Finite Group Databasebeta

← #30599162

Subgroups — #30599162

Order 15616.

362 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461759C211yesmaximal, characteristic
2D61⋊#334C211yesmaximal, characteristic
3#21461336C212yesmaximal
4#21460688C212yesmaximal
5#21454750C211yesmaximal, characteristic
6C2×#14519848—21no—
7C2×#14519847—21no—
8#16840767C2212yes—
9D61⋊(C4⋊C8)C2212yes—
10#16840624—21no—
11#16840623—21no—
12#16840622—22no—
13#16840621—22no—
14#16840316C2211yescharacteristic
15#16839892C411yescharacteristic
16#16839890—21no—
17Q8×#92418C411yescharacteristic
18#16839886—21no—
19#16839886C411yescharacteristic
20#16839787—21no—
21#16839784C2211yescharacteristic
22#16839719—21no—
23C4×C8×D61C2211yescharacteristic
24C61×#446C411yescharacteristic
25C2×#11758213—22no—
26C2×D61⋊C8—22no—
27#14519848—42no—
28#14519847—42no—
29#14519844—22no—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C2×#11758189—21no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36#14519776D411yescharacteristic
37#14519775D411yescharacteristic
38#14519767—21no—
39#14519757Q811yescharacteristic
40#14519755—21no—
41#14519753Q811yescharacteristic
42C4×Dic122—21no—
43C4×Dic122C2×C411yescharacteristic
44#14519734—21no—
45C42×D61C2311yescharacteristic
46C4⋊#92418—21no—
47C4⋊#92418C2×C411yescharacteristic
48#14519706—21no—
49#14519706—21no—
50#14519706—21no—
51#14519687—21no—
52C4×#92418—21no—
53C4×#92418C2×C411yescharacteristic
54C8×Dic61—21no—
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C4×Q8×C61C2×C411yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61C2×C411yescharacteristic
60#97×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61C4⋊C411yescharacteristic
63C2×C4×D61C2×D411yescharacteristic
64C2×C4×D61C2×Q811yescharacteristic
65C2×C4×D61#4111yescharacteristic
66C2×Dic122—21no—
67C2×Dic122C4⋊C411yescharacteristic
68C2×#92420—42no—
69C2×#92420—42no—
70#11758213—42no—
71#11758213—42no—
72D61⋊C8—82no—
73C2×C8×C61—21no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22⋊C411yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61C4⋊C411yescharacteristic
78C42×C61—21no—
79C42×C61C22×C411yescharacteristic
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61C4⋊C411yescharacteristic
84#11758196—21no—
85#11758196—21no—
86#11758196—21no—
87#11758196—21no—
88#11758196—21no—
89C4×Dic61—21no—
90C4×Dic61C2×D411yescharacteristic
91C4×Dic61C2×D411yescharacteristic
92C4×Dic61#4111yescharacteristic
93C2×#92418—21no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C22⋊C411yescharacteristic
96#11758189—41no—
97#11758189—41no—
98C8×D61—21no—
99C8×D61—21no—
100C8×D61SD1612yes—
101C8×D61Q1612yes—
102C22×D61C22⋊Q811yescharacteristic
103Q8×C61—41no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C2×C4⋊C411yescharacteristic
108C2×C4×C61#11711yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61#12111yescharacteristic
112C2×Dic61#12111yescharacteristic
113C2×Dic61C22⋊Q811yescharacteristic
114C4×D61—22no—
115C4×D61—41no—
116C4×D61C2×SD1611yescharacteristic
117C4×D61C2×Q1611yescharacteristic
118C4×D61AGL(1,ℤ/8)11yescharacteristic
119C4×D61#13711yescharacteristic
120Dic122—42no—
121Dic122—41no—
122#92420—82no—
123#92420—82no—
124C8×C61—21no—
125C8×C61—41no—
126C8×C61#10312yes—
127#92418—21no—
128#92418—41no—
129#92418#10312yes—
130#8683—611nomaximal, Sylow
131C22×C61#38011yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61#47511yescharacteristic
