Finite Group Databasebeta

← #29593708

Subgroups — #29593708

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#21448042C211yesmaximal, characteristic, complemented
3#21447851C211yesmaximal, characteristic
4#21443878C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1668C211yesmaximal, characteristic, complemented
8#16840472—21no—
9C2×#14519718—21no—
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840063—22no—
13#16840053—21no—
14C4×D488—21no—
15C4×D488C2211yescharacteristic
16C4⋊#11758185C2211yescharacteristic
17#16839563—22no—
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#460—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C2×D488D411yescharacteristic
26#14519777—21no—
27#14519769—22no—
28#14519755—42no—
29#14519753—41no—
30C4×D244—22no—
31C4×D244—21no—
32C4⋊C4×D61—41no—
33#14519718—42no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36#14519711—21no—
37#14519711D412yes—
38#14519711D411yescharacteristic
39#14519709—22no—
40#14519699—22no—
41#14519699—21no—
42C2×SD16×C61—41no—
43C2×D8×C61—21no—
44C2×D8×C61—21no—
45#127×C61—21no—
46C4×Q8×C61D411yescharacteristic
47C4⋊C8×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#102×C61—41no—
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61D811yescharacteristic
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D244—21no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×Dic122—41no—
61SD16×C61—82no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61D811yescharacteristic
71C42×C61—21no—
72C42×C61C2×D411yescharacteristic
73#11758198—42no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—22no—
77C4⋊Dic61—41no—
78#11758196—42no—
79#11758196—42no—
80D488—21no—
81D488SD1612yescomplemented
82#11758185—41no—
83#11758185—41no—
84C23×C61—81no—
85C22×D61—41no—
86Q8×C61—21no—
87Q8×C61—21no—
88D4×C61—81no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—81no—
92D4×C61—161no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—41no—
99C2×Dic61—42no—
100D244—22no—
101D244—41no—
102C4×D61—81no—
103C4×D61—81no—
104C4×D61—162no—
105Dic122—161no—
106C8×C61—21no—
107C8×C61—41no—
108C8×C61—81no—
109C8×C61C2×SD1611yescharacteristic
110C8×C61#13711yescharacteristic
111#12355—611nomaximal, Sylow
112C22×C61—161no—
113C22×C61—161no—
114C22×C61—161no—
115C22×C61#44711yescharacteristic
116C2×D61—42no—
117C2×D61—81no—
118C2×D61—81no—
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#1668D6111yescharacteristic, complemented
132#1365—611no—
133Q8⋊C16—611no—
134#1331—611no—
135C2×C61—321no—
136C2×C61#162711yescharacteristic
137C2×C61#218611yescharacteristic
138C2×C61#219211yescharacteristic
139D61—82no—
140#554—1221no—
141C2×D16—1221no—
142#500—611no—
143#499—1221no—
144#493C2×D6111yescharacteristic
145#478—1222no—
146#476—1221no—
147#460—21no—
148C8×Q8C2×D6111yescharacteristic
149C4×D8—611no—
150C4×D8—1221no—
151C4⋊C16—611no—
152#357—1221no—
153#357—1222no—
154C4×C16—611no—
155#335C2×D6111yescharacteristic
156#331—21no—
157C61#1235511yescharacteristic, complemented, Sylow
158C2×SD16—41no—
159C2×D8—21no—
160C2×D8—21no—
161C2×D8—611no—
162C4⋊Q8—1221no—
163#127—21no—
164#125—1222no—
165C22⋊Q8—2442no—
166C22⋊Q8—2441no—
167C4×Q8C22⋊D6111yescharacteristic
168C4×D4—1222no—
169C4×D4—1221no—
170C2×C4⋊C4—2441no—
171D16—2442no—
172C2×C16—1221no—
173C2×C16—1221no—
174#107—611no—
175#107—612no—
176#107—1221no—
177#106—1222no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8C22⋊D6111yescharacteristic
181#102—41no—
182#102—1222no—
183#102—1221no—
184C4×C8—21no—
185C4×C8C22×D6111yescharacteristic
186C2×Q8—2441no—
187C2×Q8#1175819911yescharacteristic
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—1221no—
192C22×C4—2442no—
193C22×C4—2441no—
194SD16—82no—
195D8—42no—
196D8—41no—
197D8—41no—
198D8—612no—
199D8—1221no—
200C2×C8—21no—
201C2×C8—41no—
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⋊C4#1175819911yescharacteristic
211C22⋊C4—2442no—
212C22⋊C4—2441no—
213C42—21no—
214C42C2×C22⋊D6111yescharacteristic
215C16—2441no—
216C16—2441no—
217C23—81no—
218C23—2441no—
219Q8—21no—
220Q8—21no—
221Q8—9761no—
222D4—81no—
223D4—81no—
224D4—81no—
225D4—81no—
226D4—161no—
227D4—1222no—
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#1451974511yescharacteristic
237C2×C4C2×#1175819911yescharacteristic
238C2×C4#1451980211yescharacteristic
239C8—21no—
240C8—41no—
241C8—81no—
242C8SD16×D6111yescharacteristic
243C8#1451980611yescharacteristic
244C22—161no—
245C22—161no—
246C22—161no—
247C22—4881no—
248C22—4881no—
249C22—2442no—
250C22#1683989511yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—4881no—
255C4—4882no—
256C4#1683989911yescharacteristic
257C4#1683993311yescharacteristic
258C4#1684019211yescharacteristic
259C4#1684019811yescharacteristic
260C2—321no—
261C2—4882no—
262C2#2144492011yescharacteristic
263C2#2144774011yescharacteristic
264C2#2144777411yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1668C2
socleC22×C61#447
prime radical#21447851C2
hypercenter#1668D61
hypocenterC61#12355
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #21458687C2semidirect
2. #21448042C2semidirect
4. #21443878C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443779C2semidirect
7. C61×#1668C2semidirect
81. D488SD16semidirect
131. #1668D61semidirect
157. C61#12355semidirect

Maximal subgroups

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

subgroupindex
#214586872
#214480422
#214478512
#214438782
Q8⋊#117581852
#214437792
C61×#16682
#1235561