Finite Group Databasebeta

← #29593712

Subgroups — #29593712

Order 15616.

312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458687C211yesmaximal, characteristic, complemented
2#21448043C211yesmaximal, characteristic, complemented
3#21447855C211yesmaximal, characteristic
4#21445179C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8#16840472—21no—
9C2×D976—21no—
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840139C2211yescharacteristic
13#16840063—22no—
14#16840053—21no—
15#16839962—21no—
16C4×D488—21no—
17C4×D488C2211yescharacteristic
18#16839564—22no—
19#16839564—21no—
20#16839515C2211yescharacteristic
21#16839505—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758201—41no—
26C2×D488—21no—
27C2×D488—21no—
28C2×D488D411yescharacteristic
29#14519777—21no—
30#14519774—21no—
31#14519769—22no—
32#14519755—42no—
33#14519753—41no—
34C4×D244—22no—
35C4×D244—21no—
36C4⋊C4×D61—41no—
37D976—42no—
38#14519711—21no—
39#14519711D412yes—
40#14519711D411yescharacteristic
41#14519709—22no—
42C4⋊#92418—21no—
43#14519699—22no—
44#14519699—21no—
45#14519697—41no—
46C4×Q8×C61D411yescharacteristic
47C2×C16×C61—21no—
48C2×C16×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61D811yescharacteristic
54C2×D244—21no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244—41no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×Dic122—41no—
61C2×C8×C61—21no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61D811yescharacteristic
66C42×C61—21no—
67C42×C61C2×D411yescharacteristic
68#11758201—82no—
69#11758198—42no—
70#11758198—41no—
71C4⋊Dic61—21no—
72C4⋊Dic61—22no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76C2×#92418—41no—
77D488—21no—
78D488—42no—
79D488—41no—
80D488—41no—
81D488SD1612yescomplemented
82C16×C61—41no—
83C16×C61—41no—
84C22×D61—41no—
85C22×D61—81no—
86Q8×C61—21no—
87Q8×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61#12011yescharacteristic
91C2×C4×C61C2×D811yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C2×Dic61—41no—
94C2×Dic61—42no—
95D244—22no—
96D244—41no—
97D244—81no—
98D244—81no—
99D244—81no—
100D244—81no—
101D244—161no—
102C4×D61—81no—
103C4×D61—81no—
104C4×D61—162no—
105Dic122—161no—
106C8×C61—21no—
107C8×C61—41no—
108C8×C61C2×SD1611yescharacteristic
109C8×C61#13711yescharacteristic
110#92418—81no—
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—41no—
121C4×C61—41no—
122C4×C61#44811yescharacteristic
123C4×C61#45411yescharacteristic
124C4×C61#50811yescharacteristic
125C4×C61#50911yescharacteristic
126Dic61—81no—
127Dic61—82no—
128#3380—611no—
129#2240—611no—
130#2206—611no—
131#1668—611no—
132#1365—611no—
133Q8⋊C16D6111yescharacteristic, complemented
134#1331—611no—
135C2×C61#162711yescharacteristic
136C2×C61#218611yescharacteristic
137C2×C61#219211yescharacteristic
138D61—82no—
139D61—321no—
140#554—1221no—
141C2×D16—1221no—
142#500—611no—
143#499—1221no—
144#493—611no—
145#478—1222no—
146#476—1221no—
147#460—1221no—
148C8×Q8C2×D6111yescharacteristic
149C4×D8—611no—
150C4×D8—1221no—
151C4⋊C16C2×D6111yescharacteristic
152#357—1221no—
153#357—1222no—
154C4×C16C2×D6111yescharacteristic
155#335—611no—
156#331—1221no—
157C61#1235511yescharacteristic, complemented, Sylow
158C2×SD16—2441no—
159C2×D8—611no—
160C2×D8—1221no—
161C2×D8—1221no—
162C4⋊Q8—1221no—
163#127—1221no—
164#125—1222no—
165C22⋊Q8—2442no—
166C22⋊Q8—2441no—
167C4×Q8D24411yescharacteristic
168C4×D4—1222no—
169C4×D4—1221no—
170C2×C4⋊C4—2441no—
171D16—2442no—
172C2×C16—21no—
173C2×C16—21no—
174#107—611no—
175#107—612no—
176#107—1221no—
177#106—1222no—
178C4⋊C8—21no—
179C4⋊C8—1221no—
180C4⋊C8D24411yescharacteristic
181#102—1222no—
182#102—1221no—
183#102—2441no—
184C4×C8—21no—
185C4×C8C22×D6111yescharacteristic
186C2×Q8—2441no—
187C2×Q8D48811yescharacteristic
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—21no—
201C2×C8—2441no—
202C2×C8D4×D6111yescharacteristic
203C2×C8D4×D6111yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—1221no—
206C4⋊C4—1222no—
207C4⋊C4—2442no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4D48811yescharacteristic
211C22⋊C4—2442no—
212C22⋊C4—2441no—
213C42—21no—
214C42C2×D24411yescharacteristic
215C16—41no—
216C16—41no—
217C23—4881no—
218C23—2441no—
219Q8—21no—
220Q8—21no—
221Q8—9761no—
222D4—1222no—
223D4—9761no—
224D4—4881no—
225D4—4881no—
226D4—4881no—
227D4—4881no—
228D4—2441no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—9762no—
232C2×C4—4881no—
233C2×C4—4881no—
234C2×C4—2441no—
235C2×C4—2442no—
236C2×C4#1451974711yescharacteristic
237C2×C4C2×D48811yescharacteristic
238C2×C4#1451980511yescharacteristic
239C8—21no—
240C8—41no—
241C8—4881no—
242C8SD16×D6111yescharacteristic
243C8#1451980911yescharacteristic
244C22—9761no—
245C22—9761no—
246C22—9761no—
247C22—4881no—
248C22—4881no—
249C22—2442no—
250C22#1683989811yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—4881no—
255C4—4882no—
256C4#1683990211yescharacteristic
257C4#1683993611yescharacteristic
258C4#1684019411yescharacteristic
259C4#1684020011yescharacteristic
260C2—19521no—
261C2—4882no—
262C2#2144492411yescharacteristic
263C2#2144774411yescharacteristic
264C2#2144777811yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61#447
prime radical#21447855C2
hypercenterQ8⋊C16D61
hypocenterC61#12355
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
1. #21458687C2semidirect
2. #21448043C2semidirect
4. #21445179C2semidirect
5. #21443876C2semidirect
6. #21443781C2semidirect
7. C61×Q8⋊C16C2semidirect
81. D488SD16semidirect
133. Q8⋊C16D61semidirect
157. C61#12355semidirect

Maximal subgroups

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

subgroupindex
#214586872
#214480432
#214478552
#214451792
#214438762
#214437812
C61×Q8⋊C162
#1235561