Finite Group Databasebeta

← #30599166

Subgroups — #30599166

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⋊#335C211yesmaximal, characteristic
3#21461336C212yesmaximal
4#21460688C212yesmaximal
5#21454750C211yesmaximal, characteristic
6C2×#14519848—21no—
7C2×#14519847—21no—
8#16840767C2212yes—
9D61⋊(C4⋊C8)C2212yes—
10#16840626—21no—
11#16840625—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—21no—
115C4×D61—21no—
116C4×D61—41no—
117C4×D61C2×SD1611yescharacteristic
118C4×D61C2×Q1611yescharacteristic
119C4×D61AGL(1,ℤ/8)11yescharacteristic
120C4×D61#13711yescharacteristic
121Dic122—41no—
122Dic122—41no—
123Dic122—41no—
124#92420—82no—
125#92420—82no—
126C8×C61—21no—
127C8×C61—41no—
128C8×C61#10312yes—
129#92418—21no—
130#92418—41no—
131#92418#10312yes—
132#8685—611nomaximal, Sylow
133C22×C61#38011yescharacteristic
134C2×D61—21no—
135C2×D61—21no—
136C2×D61#47511yescharacteristic
137C2×D61#47711yescharacteristic
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61C2×#10311yescharacteristic
143C4×C61#41711yescharacteristic
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61#46011yescharacteristic
148Dic61#46211yescharacteristic
149Dic61#47211yescharacteristic
150Dic61#47311yescharacteristic
151#2960—611no—
152#1848—611no—
153C2×#335—611no—
154#1550—612no—
155#1292—612no—
156C2×C61#180311yescharacteristic
157C2×C61#181311yescharacteristic
158C2×C61#181611yescharacteristic
159D61—21no—
160D61—21no—
161#533—611no—
162#446—611no—
163#446—1221no—
164#446#692311yescharacteristic
165C8×Q8—611no—
166C8×Q8—611no—
167C8×Q8—1221no—
168C2×#108—1221no—
169C2×#108—1221no—
170#424—1221no—
171#423—611no—
172#423—612no—
173C2×C4⋊C8—612no—
174#405—1221no—
175C2×C4×C8—611no—
176#335—1221no—
177#335—1221no—
178#333—1222no—
179#332—1222no—
180C61#868511yescharacteristic, complemented, Sylow
181C2×M16—1221no—
182C2×M16—1222no—
183C22×C8—611no—
184C22×C8—611no—
185C22×C8—1222no—
186C4⋊Q8—611no—
187C4⋊Q8—611no—
188#125—1221no—
189C22⋊Q8—611no—
190C22⋊Q8—611no—
191C22⋊Q8—1221no—
192C4×Q8—611no—
193C4×Q8—1221no—
194C4×Q8C2×#692311yescharacteristic
195#117—1221no—
196C2×C42—611no—
197#108—2442no—
198#108—2442no—
199C4⋊C8—21no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202C4⋊C8—1221no—
203C4⋊C8—1222no—
204C4⋊C8—1222no—
205C4⋊C8—1222no—
206C4⋊C8—1222no—
207C4⋊C8—1221no—
208C4⋊C8—1221no—
209C4⋊C8C2×#692311yescharacteristic
210#97—21no—
211#97—1221no—
212C4×C8—611no—
213C4×C8—611no—
214C4×C8—611no—
215C4×C8—1221no—
216C4×C8—1221no—
217C4×C8C2×#692311yescharacteristic
218C2×Q8—611no—
219C2×Q8—1221no—
220C2×Q8C4⋊#692311yescharacteristic
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224M16—2441no—
225M16—2441no—
226M16—2442no—
227M16—2442no—
228C2×C8—21no—
229C2×C8—611no—
230C2×C8—612no—
231C2×C8—612no—
232C2×C8—611no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—1221no—
236C2×C8—4882no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8C22⋊#692311yescharacteristic
240C2×C8C22⋊#692311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—611no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4C4⋊#692311yescharacteristic
250C22⋊C4—1221no—
251C22⋊C4—1221no—
252C42—21no—
253C42—611no—
254C42—611no—
255C42—611no—
256C42—1221no—
257C42C22×#692311yescharacteristic
258C23—611no—
259Q8—41no—
260Q8—2441no—
261Q8—2441no—
262Q8—2441no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—2441no—
277C2×C4C2×C22⋊#692311yescharacteristic
278C2×C4C2×C4⋊#692311yescharacteristic
279C2×C4#1451985611yescharacteristic
280C8—21no—
281C8—41no—
282C8—612no—
283C8—1221no—
284C8—4882no—
285C8—4882no—
286C8—2441no—
287C8#1451984012yes—
288C22—611no—
289C22—611no—
290C22—1221no—
291C22—1221no—
292C22#1684070411yescharacteristic
293C4—21no—
294C4—21no—
295C4—41no—
296C4—41no—
297C4—611no—
298C4—611no—
299C4—611no—
300C4—611no—
301C4—1221no—
302C4—2441no—
303C4—2441no—
304C4C2×#1451984011yescharacteristic
305C4#1684075311yescharacteristic
306C2—1221no—
307C2—1221no—
308C2#2146168811yescharacteristic
309C2#2146170411yescharacteristic
310C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radicalC22×D61C22⋊Q8
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8685
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
180. C61#8685semidirect

Maximal subgroups

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

subgroupindex
#214617592
D61⋊#3352
#214613362
#214606882
#214547502
#868561