Finite Group Databasebeta

← #29593711

Subgroups — #29593711

Order 15616.

312 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458688C211yesmaximal, characteristic, complemented
2#21448044C211yesmaximal, characteristic, complemented
3#21447855C211yesmaximal, characteristic
4#21445180C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1365C211yesmaximal, characteristic, complemented
8#16840473—21no—
9C2×D976—21no—
10#16840163—21no—
11#16840139C2211yescharacteristic
12#16840065—22no—
13#16840049—21no—
14#16839963—21no—
15C8×Dic122C2211yescharacteristic
16C4×D488C2211yescharacteristic
17#16839844—21no—
18#16839564—21no—
19#16839562—22no—
20C4×#11758185C2211yescharacteristic
21#16839505—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758190—41no—
26C2×D488—21no—
27C2×D488—21no—
28C2×D488D411yescharacteristic
29#14519774—21no—
30#14519768—22no—
31#14519757—41no—
32#14519753—42no—
33C4×Dic122D411yescharacteristic
34C4×D244—21no—
35#14519739—22no—
36C4⋊C4×D61—41no—
37D976—42no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40#14519708—22no—
41C4⋊#92418D411yescharacteristic
42#14519706—21no—
43#14519699—21no—
44#14519699—41no—
45#14519697—22no—
46C8×Dic61—21no—
47C4⋊Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61D412yes—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D244—21no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244—41no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×Dic122D811yescharacteristic
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—22no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67#11758198—42no—
68#11758198—41no—
69C4⋊Dic61—21no—
70C4⋊Dic61—42no—
71C4⋊Dic61D811yescharacteristic
72#11758196—21no—
73#11758196—42no—
74C4×Dic61—21no—
75C2×#92418—21no—
76D488—21no—
77D488—42no—
78D488—41no—
79D488—41no—
80D488SD1612yescomplemented
81#11758190—82no—
82C16×C61—41no—
83#11758185—41no—
84C22×D61—41no—
85C22×D61—81no—
86Q8×C61—161no—
87C2×C4×C61—42no—
88C2×C4×C61#12011yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—41no—
94D244—22no—
95D244—41no—
96D244—81no—
97D244—81no—
98D244—81no—
99D244—81no—
100D244—161no—
101C4×D61—81no—
102C4×D61—81no—
103C4×D61—162no—
104Dic122—21no—
105Dic122—21no—
106C8×C61—21no—
107C8×C61—81no—
108C8×C61C2×SD1611yescharacteristic
109C8×C61#13711yescharacteristic
110#92418—41no—
111#12355—611nomaximal, Sylow
112C22×C61#44711yescharacteristic
113C2×D61—42no—
114C2×D61—81no—
115C2×D61—81no—
116C2×D61—161no—
117C2×D61—161no—
118C2×D61—161no—
119C4×C61—21no—
120C4×C61—82no—
121C4×C61#44811yescharacteristic
122C4×C61#45411yescharacteristic
123C4×C61#50811yescharacteristic
124C4×C61#50911yescharacteristic
125Dic61—41no—
126Dic61—41no—
127Dic61—81no—
128#3380—611no—
129#2240—611no—
130#2206—611no—
131#1668—611no—
132#1365D6111yescharacteristic, complemented
133Q8⋊C16—611no—
134#1331—611no—
135C2×C61#162711yescharacteristic
136C2×C61#218611yescharacteristic
137C2×C61#219211yescharacteristic
138D61—82no—
139D61—321no—
140#554—1221no—
141C2×D16—1221no—
142#500C2×D6111yescharacteristic
143#499—1221no—
144#493—611no—
145#478—1222no—
146#476—1221no—
147#460—1221no—
148C8×Q8—611no—
149C4×D8—611no—
150C4×D8—1221no—
151C4⋊C16C2×D6111yescharacteristic
152#357—1221no—
153#357—1222no—
154C4×C16—611no—
155#335C2×D6111yescharacteristic
156#331—1221no—
157C61#1235511yescharacteristic, complemented, Sylow
158C2×SD16—2441no—
159C2×D8—611no—
160C2×D8—1221no—
161C2×D8—1221no—
162C4⋊Q8—21no—
163#127—1221no—
164#125—1222no—
165C22⋊Q8—2441no—
166C22⋊Q8—2442no—
167C4×Q8—611no—
168C4×D4—1222no—
169C4×D4—1221no—
170C2×C4⋊C4—2441no—
171D16—2442no—
172C2×C16—21no—
173C2×C16—1221no—
174#107—21no—
175#107—611no—
176#107D24412yes—
177#106—1222no—
178C4⋊C8—21no—
179C4⋊C8—611no—
180C4⋊C8—1221no—
181#102—1222no—
182#102—1221no—
183#102—2441no—
184C4×C8—1221no—
185C4×C8C22×D6111yescharacteristic
186C2×Q8—41no—
187C2×Q8—611no—
188C2×D4—1221no—
189C2×D4—2441no—
190C2×D4—2441no—
191C2×D4—2441no—
192C22×C4—2442no—
193C22×C4—2441no—
194SD16—4882no—
195D8—612no—
196D8—1221no—
197D8—2442no—
198D8—2441no—
199D8—2441no—
200C2×C8—41no—
201C2×C8—1221no—
202C2×C8C2×D24411yescharacteristic
203C2×C8D4×D6111yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—2442no—
210C4⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2441no—
213C42—1221no—
214C42D4×D6111yescharacteristic
215C16—41no—
216C16—2441no—
217C23—4881no—
218C23—2441no—
219Q8—161no—
220Q8—1221no—
221Q8—1221no—
222D4—1222no—
223D4—9761no—
224D4—4881no—
225D4—4881no—
226D4—4881no—
227D4—4881no—
228D4—2441no—
229C2×C4—42no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—9762no—
233C2×C4—4881no—
234C2×C4—4881no—
235C2×C4—2441no—
236C2×C4#1451974711yescharacteristic
237C2×C4D8×D6111yescharacteristic
238C2×C4#1451980411yescharacteristic
239C8—21no—
240C8—81no—
241C8—2441no—
242C8SD16×D6111yescharacteristic
243C8#1451980911yescharacteristic
244C22—9761no—
245C22—9761no—
246C22—9761no—
247C22—4881no—
248C22—4881no—
249C22—2442no—
250C22#1683989711yescharacteristic
251C4—21no—
252C4—82no—
253C4—4881no—
254C4—2441no—
255C4—2441no—
256C4#1683990211yescharacteristic
257C4#1683993711yescharacteristic
258C4#1684019511yescharacteristic
259C4#1684019911yescharacteristic
260C2—19521no—
261C2—4882no—
262C2#2144492311yescharacteristic
263C2#2144774511yescharacteristic
264C2#2144777911yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1365C2
socleC22×C61#447
prime radical#21447855C2
hypercenter#1365D61
hypocenterC61#12355
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #21458688C2semidirect
2. #21448044C2semidirect
4. #21445180C2semidirect
5. #21443797C2semidirect
6. #21443779C2semidirect
7. C61×#1365C2semidirect
80. D488SD16semidirect
132. #1365D61semidirect
157. C61#12355semidirect

Maximal subgroups

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

subgroupindex
#214586882
#214480442
#214478552
#214451802
#214437972
#214437792
C61×#13652
#1235561