Finite Group Databasebeta

← #28364015

Subgroups — #28364015

Order 13952.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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
2#20294884C211yesmaximal, characteristic
3C22⋊C4×Dic109C211yesmaximal, characteristic
4#20294793C211yesmaximal, characteristic
5#20294792C211yesmaximal, characteristic
6#20294792C211yesmaximal, characteristic
7#342×C109C211yesmaximal, characteristic
8C22×Dic218C411yescharacteristic, complemented
9C23×Dic109C2211yescharacteristic
10#16812676—21no—
11#16812676—21no—
12#16812676—21no—
13#16812676—21no—
14C2×C4⋊Dic109C411yescharacteristic, complemented
15C2×#13182008—21no—
16C2×#13182008C411yescharacteristic, complemented
17C2×#13182008C411yescharacteristic, complemented
18C2×C22⋊Dic109C2211yescharacteristic
19C2×C22⋊Dic109C2211yescharacteristic
20C2×C22⋊Dic109C2211yescharacteristic
21C2×C4×Dic109—21no—
22#16812606—21no—
23#16812606—21no—
24C2×C22⋊C4×C109C2211yescharacteristic
25C2×C22⋊C4×C109C2211yescharacteristic
26C2×C22⋊C4×C109C2211yescharacteristic
27C2×Dic218—21no—
28C2×Dic218—21no—
29C2×Dic218—42no—
30C22×Dic109—21no—
31C22×Dic109—21no—
32C22×Dic109—42no—
33C22×Dic109C2×C411yescharacteristic
34C22×Dic109C2×C411yescharacteristic
35C22×Dic109C2×C411yescharacteristic
36C22×Dic109C2×C411yescharacteristic
37C22×Dic109D411yescharacteristic
38C22×Dic109D411yescharacteristic
39C22×Dic109D411yescharacteristic
40C22×Dic109D411yescharacteristic
41C4⋊Dic109—21no—
42C4⋊Dic109—21no—
43#13182008—21no—
44#13182008—21no—
45#13182008—21no—
46#13182008—21no—
47#13182008—42no—
48C22⋊Dic109—21no—
49C22⋊Dic109—21no—
50C22⋊Dic109—21no—
51C22⋊Dic109—21no—
52C22⋊Dic109—21no—
53C22⋊Dic109Q812yescomplemented
54C4×Dic109—42no—
55C24×C109C2311yescharacteristic
56C22×C4×C109—21no—
57C22×C4×C109—21no—
58C22×C4×C109C2×C411yescharacteristic
59C22×C4×C109C2×C411yescharacteristic
60C22⋊C4×C109—21no—
61C22⋊C4×C109—21no—
62C22⋊C4×C109—21no—
63C22⋊C4×C109—21no—
64C22⋊C4×C109—21no—
65C22⋊C4×C109Q812yescomplemented
66C23×C109—41no—
67C23×C109—41no—
68C23×C109C22×C411yescharacteristic
69C23×C109C2×D411yescharacteristic
70C23×C109C2×D411yescharacteristic
71C23×C109C2×Q811yescharacteristic
72C23×C109C2×Q811yescharacteristic
73C23×C109#4111yescharacteristic
74C23×C109#4111yescharacteristic
75C2×C4×C109—21no—
76C2×C4×C109—21no—
77C2×C4×C109—22no—
78C2×C4×C109—41no—
79C2×C4×C109—41no—
80C2×C4×C109—41no—
81C2×C4×C109—41no—
82C2×C4×C109—41no—
83C2×C4×C109—41no—
84C2×C4×C109—41no—
85C2×Dic109—22no—
86C2×Dic109—22no—
87C2×Dic109—22no—
88C2×Dic109—21no—
89C2×Dic109—21no—
90C2×Dic109—22no—
91C2×Dic109—41no—
92C2×Dic109—41no—
93C2×Dic109—41no—
94C2×Dic109—41no—
95C2×Dic109—41no—
96C2×Dic109—41no—
97C2×Dic109—41no—
98C2×Dic109—41no—
99C2×Dic109—41no—
100C2×Dic109—41no—
101C2×Dic109C22⋊C411yescharacteristic
102C2×Dic109C22⋊C411yescharacteristic
103C2×Dic109C22⋊C411yescharacteristic
104C2×Dic109C22⋊C411yescharacteristic
105Dic218—42no—
106Dic218—42no—
107C22×C109—21no—
108C22×C109—21no—
109C22×C109—21no—
110C22×C109—21no—
111C22×C109—21no—
112C22×C109—21no—
113C22×C109—41no—
114C22×C109—41no—
115C22×C109—41no—
116C22×C109—41no—
117C22×C109C2×C22⋊C411yescharacteristic
118C22×C109C4×Q811yescharacteristic
119C22×C109C4×Q811yescharacteristic
120C22×C109C22⋊Q811yescharacteristic
121C22×C109C22⋊Q811yescharacteristic
122C22×C109#12411yescharacteristic
123C22×C109C4⋊Q811yescharacteristic
124C4×C109—42no—
125C4×C109—41no—
126C4×C109—41no—
127C4×C109—81no—
128Dic109—21no—
129Dic109—21no—
130Dic109—21no—
131Dic109—42no—
132Dic109—41no—
