Finite Group Databasebeta

← #28373285

Subgroups — #28373285

Order 13952.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#20295638C211yesmaximal, characteristic, complemented
2#20295500C211yesmaximal, characteristic
3#20295368C212yesmaximal, complemented
4#20295327C212yesmaximal, complemented
5#20295232C212yesmaximal, complemented
6#20295179C212yesmaximal
7#20295128C212yesmaximal, complemented
8C4×#13182018C212yesmaximal, complemented
9#433×C109C211yesmaximal, characteristic, complemented
10C22×D436C2211yescharacteristic
11C2×#13182018C2212yes—
12C2×#13182018C2212yes—
13#16812699C2211yescharacteristic, complemented
14#16812692—22no—
15#16812691C2211yescharacteristic, complemented
16#16812689—22no—
17#16812678C2212yes—
18C4×Dic218C2212yescomplemented
19C4×D436C2212yes—
20C4×D436C2212yes—
21#16812661—22no—
22#16812658C2211yescharacteristic
23C22⋊C4×D109—22no—
24#16812633C2212yescomplemented
25#16812631C2212yescomplemented
26#16812624C2212yescomplemented
27#16812624C2212yescomplemented
28#16812621C2212yes—
29#16812621C2212yes—
30#117×C109C2211yescharacteristic
31C4⋊C8×C109C2212yescomplemented
32C22⋊C8×C109C2212yes—
33#97×C109C2211yescharacteristic, complemented
34C4×C8×C109C2211yescharacteristic, complemented
35C23×D109—21no—
36C2×Dic218C2312yes—
37C2×D436—21no—
38C2×D436—24no—
39C2×D436C2312yes—
40C2×C4×D109—22no—
41C2×C4×D109—22no—
42#13182018—24no—
43#13182018—24no—
44C4⋊Dic109—22no—
45C4⋊Dic109C2312yes—
46C4⋊Dic109C2312yes—
47#13182008—22no—
48#13182008—22no—
49#13182008—22no—
50C22⋊Dic109—21no—
51C22⋊Dic109—22no—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109—21no—
55C4×Dic109—22no—
56C22×C4×C109C2311yescharacteristic
57C2×C8×C109C2312yes—
58C2×C8×C109C2312yes—
59C4⋊C4×C109D412yes—
60C22⋊C4×C109D412yes—
61C42×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C23×C109C2×D411yescharacteristic
64C22×D109—22no—
65C22×D109—24no—
66C22×D109—82no—
67C2×C4×C109—22no—
68C2×C4×C109C2×D412yes—
69C2×C4×C109C2×D412yes—
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109C2411yescharacteristic
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75D436—24no—
76D436—22no—
77D436#4114yes—
78C4×D109—82no—
79C4×D109—82no—
80Dic218—22no—
81Dic218—22no—
82C8×C109—22no—
83C8×C109—22no—
84C22×C109—21no—
85C22×C109—22no—
86C22×C109C22×D411yescharacteristic
87C2×D109—24no—
88C2×D109—42no—
89C2×D109—42no—
90C2×D109—84no—
91C4×C109—21no—
92C4×C109—22no—
93C4×C109—22no—
94C4×C109C2×#4112yes—
95Dic109—42no—
96Dic109—42no—
97Dic109—42no—
98C2×C109—41no—
99C2×C109#52511yescharacteristic
100C2×C109#57712yes—
101D109—44no—
102#3123—1091nomaximal, Sylow
103C109#312311yescharacteristic, complemented, Sylow
104#541—1091no—
105#518—1091no—
106#485—1092no—
107#478—1092no—
108#461—1092no—
109#450—1092no—
110#440—1092no—
111C4×SD16—1092no—
112#433D10911yescharacteristic, complemented
113C22×D4—1091no—
114C2×SD16—1092no—
115C2×SD16—1092no—
116C4⋊Q8—1091no—
117#126—2182no—
118#125—1091no—
119#125—2182no—
120C22⋊Q8—1092no—
121C4×Q8—1092no—
122C4×D4—1092no—
123C4×D4—1092no—
124C4×D4—2182no—
125#117—1091no—
126#117C2×D10911yescharacteristic
127C2×C22⋊C4—2182no—
128#107—1092no—
129#106—1092no—
130C4⋊C8C2×D10912yescomplemented
131#103—1092no—
132#103—1092no—
133#102—1092no—
134#102—1092no—
135C22⋊C8C2×D10912yes—
136#97C2×D10911yescharacteristic, complemented
137C4×C8C2×D10911yescharacteristic, complemented
138C24—2181no—
139C2×Q8—1092no—
140C2×D4—1092no—
141C2×D4—2184no—
142C2×D4—2181no—
143C22×C4—2182no—
144C22×C4—2182no—
145C22×C4C22×D10911yescharacteristic
146SD16—2184no—
147SD16—2184no—
148C2×C8C22×D10912yes—
149C2×C8C22×D10912yes—
150C4⋊C4—1092no—
151C4⋊C4—1092no—
152C4⋊C4—2182no—
153C4⋊C4—2182no—
154C4⋊C4—2182no—
155C4⋊C4—2182no—
156C4⋊C4D43612yes—
157C22⋊C4—2181no—
158C22⋊C4—2182no—
159C22⋊C4—2182no—
160C22⋊C4—2182no—
161C22⋊C4D43612yes—
162C42—2181no—
163C42—2182no—
164C42C22×D10911yescharacteristic
165C42C22×D10911yescharacteristic
166C23—8722no—
167C23—2184no—
168C23—2182no—
169C23C2×D43611yescharacteristic
170Q8—2182no—
171Q8—2182no—
172D4—1094no—
173D4—2184no—
174D4—2182no—
175C2×C4—22no—
176C2×C4—8722no—
177C2×C4—8722no—
178C2×C4—2182no—
179C2×C4—2182no—
180C2×C4—2182no—
181C2×C4C2×D43612yes—
182C2×C4C2×D43611yescharacteristic
183C2×C4C2×D43612yes—
184C2×C4C23×D10911yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—8724no—
190C22—4362no—
191C22—4362no—
192C22—2184no—
193C22C22×D43611yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—4362no—
198C4—4362no—
199C4—4362no—
200C4#41×D10912yes—
201C2—41no—
202C2—4364no—
203C2#2029553811yescharacteristic
204C2#2029583812yes—
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#433×C109C2
socleC22×C109C22×D4
prime radicalC22×D436C22
hypercenter#433D109
hypocenterC109#3123
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20295638C2semidirect
3. #20295368C2semidirect
4. #20295327C2semidirect
5. #20295232C2semidirect
7. #20295128C2semidirect
8. C4×#13182018C2semidirect
9. #433×C109C2semidirect
13. #16812699C22semidirect
15. #16812691C22semidirect
18. C4×Dic218C22semidirect
24. #16812633C22semidirect
25. #16812631C22semidirect
26. #16812624C22semidirect
27. #16812624C22semidirect
31. C4⋊C8×C109C22semidirect
33. #97×C109C22semidirect
34. C4×C8×C109C22semidirect
103. C109#3123semidirect
112. #433D109semidirect
130. C4⋊C8C2×D109semidirect
136. #97C2×D109semidirect
137. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956382
#202955002
#202953682
#202953272
#202952322
#202951792
#202951282
C4×#131820182
#433×C1092
#3123109