Finite Group Databasebeta

← #28361994

Subgroups — #28361994

Order 13952.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#20295625C211yesmaximal, characteristic
2#20295165C211yesmaximal, characteristic
3#20294945C211yesmaximal, characteristic, complemented
4#20294763C211yesmaximal, characteristic, complemented
5#20294761C211yesmaximal, characteristic
6#20294751C211yesmaximal, characteristic, complemented
7#451×C109C211yesmaximal, characteristic, complemented
8C2×#13182016—21no—
9#16812694—21no—
10#16812690—21no—
11#16812684—21no—
12#16812683—21no—
13#16812675—21no—
14#16812673C2211yescharacteristic
15#16812659—21no—
16C2×#13182008—21no—
17C2×#13182008C2211yescharacteristic
18#16812623—21no—
19C22⋊#11724784C2211yescharacteristic
20#16812606—21no—
21#16812606C2211yescharacteristic
22C22×Q8×C109C2211yescharacteristic
23C2×Q16×C109—21no—
24C22⋊Q8×C109C2211yescharacteristic
25#103×C109—21no—
26C22⋊C8×C109C2211yescharacteristic
27C2×D436D411yescharacteristic
28C2×C22⋊D109—21no—
29C22×Dic109—21no—
30C22×Dic109D411yescharacteristic
31C22×Dic109D411yescharacteristic
32C2×C4×D109—21no—
33#13182016—42no—
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109D411yescharacteristic
38#13182008—21no—
39#13182008—21no—
40#13182008—21no—
41#13182008—42no—
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46C4×Dic109—21no—
47C2×Q8×C109—21no—
48C2×Q8×C109—21no—
49C2×Q8×C109—42no—
50C2×Q8×C109D411yescharacteristic
51C22×C4×C109—21no—
52C22×C4×C109C2311yescharacteristic
53Q16×C109—42no—
54C2×C8×C109—21no—
55C4⋊C4×C109—21no—
56C4⋊C4×C109D411yescharacteristic
57C22⋊C4×C109—21no—
58C23×C109C2×D411yescharacteristic
59C22×D109—21no—
60Q8×C109—22no—
61Q8×C109—22no—
62Q8×C109—41no—
63Q8×C109—41no—
64Q8×C109—41no—
65C2×C4×C109—22no—
66C2×C4×C109—21no—
67C2×C4×C109—21no—
68C2×C4×C109—41no—
69C2×C4×C109—41no—
70C2×C4×C109—41no—
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109C2×D411yescharacteristic
73C22⋊D109—41no—
74C22⋊D109—41no—
75C2×Dic109—22no—
76C2×Dic109—21no—
77C2×Dic109—21no—
78C2×Dic109—21no—
79C2×Dic109—21no—
80C2×Dic109—21no—
81C2×Dic109—41no—
82C2×Dic109—41no—
83C2×Dic109—41no—
84D436—41no—
85C4×D109—81no—
86C8×C109—41no—
87#11724784—41no—
88C22×C109—21no—
89C22×C109—21no—
90C22×C109#12011yescharacteristic
91C22×C109#13511yescharacteristic
92C22×C109#13711yescharacteristic
93C2×D109—41no—
94C2×D109—41no—
95C2×D109—41no—
96C4×C109—21no—
97C4×C109—21no—
98C4×C109—41no—
99C4×C109—41no—
100C4×C109—42no—
101Dic109—42no—
102Dic109—41no—
103Dic109—41no—
104Dic109—41no—
105C2×C109—21no—
106C2×C109—21no—
107C2×C109#45211yescharacteristic
108C2×C109#45611yescharacteristic
109C2×C109B(4,𝔽2)11yescharacteristic
110D109—81no—
111#1603—1091nomaximal, Sylow
112C109#160311yescharacteristic, complemented, Sylow
113#539—1091no—
114#451D10911yescharacteristic, complemented
115#448—1091no—
116#395—1091no—
117#328—1091no—
118#327—1091no—
119#324—1091no—
120C22×Q8C2×D10911yescharacteristic
121C2×Q16—21no—
122C2×SD16—2181no—
123#126—2181no—
124#125—2181no—
125#123—2181no—
126#123—2181no—
127C22⋊Q8—2181no—
128C22⋊Q8C2×D10911yescharacteristic
129#121—1091no—
130C4×D4—2181no—
131C2×C4⋊C4—1091no—
132C2×C4⋊C4—2181no—
133#103—21no—
134#103—2181no—
135C22⋊C8—1091no—
136C22⋊C8C2×D10911yescharacteristic
137#95—1091no—
138#95—2181no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8C22⋊D10911yescharacteristic
143C2×D4—1091no—
144C2×D4—2181no—
145C22×C4—21no—
146C22×C4—1091no—
147C22×C4—1091no—
148C22×C4—2181no—
149C22×C4—2181no—
150C22×C4C22×D10911yescharacteristic
151Q16—42no—
152SD16—4362no—
153C2×C8—21no—
154C2×C8—2181no—
155C4⋊C4—21no—
156C4⋊C4—1091no—
157C4⋊C4—4362no—
158C4⋊C4—2181no—
159C4⋊C4—2181no—
160C4⋊C4—2181no—
161C4⋊C4—2181no—
162C4⋊C4—2181no—
163C4⋊C4C22⋊D10911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C22⋊C4—2181no—
168C22⋊C4—2181no—
169C42—2181no—
170C23—2181no—
171C23D4×D10911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—4361no—
178D4—4361no—
179D4—4361no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—8721no—
187C2×C4—4361no—
188C2×C4—4361no—
189C2×C4—4361no—
190C2×C4—2182no—
191C2×C4—2181no—
192C2×C4—2181no—
193C2×C4—2181no—
194C2×C4—2181no—
195C2×C4—2181no—
196C2×C4D4×D10911yescharacteristic
197C2×C4C2×C22⋊D10911yescharacteristic
198C8—41no—
199C8—4361no—
200C22—21no—
201C22—21no—
202C22—4361no—
203C22—4361no—
204C22—4361no—
205C22#1681266711yescharacteristic
206C22#1681272211yescharacteristic
207C22#1681273111yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—41no—
213C4—4362no—
214C4—4361no—
215C4—4361no—
216C4—4361no—
217C2—21no—
218C2—21no—
219C2—8721no—
220C2#2029518711yescharacteristic
221C2#2029520711yescharacteristic
222C2#2029521211yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#451×C109C2
socleC22×C109#120
prime radical#16812673C22
hypercenter#451D109
hypocenterC109#1603
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20294945C2semidirect
4. #20294763C2semidirect
6. #20294751C2semidirect
7. #451×C109C2semidirect
112. C109#1603semidirect
114. #451D109semidirect

Maximal subgroups

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

subgroupindex
#202956252
#202951652
#202949452
#202947632
#202947612
#202947512
#451×C1092
#1603109