Finite Group Databasebeta

← #13074339

Subgroups — #13074339

Order 1408.

932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#4341C211yesmaximal, characteristic, complemented
2C2×#66992C212yesmaximal, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C11×#392C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic, complemented
6#10622836C212yesmaximal, complemented
7#10622573C212yesmaximal, complemented
8#10622560C211yesmaximal, characteristic, complemented
9#10622555C212yesmaximal, complemented
10#10622286C211yesmaximal, characteristic, complemented
11#10622280C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2212yes—
18C23×Dic11C2212yes—
19C2×#4341—28no—
20C2×#4341—24no—
21C22×D44C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C22×Dic22C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2212yes—
26C2×C22⋊Dic11C2212yes—
27C2×C22⋊Dic11C2212yes—
28#66992—28no—
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2212yes—
34#66937—24no—
35C11×#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C24×C11C2312yes—
41C23×D11C2311yescharacteristic
42C23×D11C2311yescharacteristic
43C2×D4×C11—24no—
44C2×D4×C11—24no—
45C2×D4×C11—22no—
46C2×D4×C11—42no—
47C2×D4×C11—42no—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—24no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11—24no—
56C2×C22⋊D11—24no—
57C2×C22⋊D11—22no—
58C2×C22⋊D11—42no—
59C2×C22⋊D11—42no—
60C2×C22⋊D11—42no—
61C22×Dic11—24no—
62C22×Dic11—24no—
63C22×Dic11D418yescomplemented
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2312yes—
66C22×Dic11C2312yes—
67C22×Dic11C2311yescharacteristic
68#4341—232no—
69C2×D44—22no—
70C2×D44—42no—
71C2×C4×D11—24no—
72C2×C4×D11D414yescomplemented
73C2×Dic22—24no—
74C2×Dic22—22no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—42no—
77C22⋊Dic11—24no—
78C22⋊Dic11—42no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—42no—
82Dic11⋊C4—22no—
83Dic11⋊C4—24no—
84#2615—111nomaximal, Sylow
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—21no—
93C23×C11—22no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11C2×D414yes—
97C23×C11C2411yescharacteristic
98C22×D11—22no—
99C22×D11—21no—
100C22×D11—22no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11C2×D412yes—
108D4×C11—28no—
109D4×C11—48no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11C2×D412yes—
117C22⋊D11—216no—
118C22⋊D11—44no—
119C22⋊D11—48no—
120C22⋊D11—44no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—216no—
124C2×Dic11—21no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11C2×D414yes—
130C2×Dic11C2×D414yes—
131C2×Dic11C2×D412yes—
132D44—44no—
133C4×D11—28no—
134Dic22—28no—
135C22×#41—111no—
136C2×#121—112no—
137C2×#121—111no—
138#393—111no—
139#393—111no—
140#392—112no—
141#392—111no—
142#392—112no—
143#392D1111yescharacteristic, complemented
144#380—112no—
145#380—111no—
146C22×C11—24no—
147C22×C11—24no—
148C22×C11—24no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—41no—
154C22×C11—42no—
155C22×C11—41no—
156C22×C11—42no—
157C22×C11—41no—
158C22×C11C22×D412yes—
159C22×C11C22×D411yescharacteristic
160C22×C11H(5,𝔽2)12yes—
161C22×C11H(5,𝔽2)11yescharacteristic
162C22×C112−1+411yescharacteristic
163C2×D11—22no—
164C2×D11—22no—
165C2×D11—22no—
166C2×D11—42no—
167C2×D11—42no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—42no—
171C2×D11—42no—
172C2×D11—41no—
173C4×C11—22no—
174C4×C11—42no—
175C4×C11—41no—
176Dic11—24no—
177Dic11—41no—
178Dic11—42no—
179Dic11#12014yes—