133Dic109—41no—
134Dic109—81no—
135Dic109#9912yes—
136C2×C109—21no—
137C2×C109—21no—
138C2×C109—21no—
139C2×C109—21no—
140C2×C109—21no—
141C2×C109—21no—
142C2×C109#39111yescharacteristic
143C2×C109C2×#9911yescharacteristic
144C2×C109#41011yescharacteristic
145#1996—1091nomaximal, Sylow
146C109#199611yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—1091no—
148#380—1091no—
149C4×C22⋊C4—1091no—
150#342—1091no—
151#342—1091no—
152#342—1091no—
153#342D10911yescharacteristic
154C22×Q8—1091no—
155C23×C4—1091no—
156C22⋊Q8—2181no—
157C22⋊Q8—2181no—
158C22⋊Q8—2181no—
159C22⋊Q8—2181no—
160C2×C4⋊C4—1091no—
161C2×C4⋊C4—1091no—
162C2×C4⋊C4—1091no—
163C2×C4⋊C4—2181no—
164C2×C22⋊C4—1091no—
165C2×C22⋊C4—1091no—
166C2×C22⋊C4—1091no—
167C2×C22⋊C4C2×D10911yescharacteristic
168C2×C22⋊C4C2×D10911yescharacteristic
169C2×C22⋊C4C2×D10911yescharacteristic
170C2×C42—2181no—
171#95—2181no—
172#95—2181no—
173C24C22×D10911yescharacteristic
174C2×Q8—4362no—
175C2×Q8—2181no—
176C2×Q8—2181no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—1091no—
180C22×C4—1091no—
181C22×C4—1091no—
182C22×C4—1091no—
183C22×C4—1091no—
184C22×C4—1091no—
185C22×C4—1091no—
186C22×C4—1091no—
187C22×C4—4362no—
188C22×C4—2181no—
189C22×C4—2181no—
190C22×C4C4×D10911yescharacteristic
191C22×C4C4×D10911yescharacteristic
192C4⋊C4—4362no—
193C4⋊C4—2181no—
194C4⋊C4—2181no—
195C4⋊C4—2181no—
196C4⋊C4—2181no—
197C4⋊C4—2181no—
198C4⋊C4—2181no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—1092no—
205C22⋊C4—2181no—
206C22⋊C4—2181no—
207C22⋊C4—2181no—
208C22⋊C4—2181no—
209C22⋊C4—2181no—
210C22⋊C4Dic21812yescomplemented
211C42—4362no—
212C23—41no—
213C23—41no—
214C23C2×C4×D10911yescharacteristic
215C23D4×D10911yescharacteristic
216C23D4×D10911yescharacteristic
217C23Q8×D10911yescharacteristic
218C23C2×Dic21811yescharacteristic
219C23#1318202811yescharacteristic
220C23#1318202911yescharacteristic
221Q8—4362no—
222Q8—4362no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—1091no—
234C2×C4—1091no—
235C2×C4—1091no—
236C2×C4—1091no—
237C2×C4—4361no—
238C2×C4—4361no—
239C2×C4—4361no—
240C2×C4—4361no—
241C2×C4—4361no—
242C2×C4—4361no—
243C2×C4—4361no—
244C2×C4—4361no—
245C2×C4—4361no—
246C2×C4—4361no—
247C2×C4—2182no—
248C2×C4—2182no—
249C2×C4—2182no—
250C2×C4—2181no—
251C2×C4—2181no—
252C2×C4—2182no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22C22⋊C4×D10911yescharacteristic
264C22#1681266411yescharacteristic
265C22C4×Dic21811yescharacteristic
266C22#1681267611yescharacteristic
267C22#1681267711yescharacteristic
268C22#1681268511yescharacteristic
269C22#1681269811yescharacteristic
270C4—42no—
271C4—41no—
272C4—41no—
273C4—81no—
274C4—8721no—
275C4—1092no—
276C4—4362no—
277C4—4361no—
278C4—4361no—
279C4—2181no—
280C4—2181no—
281C4—2181no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—21no—
288C2#2029493011yescharacteristic
289C2#99×D10911yescharacteristic
290C2#2029499811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC24C22×D109
Fitting#342×C109C2
socleC22×C109C2×C22⋊C4
prime radical, cosocleC24×C109C23
hypercenter#342D109
hypocenterC109#1996
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C22×Dic218C4semidirect
14. C2×C4⋊Dic109C4semidirect
16. C2×#13182008C4semidirect
17. C2×#13182008C4semidirect
53. C22⋊Dic109Q8semidirect
65. C22⋊C4×C109Q8semidirect
146. C109#1996semidirect
210. C22⋊C4Dic218semidirect

Maximal subgroups

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

subgroupindex
C2×#168126762
#202948842
C22⋊C4×Dic1092
#202947932
#202947922
#342×C1092
#1996109