Finite Group Databasebeta

← #28373276

Subgroups — #28373276

Order 13952.

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

normal subgroups only

This group has 418 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#20295631C211yesmaximal, characteristic, complemented
2#20295500C211yesmaximal, characteristic, complemented
3#20295351C212yesmaximal, complemented
4#20295327C212yesmaximal, complemented
5#20295222C212yesmaximal, complemented
6#20295162C212yesmaximal, complemented
7#20295139C212yesmaximal, complemented
8C4×D872C212yesmaximal, complemented
9#433×C109C211yesmaximal, characteristic, complemented
10C22×D436C2211yescharacteristic
11C2×D872C2212yes—
12C2×D872C2212yes—
13#16812696C2211yescharacteristic, complemented
14#16812691C2211yescharacteristic, complemented
15#16812684—22no—
16#16812673C2212yes—
17#16812672—22no—
18C4×D436C2212yes—
19C4×D436C2212yes—
20C4×D436C2212yescomplemented
21#16812661—22no—
22#16812658C2211yescharacteristic
23C22⋊C4×D109—22no—
24#16812633C2212yescomplemented
25#16812631C2212yescomplemented
26#16812621C2212yes—
27#16812621C2212yes—
28#16812621C2212yescomplemented
29#16812621C2212yescomplemented
30#117×C109C2211yescharacteristic
31C4⋊C8×C109C2212yescomplemented
32C22⋊C8×C109C2212yes—
33#97×C109C2211yescharacteristic, complemented
34C4×C8×C109C2211yescharacteristic, complemented
35C23×D109—21no—
36C2×D436—21no—
37C2×D436—24no—
38C2×D436—22no—
39C2×D436C2312yes—
40C2×D436C2312yes—
41C2×C22⋊D109—22no—
42C2×C4×D109—22no—
43C2×C4×D109—22no—
44C2×C4×D109—22no—
45D872—24no—
46D872—24no—
47C4⋊Dic109C2312yes—
48C4⋊Dic109C2312yes—
49#13182008—22no—
50C22⋊Dic109—21no—
51#13182006—22no—
52#13182006—22no—
53#13182006—22no—
54#13182006—22no—
55C4×Dic109—21no—
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—22no—
67C22×D109—82no—
68C2×C4×C109—22no—
69C2×C4×C109C2×D412yes—
70C2×C4×C109C2×D412yes—
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109C2411yescharacteristic
73C22⋊D109—82no—
74C2×Dic109—22no—
75C2×Dic109—22no—
76D436—24no—
77D436—22no—
78D436—22no—
79D436—22no—
80D436—82no—
81D436#4114yes—
82C4×D109—82no—
83C4×D109—82no—
84C4×D109—82no—
85C8×C109—22no—
86C8×C109—22no—
87C22×C109—21no—
88C22×C109—22no—
89C22×C109C22×D411yescharacteristic
90C2×D109—24no—
91C2×D109—42no—
92C2×D109—42no—
93C2×D109—42no—
94C2×D109—42no—
95C2×D109—42no—
96C2×D109—84no—
97C4×C109—21no—
98C4×C109—22no—
99C4×C109—22no—
100C4×C109C2×#4112yes—
101Dic109—42no—
102Dic109—42no—
103C2×C109—41no—
104C2×C109#52511yescharacteristic
105C2×C109#57612yes—
106D109—44no—
107D109—82no—
108#3122—1091nomaximal, Sylow
109C109#312211yescharacteristic, complemented, Sylow
110#540—1091no—
111#518—1091no—
112#482—1092no—
113#478—1092no—
114#459—1092no—
115#447—1092no—
116#442—1092no—
117C4×D8—1092no—
118#433D10911yescharacteristic, complemented
119C22×D4—1091no—
120C2×D8—1092no—
121C2×D8—1092no—
122#127—1091no—
123#125—1091no—
124#123—2182no—
125#121—1092no—
126#121—2182no—
127C4×D4—1092no—
128C4×D4—1092no—
129C4×D4—1092no—
130C4×D4—2182no—
131#117—1091no—
132#117C2×D10911yescharacteristic
133C2×C22⋊C4—2182no—
134#107—1092no—
135#106—1092no—
136C4⋊C8C2×D10912yescomplemented
137#102—1092no—
138#102—1092no—
139#102—1092no—
140#102—1092no—
141C22⋊C8C2×D10912yes—
142#97C2×D10911yescharacteristic, complemented
143C4×C8C2×D10911yescharacteristic, complemented
144C24—2181no—
145C2×D4—1092no—
146C2×D4—1092no—
147C2×D4—2184no—
148C2×D4—2182no—
149C2×D4—2182no—
150C2×D4—2181no—
151C22×C4—2182no—
152C22×C4—2182no—
153C22×C4—2182no—
154C22×C4C22×D10911yescharacteristic
155D8—2184no—
156D8—2184no—
157C2×C8C22×D10912yes—
158C2×C8C22×D10912yes—
159C4⋊C4—1092no—
160C4⋊C4—1092no—
161C4⋊C4—2182no—
162C4⋊C4D43612yes—
163C22⋊C4—2181no—
164C22⋊C4—2182no—
165C22⋊C4—2182no—
166C22⋊C4—2182no—
167C22⋊C4—2182no—
168C22⋊C4D43612yes—
169C42—2181no—
170C42C22×D10911yescharacteristic
171C42C22×D10911yescharacteristic
172C23—8722no—
173C23—2184no—
174C23—2182no—
175C23—2182no—
176C23C2×D43611yescharacteristic
177D4—8722no—
178D4—8722no—
179D4—1094no—
180D4—2184no—
181D4—2182no—
182D4—2182no—
183D4—2182no—
184C2×C4—22no—
185C2×C4—8722no—
186C2×C4—8722no—
187C2×C4—8722no—
188C2×C4—2182no—
189C2×C4—2182no—
190C2×C4C2×D43611yescharacteristic
191C2×C4C2×D43612yes—
192C2×C4C2×D43612yes—
193C2×C4C23×D10911yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—8724no—
199C22—4362no—
200C22—4362no—
201C22—4362no—
202C22—4362no—
203C22—4362no—
204C22—2184no—
205C22C22×D43611yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—4362no—
210C4—4362no—
211C4#41×D10912yes—
212C2—41no—
213C2—8722no—
214C2—4364no—
215C2#2029553811yescharacteristic
216C2#2029583112yes—
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#433×C109C2
socleC22×C109C22×D4
hypercenter#433D109
hypocenterC109#3122
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. #20295631C2semidirect
2. #20295500C2semidirect
3. #20295351C2semidirect
4. #20295327C2semidirect
5. #20295222C2semidirect
6. #20295162C2semidirect
7. #20295139C2semidirect
8. C4×D872C2semidirect
9. #433×C109C2semidirect
13. #16812696C22semidirect
14. #16812691C22semidirect
20. C4×D436C22semidirect
24. #16812633C22semidirect
25. #16812631C22semidirect
28. #16812621C22semidirect
29. #16812621C22semidirect
31. C4⋊C8×C109C22semidirect
33. #97×C109C22semidirect
34. C4×C8×C109C22semidirect
109. C109#3122semidirect
118. #433D109semidirect
136. C4⋊C8C2×D109semidirect
142. #97C2×D109semidirect
143. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956312
#202955002
#202953512
#202953272
#202952222
#202951622
#202951392
C4×D8722
#433×C1092
#3122109