180C2×#41—228no—
181C2×#41—224no—
182C22×Q8—111no—
183C22×D4—111no—
184C22×D4—112no—
185C22×D4—111no—
186C22×D4—112no—
187C22×D4—111no—
188C22×D4C2×D1111yescharacteristic
189C22×D4C2×D1112yes—
190C23×C4—112no—
191C23×C4—111no—
192#121—224no—
193#121—228no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—112no—
196C2×C22⋊C4—112no—
197C2×C22⋊C4—112no—
198C2×C22⋊C4—111no—
199C2×C22⋊C4—112no—
200C2×C22⋊C4—112no—
201C2×C22⋊C4C2×D1111yescharacteristic
202C2×C22⋊C4C2×D1112yes—
203#95—112no—
204#95—112no—
205#95—111no—
206#95C2×D1111yescharacteristic
207C2×C11—44no—
208C2×C11—81no—
209C2×C11C2×#12011yescharacteristic
210C2×C11#53511yescharacteristic
211C2×C11#53512yes—
212C2×C11#53712yes—
213C2×C11#53711yescharacteristic
214D11—42no—
215D11—81no—
216C24—111no—
217C24—111no—
218C24C22×D1111yescharacteristic
219C24C22×D1112yes—
220#41—2232no—
221C2×Q8—224no—
222C2×Q8—222no—
223C2×D4—24no—
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—222no—
229C2×D4—224no—
230C2×D4—222no—
231C2×D4—224no—
232C2×D4—224no—
233C2×D4—224no—
234C2×D4—222no—
235C2×D4—224no—
236C2×D4—442no—
237C2×D4—442no—
238C2×D4—442no—
239C2×D4—442no—
240C22×C4—111no—
241C22×C4—118no—
242C22×C4—112no—
243C22×C4—114no—
244C22×C4—112no—
245C22×C4—111no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4—224no—
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1112yes—
251C22×C4C22×D1111yescharacteristic
252C4⋊C4—222no—
253C4⋊C4—224no—
254C22⋊C4—22no—
255C22⋊C4—42no—
256C22⋊C4—224no—
257C22⋊C4—224no—
258C22⋊C4—222no—
259C22⋊C4—442no—
260C22⋊C4—442no—
261C11#261511yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—112no—
274C23—222no—
275C23—221no—
276C23—222no—
277C23—221no—
278C23—221no—
279C23—222no—
280C23—222no—
281C23—221no—
282C23—221no—
283C23D4×D1114yes—
284C23C23×D1111yescharacteristic
285Q8—228no—
286D4—28no—
287D4—48no—
288D4—2216no—
289D4—444no—
290D4—444no—
291D4—448no—
292D4—444no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—112no—
300C2×C4—114no—
301C2×C4—114no—
302C2×C4—228no—
303C2×C4—2216no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—221no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4D4×D1112yes—
312C22—24no—
313C22—24no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—222no—
325C22—222no—
326C22—222no—
327C22—442no—
328C22—442no—
329C22—441no—
330C22—441no—
331C22—442no—
332C22—442no—
333C22—441no—
334C22C2×D4×D1111yescharacteristic
335C22C2×D4×D1112yes—
336C22#6703712yes—
337C22#6703711yescharacteristic
338C22#6704311yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—114no—
343C4—224no—
344C4—441no—
345C4—442no—
346C2—44no—
347C2—81no—
348C2—442no—
349C2—881no—
350C2D11×#12011yescharacteristic
351C2#1062312312yes—
352C2#1062312812yes—
353C2#1062313911yescharacteristic
354C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2615
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#4341C2semidirect
2. C2×#66992C2semidirect
3. C2×#66937C2semidirect
4. C11×#392C2semidirect
5. #10622836C2semidirect
6. #10622836C2semidirect
7. #10622573C2semidirect
8. #10622560C2semidirect
9. #10622555C2semidirect
10. #10622286C2semidirect
11. #10622280C2semidirect
63. C22×Dic11D4semidirect
72. C2×C4×D11D4semidirect
143. #392D11semidirect
261. C11#2615semidirect

Maximal subgroups

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

subgroupindex
C22×#43412
C2×#669922
C2×#669372
C11×#3922
#106228362
#106225732
#106225602
#106225552
#106222862
#106222802
#261511