Finite Group Databasebeta

← #29600384

Subgroups — #29600384

Order 15616.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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#21456140C211yesmaximal, characteristic
2#21447501C211yesmaximal, characteristic
3#21447483C211yesmaximal, characteristic
4#21443995C211yesmaximal, characteristic, complemented
5#21443994C211yesmaximal, characteristic, complemented
6#21443993C211yesmaximal, characteristic, complemented
7C61×#1414C211yesmaximal, characteristic, complemented
8#16840318C411yescharacteristic, complemented
9#16840311C2211yescharacteristic
10#16840119C411yescharacteristic, complemented
11#16840117C411yescharacteristic, complemented
12#16840116C2211yescharacteristic
13#16840111—21no—
14#16840107—21no—
15#16839757—21no—
16#16839755—21no—
17#16839745—21no—
18#16839734—21no—
19C4×C8×D61C411yescharacteristic, complemented
20#16839560—21no—
21#16839559C2211yescharacteristic
22#16839557C2211yescharacteristic
23#16839554—21no—
24C61×#488C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×#11758226D411yescharacteristic
28C2×#11758224D411yescharacteristic
29M16×D61—41no—
30C2×C8×D61—21no—
31#14519776—21no—
32#14519775D411yescharacteristic
33#14519773D411yescharacteristic
34#14519769C2×C411yescharacteristic
35#14519765C2×C411yescharacteristic
36#14519755—41no—
37#14519750—41no—
38#14519742—41no—
39#14519737—41no—
40#14519735—21no—
41#14519733—41no—
42C42×D61C2×C411yescharacteristic
43#14519702—21no—
44#14519701—21no—
45#14519700—21no—
46#14519699—21no—
47#14519698—21no—
48#14519697—21no—
49#14519696—21no—
50#14519693—41no—
51#14519692—21no—
52#14519691—41no—
53C4×#92418C2×C411yescharacteristic
54C8×Dic61—21no—
55#125×C61C2×C411yescharacteristic
56#124×C61C2311yescharacteristic
57#103×C61—21no—
58#102×C61—21no—
59#101×C61—21no—
60#99×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61C2×D411yescharacteristic
63C2×D4×C61C2×D411yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—41no—
66C22×Dic61—21no—
67#11758226—41no—
68#11758226—41no—
69#11758224—41no—
70#11758224—41no—
71C2×D244—21no—
72C2×D244C22⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C22⋊C411yescharacteristic
76C2×Dic122—41no—
77C2×Dic122C22⋊C411yescharacteristic
78M16×C61—41no—
79C2×C8×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C42×C61C22×C411yescharacteristic
85C22⋊Dic61—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—21no—
89#11758196—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—81no—
93C4×Dic61—21no—
94C4×Dic61—41no—
95C4×Dic61—81no—
96C4×Dic61C22⋊C411yescharacteristic
97#11758194—41no—
98C2×#92418—21no—
99#11758189—81no—
100C8×D61—41no—
101C8×D61—41no—
102C8×D61—81no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61#9911yescharacteristic
106Q8×C61—41no—
107D4×C61—41no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—81no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C22⋊D61—82no—
114C22⋊D61—81no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—81no—
121C2×Dic61#9911yescharacteristic
122D244—41no—
123D244—81no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—42no—
127C4×D61—41no—
128C4×D61—41no—
129Dic122—41no—
130Dic122—82no—
131C8×C61—41no—
132C8×C61—81no—
133#92418—41no—
134#92418—81no—
135#13602—611nomaximal, Sylow
136C22×C61—41no—
137C22×C61—81no—
138C22×C61C2×#9911yescharacteristic
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—81no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61—161no—
148Dic61—22no—
149Dic61—41no—
150Dic61—81no—
151Dic61—161no—
152Dic61#35411yescharacteristic
