Finite Group Databasebeta

← #29594118

Subgroups — #29594118

Order 15616.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458775C211yesmaximal, characteristic
2#21448105C211yesmaximal, characteristic, complemented
3#21447966C211yesmaximal, characteristic
4#21445338C211yesmaximal, characteristic, complemented
5#21443872C211yesmaximal, characteristic, complemented
6#21443802C211yesmaximal, characteristic, complemented
7C61×#1333C211yesmaximal, characteristic
8#16840471—21no—
9#16840170—21no—
10#16840167C2211yescharacteristic
11#16840164C2211yescharacteristic
12#16840062—21no—
13#16840060—21no—
14#16840040—21no—
15#16839973—21no—
16#16839892C2211yescharacteristic
17#16839874—21no—
18#16839590—21no—
19#16839589—21no—
20#16839588—21no—
21C4⋊#11758185C2211yescharacteristic
22#16839563—21no—
23#16839509—21no—
24C4×D8×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244—41no—
28#14519777—21no—
29#14519776—21no—
30#14519769—21no—
31#14519768—21no—
32#14519756—41no—
33#14519754—41no—
34#14519754—41no—
35C4×Dic122D411yescharacteristic
36D4×Dic61—21no—
37D4×Dic61—21no—
38C2×#11758196—41no—
39C2×#11758185—21no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—21no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519702—41no—
50#14519698—21no—
51#14519698—21no—
52#14519687—21no—
53C2×D8×C61D411yescharacteristic
54C4×D4×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57C4⋊C8×C61—21no—
58#102×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C22×C4×C61—41no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×Dic122D811yescharacteristic
67D8×C61—21no—
68D8×C61Q1612yescomplemented
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C22⋊C4×C61—41no—
74C42×C61C2×D411yescharacteristic
75C22⋊Dic61—41no—
76C22⋊Dic61—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61D811yescharacteristic
83#11758196—21no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—21no—
89C2×#92418—21no—
90Dic244—82no—
91C16×C61—22no—
92#11758185—41no—
93C23×C61—41no—
94D4×C61—22no—
95D4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—161no—
98C2×C4×C61#12011yescharacteristic
99C2×C4×C61C2×D811yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—82no—
106C2×Dic61—81no—
107C2×Dic61—161no—
108Dic122—41no—
109Dic122—81no—
110Dic122—81no—
111Dic122—161no—
112C8×C61—21no—
113C8×C61—81no—
114C8×C61C2×Q1611yescharacteristic
115C8×C61#13711yescharacteristic
116#92418—41no—
117#12414—611nomaximal, Sylow
118C22×C61—42no—
119C22×C61—81no—
120C22×C61—81no—
121C22×C61#44711yescharacteristic
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—81no—
125C4×C61#45111yescharacteristic
126C4×C61#45611yescharacteristic
127Dic61—41no—
128Dic61—41no—
129Dic61—81no—
130Dic61—81no—
131Dic61—161no—
132#3389—611no—
133#2255—611no—
134#2226—611no—
135#1694—611no—
136#1363—611no—
137#1338—611no—
138#1333D6111yescharacteristic
139C2×C61—82no—
140C2×C61#164911yescharacteristic
141C2×C61#219011yescharacteristic
142C2×C61#219411yescharacteristic
143#554—1221no—
144#501—1221no—
145#500—611no—
146#499—611no—
147#478—1221no—
148#478—1221no—
149#474—1221no—
150#462—1221no—
151#446—611no—
152#442—1221no—
153C4×D8C2×D6111yescharacteristic
154#367—1221no—
155#367—1221no—
156#366—1221no—
157C4⋊C16—611no—
158#357—1221no—
159#346C2×D6111yescharacteristic
160#334C2×D6111yescharacteristic
161#332—1221no—
162C61#1241411yescharacteristic, complemented, Sylow
163C2×Q16—2441no—
164C2×D8D24411yescharacteristic
165C4⋊Q8—1221no—
166C4⋊Q8—1221no—
167#125—1221no—
168#125—1221no—
169C22⋊Q8—2441no—
170C22⋊Q8—2441no—
171C22⋊Q8—2441no—
172C4×Q8—611no—
173C4×D4—21no—
174C4×D4—1221no—
175C4×D4—1221no—
176C2×C4⋊C4—2441no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—611no—
180#107—611no—
181#107—1221no—
182#107—1221no—
183#107—1221no—
184#107D24411yescharacteristic
185#106—1221no—
186#106—1221no—
187C4⋊C8—21no—
188C4⋊C8—611no—
189C4⋊C8—1221no—
190#103—2441no—
191#102—21no—
192#102—1221no—
193#102—1221no—
194#97—1221no—
195C4×C8C22×D6111yescharacteristic
196C2×Q8—611no—
197C2×Q8—2441no—
198C2×Q8—2441no—
199C2×D4—21no—
200C22×C4—41no—
201C22×C4—2441no—
202C22×C4—2441no—
203Q16—4882no—
204D8—21no—
205D8Dic24412yescomplemented
206C2×C8—41no—
207C2×C8—1221no—
208C2×C8C2×D24411yescharacteristic
209C2×C8D4×D6111yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—611no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C22⋊C4—41no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C42—1221no—
226C42D4×D6111yescharacteristic
227C16—22no—
228C16—2441no—
229C23—41no—
230Q8—9761no—
231Q8—4881no—
232Q8—4881no—
233Q8—2441no—
234D4—22no—
235D4—41no—
236C2×C4—41no—
237C2×C4—161no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—9761no—
241C2×C4—4881no—
242C2×C4—4882no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451974711yescharacteristic
246C2×C4D8×D6111yescharacteristic
247C2×C4#1451980411yescharacteristic
248C8—21no—
249C8—81no—
250C8—2441no—
251C8C2×Dic24411yescharacteristic
252C8#1451981011yescharacteristic
253C22—42no—
254C22—81no—
255C22—81no—
256C22#1683989711yescharacteristic
257C4—21no—
258C4—21no—
259C4—81no—
260C4—9761no—
261C4—4881no—
262C4—4881no—
263C4—2441no—
264C4—2441no—
265C4#1683992011yescharacteristic
266C4#1683994611yescharacteristic
267C2—82no—
268C2#2144507111yescharacteristic
269C2#2144776611yescharacteristic
270C2#2144779311yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1333C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1333D61
hypocenterC61#12414
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
2. #21448105C2semidirect
4. #21445338C2semidirect
5. #21443872C2semidirect
6. #21443802C2semidirect
68. D8×C61Q16semidirect
162. C61#12414semidirect
205. D8Dic244semidirect

Maximal subgroups

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

subgroupindex
#214587752
#214481052
#214479662
#214453382
#214438722
#214438022
C61×#13332
#1241461