Finite Group Databasebeta

← #28363489

Subgroups — #28363489

Order 13952.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16812683C211yesmaximal, characteristic
2C2×#16812655C211yesmaximal, characteristic, complemented
3C2×#16812613C211yesmaximal, characteristic
4C2×#16812613C211yesmaximal, characteristic
5#20294887C211yesmaximal, characteristic, complemented
6#20294793C211yesmaximal, characteristic, complemented
7#342×C109C211yesmaximal, characteristic, complemented
8C22×C22⋊D109C2211yescharacteristic
9C23×Dic109C2211yescharacteristic
10#16812683—22no—
11#16812683—21no—
12#16812683—21no—
13#16812655—22no—
14#16812655—22no—
15C2×C4⋊Dic109C412yescomplemented
16C2×#13182008—21no—
17C2×C22⋊Dic109C2211yescharacteristic
18C2×C22⋊Dic109C2211yescharacteristic
19C2×#13182006C412yescomplemented
20C2×C4×Dic109—21no—
21#16812613—22no—
22#16812613—22no—
23#16812606—22no—
24C2×C22⋊C4×C109C2211yescharacteristic
25C2×C22⋊C4×C109C2211yescharacteristic
26C2×C22⋊C4×C109C2211yescharacteristic
27C23×D109C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C22×Dic109—21no—
35C22×Dic109—21no—
36C22×Dic109—21no—
37C22×Dic109—21no—
38C22×Dic109—21no—
39C22×Dic109—21no—
40C22×Dic109C2×C411yescharacteristic
41C22×Dic109C2×C412yes—
42C22×Dic109D412yes—
43C22×Dic109D411yescharacteristic
44C22×Dic109D411yescharacteristic
45C4⋊Dic109—22no—
46C4⋊Dic109—22no—
47#13182008—24no—
48C22⋊Dic109—21no—
49C22⋊Dic109—21no—
50C22⋊Dic109—21no—
51C22⋊Dic109D412yes—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109—24no—
55C24×C109C2311yescharacteristic
56C22×C4×C109—21no—
57C22×C4×C109—21no—
58C22×C4×C109C2×C412yes—
59C22⋊C4×C109—21no—
60C22⋊C4×C109—21no—
61C22⋊C4×C109—21no—
62C22⋊C4×C109—21no—
63C22⋊C4×C109—21no—
64C22⋊C4×C109D412yes—
65C23×C109—42no—
66C23×C109C22×C411yescharacteristic
67C23×C109C2×D411yescharacteristic
68C23×C109C2×D411yescharacteristic
69C23×C109C2×D411yescharacteristic
70C23×C109C2×D411yescharacteristic
71C23×C109#4111yescharacteristic
72C23×C109#4111yescharacteristic
73C22×D109—21no—
74C22×D109—21no—
75C22×D109—21no—
76C22×D109—42no—
77C2×C4×C109—22no—
78C2×C4×C109—22no—
79C2×C4×C109—42no—
80C2×C4×C109—42no—
81C2×C4×C109—42no—
82C2×C4×C109—41no—
83C22⋊D109—41no—
84C22⋊D109—41no—
85C22⋊D109—41no—
86C22⋊D109—41no—
87C2×Dic109—22no—
88C2×Dic109—22no—
89C2×Dic109—21no—
90C2×Dic109—21no—
91C2×Dic109—22no—
92C2×Dic109—22no—
93C2×Dic109—21no—
94C2×Dic109—21no—
95C2×Dic109—21no—
96C2×Dic109—21no—
97C2×Dic109—21no—
98C2×Dic109—22no—
99C2×Dic109—42no—
100C2×Dic109—42no—
101C2×Dic109—41no—
102C2×Dic109C22⋊C412yes—
103C2×Dic109C22⋊C412yes—
104C22×C109—22no—
105C22×C109—22no—
106C22×C109—22no—
107C22×C109—41no—
108C22×C109—41no—
109C22×C109—41no—
110C22×C109—41no—
111C22×C109C2×C22⋊C411yescharacteristic
112C22×C109C4×D411yescharacteristic
113C22×C109C4×D411yescharacteristic
114C22×C109#12011yescharacteristic
115C22×C109#12111yescharacteristic
116C22×C109#12111yescharacteristic
117C22×C109#12311yescharacteristic
118C2×D109—41no—
119C2×D109—42no—
120C2×D109—81no—
121C2×D109—81no—
122C4×C109—42no—
123C4×C109—42no—
124C4×C109—81no—
125Dic109—22no—
126Dic109—22no—
127Dic109—42no—
128Dic109—41no—
129Dic109—81no—
130C2×C109—21no—
131C2×C109—21no—
132C2×C109—21no—
133C2×C109—21no—