153Dic61#35411yescharacteristic
154#3131—611no—
155#2132—611no—
156#2126—611no—
157#1414—611no—
158#1414—611no—
159#1414—611no—
160#1414D6111yescharacteristic, complemented
161C2×C61—21no—
162C2×C61—81no—
163C2×C61C2×#35411yescharacteristic
164D61—41no—
165D61—81no—
166#533—611no—
167#532—611no—
168#488—611no—
169#488—611no—
170#488—611no—
171#488C2×D6111yescharacteristic
172#487—1221no—
173#486—1221no—
174#416—1221no—
175#416—1221no—
176#413—1221no—
177#410—1221no—
178C2×C4×C8—611no—
179#356—1221no—
180#355—611no—
181#355C2×D6111yescharacteristic
182#354—611no—
183#354C2×D6111yescharacteristic
184#353—1221no—
185C61#1360211yescharacteristic, complemented, Sylow
186C2×#41—611no—
187C2×#41—611no—
188C2×M16—2441no—
189C22×C8—1221no—
190C4⋊Q8—611no—
191C4⋊Q8—1221no—
192#127—611no—
193#125—611no—
194#125C4×D6111yescharacteristic
195#124—611no—
196#124C22×D6111yescharacteristic
197C22⋊Q8—2441no—
198#121—2441no—
199C4×Q8—2441no—
200C4×D4—2441no—
201#117—1221no—
202#117—2441no—
203C2×C42—611no—
204#103—21no—
205#103—1221no—
206#103—1221no—
207#103—1221no—
208#102—21no—
209#102—1221no—
210#102—1221no—
211#102—1221no—
212#101—21no—
213#101—1221no—
214#100—2441no—
215#99—21no—
216#99—1221no—
217#99—2441no—
218C4×C8—611no—
219C4×C8—1221no—
220C4×C8C4×D6111yescharacteristic
221#41—2441no—
222#41—2441no—
223#41—2441no—
224#41—2441no—
225C2×Q8—611no—
226C2×Q8—2441no—
227C2×Q8D4×D6111yescharacteristic
228C2×D4—611no—
229C2×D4—1221no—
230C2×D4—1221no—
231C2×D4—2441no—
232C2×D4D4×D6111yescharacteristic
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237M16—41no—
238M16—4881no—
239M16—2441no—
240C2×C8—21no—
241C2×C8—1221no—
242C2×C8—4881no—
243C2×C8—2441no—
244C2×C8—2441no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—1221no—
248C4⋊C4—4881no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—2441no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C42—611no—
258C42—1221no—
259C42—4881no—
260C42—2441no—
261C42C2×C4×D6111yescharacteristic
262C23—21no—
263C23—611no—
264C23—1221no—
265Q8—41no—
266Q8—4882no—
267Q8—2441no—
268D4—41no—
269D4—4881no—
270D4—4882no—
271D4—4881no—
272D4—2441no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—611no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—4881no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2442no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4C22⋊C4×D6111yescharacteristic
290C8—41no—
291C8—81no—
292C8—4881no—
293C8—2441no—
294C22—41no—
295C22—81no—
296C22—1221no—
297C22—4881no—
298C22—2441no—
299C22—2441no—
300C22#99×D6111yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—161no—
306C4—611no—
307C4—611no—
308C4—1222no—
309C4—9761no—
310C4—4881no—
311C4—2441no—
312C2—21no—
313C2—81no—
314C2—4881no—
315C2—2441no—
316C2#354×D6111yescharacteristic
subgroupG/H
centerC2#354×D61
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1414C2
socleC2×C61C2×#354
prime radical#16840311C22
cosocle#124×C61C23
hypercenter#1414D61
hypocenterC61#13602
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1414

Complements

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

NH ≅ G/Ntype
4. #21443995C2semidirect
5. #21443994C2semidirect
6. #21443993C2semidirect
7. C61×#1414C2semidirect
8. #16840318C4semidirect
10. #16840119C4semidirect
11. #16840117C4semidirect
19. C4×C8×D61C4semidirect
160. #1414D61semidirect
185. C61#13602semidirect

Maximal subgroups

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

subgroupindex
#214561402
#214475012
#214474832
#214439952
#214439942
#214439932
C61×#14142
#1360261