135C2×D61#47711yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61C2×#10311yescharacteristic
141C4×C61#41711yescharacteristic
142Dic61—21no—
143Dic61—41no—
144Dic61—41no—
145Dic61#46011yescharacteristic
146Dic61#46211yescharacteristic
147Dic61#47112yes—
148#2960—611no—
149#1848—611no—
150C2×#334—611no—
151#1550—612no—
152#1292—612no—
153C2×C61#180311yescharacteristic
154C2×C61#181311yescharacteristic
155C2×C61#181511yescharacteristic
156D61—21no—
157D61—21no—
158#533—611no—
159#446—611no—
160#446—1221no—
161#446#692311yescharacteristic
162C8×Q8—611no—
163C8×Q8—611no—
164C8×Q8—1221no—
165C2×#108—1221no—
166C2×#108—1221no—
167#424—1221no—
168#423—611no—
169#423—612no—
170C2×C4⋊C8—612no—
171#405—1221no—
172C2×C4×C8—611no—
173#334—1221no—
174#334—1221no—
175#333—1222no—
176#332—1222no—
177C61#868311yescharacteristic, complemented, Sylow
178C2×M16—1221no—
179C2×M16—1222no—
180C22×C8—611no—
181C22×C8—611no—
182C22×C8—1222no—
183C4⋊Q8—611no—
184C4⋊Q8—611no—
185#125—1221no—
186C22⋊Q8—611no—
187C22⋊Q8—611no—
188C22⋊Q8—1221no—
189C4×Q8—611no—
190C4×Q8—1221no—
191C4×Q8C2×#692311yescharacteristic
192#117—1221no—
193C2×C42—611no—
194#108—2442no—
195#108—2442no—
196C4⋊C8—21no—
197C4⋊C8—611no—
198C4⋊C8—1221no—
199C4⋊C8—1221no—
200C4⋊C8—1222no—
201C4⋊C8—1222no—
202C4⋊C8—1222no—
203C4⋊C8—1222no—
204C4⋊C8—1221no—
205C4⋊C8—1221no—
206C4⋊C8C2×#692311yescharacteristic
207#97—21no—
208#97—1221no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8—611no—
212C4×C8—1221no—
213C4×C8—1221no—
214C4×C8C2×#692311yescharacteristic
215C2×Q8—611no—
216C2×Q8—1221no—
217C2×Q8C4⋊#692311yescharacteristic
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221M16—2441no—
222M16—2441no—
223M16—2442no—
224M16—2442no—
225C2×C8—21no—
226C2×C8—611no—
227C2×C8—612no—
228C2×C8—612no—
229C2×C8—611no—
230C2×C8—1221no—
231C2×C8—1221no—
232C2×C8—1221no—
233C2×C8—4882no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8C22⋊#692311yescharacteristic
237C2×C8C22⋊#692311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—611no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4C4⋊#692311yescharacteristic
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C42—21no—
250C42—611no—
251C42—611no—
252C42—611no—
253C42—1221no—
254C42C22×#692311yescharacteristic
255C23—611no—
256Q8—41no—
257Q8—2441no—
258Q8—2442no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—2441no—
272C2×C4C2×C22⋊#692311yescharacteristic
273C2×C4C2×C4⋊#692311yescharacteristic
274C2×C4#1451985611yescharacteristic
275C8—21no—
276C8—41no—
277C8—612no—
278C8—1221no—
279C8—4882no—
280C8—4882no—
281C8—2441no—
282C8#1451984012yes—
283C22—611no—
284C22—611no—
285C22—1221no—
286C22—1221no—
287C22#1684070411yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—611no—
293C4—611no—
294C4—612no—
295C4—1221no—
296C4—2441no—
297C4—2441no—
298C4C2×#1451984011yescharacteristic
299C4#1684075311yescharacteristic
300C2—1221no—
301C2—1221no—
302C2#2146168811yescharacteristic
303C2#2146170411yescharacteristic
304C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radicalC22×D61C22⋊Q8
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8683
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
177. C61#8683semidirect

Maximal subgroups

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

subgroupindex
#214617592
D61⋊#3342
#214613362
#214606882
#214547502
#868361