Finite Group Databasebeta

← #30602007

Subgroups — #30602007

Order 15616.

466 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462011C212yesmaximal
2#21461373C211yesmaximal, characteristic
3#21461332C212yesmaximal
4#21461028C211yesmaximal, characteristic
5C2×#16840140C211yesmaximal, characteristic
6#16840779C2211yescharacteristic
7#16840765C2212yes—
8C4×#11758217C2211yescharacteristic
9#16840642—24no—
10#16840624—21no—
11#16840623—21no—
12#16840622—24no—
13#92420⋊C8—21no—
14#16840603—21no—
15C22×Dic244C411yescharacteristic
16C22×#11758202C412yes—
17C2×#14519775C2212yes—
18#16840140—21no—
19#16840140—21no—
20#16840140—21no—
21#16840140—21no—
22C2×C8×Dic61C2211yescharacteristic
23C22×Q16×C61C411yescharacteristic
24C2×#11758217—22no—
25C2×#11758217D412yes—
26#14519844—22no—
27#14519844D412yes—
28C4⋊#92420—22no—
29C22⋊#92420—21no—
30#14519832—21no—
31C4×#92420—21no—
32C4×#92420—21no—
33C22×Dic122C2×C412yes—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244—42no—
37C2×#11758202—22no—
38C2×#11758202—22no—
39C2×#11758202—44no—
40C22×#92418C2×C411yescharacteristic
41#14519775—22no—
42#14519775—22no—
43#14519775—22no—
44#14519775—22no—
45C2×#11758196—22no—
46C2×#11758196—22no—
47C2×C4×Dic61C2311yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C22×Q8×C61C2×C412yes—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—42no—
56C22×C8×C61C2×C411yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61—42no—
60C2×Q8×C61—42no—
61C22×C4×C61—22no—
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61#4111yescharacteristic
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70#11758217—24no—
71#11758217—44no—
72C2×#92420—22no—
73C2×#92420—22no—
74C2×#92420—42no—
75Q16×C61—42no—
76Q16×C61—42no—
77C2×C8×C61—22no—
78C2×C8×C61C22⋊C411yescharacteristic
79C2×C8×C61C22⋊C411yescharacteristic
80#11758202—44no—
81#11758202—44no—
82#11758196—42no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61C2×D411yescharacteristic
87C4×Dic61C2×D411yescharacteristic
88C4×Dic61C2×D411yescharacteristic
89C4×Dic61#4111yescharacteristic
90C2×#92418—22no—
91C2×#92418C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93Dic244—42no—
94Dic244—42no—
95C23×C61C4×D411yescharacteristic
96Q8×C61—42no—
97Q8×C61—42no—
98Q8×C61—82no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—42no—
102C2×C4×C61—82no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61C4×D411yescharacteristic
105C2×Dic61—22no—
106C2×Dic61—42no—
107C2×Dic61—82no—
108C2×Dic61#12111yescharacteristic
109C2×Dic61#12111yescharacteristic
110C2×Dic61#12411yescharacteristic
111C2×Dic61#12711yescharacteristic
112C2×Dic61#13714yes—
113Dic122—42no—
114Dic122—42no—
115Dic122—82no—
116#92420—42no—
117#92420—42no—
118#92420—82no—
119C8×C61—21no—
120C8×C61#10012yes—
121#92418—21no—
122#92418#10012yes—
123#9807—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61#39011yescharacteristic
127C22×C61#44112yes—
128C4×C61—21no—
129C4×C61—82no—
130C4×C61C2×#10011yescharacteristic
131C4×C61C2×#10011yescharacteristic
132Dic61—21no—
133Dic61—82no—
134Dic61#47012yes—
135Dic61#47312yes—
136Dic61#49712yes—
137C2×#494—611no—
138#1997—612no—
139#1566—611no—
140#1548—612no—
141#1451—611no—
142C2×C61—22no—
143C2×C61#196511yescharacteristic
144C2×C61#197111yescharacteristic
145C2×C61#197911yescharacteristic
146C22×Q16—612no—
147C22×Q16—611no—
148C22×Q16#692311yescharacteristic
149C2×C4⋊Q8—612no—
150#494—1221no—
151#494—1221no—
152#494—1221no—
153#494—1221no—
154#431—611no—
155#423—612no—
156C4×M16—611no—
157C2×C4×C8—611no—
158#343—1224no—
159#334—1221no—
160#334—1221no—
161#333—1224no—
162#322—1221no—
163#322—1221no—
164C61#980711yescharacteristic, complemented, Sylow
165C22×Q8—612no—
166C22×Q8C2×#692312yes—
167C2×Q16—21no—
168C2×Q16—21no—
169C2×Q16—42no—
170C2×Q16—1222no—
171C2×Q16—1222no—
172C2×Q16—1221no—
173C2×Q16—1221no—
174C2×Q16—2442no—
175C2×Q16—2444no—
176C2×M16—612no—
177C2×M16—1222no—
178C22×C8—611no—
179C22×C8C2×#692311yescharacteristic
180C4⋊Q8—1222no—
181C4⋊Q8—1222no—
182C4⋊Q8—1222no—
183C4⋊Q8—1222no—
184C2×C4⋊C4—1222no—
185C2×C4⋊C4—1222no—
186C2×C42—611no—
187C4⋊C8—612no—
188C4⋊C8—1222no—
189C4⋊C8—1222no—
190C22⋊C8—1221no—
191#97—1221no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8—1221no—
197C4×C8—1221no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—1222no—
203C2×Q8—1222no—
204C2×Q8—2442no—
205C2×Q8—2442no—
206C22×C4—22no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1222no—
210C22×C4C22×#692311yescharacteristic
211Q16—42no—
212Q16—42no—
213Q16—2442no—
214Q16—2444no—
215Q16—2444no—
216Q16—2442no—
217M16—1224no—
218M16—2444no—
219C2×C8—22no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—1222no—
223C2×C8—1222no—
224C2×C8—1222no—
225C2×C8—2442no—
226C2×C8C22⋊#692311yescharacteristic
227C2×C8C22⋊#692311yescharacteristic
228C4⋊C4—2442no—
229C4⋊C4—2442no—
230C4⋊C4—2442no—
231C4⋊C4—2442no—
232C42—611no—
233C42—611no—
234C42—611no—
235C42—611no—
236C23D4×#692311yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—82no—
240Q8—4882no—
241Q8—2442no—
242Q8—2442no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—82no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—614no—
251C2×C4—611no—
252C2×C4—1222no—
253C2×C4—4882no—
254C2×C4—2442no—
255C2×C4C2×C22⋊#692311yescharacteristic
256C2×C4D4×#692311yescharacteristic
257C8—21no—
258C8—612no—
259C8—1221no—
260C8—4882no—
261C8—2442no—
262C8—2442no—
263C8#1451983712yes—
264C22—21no—
265C22—21no—
266C22#1684071411yescharacteristic
267C22#1684080212yes—
268C4—21no—
269C4—82no—
270C4—612no—
271C4—612no—
272C4—612no—
273C4—1221no—
274C4—4882no—
275C4C2×#1451983711yescharacteristic
276C4D61⋊#10011yescharacteristic
277C2—22no—
278C2#2146196111yescharacteristic
279C2#2146196711yescharacteristic
280C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×Q16×C61C4
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC22×Q16#6923
hypocenterC61#9807
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
164. C61#9807semidirect

Maximal subgroups

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

subgroupindex
#214620112
#214613732
#214613322
#214610282
C2×#168401402
#980761