Finite Group Databasebeta

← #28364158

Subgroups — #28364158

Order 13952.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#20295588C211yesmaximal, characteristic, complemented
2C2×#16812668C212yesmaximal, complemented
3C2×#16812613C212yesmaximal, complemented
4#20294793C211yesmaximal, characteristic, complemented
5#379×C109C211yesmaximal, characteristic, complemented
6C22×C22⋊D109—22no—
7C22×C22⋊D109C2212yes—
8#16812683—22no—
9#16812673—22no—
10#16812669—22no—
11#16812668—24no—
12#16812668—24no—
13C2×C22⋊Dic109—22no—
14C2×C22⋊Dic109C2212yes—
15#16812613—24no—
16C25×C109C2211yescharacteristic
17C2×C22⋊C4×C109—22no—
18C2×C22⋊C4×C109C2211yescharacteristic
19C2×C22⋊C4×C109C2211yescharacteristic
20C23×D109D412yescomplemented
21C2×D436—22no—
22C2×C22⋊D109—28no—
23C2×C22⋊D109—22no—
24C2×C22⋊D109—22no—
25C2×C22⋊D109—22no—
26C2×C22⋊D109—22no—
27C2×C22⋊D109—22no—
28C2×C22⋊D109—22no—
29C2×C22⋊D109—48no—
30C22×Dic109—22no—
31C22×Dic109D412yescomplemented
32C4⋊Dic109—22no—
33C22⋊Dic109—28no—
34C22⋊Dic109—22no—
35C22⋊Dic109D414yescomplemented
36#13182006—24no—
37C24×C109—21no—
38C24×C109—22no—
39C24×C109—22no—
40C24×C109—21no—
41C24×C109—44no—
42C24×C109D412yescomplemented
43C24×C109C2311yescharacteristic
44C22×C4×C109—21no—
45C22×C4×C109D412yescomplemented
46C22⋊C4×C109—22no—
47C22⋊C4×C109—22no—
48C22⋊C4×C109—44no—
49C23×C109—24no—
50C23×C109—28no—
51C23×C109—24no—
52C23×C109—22no—
53C23×C109—44no—
54C23×C109—42no—
55C23×C109—44no—
56C23×C109—42no—
57C23×C109—48no—
58C23×C109—44no—
59C23×C109—41no—
60C23×C109—42no—
61C23×C109—41no—
62C23×C109C2×D412yes—
63C23×C109C2×D412yes—
64C23×C109C2×D411yescharacteristic
65C23×C109C2×D411yescharacteristic
66C23×C109#4111yescharacteristic
67C22×D109—22no—
68C22×D109—22no—
69C22×D109—22no—
70C22×D109—44no—
71C2×C4×C109—22no—
72C2×C4×C109—42no—
73C2×C4×C109—42no—
74C2×C4×C109—41no—
75C22⋊D109—416no—
76C22⋊D109—42no—
77C22⋊D109—42no—
78C22⋊D109—42no—
79C22⋊D109—42no—
80C2×Dic109—22no—
81C2×Dic109—22no—
82C2×Dic109—24no—
83C2×Dic109—22no—
84C2×Dic109—44no—
85D436—82no—
86C22×C109—24no—
87C22×C109—22no—
88C22×C109—28no—
89C22×C109—24no—
90C22×C109—42no—
91C22×C109—41no—
92C22×C109—41no—
93C22×C109—44no—
94C22×C109—44no—
95C22×C109—48no—
96C22×C109—42no—
97C22×C109—42no—
98C22×C109—44no—
99C22×C109#12011yescharacteristic
100C22×C109#12012yes—
101C22×C109#12112yes—
102C22×C109#12111yescharacteristic
103C22×C109#12711yescharacteristic
104C2×D109—44no—
105C2×D109—42no—
106C2×D109—44no—
107C2×D109—82no—
108C4×C109—42no—
109C4×C109—81no—
110Dic109—44no—
111Dic109—42no—
112C2×C109—22no—
113C2×C109—21no—
114C2×C109—22no—
115C2×C109—21no—
116C2×C109—44no—
117C2×C109#39211yescharacteristic
118C2×C109B(4,𝔽2)12yes—
119D109—82no—
120#2021—1091nomaximal, Sylow
121C109#202111yescharacteristic, complemented, Sylow
122#534—1091no—
123C2×#120—1092no—
124C2×#99—1092no—
125#379D10911yescharacteristic, complemented
126#342—1091no—
127C25C2×D10911yescharacteristic
128C22×D4—1092no—
129C22×D4—2182no—
130#123—2182no—
131#121—2182no—
132#120—2182no—
133#120—2184no—
134#120—2184no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—1092no—
137C2×C22⋊C4—2182no—
138C2×C22⋊C4C2×D10911yescharacteristic
139C2×C22⋊C4C2×D10911yescharacteristic
140#99—2184no—
141C24—22no—
142C24—21no—
143C24—22no—
144C24—21no—
145C24—44no—
146C24—1092no—
147C24D43612yescomplemented
148C24C22×D10911yescharacteristic
149C2×D4—4368no—
150C2×D4—2182no—
151C2×D4—2188no—
152C2×D4—2182no—
153C2×D4—2182no—
154C2×D4—2182no—
155C2×D4—2182no—
156C2×D4—2182no—
157C2×D4—2182no—
158C22×C4—21no—
159C22×C4—1092no—
160C22×C4—2182no—
161C22×C4C22⋊D10912yescomplemented
162C4⋊C4—2182no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—1094no—
167C22⋊C4—2184no—
168C22⋊C4—2188no—
169C22⋊C4—2182no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—42no—
182C23—41no—
183C23—4364no—
184C23—2182no—
185C23—2182no—
186C23—2182no—
187C23D4×D10912yes—
188C23D4×D10912yes—
189C23C2×C22⋊D10911yescharacteristic
190C23C2×D43611yescharacteristic
191C23#1318202911yescharacteristic
192D4—8722no—
193D4—43616no—
194D4—4362no—
195D4—4362no—
196D4—4362no—
197D4—4362no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—4364no—
203C2×C4—2182no—
204C2×C4—2184no—
205C2×C4—2182no—
206C2×C4—2182no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—8722no—
221C22—4364no—
222C22—4362no—
223C22—4364no—
224C22#1681266711yescharacteristic
225C22#1681266912yes—
226C22#1681267212yes—
227C22#1681267311yescharacteristic
228C22#1681269511yescharacteristic
229C4—42no—
230C4—81no—
231C4—4364no—
232C4—4362no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—8722no—
239C2#2029493511yescharacteristic
240C2#2029521212yes—
subgroupG/H
centerC22#16812667
commutator, cosocleC24×C109C23
FrattiniC24C22×D109
Fitting#379×C109C2
socleC22×C109#120
hypercenter#379D109
hypocenterC109#2021
LCSG ▷ C24×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #20295588C2semidirect
2. C2×#16812668C2semidirect
3. C2×#16812613C2semidirect
4. #20294793C2semidirect
5. #379×C109C2semidirect
20. C23×D109D4semidirect
31. C22×Dic109D4semidirect
35. C22⋊Dic109D4semidirect
42. C24×C109D4semidirect
45. C22×C4×C109D4semidirect
121. C109#2021semidirect
125. #379D109semidirect
147. C24D436semidirect
161. C22×C4C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202955882
C2×#168126682
C2×#168126132
#202947932
#379×C1092
#2021109