Finite Group Databasebeta

← #30607891

Subgroups — #30607891

Order 15616.

296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#16840681C211yesmaximal, characteristic
2#21462039C211yesmaximal, characteristic
3#21461981C211yesmaximal, characteristic
4#21461938C211yesmaximal, characteristic
5#21460897C211yesmaximal, characteristic
6#21460896C211yesmaximal, characteristic
7#362×D61C211yesmaximal, characteristic
8C2×#14519852C2211yescharacteristic
9#16840777—21no—
10D61⋊#108C2211yescharacteristic
11C2×#14519847C2211yescharacteristic
12#16840755—21no—
13D61⋊#101—21no—
14#16840725C2211yescharacteristic
15#16840681—21no—
16#16840681—21no—
17#16840653—21no—
18#16840652—21no—
19#16840645—21no—
20C2×Q16×D61C2211yescharacteristic
21M32×D61C2211yescharacteristic
22#108×D61C2211yescharacteristic
23#16839579C411yescharacteristic, complemented
24#16839578C411yescharacteristic, complemented
25#16839577C411yescharacteristic, complemented
26C61×#362C411yescharacteristic, complemented
27C2×#11758213—21no—
28D61⋊M16—21no—
29D61⋊M16D411yescharacteristic
30#14519856D411yescharacteristic
31#14519852—21no—
32#14519852D411yescharacteristic
33#14519852D411yescharacteristic
34C2×#11758187—21no—
35#14519848—21no—
36#14519848—41no—
37#14519847—21no—
38#14519847—21no—
39#14519847—21no—
40#14519847—41no—
41#14519840—42no—
42#14519838—42no—
43#14519831—21no—
44C8×#6923—21no—
45C2×Q8×D61—21no—
46C2×Dic244C2×C411yescharacteristic
47C2×#11758202—21no—
48Q16×D61—21no—
49Q16×D61—21no—
50Q16×D61—21no—
51Q16×D61—21no—
52M16×D61—21no—
53C2×C8×D61C2311yescharacteristic
54#14519717C2×C411yescharacteristic
55#14519716—21no—
56C16×D61—21no—
57#14519713C2×C411yescharacteristic
58#14519712—21no—
59C2×Q16×C61C2×C411yescharacteristic
60M32×C61C2×C411yescharacteristic
61#108×C61C2×C411yescharacteristic
62C2×Q8×C61—21no—
63Q8×D61—41no—
64Q8×D61—41no—
65Q8×D61—41no—
66Q8×D61—41no—
67C2×C4×D61—41no—
68C2×C4×D61C2×D411yescharacteristic
69C2×Dic122—21no—
70C2×Dic122—41no—
71C22⋊#6923—21no—
72#11758217—21no—
73#11758217—41no—
74C2×#92420—41no—
75C4⋊#6923—21no—
76C4×#6923—21no—
77#11758213—21no—
78#11758213—41no—
79#11758213—41no—
80#11758213—41no—
81D61⋊C8—21no—
82D61⋊C8—41no—
83Q16×C61—21no—
84Q16×C61—21no—
85M16×C61—21no—
86C2×C8×C61C22×C411yescharacteristic
87#11758202—41no—
88#11758202—41no—
89#11758194—21no—
90C2×#92418#4111yescharacteristic
91Dic244—21no—
92Dic244—21no—
93#11758189—41no—
94C8×D61—41no—
95C8×D61C2×D411yescharacteristic
96C8×D61#4111yescharacteristic
97C8×D61#4111yescharacteristic
98C8×D61#4111yescharacteristic
99#11758187—21no—
100#11758187—21no—
101C16×C61—21no—
102#11758185—21no—
103C22×D61#13711yescharacteristic
104C2×#6923—41no—
105Q8×C61—41no—
106Q8×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C4×D411yescharacteristic
109C2×Dic61—41no—
110C2×Dic61AGL(1,ℤ/8)11yescharacteristic
111C4×D61—81no—
112C4×D61—81no—
113C4×D61#12111yescharacteristic
114C4×D61#12411yescharacteristic
115C4×D61AGL(1,ℤ/8)11yescharacteristic
116C4×D61AGL(1,ℤ/8)11yescharacteristic
117Dic122—41no—
118Dic122—41no—
119Dic122—81no—
120Dic122—81no—
121#92420—41no—
122#92420—81no—
123#92420—81no—
124C8×C61—41no—
125C8×C61#11711yescharacteristic
126C8×C61C4×D411yescharacteristic
127#92418—41no—
128#92418#12311yescharacteristic
129#92418#12611yescharacteristic
130#13157—611nomaximal, Sylow
131C22×C61#44011yescharacteristic
132C2×D61—41no—
