Finite Group Databasebeta

← #30608425

Subgroups — #30608425

Order 15616.

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

normal subgroups only

This group has 322 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
1#21462113C211yesmaximal, characteristic
2#21462091C211yesmaximal, characteristic
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460965C211yesmaximal, characteristic, complemented
6#21460964C211yesmaximal, characteristic, complemented
7#21456216C211yesmaximal, characteristic
8#16840749—21no—
9#16840743—21no—
10#16840672—21no—
11#16840671C2211yescharacteristic
12#16840671C2211yescharacteristic
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840666—21no—
16#16840311C2211yescharacteristic
17#125×D61C411yescharacteristic, complemented
18#16840129—21no—
19#16840125—21no—
20#16840119C2211yescharacteristic
21#16840117C2211yescharacteristic
22#16840116C411yescharacteristic, complemented
23#16839762—21no—
24#16839760—21no—
25C4×#11758189C411yescharacteristic, complemented
26C61×#488C411yescharacteristic, complemented
27C2×#11758217—41no—
28#14519856—41no—
29#14519838—21no—
30#14519838—21no—
31#14519837—41no—
32#14519836—21no—
33#14519836—21no—
34#14519836—41no—
35C2×#11758226D411yescharacteristic
36C2×#11758224D411yescharacteristic
37C2×#11758189—21no—
38#14519775D411yescharacteristic
39#14519773D411yescharacteristic
40#14519769C2×C411yescharacteristic
41#14519768—21no—
42#14519767—41no—
43#14519765C2311yescharacteristic
44#14519750—41no—
45#14519737—41no—
46C4⋊C4×D61—21no—
47C4⋊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
57#125×C61C2×C411yescharacteristic
58#124×C61C2×C411yescharacteristic
59#103×C61—21no—
60#102×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61C22⋊C411yescharacteristic
63C2×D4×C61C22⋊C411yescharacteristic
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×D244C2×D411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—41no—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×Dic122C2×D411yescharacteristic
78C22⋊#6923—41no—
79C22⋊#6923—41no—
80#11758217—41no—
81#11758217—41no—
82#11758217—81no—
83C2×#92420—81no—
84C4⋊#6923—81no—
85C4×#6923—81no—
86C2×C8×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C42×C61C22×C411yescharacteristic
91#11758198—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61C22⋊C411yescharacteristic
100C2×#92418—21no—
101#11758189—41no—
102#11758189—41no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61#9911yescharacteristic
106C2×#6923—81no—
107C2×#6923—81no—
108Q8×C61—41no—
109D4×C61—41no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C22⋊D61—81no—
115C22⋊D61—82no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61#9911yescharacteristic
122D244—41no—
123D244—81no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—41no—
127C4×D61—41no—
128C4×D61—81no—
129C4×D61—82no—
130Dic122—41no—
131#92420—81no—
132#92420—81no—
133C8×C61—41no—
134#92418—41no—
135#13604—611nomaximal, Sylow
136C22×C61—41no—
137C22×C61—81no—
138C22×C61C2×#9911yescharacteristic
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—81no—
143#6923—161no—
144#6923—161no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—81no—
149Dic61—41no—
150Dic61—41no—
151Dic61—81no—
152Dic61#35411yescharacteristic
153Dic61#35411yescharacteristic
154#3142—611no—
155#2132—611no—
156#2126—611no—
157#1414—611no—
158#1414—611no—
159#1414—611no—
160#1414—611no—
161C2×C61—21no—
162C2×C61—81no—
163C2×C61C2×#35411yescharacteristic
164D61—41no—
165D61—81no—
166#532—611no—
167C2×#125—611no—
168#491—1221no—
169#490—1221no—
170#488—611no—
171#488—611no—
172#488—611no—
173#488#692311yescharacteristic, complemented
174#417—1221no—
175#417—1221no—
176#413—1221no—
177#410—1221no—
178C4×M16—611no—
179#356—1221no—
180#355—611no—
181#355—611no—
182#354—611no—
183#354—611no—
184#353—1221no—
185C61#1360411yescharacteristic, complemented, Sylow
186C2×#41—611no—
187C2×#41—611no—
188C2×M16—1221no—
189C2×M16—2441no—
190C4⋊Q8—611no—
191#127—611no—
192#125—611no—
193#125—1221no—
194#125—2441no—
195#125C2×#692311yescharacteristic
196#124—611no—
197#124C2×#692311yescharacteristic
198#121—2441no—
199C4×D4—2441no—
200#117—2441no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—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—1221no—
213#101—1221no—
214#100—2441no—
215#99—1221no—
216#99—1221no—
217#99—2441no—
218#97—1221no—
219C4×C8—611no—
220C4×C8C2×#692311yescharacteristic
221#41—2441no—
222#41—2441no—
223#41—2441no—
224#41—2441no—
225C2×Q8—611no—
226C2×Q8C22⋊#692311yescharacteristic
227C2×D4—611no—
228C2×D4—1221no—
229C2×D4—1221no—
230C2×D4—2441no—
231C2×D4C22⋊#692311yescharacteristic
232C22×C4—611no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—2441no—
237M16—4881no—
238M16—2441no—
239M16—2441no—
240M16—2441no—
241M16—2441no—
242C2×C8—21no—
243C2×C8—1221no—
244C2×C8—4881no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—1221no—
248C4⋊C4—4881no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C22⋊C4—41no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C42—611no—
259C42—1221no—
260C42—4881no—
261C42C22×#692311yescharacteristic
262C23—21no—
263C23—611no—
264C23—1221no—
265Q8—41no—
266Q8—2441no—
267D4—41no—
268D4—4881no—
269D4—4881no—
270D4—4882no—
271D4—2441no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—611no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—4881no—
281C2×C4—4882no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4C2×C22⋊#692311yescharacteristic
290C8—41no—
291C8—4881no—
292C8—4881no—
293C8—2441no—
294C22—41no—
295C22—81no—
296C22—1221no—
297C22—4881no—
298C22—2441no—
299C22—2441no—
300C22D61⋊#9911yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—611no—
306C4—611no—
307C4—9761no—
308C4—9761no—
309C4—4881no—
310C4—2441no—
311C4—2441no—
312C2—21no—
313C2—81no—
314C2—4881no—
315C2—2441no—
316C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#488C4
socleC2×C61C2×#354
prime radical#16840311C22
cosocle#14519765C23
hypercenter#488#6923
hypocenterC61#13604
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
17. #125×D61C4semidirect
22. #16840116C4semidirect
25. C4×#11758189C4semidirect
26. C61×#488C4semidirect
173. #488#6923semidirect
185. C61#13604semidirect

Maximal subgroups

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

subgroupindex
#214621132
#214620912
#214609672
#214609662
#214609652
#214609642
#214562162
#1360461