Finite Group Databasebeta

← #28374468

Subgroups — #28374468

Order 13952.

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

normal subgroups only

This group has 370 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#20295629C212yesmaximal, complemented
2#20295328C212yesmaximal, complemented
3#20295325C212yesmaximal, complemented
4#20295279C211yesmaximal, characteristic, complemented
5#20295260C212yesmaximal, complemented
6#20295220C212yesmaximal, complemented
7#20295219C212yesmaximal, complemented
8#20295054C211yesmaximal, characteristic, complemented
9#469×C109C211yesmaximal, characteristic, complemented
10C2×D872C2211yescharacteristic
11C2×#13182014C2212yes—
12C22×#11724784C2211yescharacteristic
13#16812695C2212yes—
14#16812690C2212yes—
15#16812683—22no—
16#16812681—22no—
17#16812673C2212yes—
18#16812671—22no—
19#16812670—22no—
20D4×Dic109C2212yes—
21#16812661C2212yes—
22#16812658C2211yescharacteristic
23#16812632C2212yes—
24#16812631C2211yescharacteristic
25#16812628C2212yes—
26#16812628C2212yes—
27#16812621C2212yes—
28#16812620C2212yes—
29#16812619C2212yes—
30C2×D8×C109C2211yescharacteristic
31C2×M16×C109C2211yescharacteristic
32#121×C109C2212yes—
33#106×C109C2211yescharacteristic
34#102×C109C2212yes—
35C2×D436C2312yes—
36C2×C22⋊D109—22no—
37C2×C22⋊D109—22no—
38C2×C22⋊D109—22no—
39C22×Dic109—22no—
40C2×C4×D109—22no—
41D872—41no—
42#13182014—42no—
43C2×#11724784—41no—
44C2×#11724784C2312yes—
45C4⋊Dic109—22no—
46C4⋊Dic109D412yes—
47C4⋊Dic109C2312yes—
48#13182008—22no—
49C22⋊Dic109—22no—
50C22⋊Dic109D411yescharacteristic
51C22⋊Dic109D411yescharacteristic
52#13182006—22no—
53#13182006—22no—
54C4×Dic109C2312yes—
55C2×D4×C109—22no—
56C2×D4×C109C2312yes—
57C22×C4×C109C2311yescharacteristic
58D8×C109—41no—
59M16×C109—41no—
60C2×C8×C109C2311yescharacteristic
61C2×C8×C109C2311yescharacteristic
62C4⋊C4×C109C2312yes—
63C22⋊C4×C109—22no—
64C23×C109—22no—
65C23×C109C2×D411yescharacteristic
66C22×D109—22no—
67D4×C109—22no—
68D4×C109—22no—
69D4×C109—82no—
70C2×C4×C109—21no—
71C2×C4×C109—21no—
72C2×C4×C109—22no—
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109C2411yescharacteristic
75C22⋊D109—82no—
76C22⋊D109—82no—
77C22⋊D109—82no—
78C2×Dic109—22no—
79C2×Dic109—82no—
80C2×Dic109C2×D412yes—
81C2×Dic109C2×D412yes—
82D436—22no—
83D436—22no—
84C4×D109—82no—
85C8×C109—21no—
86C8×C109—21no—
87#11724784—22no—
88C22×C109—21no—
89C22×C109—22no—
90C22×C109—42no—
91C22×C109—42no—
92C22×C109—42no—
93C22×C109C22×D411yescharacteristic
94C2×D109—42no—
95C2×D109—42no—
96C2×D109—42no—
97C4×C109—21no—
98C4×C109—42no—
99C4×C109H(5,𝔽2)11yescharacteristic
100C4×C1092−1+411yescharacteristic
101Dic109—22no—
102Dic109—22no—
103Dic109—42no—
104C2×C109—41no—
105C2×C109—82no—
106C2×C109#53711yescharacteristic
107C2×C109#57612yes—
108D109—82no—
109#3259—1091nomaximal, Sylow
110C109#325911yescharacteristic, complemented, Sylow
111#540—1092no—
112#478—1092no—
113#478—1092no—
114#469—1091no—
115#469D10911yescharacteristic, complemented
116#466—1092no—
117#459—1092no—
118#459—1092no—
119#424—1091no—
120C2×D8—1092no—
121C2×D8—1091no—
122C2×D8C2×D10911yescharacteristic
123C2×M16C2×D10911yescharacteristic
124C22×C8—1091no—
125#127—1092no—
126#125—1092no—
127#123—2182no—
128#123—2182no—
129#121—1092no—
130#121—2182no—
131#121—2182no—
132#121C2×D10912yes—
133C4×D4—1092no—
134C4×D4—1092no—
135#117—1091no—
136#107—1092no—
137#106—1091no—
138#106C2×D10911yescharacteristic
139C4⋊C8—1092no—
140C4⋊C8—1092no—
141#102—1092no—
142#102—1092no—
143#102—1092no—
144#102C2×D10912yes—
145C2×D4—22no—
146C2×D4—1092no—
147C2×D4—2182no—
148C2×D4—2182no—
149C2×D4—2182no—
150C2×D4C22×D10912yes—
151C22×C4—2182no—
152C22×C4—2182no—
153C22×C4C22×D10911yescharacteristic
154D8—41no—
155D8—4361no—
156D8—4362no—
157M16—41no—
158C2×C8—1092no—
159C2×C8—4361no—
160C2×C8C22×D10911yescharacteristic
161C2×C8C22×D10911yescharacteristic
162C4⋊C4—1092no—
163C4⋊C4—1092no—
164C4⋊C4—2182no—
165C4⋊C4—2182no—
166C4⋊C4C22×D10912yes—
167C22⋊C4—22no—
168C22⋊C4—1091no—
169C22⋊C4—1091no—
170C22⋊C4—2182no—
171C22⋊C4—2182no—
172C22⋊C4—2182no—
173C42—1092no—
174C23—22no—
175C23—2182no—
176C23D4×D10911yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—8722no—
181D4—8722no—
182D4—8722no—
183D4—2182no—
184D4—2182no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—8722no—
189C2×C4—8722no—
190C2×C4—1092no—
191C2×C4—1092no—
192C2×C4—2182no—
193C2×C4D4×D10911yescharacteristic
194C2×C4C23×D10911yescharacteristic
195C8—21no—
196C8—21no—
197C8—2182no—
198C22—22no—
199C22—21no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—4362no—
204C22—4362no—
205C22—4362no—
206C22C2×D4×D10911yescharacteristic
207C4—21no—
208C4—42no—
209C4—4362no—
210C4—2182no—
211C4—2182no—
212C4#1681274411yescharacteristic
213C4#1681274611yescharacteristic
214C2—41no—
215C2—82no—
216C2—8722no—
217C2#2029560311yescharacteristic
218C2#2029583012yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#469×C109C2
socleC22×C109C22×D4
hypercenter#469D109
hypocenterC109#3259
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20295629C2semidirect
2. #20295328C2semidirect
3. #20295325C2semidirect
4. #20295279C2semidirect
5. #20295260C2semidirect
6. #20295220C2semidirect
7. #20295219C2semidirect
8. #20295054C2semidirect
9. #469×C109C2semidirect
110. C109#3259semidirect
115. #469D109semidirect

Maximal subgroups

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

subgroupindex
#202956292
#202953282
#202953252
#202952792
#202952602
#202952202
#202952192
#202950542
#469×C1092
#3259109