Finite Group Databasebeta

← #28373279

Subgroups — #28373279

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#20295500C211yesmaximal, characteristic
2#20295364C212yesmaximal, complemented
3#20295323C212yesmaximal, complemented
4#20295228C212yesmaximal, complemented
5#20295176C212yesmaximal
6#20295124C212yesmaximal, complemented
7C4×#13182016C212yesmaximal, complemented
8#20295087C211yesmaximal, characteristic, complemented
9#541×C109C211yesmaximal, characteristic, complemented
10C22×D436C2211yescharacteristic
11C2×#13182016C2212yes—
12C2×#13182016C2212yes—
13C4×D436C2212yes—
14C4×D436C2212yes—
15#16812661—22no—
16#16812658C2211yescharacteristic
17C22⋊C4×D109—22no—
18#16812632C2212yescomplemented
19#16812630C2212yescomplemented
20C4⋊#11724784C2212yescomplemented
21#16812623C2212yescomplemented
22#16812623C2212yescomplemented
23#16812619C2212yes—
24#16812619C2212yes—
25C22⋊#11724784C2212yes—
26#16812610C2211yescharacteristic, complemented
27C4×#11724784C2211yescharacteristic, complemented
28C4⋊Q8×C109C2211yescharacteristic, complemented
29#126×C109—22no—
30#125×C109—22no—
31#125×C109C2211yescharacteristic, complemented
32C22⋊Q8×C109C2212yes—
33C4×Q8×C109C2212yescomplemented
34#117×C109C2211yescharacteristic
35C23×D109—21no—
36C2×D436—21no—
37C2×D436—24no—
38C2×D436C2312yes—
39C2×C4×D109—22no—
40C2×C4×D109—22no—
41#13182016—24no—
42#13182016—24no—
43C2×#11724784C2312yes—
44C2×#11724784C2312yes—
45C4⋊Dic109C2312yes—
46C22⋊Dic109—21no—
47#13182006—22no—
48#13182006—22no—
49C4×Dic109—21no—
50C2×Q8×C109C2312yes—
51C22×C4×C109C2311yescharacteristic
52C4⋊C4×C109—22no—
53C4⋊C4×C109—22no—
54C4⋊C4×C109—22no—
55C4⋊C4×C109—22no—
56C4⋊C4×C109D412yes—
57C4⋊C4×C109C2312yes—
58C22⋊C4×C109—22no—
59C22⋊C4×C109D412yes—
60C42×C109—22no—
61C42×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C23×C109C2×D411yescharacteristic
64C22×D109—22no—
65C22×D109—24no—
66C22×D109—82no—
67Q8×C109—22no—
68Q8×C109—22no—
69C2×C4×C109—22no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D412yes—
73C2×C4×C109C2×D412yes—
74C2×C4×C109C2×D411yescharacteristic
75C2×C4×C109C2411yescharacteristic
76C2×Dic109—22no—
77D436—24no—
78D436—22no—
79D436#4114yes—
80C4×D109—82no—
81C4×D109—82no—
82#11724784—22no—
83#11724784—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×C109—42no—
95C4×C109—42no—
96C4×C109C2×#4112yes—
97Dic109—42no—
98C2×C109—41no—
99C2×C109#52511yescharacteristic
100C2×C109#57712yes—
101D109—44no—
102#3123—1091nomaximal, Sylow
103C109#312311yescharacteristic, complemented, Sylow
104#541D10911yescharacteristic, complemented
105#518—1091no—
106#485—1092no—
107#478—1092no—
108#461—1092no—
109#450—1092no—
110#440—1092no—
111C4×SD16—1092no—
112#433—1091no—
113C22×D4—1091no—
114C2×SD16—1092no—
115C2×SD16—1092no—
116C4⋊Q8C2×D10911yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D10911yescharacteristic, complemented
120C22⋊Q8C2×D10912yes—
121C4×Q8C2×D10912yescomplemented
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⋊C8—1092no—
131#103—1092no—
132#103—1092no—
133#102—1092no—
134#102—1092no—
135C22⋊C8—1092no—
136#97—1091no—
137C4×C8—1091no—
138C24—2181no—
139C2×Q8C22×D10912yes—
140C2×D4—1092no—
141C2×D4—2184no—
142C2×D4—2181no—
143C22×C4—2182no—
144C22×C4—2182no—
145C22×C4C22×D10911yescharacteristic
146SD16—2184no—
147SD16—2184no—
148C2×C8—1092no—
149C2×C8—1092no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—1092no—
155C4⋊C4C22⋊D10912yes—
156C4⋊C4C22×D10912yes—
157C22⋊C4—22no—
158C22⋊C4—2181no—
159C22⋊C4—2182no—
160C22⋊C4—2182no—
161C22⋊C4C22⋊D10912yes—
162C42—22no—
163C42—2181no—
164C42C22×D10911yescharacteristic
165C42C22×D10911yescharacteristic
166C23—8722no—
167C23—2184no—
168C23—2182no—
169C23C2×C22⋊D10911yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—1094no—
173D4—2184no—
174D4—2182no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—8722no—
179C2×C4—8722no—
180C2×C4—2182no—
181C2×C4C2×C22⋊D10912yes—
182C2×C4C2×C22⋊D10911yescharacteristic
183C2×C4C2×C22⋊D10912yes—
184C2×C4C23×D10911yescharacteristic
185C8—2182no—
186C8—2182no—
187C22—21no—
188C22—22no—
189C22—8724no—
190C22—4362no—
191C22—4362no—
192C22—2184no—
193C22C22×C22⋊D10911yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—4362no—
200C4#41×D10912yes—
201C2—41no—
202C2—4364no—
203C2#2029553311yescharacteristic
204C2#2029583412yes—
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#541×C109C2
socleC22×C109C22×D4
prime radicalC22×D436C22
hypercenter#541D109
hypocenterC109#3123
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20295364C2semidirect
3. #20295323C2semidirect
4. #20295228C2semidirect
6. #20295124C2semidirect
7. C4×#13182016C2semidirect
8. #20295087C2semidirect
9. #541×C109C2semidirect
18. #16812632C22semidirect
19. #16812630C22semidirect
20. C4⋊#11724784C22semidirect
21. #16812623C22semidirect
22. #16812623C22semidirect
26. #16812610C22semidirect
27. C4×#11724784C22semidirect
28. C4⋊Q8×C109C22semidirect
31. #125×C109C22semidirect
33. C4×Q8×C109C22semidirect
103. C109#3123semidirect
104. #541D109semidirect
116. C4⋊Q8C2×D109semidirect
119. #125C2×D109semidirect
121. C4×Q8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955002
#202953642
#202953232
#202952282
#202951762
#202951242
C4×#131820162
#202950872
#541×C1092
#3123109