Finite Group Databasebeta

← #28374494

Subgroups — #28374494

Order 13952.

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

normal subgroups only

This group has 346 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#20295649C212yesmaximal, complemented
2#20295319C212yesmaximal, complemented
3#20295305C212yesmaximal, complemented
4#20295274C212yesmaximal, complemented
5#20295262C211yesmaximal, characteristic
6#20295250C212yesmaximal, complemented
7#20295244C212yesmaximal, complemented
8#20295052C211yesmaximal, characteristic, complemented
9#467×C109C211yesmaximal, characteristic, complemented
10C2×#13182016C2212yes—
11C2×D872C2211yescharacteristic
12C2×#13182013C2211yescharacteristic
13#16812698C2212yes—
14#16812694—22no—
15#16812688C2212yes—
16#16812685—22no—
17#16812681—22no—
18#16812679—22no—
19#16812673C2212yes—
20Q8×Dic109C2212yes—
21#16812661C2212yes—
22#16812658C2211yescharacteristic
23#16812633C2211yescharacteristic
24#16812632C2212yes—
25#16812628C2212yes—
26#16812628C2212yes—
27#16812623C2212yes—
28#16812621C2212yes—
29#16812619C2212yes—
30C2×Q16×C109C2211yescharacteristic
31C22×C8×C109C2211yescharacteristic
32C22⋊Q8×C109C2212yes—
33#107×C109C2211yescharacteristic
34#103×C109C2212yes—
35C2×Dic218—22no—
36C2×D436C2312yes—
37C2×C22⋊D109—22no—
38C2×C4×D109—22no—
39#13182016—42no—
40D872—41no—
41#13182013—41no—
42C2×#11724784C2312yes—
43C4⋊Dic109—22no—
44C4⋊Dic109D411yescharacteristic
45C4⋊Dic109D411yescharacteristic
46C4⋊Dic109C2312yes—
47#13182008—22no—
48C22⋊Dic109D412yes—
49#13182006—22no—
50#13182006—22no—
51#13182006—22no—
52#13182006—22no—
53C4×Dic109—22no—
54C4×Dic109C2312yes—
55C2×Q8×C109C2312yes—
56C22×C4×C109C2311yescharacteristic
57Q16×C109—41no—
58C2×C8×C109—41no—
59C2×C8×C109C2311yescharacteristic
60C2×C8×C109C2311yescharacteristic
61C4⋊C4×C109—22no—
62C4⋊C4×C109C2312yes—
63C22⋊C4×C109—22no—
64C23×C109C2×D411yescharacteristic
65C22×D109—22no—
66Q8×C109—22no—
67Q8×C109—22no—
68C2×C4×C109—21no—
69C2×C4×C109—21no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2411yescharacteristic
74C22⋊D109—82no—
75C2×Dic109—22no—
76C2×Dic109C2×D412yes—
77C2×Dic109C2×D412yes—
78D436—22no—
79D436—22no—
80C4×D109—82no—
81Dic218—82no—
82C8×C109—21no—
83C8×C109—21no—
84#11724784—22no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109—21no—
88C22×C109C22×D411yescharacteristic
89C2×D109—42no—
90C2×D109—42no—
91C2×D109—42no—
92C4×C109—21no—
93C4×C109—42no—
94C4×C109—42no—
95C4×C109H(5,𝔽2)11yescharacteristic
96C4×C1092−1+411yescharacteristic
97Dic109—22no—
98Dic109—22no—
99Dic109—42no—
100C2×C109—41no—
101C2×C109#53711yescharacteristic
102C2×C109#57611yescharacteristic
103C2×C109#57811yescharacteristic
104D109—82no—
105#3262—1091nomaximal, Sylow
106C109#326211yescharacteristic, complemented, Sylow
107#542—1092no—
108#477—1092no—
109#474—1092no—
110#468—1092no—
111#467D10911yescharacteristic, complemented
112#466—1091no—
113#464—1092no—
114#463—1092no—
115#424—1091no—
116C2×Q16C2×D10911yescharacteristic
117C2×SD16—1092no—
118C2×D8—1091no—
119C2×M16—1091no—
120C22×C8C2×D10911yescharacteristic
121C4⋊Q8—1092no—
122#126—2182no—
123#124—1092no—
124#124—2182no—
125#123—2182no—
126C22⋊Q8—2182no—
127C22⋊Q8C2×D10912yes—
128#121—1092no—
129C4×Q8—1092no—
130C4×D4—1092no—
131#117—1091no—
132#107—1091no—
133#107—1092no—
134#107C2×D10911yescharacteristic
135C4⋊C8—1092no—
136C4⋊C8—1092no—
137#103—1092no—
138#103C2×D10912yes—
139#102—1092no—
140#102—1092no—
141C2×Q8—2182no—
142C2×Q8C22×D10912yes—
143C2×D4—1092no—
144C2×D4—2182no—
145C22×C4—2182no—
146C22×C4C22×D10911yescharacteristic
147Q16—41no—
148SD16—4362no—
149D8—4361no—
150M16—4361no—
151C2×C8—41no—
152C2×C8—1092no—
153C2×C8C22×D10911yescharacteristic
154C2×C8C22×D10911yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—1091no—
157C4⋊C4—1091no—
158C4⋊C4—1092no—
159C4⋊C4—2182no—
160C4⋊C4—2182no—
161C4⋊C4C22×D10912yes—
162C22⋊C4—22no—
163C22⋊C4—1092no—
164C22⋊C4—2182no—
165C22⋊C4—2182no—
166C22⋊C4—2182no—
167C22⋊C4—2182no—
168C42—1092no—
169C42—2182no—
170C23—2182no—
171C23D4×D10911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—8722no—
175D4—8722no—
176D4—2182no—
177D4—2182no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—8722no—
183C2×C4—1092no—
184C2×C4—1092no—
185C2×C4—2182no—
186C2×C4D4×D10911yescharacteristic
187C2×C4C23×D10911yescharacteristic
188C8—21no—
189C8—21no—
190C8—2182no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—4362no—
195C22—4362no—
196C22—4362no—
197C22C2×D4×D10911yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—4362no—
202C4—2182no—
203C4—2182no—
204C4#1681274411yescharacteristic
205C4#1681274611yescharacteristic
206C2—41no—
207C2—8722no—
208C2#2029560311yescharacteristic
209C2#2029582811yescharacteristic
210C2#2029583911yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#467×C109C2
socleC22×C109C22×D4
prime radical#20295262C2
hypercenter#467D109
hypocenterC109#3262
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20295649C2semidirect
2. #20295319C2semidirect
3. #20295305C2semidirect
4. #20295274C2semidirect
6. #20295250C2semidirect
7. #20295244C2semidirect
8. #20295052C2semidirect
9. #467×C109C2semidirect
106. C109#3262semidirect
111. #467D109semidirect

Maximal subgroups

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

subgroupindex
#202956492
#202953192
#202953052
#202952742
#202952622
#202952502
#202952442
#202950522
#467×C1092
#3262109