Finite Group Databasebeta

← #27195673

Subgroups — #27195673

Order 13184.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#20268355C211yesmaximal, characteristic
2#20268265C211yesmaximal, characteristic, complemented
3#20267808C211yesmaximal, characteristic, complemented
4C2×#15692937C211yesmaximal, characteristic, complemented
5#20267548C211yesmaximal, characteristic, complemented
6#20267547C211yesmaximal, characteristic, complemented
7#421×C103C211yesmaximal, characteristic, complemented
8C22×D412C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15693017C412yescomplemented
11#15693010C412yescomplemented
12#15692995—22no—
13#15692989—22no—
14C4×D412—22no—
15#15692983—22no—
16#15692980C2211yescharacteristic
17#15692980C2211yescharacteristic
18C22⋊C4×D103—22no—
19#15692948—22no—
20#15692937—22no—
21C2×#41×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic
23#117×C103C2211yescharacteristic
24#104×C103—22no—
25C23×D103D412yes—
26C2×D412—21no—
27C2×D412—21no—
28C2×D412—21no—
29C2×D412—21no—
30C2×D412C2×C412yes—
31C2×D412D412yes—
32C2×C22⋊D103—24no—
33C2×C4×D103—24no—
34#13110089—21no—
35#13110089—21no—
36C2×C103⋊C8—21no—
37C4⋊Dic103—21no—
38C4⋊Dic103—21no—
39C22⋊Dic103—21no—
40C22⋊Dic103—21no—
41(C2×D103)⋊C4—24no—
42(C2×D103)⋊C4—24no—
43C4×Dic103C2×C412yescomplemented
44C4×Dic103D412yescomplemented
45#41×C103—21no—
46#41×C103—21no—
47#41×C103—21no—
48#41×C103—21no—
49C2×Q8×C103C2×C411yescharacteristic, complemented
50C2×D4×C103—21no—
51C2×D4×C103C2×C411yescharacteristic, complemented
52C22×C4×C103—21no—
53C22×C4×C103C2311yescharacteristic
54M16×C103—21no—
55M16×C103—21no—
56C2×C8×C103—21no—
57C4⋊C4×C103—21no—
58C22⋊C4×C103—21no—
59C42×C103D412yescomplemented
60C23×C103—21no—
61C23×C103C2×D411yescharacteristic
62C22×D103—22no—
63C22×D103—22no—
64C22×D103—82no—
65C22×D103C22⋊C414yes—
66Q8×C103—21no—
67Q8×C103—21no—
68D4×C103—21no—
69D4×C103—21no—
70D4×C103—41no—
71D4×C103—41no—
72C2×C4×C103—21no—
73C2×C4×C103—22no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103C22×C411yescharacteristic
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103#4111yescharacteristic
81C2×C4×C103#4111yescharacteristic
82C22⋊D103—84no—
83C2×Dic103—22no—
84C2×Dic103—22no—
85D412—22no—
86D412—22no—
87D412—22no—
88D412—22no—
89C4×D103—84no—
90C8×C103—41no—
91C103⋊C8—41no—
92C22×C103—41no—
93C22×C103—42no—
94C22×C103—41no—
95C22×C103C2×C22⋊C411yescharacteristic
96C22×C103#12011yescharacteristic
97C22×C103#12311yescharacteristic
98C2×D103—24no—
99C2×D103—44no—
100C2×D103—44no—
101C2×D103—82no—
102C4×C103—42no—
103C4×C103—41no—
104C4×C103C4×D411yescharacteristic
105C4×C103C4×D411yescharacteristic
106C4×C103#12111yescharacteristic
107C4×C103#12111yescharacteristic
108Dic103—42no—
109Dic103—42no—
110C2×C103—21no—
111C2×C103—21no—
112C2×C103—21no—
113C2×C103—81no—
114C2×C103#38611yescharacteristic
115D103—44no—
116#1911—1031nomaximal, Sylow
117C103#191111yescharacteristic, complemented, Sylow
118#535—1031no—
119#518—1031no—
120#421—1031no—
