Finite Group Databasebeta

← #28371368

Subgroups — #28371368

Order 13952.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#16812676C211yesmaximal, characteristic
2C22×C4×Dic109C211yesmaximal, characteristic
3#20294930C212yesmaximal, complemented
4#20294921C212yesmaximal, complemented
5#20294912C212yesmaximal, complemented
6#20294908C212yesmaximal, complemented
7#20294899C211yesmaximal, characteristic
8#20294887C211yesmaximal, characteristic
9#20294887C211yesmaximal, characteristic
10#20294884C211yesmaximal, characteristic
11#385×C109C211yesmaximal, characteristic
12C22×Dic218C2211yescharacteristic
13C23×Dic109C2211yescharacteristic
14C23×Dic109C2211yescharacteristic
15#16812676—24no—
16C2×C4⋊Dic109C2211yescharacteristic
17C2×#13182008C2211yescharacteristic
18C2×#13182008C2212yes—
19C2×#13182008C2212yes—
20C2×#13182008C2211yescharacteristic
21C2×C22⋊Dic109C2211yescharacteristic
22C2×C22⋊Dic109C2211yescharacteristic
23C2×C4×Dic109—24no—
24C2×C4×Dic109C2212yes—
25C2×C4×Dic109C2212yes—
26#16812606C2212yes—
27#16812606C2212yes—
28#16812606C2212yes—
29#16812606C2212yes—
30#16812606C2212yes—
31#16812606C2212yes—
32C23×C4×C109C2211yescharacteristic
33C2×C4⋊C4×C109C2212yes—
34C2×C22⋊C4×C109C2211yescharacteristic
35C2×C22⋊C4×C109C2211yescharacteristic
36#95×C109C2212yes—
37C2×Dic218—22no—
38C2×Dic218—24no—
39C22×Dic109—22no—
40C22×Dic109—22no—
41C22×Dic109—24no—
42C22×Dic109D414yes—
43C22×Dic109Q814yescomplemented
44C22×Dic109C2312yes—
45C22×Dic109C2311yescharacteristic
46C22×Dic109C2311yescharacteristic
47C22×Dic109C2311yescharacteristic
48C22×Dic109C2312yes—
49C22×Dic109C2311yescharacteristic
50C4⋊Dic109—22no—
51#13182008—24no—
52#13182008—22no—
53#13182008—22no—
54#13182008—24no—
55C22⋊Dic109—22no—
56C22⋊Dic109—22no—
57C4×Dic109—24no—
58C4×Dic109—24no—
59C24×C109C2311yescharacteristic
60C22×C4×C109—22no—
61C22×C4×C109—24no—
62C22×C4×C109C2311yescharacteristic
63C22×C4×C109C2312yes—
64C22×C4×C109C2311yescharacteristic
65C22×C4×C109C2312yes—
66C4⋊C4×C109—24no—
67C22⋊C4×C109—22no—
68C22⋊C4×C109—22no—
69C23×C109—22no—
70C23×C109—22no—
71C23×C109C2×D412yes—
72C23×C109C2×Q812yes—
73C23×C109#4112yes—
74C23×C109C2411yescharacteristic
75C2×C4×C109—28no—
76C2×C4×C109—22no—
77C2×C4×C109—22no—
78C2×C4×C109—21no—
79C2×C4×C109—21no—
80C2×C4×C109—22no—
81C2×C4×C109—22no—
82C2×C4×C109—22no—
83C2×C4×C109—22no—
84C2×C4×C109—22no—
85C2×C4×C109#4114yes—
86C2×Dic109—28no—
87C2×Dic109—22no—
88C2×Dic109—22no—
89C2×Dic109—22no—
90C2×Dic109—28no—
91C2×Dic109—21no—
92C2×Dic109—21no—
93C2×Dic109—22no—
94C2×Dic109—22no—
95C2×Dic109—22no—
96C2×Dic109—22no—
97C2×Dic109—22no—
98C2×Dic109C2×D412yes—
99C2×Dic109C2×D412yes—
100C2×Dic109C2×Q814yes—
101C2×Dic109#4114yes—
102Dic218—44no—
103C22×C109—22no—
104C22×C109—22no—
105C22×C109—24no—
106C22×C109—24no—
107C22×C109C22⋊Q814yes—
108C22×C109C22×D411yescharacteristic
109C22×C109C22×Q811yescharacteristic
110C22×C109C2×#4112yes—
111C22×C109C2×#4112yes—
112C22×C109C2×#4111yescharacteristic
113C4×C109—24no—
114C4×C109—41no—
115C4×C109—41no—
116C4×C109—42no—
117Dic109—24no—
118Dic109—22no—
119Dic109—41no—
120Dic109—41no—
121Dic109—42no—
122Dic109#12314yes—
