Finite Group Databasebeta

← #27206034

Subgroups — #27206034

Order 13184.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268364C212yesmaximal
2#20268134C212yesmaximal, complemented
3#20268131C212yesmaximal, complemented
4#20268047C212yesmaximal, complemented
5#20268032C211yesmaximal, characteristic, complemented
6#20267948C212yesmaximal, complemented
7#20267945C212yesmaximal, complemented
8#20267757C211yesmaximal, characteristic
9#467×C103C211yesmaximal, characteristic, complemented
10C2×#13110105C2211yescharacteristic
11C2×Q8×D103C2212yes—
12C2×Dic412C2211yescharacteristic
13C2×#13110095C2212yes—
14C2×#13110089C2211yescharacteristic
15#15693020—22no—
16#15693007—22no—
17#15693006—22no—
18#15693003—22no—
19#15693001C2212yes—
20#15693000C2212yes—
21#15692997C2212yes—
22#15692979C2212yes—
23#15692955C2211yescharacteristic
24#15692952C2212yes—
25#15692946C2212yes—
26#15692945C2212yes—
27#15692944C2212yes—
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic
31C22×C8×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#107×C103C2211yescharacteristic
34#103×C103C2212yes—
35#13110105—41no—
36#13110105—41no—
37C2×Dic206—22no—
38C2×Dic206D411yescharacteristic
39C2×Dic206C2312yes—
40Q8×D103—42no—
41Q8×D103—42no—
42C2×D412D411yescharacteristic
43C2×C22⋊D103D412yes—
44C2×C4×D103—22no—
45C2×C4×D103C2312yes—
46Dic412—41no—
47#13110095—42no—
48#13110089—41no—
49C2×C103⋊C8C2312yes—
50C4⋊Dic103—22no—
51C4⋊Dic103C2312yes—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54C22⋊Dic103—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103—22no—
59C2×Q8×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61Q16×C103—41no—
62C2×C8×C103—41no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103C2×D411yescharacteristic
69C22×D103C2×D412yes—
70Q8×C103—22no—
71Q8×C103—22no—
72C2×C4×C103—21no—
73C2×C4×C103—21no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—42no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103C2×D412yes—
82D412—41no—
83C4×D103—22no—
84C4×D103—22no—
85C4×D103—44no—
86Dic206—22no—
87Dic206—22no—
88Dic206—41no—
89Dic206—44no—
90C8×C103—21no—
91C8×C103—21no—
92C103⋊C8—22no—
93C22×C103—21no—
94C22×C103—21no—
95C22×C103—21no—
96C22×C103C22×D411yescharacteristic
97C2×D103—22no—
98C2×D103—22no—
99C2×D103—22no—
100C4×C103—21no—
101C4×C103—42no—
102C4×C103—42no—
103C4×C103H(5,𝔽2)11yescharacteristic
104C4×C103H(5,𝔽2)11yescharacteristic
105Dic103—22no—
106Dic103—42no—
107Dic103—42no—
108C2×C103—41no—
109C2×C103#53411yescharacteristic
110C2×C103#57811yescharacteristic
111C2×C103#57811yescharacteristic
112D103—42no—
113#3202—1031nomaximal, Sylow
114C103#320211yescharacteristic, complemented, Sylow
115#536—1032no—
116#485—1032no—
117#485—1032no—
118#470—1032no—
119#467—1031no—
120#467D10311yescharacteristic, complemented
121#451—1032no—
122#451—1032no—
123#408—1031no—
124C2×#41—1031no—
125C22×Q8—1032no—
126C2×Q16—1032no—
127C2×Q16—1031no—
128C2×Q16C2×D10311yescharacteristic
129C2×M16—1031no—
130C22×C8C2×D10311yescharacteristic
131C4⋊Q8—2062no—
132#124—2062no—
133#123—2062no—
134#123—2062no—
135C22⋊Q8—1032no—
136C22⋊Q8—1032no—
137C22⋊Q8—1032no—
138C22⋊Q8C2×D10312yes—
139#117—1032no—
140#107—1031no—
141#107C2×D10311yescharacteristic
142#106—1032no—
143#103—1032no—
144#103—1032no—
145#103—1032no—
146#103C2×D10312yes—
147C22⋊C8—1032no—
148C22⋊C8—1032no—
149#41—4121no—
150#41—4121no—
151C2×Q8—1031no—
152C2×Q8—1032no—
153C2×Q8—4122no—
154C2×Q8—4122no—
155C2×Q8—2062no—
156C2×Q8C22×D10312yes—
157C2×D4—1032no—
158C2×D4—1031no—
159C22×C4—1032no—
160C22×C4—2062no—
161C22×C4C22×D10311yescharacteristic
162Q16—41no—
163Q16—4121no—
164Q16—4122no—
165M16—4121no—
166C2×C8—41no—
167C2×C8—1032no—
168C2×C8C22×D10311yescharacteristic
169C2×C8C22×D10311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—1032no—
172C4⋊C4—2062no—
173C4⋊C4—2062no—
174C4⋊C4—2062no—
175C4⋊C4C22×D10312yes—
176C22⋊C4—22no—
177C22⋊C4—2062no—
178C22⋊C4—2062no—
179C22⋊C4—2062no—
180C22⋊C4—2062no—
181C42—2062no—
182C23—1032no—
183C23D4×D10311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—4121no—
187Q8—4124no—
188Q8—2062no—
189Q8—2062no—
190D4—4121no—
191D4—4122no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1032no—
197C2×C4—4124no—
198C2×C4—2062no—
199C2×C4—2062no—
200C2×C4—2062no—
201C2×C4—2062no—
202C2×C4D4×D10311yescharacteristic
203C2×C4C23×D10311yescharacteristic
204C8—21no—
205C8—21no—
206C8—2062no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—2062no—
211C22—2062no—
212C22—2062no—
213C22C2×D4×D10311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—4122no—
218C4—4122no—
219C4—2062no—
220C4#1569306611yescharacteristic
221C4#1569306711yescharacteristic
222C2—41no—
223C2—4122no—
224C2#2026834911yescharacteristic
225C2#2026860411yescharacteristic
226C2#2026860511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#467×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110105C22
hypercenter#467D103
hypocenterC103#3202
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #20268134C2semidirect
3. #20268131C2semidirect
4. #20268047C2semidirect
5. #20268032C2semidirect
6. #20267948C2semidirect
7. #20267945C2semidirect
9. #467×C103C2semidirect
114. C103#3202semidirect
120. #467D103semidirect

Maximal subgroups

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

subgroupindex
#202683642
#202681342
#202681312
#202680472
#202680322
#202679482
#202679452
#202677572
#467×C1032
#3202103