133C2×D61#46811yescharacteristic
134C2×D61#48911yescharacteristic
135#6923—81no—
136C4×C61—81no—
137C4×C61#38811yescharacteristic
138C4×C61#44211yescharacteristic
139Dic61—81no—
140Dic61#46911yescharacteristic
141Dic61#49011yescharacteristic
142C2×#362—611no—
143C2×#362—611no—
144#2110—611no—
145#1979—611no—
146#1953—611no—
147#1388—611no—
148#1388—611no—
149C2×C61—21no—
150C2×C61#193611yescharacteristic
151D61—21no—
152D61—21no—
153C22×Q16—611no—
154C2×M32—611no—
155C2×M32—611no—
156#430—1221no—
157C2×#108—611no—
158C2×#108—611no—
159C2×#108—611no—
160#419—1221no—
161C2×#101—1221no—
162#405—611no—
163#362—611no—
164#362—611no—
165#362—611no—
166#362—1221no—
167#362—1221no—
168#362#692311yescharacteristic, complemented
169#347—1221no—
170#347—1221no—
171#344—1221no—
172C61#1315711yescharacteristic, complemented, Sylow
173C22×Q8—1221no—
174C2×Q16—611no—
175C2×Q16—1221no—
176C2×Q16—1221no—
177C2×Q16—1221no—
178C2×Q16—1221no—
179C2×Q16—1221no—
180C2×Q16C2×#692311yescharacteristic
181C2×M16—611no—
182C2×M16—1221no—
183C2×M16—1221no—
184C2×M16—1221no—
185C22×C8—611no—
186#117—611no—
187M32—611no—
188M32—611no—
189M32—611no—
190M32—1221no—
191M32—1221no—
192M32C2×#692311yescharacteristic
193C2×C16—1221no—
194C2×C16—1221no—
195#108—611no—
196#108—1221no—
197#108—1221no—
198#108—1221no—
199#108—1221no—
200#108—1221no—
201#108—2441no—
202#108—2441no—
203#108C2×#692311yescharacteristic
204#103—2442no—
205#101—2442no—
206#97—1221no—
207C4×C8—1221no—
208C2×Q8—21no—
209C2×Q8—1221no—
210C2×Q8—2441no—
211C2×Q8—2441no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C22×C4—611no—
216C22×C4—2441no—
217Q16—21no—
218Q16—21no—
219Q16—1221no—
220Q16—1221no—
221Q16—2441no—
222Q16—2441no—
223M16—21no—
224M16—1221no—
225M16—1221no—
226M16—1221no—
227M16—2441no—
228M16—2441no—
229M16—2441no—
230M16—2441no—
231M16—2441no—
232C2×C8—611no—
233C2×C8—611no—
234C2×C8—611no—
235C2×C8—611no—
236C2×C8—611no—
237C2×C8—1221no—
238C2×C8—2441no—
239C2×C8—2441no—
240C2×C8—2441no—
241C2×C8C22×#692311yescharacteristic
242C4⋊C4—1221no—
243C22⋊C4—1221no—
244C42—1221no—
245C16—21no—
246C16—1221no—
247C16—1221no—
248C16—1221no—
249C23—611no—
250Q8—41no—
251Q8—41no—
252Q8—4881no—
253Q8—4881no—
254Q8—2441no—
255Q8—2441no—
256C2×C4—41no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4D4×#692311yescharacteristic
267C8—41no—
268C8—611no—
269C8—611no—
270C8—4881no—
271C8—4881no—
272C8—2441no—
273C8—2441no—
274C8#1451985611yescharacteristic
275C8D4×#692311yescharacteristic
276C22—611no—
277C22—611no—
278C22—2441no—
279C22#1684080111yescharacteristic
280C4—81no—
281C4—611no—
282C4—611no—
283C4—4881no—
284C4—4881no—
285C4#1684071211yescharacteristic
286C4#1684080311yescharacteristic
287C2—21no—
288C2—1221no—
289C2—1221no—
290C2#2146191111yescharacteristic
subgroupG/H
centerC2#21461911
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#362C4
socleC2×C61#1936
prime radicalC22×D61#137
cosocleC2×C8×D61C23
hypercenter#362#6923
hypocenterC61#13157
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
23. #16839579C4semidirect
24. #16839578C4semidirect
25. #16839577C4semidirect
26. C61×#362C4semidirect
168. #362#6923semidirect
172. C61#13157semidirect

Maximal subgroups

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

subgroupindex
C2×#168406812
#214620392
#214619812
#214619382
#214608972
#214608962
#362×D612
#1315761