123C2×C109—24no—
124C2×C109C2×C22⋊Q811yescharacteristic
125C2×C109C2×#12311yescharacteristic
126C2×C109#52511yescharacteristic
127C2×C109#52912yes—
128C2×C109#53312yes—
129#2855—1091nomaximal, Sylow
130C109#285511yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—1091no—
132C22×C42—1091no—
133#391—1092no—
134#389—1092no—
135#387—1092no—
136#387—1092no—
137#385—1091no—
138#385D10911yescharacteristic
139#381—1091no—
140#381—1091no—
141#380—1091no—
142C22×Q8—1091no—
143C23×C4—1091no—
144C23×C4—1091no—
145C23×C4C2×D10911yescharacteristic
146C22⋊Q8—2184no—
147C2×C4⋊C4—1091no—
148C2×C4⋊C4—1091no—
149C2×C4⋊C4—1091no—
150C2×C4⋊C4—1092no—
151C2×C4⋊C4—1092no—
152C2×C4⋊C4C2×D10912yes—
153C2×C22⋊C4—1091no—
154C2×C22⋊C4—1091no—
155C2×C22⋊C4C2×D10911yescharacteristic
156C2×C22⋊C4C2×D10911yescharacteristic
157C2×C42—1092no—
158C2×C42—1092no—
159C2×C42—2184no—
160#95—1092no—
161#95—1092no—
162#95—1092no—
163#95—1092no—
164#95—1092no—
165#95—1092no—
166#95C2×D10912yes—
167C24C22×D10911yescharacteristic
168C2×Q8—2182no—
169C2×Q8—2184no—
170C22×C4—22no—
171C22×C4—24no—
172C22×C4—1091no—
173C22×C4—1094no—
174C22×C4—1094no—
175C22×C4—1092no—
176C22×C4—1091no—
177C22×C4—1092no—
178C22×C4—1091no—
179C22×C4—1091no—
180C22×C4—2184no—
181C22×C4—2182no—
182C22×C4—2182no—
183C22×C4C22×D10912yes—
184C22×C4C22×D10911yescharacteristic
185C22×C4C22×D10911yescharacteristic
186C22×C4C22×D10912yes—
187C4⋊C4—24no—
188C4⋊C4—2184no—
189C4⋊C4—2182no—
190C4⋊C4—2182no—
191C4⋊C4—2182no—
192C4⋊C4—2184no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—2182no—
196C22⋊C4—2182no—
197C42—2184no—
198C42—2184no—
199C23—22no—
200C23—22no—
201C23D4×D10912yes—
202C23Q8×D10912yes—
203C23#1318202912yes—
204C23C23×D10911yescharacteristic
205Q8—4364no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—1092no—
217C2×C4—1094no—
218C2×C4—1092no—
219C2×C4—1094no—
220C2×C4—2188no—
221C2×C4—2181no—
222C2×C4—2181no—
223C2×C4—2182no—
224C2×C4—2182no—
225C2×C4—2182no—
226C2×C4—2182no—
227C2×C4—2182no—
228C2×C4—2188no—
229C2×C4—2182no—
230C2×C4—2182no—
231C2×C4—2182no—
232C2×C4#1318202814yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1681267714yes—
238C22C2×D4×D10911yescharacteristic
239C22C2×Q8×D10911yescharacteristic
240C22#41×D10912yes—
241C22C2×#1318202812yes—
242C22C2×#1318202911yescharacteristic
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—1094no—
248C4—4361no—
249C4—4361no—
250C4—4362no—
251C4—2184no—
252C4—2182no—
253C2—24no—
254C2C2×#1681267711yescharacteristic
255C2#123×D10911yescharacteristic
256C2#2029553211yescharacteristic
257C2#2029555612yes—
258C2#2029557812yes—
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#385×C109C2
prime radicalC24×C109C23
hypercenter#385D109
hypocenterC109#2855
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #20294930C2semidirect
4. #20294921C2semidirect
5. #20294912C2semidirect
6. #20294908C2semidirect
43. C22×Dic109Q8semidirect
130. C109#2855semidirect

Maximal subgroups

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

subgroupindex
C2×#168126762
C22×C4×Dic1092
#202949302
#202949212
#202949122
#202949082
#202948992
#202948872
#202948842
#385×C1092
#2855109