Finite Group Databasebeta

← #28374487

Subgroups — #28374487

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#20295643C212yesmaximal, complemented
2#20295320C212yesmaximal, complemented
3#20295304C212yesmaximal, complemented
4#20295270C212yesmaximal, complemented
5#20295267C211yesmaximal, characteristic, complemented
6#20295247C212yesmaximal, complemented
7#20295239C212yesmaximal, complemented
8#20295052C211yesmaximal, characteristic, complemented
9#466×C109C211yesmaximal, characteristic
10C2×Dic436C2211yescharacteristic
11C2×#13182017C2212yes—
12C2×#13182013C2211yescharacteristic
13#16812698C2212yes—
14#16812692—22no—
15#16812686—22no—
16#16812686C2212yes—
17#16812680—22no—
18#16812678C2212yes—
19#16812676—22no—
20#16812664C2212yes—
21D4×Dic109C2212yes—
22#16812658C2211yescharacteristic
23#16812633C2211yescharacteristic
24#16812632C2212yes—
25#16812628C2212yes—
26#16812628C2212yes—
27#16812624C2212yes—
28#16812622C2212yes—
29#16812620C2212yes—
30C2×D8×C109C2211yescharacteristic
31C22×C8×C109C2211yescharacteristic
32#121×C109C2212yes—
33#107×C109C2211yescharacteristic
34#102×C109C2212yes—
35C2×Dic218—22no—
36C2×Dic218C2312yes—
37C22×Dic109—22no—
38Dic436—41no—
39#13182017—42no—
40#13182013—41no—
41C2×#11724784C2312yes—
42C4⋊Dic109D411yescharacteristic
43C4⋊Dic109D411yescharacteristic
44C4⋊Dic109C2312yes—
45#13182008—22no—
46#13182008—22no—
47#13182008—22no—
48C22⋊Dic109—22no—
49C22⋊Dic109—22no—
50C22⋊Dic109—22no—
51C22⋊Dic109—22no—
52C22⋊Dic109D412yes—
53C4×Dic109—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
66D4×C109—22no—
67D4×C109—22no—
68D4×C109—82no—
69C2×C4×C109—21no—
70C2×C4×C109—21no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2411yescharacteristic
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—82no—
77C2×Dic109C2×D412yes—
78C2×Dic109C2×D412yes—
79Dic218—22no—
80Dic218—22no—
81Dic218—82no—
82C8×C109—21no—
83C8×C109—21no—
84#11724784—22no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109—21no—
88C22×C109—42no—
89C22×C109—42no—
90C22×C109—42no—
91C22×C109C22×D411yescharacteristic
92C4×C109—21no—
93C4×C109—42no—
94C4×C109H(5,𝔽2)11yescharacteristic
95C4×C1092−1+411yescharacteristic
96Dic109—22no—
97Dic109—22no—
98Dic109—42no—
99Dic109—42no—
100C2×C109—41no—
101C2×C109—82no—
102C2×C109#53711yescharacteristic
103C2×C109#57611yescharacteristic
104C2×C109#57811yescharacteristic
105#3262—1091nomaximal, Sylow
106C109#326211yescharacteristic, complemented, Sylow
107#542—1092no—
108#477—1092no—
109#474—1092no—
110#468—1092no—
111#467—1091no—
112#466D10911yescharacteristic
113#464—1092no—
114#463—1092no—
115#424—1091no—
116C2×Q16—1091no—
117C2×SD16—1092no—
118C2×D8C2×D10911yescharacteristic
119C2×M16—1091no—
120C22×C8C2×D10911yescharacteristic
121C4⋊Q8—1092no—
122#126—2182no—
123#124—1092no—
124#124—2182no—
125#123—2182no—
126C22⋊Q8—1092no—
127C22⋊Q8—2182no—
128#121C2×D10912yes—
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#103—1092no—
139#102—1092no—
140#102C2×D10912yes—
141C2×Q8—1092no—
142C2×Q8—2182no—
143C2×D4—22no—
144C2×D4C22×D10912yes—
145C22×C4—2182no—
146C22×C4C22×D10911yescharacteristic
147Q16—4361no—
148SD16—4362no—
149D8—41no—
150M16—4361no—
151C2×C8—41no—
152C2×C8—1092no—
153C2×C8C22×D10911yescharacteristic
154C2×C8C22×D10911yescharacteristic
155C4⋊C4—1091no—
156C4⋊C4—1091no—
157C4⋊C4—1092no—
158C4⋊C4—2182no—
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—22no—
171C23D4×D10911yescharacteristic
172Q8—8722no—
173Q8—2182no—
174Q8—2182no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—8722no—
182C2×C4—1092no—
183C2×C4—1092no—
184C2×C4—2182no—
185C2×C4—2182no—
186C2×C4D4×D10911yescharacteristic
187C2×C4C23×D10911yescharacteristic
188C8—21no—
189C8—21no—
190C8—2182no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D10911yescharacteristic
198C4—21no—
199C4—42no—
200C4—4362no—
201C4—4362no—
202C4—2182no—
203C4—2182no—
204C4#1681274411yescharacteristic
205C4#1681274611yescharacteristic
206C2—41no—
207C2—82no—
208C2#2029560311yescharacteristic
209C2#2029582711yescharacteristic
210C2#2029584011yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting, prime radical#466×C109C2
socleC22×C109C22×D4
hypercenter#466D109
hypocenterC109#3262
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. #20295643C2semidirect
2. #20295320C2semidirect
3. #20295304C2semidirect
4. #20295270C2semidirect
5. #20295267C2semidirect
6. #20295247C2semidirect
7. #20295239C2semidirect
8. #20295052C2semidirect
106. C109#3262semidirect

Maximal subgroups

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

subgroupindex
#202956432
#202953202
#202953042
#202952702
#202952672
#202952472
#202952392
#202950522
#466×C1092
#3262109