Finite Group Databasebeta

← #30608421

Subgroups — #30608421

Order 15616.

334 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 56 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
1D61⋊#355C211yesmaximal, characteristic
2D61⋊#354C211yesmaximal, characteristic
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460965C211yesmaximal, characteristic, complemented
6#21460964C211yesmaximal, characteristic, complemented
7#21456202C211yesmaximal, characteristic
8D61⋊#101—21no—
9D61⋊#99—21no—
10#16840671C2211yescharacteristic
11#16840671C2211yescharacteristic
12#16840670—21no—
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840668—21no—
16#16840318C411yescharacteristic, complemented
17#124×D61C2211yescharacteristic
18#16840123—21no—
19#16840120—21no—
20#16840119C2211yescharacteristic
21#16840117C2211yescharacteristic
22#16840116C411yescharacteristic, complemented
23#16839769—21no—
24#16839765—21no—
25C4×#11758189C411yescharacteristic, complemented
26C61×#488C411yescharacteristic, complemented
27D61⋊M16—41no—
28C2×C22⋊#6923—41no—
29#14519838—21no—
30#14519838—21no—
31#14519838—41no—
32#14519836—21no—
33#14519836—21no—
34#14519835—41no—
35C2×Q8×D61D411yescharacteristic
36C2×D4×D61D411yescharacteristic
37C2×#11758189—21no—
38#14519776—21no—
39#14519769C2×C411yescharacteristic, complemented
40#14519766D411yescharacteristic
41#14519765C2311yescharacteristic
42#14519764D411yescharacteristic
43#14519763—41no—
44#14519755—41no—
45#14519742—41no—
46#14519735—21no—
47C22⋊C4×D61—41no—
48C42×D61C2×C411yescharacteristic
49#14519702—21no—
50#14519701—21no—
51#14519700—21no—
52#14519699—21no—
53#14519698—21no—
54#14519697—21no—
55#14519687—21no—
56C4×#92418C2×C411yescharacteristic, complemented
57#125×C61C2×C411yescharacteristic, complemented
58#124×C61C2×C411yescharacteristic
59#103×C61—21no—
60#102×C61—21no—
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C22×#6923—81no—
64C2×Q8×C61C22⋊C411yescharacteristic
65C2×D4×C61C22⋊C411yescharacteristic
66C2×C22⋊D61—21no—
67Q8×D61—41no—
68Q8×D61—41no—
69D4×D61—41no—
70D4×D61—41no—
71C2×D244C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×Dic122—21no—
76C2×Dic122—41no—
77C2×Dic122C2×D411yescharacteristic
78C22⋊#6923—41no—
79C22⋊#6923—41no—
80C22⋊#6923—81no—
81#11758217—41no—
82#11758217—41no—
83#11758213—81no—
84D61⋊C8—81no—
85C2×C8×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61C22×C411yescharacteristic
90C22⋊Dic61—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—21no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61C22⋊C411yescharacteristic
100C2×#92418—21no—
101#11758189—41no—
102#11758189—41no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—82no—
108C22×D61#9911yescharacteristic
109C2×#6923—81no—
110C2×#6923—81no—
111C2×#6923—162no—
112Q8×C61—41no—
113D4×C61—41no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61C2×C22⋊C411yescharacteristic
118C22⋊D61—81no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61#9911yescharacteristic
123D244—41no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—41no—
127C4×D61—41no—
128C4×D61—81no—
129Dic122—41no—
130Dic122—81no—
131Dic122—82no—
132#92420—81no—
133#92420—81no—
134C8×C61—41no—
135#92418—41no—
136#13603—611nomaximal, Sylow
137C22×C61—41no—
138C22×C61—81no—
139C22×C61C2×#9911yescharacteristic
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—82no—
143C2×D61—81no—
144C2×D61—161no—
145C2×D61#35411yescharacteristic
146C2×D61#35411yescharacteristic
147#6923—161no—
148#6923—161no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153Dic61—21no—
154Dic61—41no—
155Dic61—41no—
156Dic61—81no—
