Finite Group Databasebeta

← #28374466

Subgroups — #28374466

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#20295329C212yesmaximal, complemented
3#20295324C212yesmaximal, complemented
4#20295277C212yesmaximal, complemented
5#20295262C211yesmaximal, characteristic, complemented
6#20295220C212yesmaximal, complemented
7#20295219C212yesmaximal, complemented
8#20295052C211yesmaximal, characteristic, complemented
9#466×C109C211yesmaximal, characteristic, complemented
10C2×D872C2211yescharacteristic
11C2×#13182014C2212yes—
12C2×#13182013C2211yescharacteristic
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#16812633C2211yescharacteristic
24#16812630C2212yes—
25#16812628C2212yes—
26#16812628C2212yes—
27#16812621C2212yes—
28#16812620C2212yes—
29#16812619C2212yes—
30C2×D8×C109C2211yescharacteristic
31C22×C8×C109C2211yescharacteristic
32#121×C109C2212yes—
33#107×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—
43#13182013—41no—
44C2×#11724784C2312yes—
45C4⋊Dic109—22no—
46C4⋊Dic109D411yescharacteristic
47C4⋊Dic109D411yescharacteristic
48C4⋊Dic109C2312yes—
49#13182008—22no—
50C22⋊Dic109—22no—
51C22⋊Dic109D412yes—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109C2312yes—
55C2×D4×C109—22no—
56C2×D4×C109C2312yes—
57C22×C4×C109C2311yescharacteristic
58D8×C109—41no—
59C2×C8×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—21no—
90C22×C109—21no—
91C22×C109—42no—
92C22×C109—42no—
93C22×C109—42no—
94C22×C109C22×D411yescharacteristic
95C2×D109—42no—
96C2×D109—42no—
97C2×D109—42no—
98C4×C109—21no—
99C4×C109—42no—
100C4×C109H(5,𝔽2)11yescharacteristic
101C4×C1092−1+411yescharacteristic
102Dic109—22no—
103Dic109—22no—
104Dic109—42no—
105C2×C109—41no—
106C2×C109—82no—
107C2×C109#53711yescharacteristic
108C2×C109#57611yescharacteristic
109C2×C109#57611yescharacteristic
110D109—82no—
111#3259—1091nomaximal, Sylow
112C109#325911yescharacteristic, complemented, Sylow
113#540—1092no—
114#478—1092no—
115#478—1092no—
116#469—1092no—
117#466—1091no—
118#466D10911yescharacteristic, complemented
119#459—1092no—
120#459—1092no—
121#424—1091no—
122C2×D8—1092no—
123C2×D8—1091no—
124C2×D8C2×D10911yescharacteristic
125C2×M16—1091no—
126C22×C8C2×D10911yescharacteristic
127#127—1092no—
128#125—1092no—
129#123—2182no—
130#123—2182no—
131#121—1092no—
132#121—2182no—
133#121—2182no—
134#121C2×D10912yes—
135C4×D4—1092no—
136C4×D4—1092no—
137#117—1091no—
138#107—1091no—
139#107C2×D10911yescharacteristic
140#106—1092no—
141C4⋊C8—1092no—
142C4⋊C8—1092no—
143#102—1092no—
144#102—1092no—
145#102—1092no—
146#102C2×D10912yes—
147C2×D4—22no—
148C2×D4—1092no—
149C2×D4—2182no—
150C2×D4—2182no—
151C2×D4—2182no—
152C2×D4C22×D10912yes—
153C22×C4—2182no—
154C22×C4—2182no—
155C22×C4C22×D10911yescharacteristic
156D8—41no—
157D8—4361no—
158D8—4362no—
159M16—4361no—
160C2×C8—41no—
161C2×C8—1092no—
162C2×C8C22×D10911yescharacteristic
163C2×C8C22×D10911yescharacteristic
164C4⋊C4—1091no—
165C4⋊C4—1091no—
166C4⋊C4—1092no—
167C4⋊C4—2182no—
168C4⋊C4—2182no—
169C4⋊C4C22×D10912yes—
170C22⋊C4—22no—
171C22⋊C4—1092no—
172C22⋊C4—2182no—
173C22⋊C4—2182no—
174C22⋊C4—2182no—
175C42—1092no—
176C23—22no—
177C23—2182no—
178C23D4×D10911yescharacteristic
179D4—22no—
180D4—22no—
181D4—82no—
182D4—8722no—
183D4—8722no—
184D4—8722no—
185D4—2182no—
186D4—2182no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—8722no—
191C2×C4—8722no—
192C2×C4—1092no—
193C2×C4—1092no—
194C2×C4—2182no—
195C2×C4D4×D10911yescharacteristic
196C2×C4C23×D10911yescharacteristic
197C8—21no—
198C8—21no—
199C8—2182no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—4362no—
207C22—4362no—
208C22—4362no—
209C22C2×D4×D10911yescharacteristic
210C4—21no—
211C4—42no—
212C4—4362no—
213C4—2182no—
214C4—2182no—
215C4#1681274411yescharacteristic
216C4#1681274611yescharacteristic
217C2—41no—
218C2—82no—
219C2—8722no—
220C2#2029560311yescharacteristic
221C2#2029582711yescharacteristic
222C2#2029582811yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#466×C109C2
socleC22×C109C22×D4
hypercenter#466D109
hypocenterC109#3259
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20295629C2semidirect
2. #20295329C2semidirect
3. #20295324C2semidirect
4. #20295277C2semidirect
5. #20295262C2semidirect
6. #20295220C2semidirect
7. #20295219C2semidirect
8. #20295052C2semidirect
9. #466×C109C2semidirect
112. C109#3259semidirect
118. #466D109semidirect

Maximal subgroups

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

subgroupindex
#202956292
#202953292
#202953242
#202952772
#202952622
#202952202
#202952192
#202950522
#466×C1092
#3259109