134C2×C109—21no—
135C2×C109—21no—
136C2×C109#38611yescharacteristic
137C2×C109#41012yes—
138D109—81no—
139#1899—1091nomaximal, Sylow
140C109#189911yescharacteristic, complemented, Sylow
141C2×#123—1091no—
142C2×#117—1091no—
143C2×#99—1091no—
144C2×#99—1091no—
145#381—1091no—
146#342—1091no—
147#342D10911yescharacteristic, complemented
148C22×D4—1091no—
149C23×C4—1091no—
150#123—2182no—
151#123—2181no—
152#123—2181no—
153#117—2182no—
154#117—2182no—
155C2×C4⋊C4—1092no—
156C2×C4⋊C4—2181no—
157C2×C22⋊C4—1091no—
158C2×C22⋊C4—1092no—
159C2×C22⋊C4—1091no—
160C2×C22⋊C4C2×D10911yescharacteristic
161C2×C22⋊C4C2×D10911yescharacteristic
162C2×C22⋊C4C2×D10911yescharacteristic
163C2×C42—2181no—
164#99—2182no—
165#99—2182no—
166#95—2182no—
167C24—1091no—
168C24C22×D10911yescharacteristic
169C2×D4—2181no—
170C2×D4—2181no—
171C2×D4—2181no—
172C2×D4—2181no—
173C2×D4—2181no—
174C2×D4—2181no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—1092no—
178C22×C4—1092no—
179C22×C4—1091no—
180C22×C4—1091no—
181C22×C4—1091no—
182C22×C4—2181no—
183C22×C4—2181no—
184C22×C4—2181no—
185C22×C4—2181no—
186C22×C4—2181no—
187C22×C4—2181no—
188C22×C4C4×D10912yes—
189C4⋊C4—2182no—
190C4⋊C4—2182no—
191C4⋊C4—2184no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—1092no—
198C22⋊C4—2182no—
199C22⋊C4—2182no—
200C22⋊C4—2181no—
201C22⋊C4—2181no—
202C22⋊C4—2181no—
203C22⋊C4D43612yes—
204C42—2184no—
205C23—42no—
206C23—4362no—
207C23—2181no—
208C23—2181no—
209C23—2181no—
210C23C2×C4×D10911yescharacteristic
211C23D4×D10911yescharacteristic
212C23D4×D10911yescharacteristic
213C23D4×D10911yescharacteristic
214C23C2×D43611yescharacteristic
215C23#1318202911yescharacteristic
216C23#1318203011yescharacteristic
217D4—4361no—
218D4—4361no—
219D4—4361no—
220D4—4361no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—1092no—
228C2×C4—1092no—
229C2×C4—4362no—
230C2×C4—4361no—
231C2×C4—4362no—
232C2×C4—2181no—
233C2×C4—2181no—
234C2×C4—2181no—
235C2×C4—2182no—
236C2×C4—2182no—
237C2×C4—2182no—
238C2×C4—2181no—
239C2×C4—2181no—
240C2×C4—2182no—
241C2×C4—2182no—
242C2×C4—2181no—
243C2×C4—2181no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—8721no—
252C22—8721no—
253C22—4362no—
254C22—4361no—
255C22C22⋊C4×D10911yescharacteristic
256C22#1681266111yescharacteristic
257C22C4×D43611yescharacteristic
258C22#1681266911yescharacteristic
259C22#1681267211yescharacteristic
260C22#1681267411yescharacteristic
261C22#1681268411yescharacteristic
262C4—42no—
263C4—42no—
264C4—81no—
265C4—8721no—
266C4—4362no—
267C4—4361no—
268C4—2182no—
269C4—2182no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—8721no—
277C2#2029490411yescharacteristic
278C2#2029499812yes—
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC24C22×D109
Fitting#342×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C22
cosocleC24×C109C23
hypercenter#342D109
hypocenterC109#1899
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#16812655C2semidirect
5. #20294887C2semidirect
6. #20294793C2semidirect
7. #342×C109C2semidirect
15. C2×C4⋊Dic109C4semidirect
19. C2×#13182006C4semidirect
140. C109#1899semidirect
147. #342D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126832
C2×#168126552
C2×#168126132
#202948872
#202947932
#342×C1092
#1899109