121#421D10311yescharacteristic, complemented
122C2×#100—1031no—
123H(3,ℤ/4)—1031no—
124H(3,ℤ/4)—1031no—
125C2×#41C2×D10311yescharacteristic
126C22×D4—1031no—
127C2×M16—1031no—
128C2×M16C2×D10311yescharacteristic
129#127—1032no—
130#124—1032no—
131#121—2062no—
132#120—2062no—
133C4×D4—2062no—
134C4×D4—2062no—
135#117—1031no—
136#117—1031no—
137#117C2×D10311yescharacteristic
138C2×C22⋊C4—2062no—
139#104—22no—
140#104—2062no—
141#100—2062no—
142C24—1032no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C4×D10311yescharacteristic, complemented
148C2×D4—21no—
149C2×D4—1032no—
150C2×D4—1032no—
151C2×D4—2064no—
152C2×D4—2061no—
153C2×D4—2061no—
154C2×D4—2061no—
155C2×D4—2061no—
156C2×D4C4×D10311yescharacteristic, complemented
157C22×C4—21no—
158C22×C4—2064no—
159C22×C4C22×D10311yescharacteristic
160M16—21no—
161M16—21no—
162M16—2061no—
163M16—2061no—
164C2×C8—21no—
165C2×C8—2061no—
166C4⋊C4—21no—
167C4⋊C4—2061no—
168C4⋊C4—2061no—
169C22⋊C4—21no—
170C22⋊C4—2064no—
171C22⋊C4—2064no—
172C22⋊C4—2061no—
173C22⋊C4—2061no—
174C42—1032no—
175C42—1032no—
176C42C22⋊D10312yescomplemented
177C23—21no—
178C23—8242no—
179C23—1034no—
180C23—2062no—
181C23—2062no—
182C23D4×D10311yescharacteristic
183Q8—21no—
184Q8—21no—
185D4—21no—
186D4—21no—
187D4—41no—
188D4—41no—
189D4—8244no—
190D4—2062no—
191D4—2062no—
192D4—2062no—
193D4—2062no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—8244no—
199C2×C4—2062no—
200C2×C4—2062no—
201C2×C4C2×C4×D10311yescharacteristic
202C2×C4D4×D10311yescharacteristic
203C2×C4D4×D10311yescharacteristic
204C2×C4C2×C22⋊D10311yescharacteristic
205C2×C4#1311010411yescharacteristic
206C2×C4#1311010511yescharacteristic
207C8—41no—
208C8—4121no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—8242no—
213C22—4124no—
214C22—4124no—
215C22—2064no—
216C22C22⋊C4×D10311yescharacteristic
217C22#1569298911yescharacteristic
218C22#1569300311yescharacteristic
219C4—42no—
220C4—41no—
221C4—4122no—
222C4—4122no—
223C4(C22⋊D103)⋊C411yescharacteristic
224C4C4×C22⋊D10311yescharacteristic
225C4#1569299211yescharacteristic
226C4#1569299411yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—81no—
231C2—4124no—
232C2#2026766711yescharacteristic
subgroupG/H
centerC2#20267667
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#421×C103C2
socleC2×C103#386
prime radical#20268355C2
cosocleC22×C4×C103C23
hypercenter#421D103
hypocenterC103#1911
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #20268265C2semidirect
3. #20267808C2semidirect
4. C2×#15692937C2semidirect
5. #20267548C2semidirect
6. #20267547C2semidirect
7. #421×C103C2semidirect
10. #15693017C4semidirect
11. #15693010C4semidirect
43. C4×Dic103C2×C4semidirect
44. C4×Dic103D4semidirect
49. C2×Q8×C103C2×C4semidirect
51. C2×D4×C103C2×C4semidirect
59. C42×C103D4semidirect
117. C103#1911semidirect
121. #421D103semidirect
147. C2×Q8C4×D103semidirect
156. C2×D4C4×D103semidirect
176. C42C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202682652
#202678082
C2×#156929372
#202675482
#202675472
#421×C1032
#1911103