1566—611no—
145#1333—612no—
146#1333—612no—
147C2×C61—41no—
148C2×C61—161no—
149C2×C61#149211yescharacteristic
150C2×C61C2×#36011yescharacteristic
151C2×C61C2×#36111yescharacteristic
152D61—161no—
153#532—1221no—
154C2×M32—1221no—
155#500—611no—
156#493—611no—
157#486—1221no—
158#466—611no—
159#466—1221no—
160#466#692311yescharacteristic
161C4×D8—611no—
162C4×D8—611no—
163C4×D8—1221no—
164#423—1221no—
165C2×C4×C8—611no—
166#346—612no—
167C4×C16—1221no—
168#334—612no—
169#334—1221no—
170C61#1168011yescharacteristic, complemented, Sylow
171C2×#41—2441no—
172C2×D8—611no—
173C2×D8—1221no—
174C2×D8C2×#692311yescharacteristic
175C2×M16—2441no—
176C22×C8—611no—
177C22×C8C2×#692311yescharacteristic
178C4⋊Q8—1221no—
179#127—1221no—
180#124—2441no—
181#121—21no—
182#121—1221no—
183#121—2441no—
184C4×D4—1221no—
185C4×D4—1221no—
186C4×D4—2441no—
187C2×C42—611no—
188M32—1224no—
189C2×C16—1222no—
190#107—611no—
191#107—1221no—
192#107C2×#692311yescharacteristic
193C4⋊C8—1222no—
194C4⋊C8—2441no—
195#102—21no—
196#102—1221no—
197#102—1221no—
198#102—1221no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—611no—
202C4×C8—611no—
203#41—4884no—
204C2×Q8—2441no—
205C2×D4—21no—
206C2×D4—41no—
207C2×D4—1221no—
208C2×D4—2441no—
209C2×D4—2441no—
210C2×D4—2441no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—2441no—
214C22×C4—2441no—
215C22×C4C22⋊#692311yescharacteristic
216D8—22no—
217D8—1222no—
218D8—2442no—
219M16—4882no—
220C2×C8—22no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—1222no—
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—
237C42—611no—
238C16—1224no—
239C23—41no—
240C23—2441no—
241C23#1451983911yescharacteristic
242Q8—4882no—
243D4—41no—
244D4—41no—
245D4—82no—
246D4—4882no—
247D4—4882no—
248D4—4882no—
249D4—2441no—
250D4—2441no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—611no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—4882no—
261C2×C4—4882no—
262C2×C4—2441no—
263C2×C4#1451983911yescharacteristic
264C2×C4C2×C22⋊#692311yescharacteristic
265C8—21no—
266C8—612no—
267C8—1221no—
268C8—4882no—
269C8#1451986412yes—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22—4881no—
277C22—4881no—
278C22—4881no—
279C22C2×#1451983911yescharacteristic
280C4—21no—
281C4—81no—
282C4—612no—
283C4—612no—
284C4—1221no—
285C4—1221no—
286C4—4881no—
287C4#1684073511yescharacteristic
288C4D61⋊#10411yescharacteristic
289C2—41no—
290C2—161no—
291C2—9761no—
292C2#2146116411yescharacteristic
293C2D61⋊#36011yescharacteristic
294C2D61⋊#36111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#466C4
socleC22×C61C2×#102
prime radical#21456393C2
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11680
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #21462025C2semidirect
2. #21461373C2semidirect
3. #21460778C2semidirect
4. #21460777C2semidirect
170. C61#11680semidirect

Maximal subgroups

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

subgroupindex
#214620252
#214613732
#214607782
#214607772
#214563932
#1168061