Finite Group Databasebeta

← #28373356

Subgroups — #28373356

Order 13952.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295581C211yesmaximal, characteristic, complemented
2#20295577C211yesmaximal, characteristic
3#20295382C214yesmaximal, complemented
4#20295376C211yesmaximal, characteristic, complemented
5#20295374C211yesmaximal, characteristic, complemented
6#20295373C211yesmaximal, characteristic, complemented
7#20295021C214yesmaximal, complemented
8C4×C8×D109C211yesmaximal, characteristic, complemented
9#487×C109C211yesmaximal, characteristic, complemented
10C2×#13182030C2212yes—
11C2×C8×D109C2212yes—
12#16812699C2211yescharacteristic
13#16812696C2211yescharacteristic
14#16812690C2212yes—
15#16812688C2212yes—
16#16812679—21no—
17#16812675—21no—
18#16812674—21no—
19#16812674—21no—
20Q8×Dic109—21no—
21#16812664—21no—
22#16812661—21no—
23#16812661—21no—
24#16812657C2212yes—
25C42×D109C2211yescharacteristic
26#16812623C2214yes—
27#16812621C2214yes—
28#16812619C2214yes—
29C4×#11724784C2211yescharacteristic
30C8×Dic109C2212yes—
31C4⋊Q8×C109C2211yescharacteristic
32C4⋊Q8×C109C2211yescharacteristic
33#103×C109C2214yes—
34C4×C8×C109C2211yescharacteristic
35#13182030—28no—
36C2×Dic218—21no—
37C2×D436—22no—
38C2×D436—21no—
39C2×D436—21no—
40C2×D436C2312yes—
41C2×C4×D109—22no—
42C2×C4×D109D411yescharacteristic
43C2×C4×D109D411yescharacteristic
44C2×C4×D109C2311yescharacteristic
45C2×#11724784C2312yes—
46C8×D109—24no—
47C4⋊Dic109—21no—
48C4⋊Dic109—22no—
49C4⋊Dic109C2312yes—
50#13182008—22no—
51#13182006—22no—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109—22no—
55C4×Dic109D411yescharacteristic
56C4×Dic109D411yescharacteristic
57C4×Dic109C2311yescharacteristic
58C2×Q8×C109—21no—
59C2×Q8×C109C2312yes—
60C2×C8×C109C2312yes—
61C4⋊C4×C109—21no—
62C4⋊C4×C109—21no—
63C4⋊C4×C109—21no—
64C4⋊C4×C109C2312yes—
65C42×C109C2311yescharacteristic
66C22×D109—22no—
67C22×D109C2×D411yescharacteristic
68Q8×C109—24no—
69Q8×C109—42no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109C2411yescharacteristic
75C2×Dic109—22no—
76C2×Dic109C2×D411yescharacteristic
77C2×Dic109C2×D411yescharacteristic
78C2×Dic109C2×D411yescharacteristic
79D436—24no—
80D436—44no—
81D436—42no—
82D436—42no—
83C4×D109—22no—
84C4×D109—22no—
85C4×D109—44no—
86C4×D109#4114yes—
87Dic218—42no—
88C8×C109—22no—
89#11724784—22no—
90C22×C109C22×D411yescharacteristic
91C2×D109—21no—
92C2×D109—21no—
93C2×D109—42no—
94C2×D109—42no—
95C2×D109—42no—
96C2×D109#12412yes—
97C4×C109—42no—
98C4×C109—42no—
99C4×C109#13512yes—
100C4×C109#13512yes—
101C4×C109C2×#4112yes—
102Dic109—21no—
103Dic109—21no—
104Dic109—42no—
105Dic109#12412yes—
106C2×C109C2×#12411yescharacteristic
107C2×C109C2×#13511yescharacteristic
108C2×C109C2×#13511yescharacteristic
109D109—22no—
110D109—82no—
111#3131—1091nomaximal, Sylow
112C109#313111yescharacteristic, complemented, Sylow
113#533—1091no—
114#532—1091no—
115#488—1094no—
116#487—1091no—
117#487D10911yescharacteristic, complemented
118#486—1091no—
119#486—1091no—
120#416—1094no—
121C2×C4×C8—1091no—
122C2×#41—1092no—
123C22×C8—1092no—
124C4⋊Q8—1091no—
125C4⋊Q8C2×D10911yescharacteristic
126C4⋊Q8C2×D10911yescharacteristic
127#127—1091no—
128#125—1092no—
129#124—1092no—
130C22⋊Q8—2181no—
131C22⋊Q8—2181no—
132#121—2181no—
133#121—2181no—
134C4×Q8—2181no—
135C4×Q8—2181no—
136C4×D4—2181no—
137C4×D4—2181no—
138#117—1092no—
139C2×C42—1091no—
140#103—1094no—
141#103C2×D10914yes—
142#102—1094no—
143#102—1094no—
144C4×C8—1092no—
145C4×C8—1091no—
146C4×C8C2×D10911yescharacteristic
147#41—2188no—
148C2×Q8—21no—
149C2×Q8—2181no—
150C2×Q8C22×D10912yes—
151C2×D4—1092no—
152C2×D4—2182no—
153C2×D4—2181no—
154C2×D4—2181no—
155C22×C4—1091no—
156C22×C4—1091no—
157C22×C4—1091no—
158C22×C4—2182no—
159C2×C8—1092no—
160C2×C8—2184no—
161C2×C8C22×D10912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—1092no—
166C4⋊C4—2182no—
167C4⋊C4—2182no—
168C4⋊C4—2181no—
169C4⋊C4C22×D10912yes—
170C22⋊C4—2182no—
171C22⋊C4—2182no—
172C22⋊C4—2182no—
173C42—1091no—
174C42—1091no—
175C42—1091no—
176C42—2182no—
177C42C22×D10911yescharacteristic
178C23—1091no—
179C23—2182no—
180Q8—24no—
181Q8—42no—
182Q8—4362no—
183D4—4364no—
184D4—4362no—
185D4—4362no—
186D4—2184no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—1091no—
190C2×C4—1094no—
191C2×C4—1091no—
192C2×C4—1091no—
193C2×C4—4364no—
194C2×C4—2182no—
195C2×C4—2182no—
196C2×C4—2182no—
197C2×C4D4×D10911yescharacteristic
198C2×C4D4×D10911yescharacteristic
199C2×C4C23×D10911yescharacteristic
200C8—22no—
201C8—2182no—
202C22—1092no—
203C22—4362no—
204C22—4362no—
205C22—4362no—
206C22—2181no—
207C22—2181no—
208C22C2×D4×D10911yescharacteristic
209C4—42no—
210C4—42no—
211C4—1092no—
212C4—4362no—
213C4—2181no—
214C4—2181no—
215C4#1681272012yes—
216C4#1681272212yes—
217C4#41×D10912yes—
218C2—8722no—
219C2—2182no—
220C2#124×D10911yescharacteristic
221C2C2×#1681272011yescharacteristic
222C2C2×#1681272211yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#487×C109C2
socleC22×C109C22×D4
prime radical#20295577C2
hypercenter#487D109
hypocenterC109#3131
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #20295581C2semidirect
3. #20295382C2semidirect
4. #20295376C2semidirect
5. #20295374C2semidirect
6. #20295373C2semidirect
7. #20295021C2semidirect
8. C4×C8×D109C2semidirect
9. #487×C109C2semidirect
112. C109#3131semidirect
117. #487D109semidirect

Maximal subgroups

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

subgroupindex
#202955812
#202955772
#202953822
#202953762
#202953742
#202953732
#202950212
C4×C8×D1092
#487×C1092
#3131109