Finite Group Databasebeta

← #27197088

Subgroups — #27197088

Order 13184.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#20268588C211yesmaximal, characteristic, complemented
2#20268227C211yesmaximal, characteristic, complemented
3#20268041C211yesmaximal, characteristic, complemented
4#20267602C211yesmaximal, characteristic, complemented
5#20267601C211yesmaximal, characteristic, complemented
6#20267572C211yesmaximal, characteristic, complemented
7#509×C103C211yesmaximal, characteristic, complemented
8#41×D103—21no—
9#15693053—21no—
10#15693050—21no—
11#15693048—21no—
12#15693045—21no—
13#15693043C2211yescharacteristic
14#15693041—21no—
15C2×#13110088C2211yescharacteristic
16#15692992—21no—
17#15692965—21no—
18#15692962—21no—
19#15692961C2211yescharacteristic, complemented
20#15692953C2211yescharacteristic, complemented
21#15692942—21no—
22#135×C103C2211yescharacteristic
23C2×D8×C103C2211yescharacteristic, complemented
24SD32×C103—21no—
25D16×C103—21no—
26M32×C103C2211yescharacteristic, complemented
27#13110106—21no—
28#13110105—21no—
29#13110105—41no—
30#13110104—21no—
31#13110104—41no—
32Q8×D103—21no—
33C2×C22⋊D103—41no—
34D4×D103—21no—
35D4×D103—41no—
36C2×C4×D103—41no—
37C2×C4×D103D411yescharacteristic
38Dic412D411yescharacteristic, complemented
39#13110095—21no—
40#13110094—21no—
41#13110093—21no—
42#13110092—21no—
43D824D411yescharacteristic, complemented
44#13110090—21no—
45#13110088—21no—
46#13110088—21no—
47C2×C103⋊C8D411yescharacteristic
48C4⋊Dic103—21no—
49C22⋊Dic103—41no—
50C103⋊C16—21no—
51#41×C103—21no—
52C2×D4×C103—21no—
53Q16×C103D411yescharacteristic, complemented
54SD16×C103—21no—
55D8×C103—21no—
56D8×C103—21no—
57D8×C103D411yescharacteristic, complemented
58C2×C8×C103C2311yescharacteristic
59C16×C103—21no—
60C23×C103—41no—
61C22×D103—41no—
62C22×D103D811yescharacteristic
63Q8×C103—21no—
64D4×C103—21no—
65D4×C103—41no—
66D4×C103—41no—
67D4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103C2×D411yescharacteristic
70C22⋊D103—41no—
71C22⋊D103—41no—
72C22⋊D103—41no—
73C22⋊D103—82no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103D811yescharacteristic
77D412—21no—
78D412—41no—
79C4×D103—21no—
80C4×D103—21no—
81C4×D103—41no—
82C4×D103—41no—
83C4×D103—41no—
84Dic206—21no—
85Dic206—41no—
86C8×C103C2×D411yescharacteristic
87C8×C103C2×D411yescharacteristic
88C103⋊C8—21no—
89C22×C103—41no—
90C22×C103—81no—
91C22×C103—81no—
92C22×C103—81no—
93C22×C103C2×D811yescharacteristic
94C2×D103—21no—
95C2×D103—41no—
96C2×D103—41no—
97C2×D103—82no—
98C4×C103—41no—
99C4×C103#12011yescharacteristic
100C4×C103AGL(1,ℤ/8)11yescharacteristic
101Dic103—21no—
102Dic103—41no—
103Dic103—81no—
104C2×C103—21no—
105C2×C103—81no—
106C2×C103—161no—
107C2×C103#44711yescharacteristic
108D103—41no—
109D103—81no—
110#2190—1031nomaximal, Sylow
111C103#219011yescharacteristic, complemented, Sylow
112#575—1031no—
113#509—1031no—
114#509D10311yescharacteristic, complemented
115#469—1031no—
116#360—1031no—
117#360—1031no—
118#349—1031no—
119C2×#41—2061no—
120#137—2061no—
121#137—2061no—
122AGL(1,ℤ/8)—2061no—
123AGL(1,ℤ/8)—2061no—
124#135—1031no—
125#135—2061no—
126#135C2×D10311yescharacteristic
127C2×D8C2×D10311yescharacteristic, complemented
128C2×M16—1031no—
129#121—2061no—
130SD32—21no—
131SD32—2061no—
132D16—21no—
133D16—2061no—
134M32—1031no—
135M32C2×D10311yescharacteristic, complemented
136#106—1031no—
137#102—2061no—
138#41—21no—
139#41—4121no—
140#41—4121no—
141#41—2061no—
142#41—2061no—
143#41—2061no—
144C2×Q8—2061no—
145C2×D4—21no—
146C2×D4—4121no—
147C2×D4—4121no—
148C2×D4—2061no—
149C22×C4—1031no—
150C22×C4—4121no—
151Q16—1031no—
152Q16—2061no—
153Q16C22⋊D10311yescharacteristic, complemented
154SD16—21no—
155SD16—2061no—
156SD16—2061no—
157SD16—2061no—
158D8—21no—
159D8—21no—
160D8—1031no—
161D8—2061no—
162D8C22⋊D10311yescharacteristic, complemented
163M16—2061no—
164M16—2061no—
165C2×C8—1031no—
166C2×C8C22×D10311yescharacteristic
167C4⋊C4—2061no—
168C22⋊C4—4121no—
169C16—21no—
170C16—2061no—
171C23—41no—
172C23—1031no—
173C23—4121no—
174Q8—21no—
175Q8—4121no—
176Q8—2061no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—8242no—
182D4—4121no—
183D4—4121no—
184D4—4121no—
185D4—4121no—
186D4—2061no—
187C2×C4—41no—
188C2×C4—1031no—
189C2×C4—4121no—
190C2×C4—4121no—
191C2×C4—4121no—
192C2×C4—4121no—
193C2×C4—4121no—
194C2×C4—2061no—
195C2×C4—2061no—
196C2×C4D4×D10311yescharacteristic
197C8—2061no—
198C8D4×D10311yescharacteristic
199C8C2×C22⋊D10311yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—8242no—
205C22—4121no—
206C22—4121no—
207C22—2061no—
208C22D8×D10311yescharacteristic
209C4—41no—
210C4—8241no—
211C4—4121no—
212C4—2061no—
213C4#1569298911yescharacteristic
214C4#1569304511yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—8241no—
219C2—4121no—
220C2#2026792311yescharacteristic
subgroupG/H
centerC2#20267923
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#509×C103C2
socleC2×C103#447
hypercenter#509D103
hypocenterC103#2190
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20268588C2semidirect
2. #20268227C2semidirect
3. #20268041C2semidirect
4. #20267602C2semidirect
5. #20267601C2semidirect
6. #20267572C2semidirect
7. #509×C103C2semidirect
19. #15692961C22semidirect
20. #15692953C22semidirect
23. C2×D8×C103C22semidirect
26. M32×C103C22semidirect
38. Dic412D4semidirect
43. D824D4semidirect
53. Q16×C103D4semidirect
57. D8×C103D4semidirect
111. C103#2190semidirect
114. #509D103semidirect
127. C2×D8C2×D103semidirect
135. M32C2×D103semidirect
153. Q16C22⋊D103semidirect
162. D8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202685882
#202682272
#202680412
#202676022
#202676012
#202675722
#509×C1032
#2190103