157#3140—611no—
158C2×#355—611no—
159C2×#354—611no—
160#1414—611no—
161#1414—611no—
162#1414—611no—
163#1414—611no—
164C2×C61—21no—
165C2×C61—81no—
166C2×C61C2×#35411yescharacteristic
167D61—21no—
168D61—21no—
169D61—81no—
170#533—611no—
171C2×#124—611no—
172#489—1221no—
173#489—1221no—
174#488—611no—
175#488—611no—
176#488—611no—
177#488#692311yescharacteristic, complemented
178#419—1221no—
179#418—1221no—
180C2×#101—1221no—
181C2×#99—1221no—
182C4×M16—611no—
183#355—611no—
184#355—611no—
185#355—1221no—
186#354—611no—
187#354—611no—
188#354—1221no—
189C61#1360311yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C22×D4—611no—
192C2×M16—1221no—
193C2×M16—2441no—
194C4⋊Q8—1221no—
195#125—611no—
196#125C2×#692311yescharacteristic, complemented
197#124—611no—
198#124—611no—
199#124—611no—
200#124—2441no—
201#124C2×#692311yescharacteristic
202C22⋊Q8—2441no—
203C4×Q8—2441no—
204#117—1221no—
205C2×C22⋊C4—2441no—
206C2×C22⋊C4—2441no—
207C2×C42—611no—
208#103—21no—
209#103—1221no—
210#103—1221no—
211#103—1221no—
212#102—21no—
213#102—1221no—
214#102—1221no—
215#102—1221no—
216#101—1221no—
217#101—1221no—
218#101—2441no—
219#99—1221no—
220#99—1221no—
221#99—2441no—
222#97—1221no—
223C4×C8—611no—
224C4×C8C2×#692311yescharacteristic, complemented
225C24—1221no—
226C2×Q8—611no—
227C2×Q8—1221no—
228C2×Q8—2441no—
229C2×Q8—2441no—
230C2×Q8—2441no—
231C2×Q8C22⋊#692311yescharacteristic
232C2×D4—611no—
233C2×D4—1221no—
234C2×D4—2441no—
235C2×D4—2441no—
236C2×D4C22⋊#692311yescharacteristic
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—4881no—
241M16—4881no—
242M16—2441no—
243M16—2441no—
244M16—2441no—
245M16—2441no—
246C2×C8—21no—
247C2×C8—1221no—
248C2×C8—4881no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—1221no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C22⋊C4—41no—
255C22⋊C4—4881no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C42—611no—
263C42—1221no—
264C42—2441no—
265C42C22×#692311yescharacteristic
266C23—21no—
267C23—611no—
268C23—1221no—
269C23—4882no—
270C23—2441no—
271C23—2441no—
272Q8—41no—
273Q8—4881no—
274Q8—4882no—
275Q8—2441no—
276D4—41no—
277D4—4881no—
278D4—2441no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—611no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—9762no—
288C2×C4—4881no—
289C2×C4—4881no—
290C2×C4—4881no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4C2×C22⋊#692311yescharacteristic
295C8—41no—
296C8—4881no—
297C8—4881no—
298C8—2441no—
299C22—41no—
300C22—81no—
301C22—611no—
302C22—611no—
303C22—9761no—
304C22—4881no—
305C22—4882no—
306C22—2441no—
307C22—2441no—
308C22D61⋊#9911yescharacteristic
309C4—21no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—1221no—
314C4—9761no—
315C4—9761no—
316C4—4881no—
317C4—2441no—
318C4—2441no—
319C2—21no—
320C2—81no—
321C2—1221no—
322C2—1221no—
323C2—4881no—
324C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#488C4
socleC2×C61C2×#354
prime radicalC2×D4×D61D4
cosocle#14519765C23
hypercenter#488#6923
hypocenterC61#13603
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
3. #21460967C2semidirect
4. #21460966C2semidirect
5. #21460965C2semidirect
6. #21460964C2semidirect
16. #16840318C4semidirect
22. #16840116C4semidirect
25. C4×#11758189C4semidirect
26. C61×#488C4semidirect
39. #14519769C2×C4semidirect
56. C4×#92418C2×C4semidirect
57. #125×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
177. #488#6923semidirect
189. C61#13603semidirect
196. #125C2×#6923semidirect
224. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3552
D61⋊#3542
#214609672
#214609662
#214609652
#214609642
#214562022
#1360361