Finite Group Databasebeta

← #28361993

Subgroups — #28361993

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#20295623C211yesmaximal, characteristic
2#20295182C211yesmaximal, characteristic, complemented
3#20295165C211yesmaximal, characteristic
4#20294762C211yesmaximal, characteristic, complemented
5#20294759C211yesmaximal, characteristic
6#20294752C211yesmaximal, characteristic, complemented
7#395×C109C211yesmaximal, characteristic, complemented
8C2×#13182019—21no—
9C2×#13182016—21no—
10#16812694—21no—
11#16812689—21no—
12#16812684—21no—
13#16812682—21no—
14#16812678C2211yescharacteristic
15#16812677—21no—
16#16812673C2211yescharacteristic
17C4×C22⋊D109—21no—
18#16812623—21no—
19#16812623—21no—
20C22⋊#11724784C2211yescharacteristic
21C22⋊#11724784C2211yescharacteristic
22C22×Q8×C109C2211yescharacteristic
23C2×C4⋊C4×C109—21no—
24C2×C4⋊C4×C109C2211yescharacteristic
25#95×C109—21no—
26#95×C109C2211yescharacteristic
27C2×Dic218D411yescharacteristic
28C2×D436D411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C4×D109—21no—
31#13182019—42no—
32#13182016—42no—
33C2×#11724784—21no—
34C2×#11724784—21no—
35C4⋊Dic109D411yescharacteristic
36C4⋊Dic109D411yescharacteristic
37#13182008—21no—
38#13182008—21no—
39#13182008—21no—
40#13182008—21no—
41C22⋊Dic109—21no—
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—
50C22×C4×C109—21no—
51C22×C4×C109—21no—
52C22×C4×C109D411yescharacteristic
53C22×C4×C109D411yescharacteristic
54C22×C4×C109C2311yescharacteristic
55C4⋊C4×C109—21no—
56C4⋊C4×C109—21no—
57C4⋊C4×C109—42no—
58C23×C109C2×D411yescharacteristic
59C22×D109—21no—
60Q8×C109—22no—
61Q8×C109—22no—
62Q8×C109—41no—
63Q8×C109—41no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109—21no—
67C2×C4×C109—21no—
68C2×C4×C109—21no—
69C2×C4×C109—21no—
70C2×C4×C109—41no—
71C2×C4×C109—41no—
72C2×C4×C109—41no—
73C2×C4×C109—41no—
74C2×C4×C109—41no—
75C2×C4×C109—41no—
76C2×C4×C109C2×D411yescharacteristic
77C2×C4×C109C2×D411yescharacteristic
78C22⋊D109—41no—
79C22⋊D109—41no—
80C2×Dic109—21no—
81C2×Dic109—21no—
82C2×Dic109—21no—
83D436—41no—
84C4×D109—81no—
85Dic218—41no—
86#11724784—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—42no—
99C4×C109—41no—
100C4×C109—41no—
101C4×C109—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#451—1091no—
115#448—1091no—
116#395D10911yescharacteristic, complemented
117#328—1091no—
118#327—1091no—
119#324—1091no—
120C22×Q8C2×D10911yescharacteristic
121C2×Q16—2181no—
122C2×SD16—2181no—
123#126—2181no—
124#125—2181no—
125#123—2181no—
126#123—2181no—
127C22⋊Q8—1091no—
128C22⋊Q8—2181no—
129#121—1091no—
130C4×D4—2181no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D10911yescharacteristic
133#103—2181no—
134#103—2181no—
135C22⋊C8—1091no—
136C22⋊C8—1091no—
137#95—21no—
138#95C2×D10911yescharacteristic
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—1091no—
143C2×D4—1091no—
144C2×D4—2181no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—2181no—
148C22×C4C22⋊D10911yescharacteristic
149C22×C4C22⋊D10911yescharacteristic
150C22×C4C22×D10911yescharacteristic
151Q16—4362no—
152SD16—4362no—
153C2×C8—2181no—
154C2×C8—2181no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—1091no—
159C4⋊C4—1091no—
160C4⋊C4—2181no—
161C4⋊C4—2181no—
162C4⋊C4—2181no—
163C4⋊C4—2181no—
164C22⋊C4—2181no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C22⋊C4—2181no—
168C22⋊C4—2181no—
169C42—2181no—
170C23—2181no—
171C23C2×C22⋊D10911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—4361no—
177D4—4361no—
178D4—4361no—
179D4—4361no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—8721no—
193C2×C4—2181no—
194C2×C4—2181no—
195C2×C4—2181no—
196C2×C4D4×D10911yescharacteristic
197C2×C4D4×D10911yescharacteristic
198C8—4361no—
199C8—4361no—
200C22—21no—
201C22—21no—
202C22—4361no—
203C22—4361no—
204C22—4361no—
205C22#1681266711yescharacteristic
206C22#1681271911yescharacteristic
207C22#1681273011yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—42no—
213C4—41no—
214C4—4361no—
215C4—4361no—
216C4—4361no—
217C2—21no—
218C2—21no—
219C2—8721no—
220C2#2029518611yescharacteristic
221C2#2029520811yescharacteristic
222C2#2029521211yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#395×C109C2
socleC22×C109#120
prime radical#16812673C22
hypercenter#395D109
hypocenterC109#1603
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #20295182C2semidirect
4. #20294762C2semidirect
6. #20294752C2semidirect
7. #395×C109C2semidirect
112. C109#1603semidirect
116. #395D109semidirect

Maximal subgroups

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

subgroupindex
#202956232
#202951822
#202951652
#202947622
#202947592
#202947522
#395×C1092
#1603109