Finite Group Databasebeta

← #13073554

Subgroups — #13073554

Order 1408.

760 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic, complemented
3C2×#66999C211yesmaximal, characteristic, complemented
4C2×#66983C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6C2×#66948C211yesmaximal, characteristic, complemented
7#10622605C212yesmaximal, complemented
8#10622601C212yesmaximal, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622573C212yesmaximal, complemented
11#10622570C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×D44C2211yescharacteristic
17C22×D44C2212yes—
18C22×C4×D11C2211yescharacteristic
19C11×C22⋊Q8—24no—
20C2×C11×C4⋊C4C2212yes—
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2212yes—
23C2×C22⋊Dic11C2211yescharacteristic
24#67000—24no—
25#66999—24no—
26#66983—24no—
27C4×C22⋊D11—24no—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×(C2×D11)⋊C4C2212yes—
34C2×C4⋊Dic11C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2212yes—
37C2×C4×Dic11C2212yes—
38C2×C4×Dic11C2211yescharacteristic
39#66948—24no—
40C11⋊#95C2212yes—
41C24×C11C2311yescharacteristic
42C23×D11C2312yes—
43C23×D11C2311yescharacteristic
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11C2312yes—
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2312yes—
53C22×C4×C11C2311yescharacteristic
54C2×C22⋊D11—22no—
55C2×C22⋊D11—24no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—22no—
59C2×C22⋊D11—42no—
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2312yes—
63C22×Dic11C2311yescharacteristic
64C2×D44—24no—
65C2×D44—24no—
66C2×D44—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—42no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C11×C4⋊C4—24no—
74C11×C4⋊C4D414yescomplemented
75C11×C22⋊C4—24no—
76C22⋊Dic11—22no—
77(C2×D11)⋊C4—22no—
78(C2×D11)⋊C4—24no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4—24no—
81(C2×D11)⋊C4—24no—
82(C2×D11)⋊C4—24no—
83C4⋊Dic11D414yescomplemented
84Dic11⋊C4—22no—
85Dic11⋊C4—24no—
86C4×Dic11—42no—
87C4×Dic11D414yescomplemented
88#2540—111nomaximal, Sylow
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11#4112yes—
96C23×C11C2411yescharacteristic
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—22no—
110C22×D11#4112yes—
111Q8×C11—44no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—44no—
121C2×C4×C11C2×D412yes—
122C2×C4×C11C2×D412yes—
123C2×C4×C11C2×D414yes—
124C2×C4×C11C2×D412yes—
125C22⋊D11—28no—
126C22⋊D11—48no—
127C2×Dic11—21no—
128C2×Dic11—22no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11C2×D412yes—
137C2×Dic11C2×D412yes—
138C2×Dic11C2×D414yes—
139D44—48no—
140D44—44no—
141C4×D11—44no—
142C2×#124—111no—
143C2×C22⋊Q8—111no—
144C2×C22⋊Q8D1111yescharacteristic, complemented
145C2×#121—111no—
146C2×#121—111no—
147C2×C4×D4—111no—
148#399—112no—
149#392—112no—
150#390—112no—
151#390—112no—
152C4×C4⋊C4—111no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C22×C11C22×D411yescharacteristic
162C22×C11C22×D411yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11H(5,𝔽2)11yescharacteristic
166C22×C112−1+411yescharacteristic
167C2×D11—22no—
168C2×D11—22no—
169C2×D11—22no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C4×C11—24no—
182C4×C11—41no—
183C4×C11—42no—
184C4×C11#12714yes—
185Dic11—22no—
186Dic11—22no—
187Dic11—24no—
188Dic11—41no—
189C22×Q8C2×D1111yescharacteristic
190C22×D4—111no—
191C22×D4—112no—
192C22×D4—111no—
193C22×D4—112no—
194C23×C4—111no—
195C23×C4C2×D1111yescharacteristic
196#124—224no—
197C22⋊Q8—24no—
198C22⋊Q8—224no—
199#121—224no—
200#121—224no—
201C4×D4—224no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—112no—
205C2×C4⋊C4C2×D1112yes—
206C2×C4⋊C4C2×D1111yescharacteristic
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—112no—
212C2×C22⋊C4—112no—
213C2×C22⋊C4—112no—
214C2×C22⋊C4C2×D1112yes—
215C2×C42—111no—
216C2×C42—112no—
217#95—112no—
218C2×C11—42no—
219C2×C11#52511yescharacteristic
220C2×C11C2×#12711yescharacteristic
221C2×C11#53711yescharacteristic
222C2×C11#54611yescharacteristic
223C2×C11#54611yescharacteristic
224C2×C11#54811yescharacteristic
225C2×C11#54811yescharacteristic
226D11—42no—
227D11—82no—
228C24—111no—
229C24—112no—
230C24C22×D1111yescharacteristic
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×D4—224no—
235C2×D4—222no—
236C2×D4—224no—
237C2×D4—222no—
238C2×D4—222no—
239C2×D4—224no—
240C2×D4—222no—
241C2×D4—222no—
242C2×D4—224no—
243C2×D4—222no—
244C2×D4—442no—
245C2×D4—442no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—111no—
250C22×C4—112no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—222no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4C22×D1112yes—
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1112yes—
259C22×C4C22×D1111yescharacteristic
260C4⋊C4—24no—
261C4⋊C4—114no—
262C4⋊C4—222no—
263C4⋊C4—224no—
264C4⋊C4C22⋊D1114yescomplemented
265C22⋊C4—24no—
266C22⋊C4—222no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C22⋊C4—224no—
271C22⋊C4—222no—
272C22⋊C4—224no—
273C42—114no—
274C42—442no—
275C11#254011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—112no—
283C23—221no—
284C23—221no—
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23—222no—
293C23—222no—
294C23—222no—
295C23—222no—
296C23#434312yes—
297C23C23×D1111yescharacteristic
298Q8—44no—
299D4—228no—
300D4—448no—
301D4—448no—
302D4—444no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—114no—
315C2×C4—221no—
316C2×C4—222no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—222no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—444no—
325C2×C4D4×D1112yes—
326C2×C4D4×D1112yes—
327C2×C4C2×C22⋊D1114yes—
328C2×C4C2×C22⋊D1112yes—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—222no—
337C22—222no—
338C22—222no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22C2×D4×D1111yescharacteristic
351C22C2×D4×D1111yescharacteristic
352C22C2×#434311yescharacteristic
353C22#6704011yescharacteristic
354C22#41×D1111yescharacteristic
355C22#6704211yescharacteristic
356C22C22×C22⋊D1111yescharacteristic
357C4—24no—
358C4—41no—
359C4—42no—
360C4—222no—
361C4—222no—
362C4—224no—
363C4—441no—
364C4#6699314yes—
365C2—42no—
366C2—442no—
367C2—882no—
368C2#1062315811yescharacteristic
369C2#1062316011yescharacteristic
370C2#1062316111yescharacteristic
371C2#1062316411yescharacteristic
372C2C2×#6699311yescharacteristic
373C2#1062334811yescharacteristic
374C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
hypercenterC2×C22⋊Q8D11
hypocenterC11#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#67000C2semidirect
3. C2×#66999C2semidirect
4. C2×#66983C2semidirect
5. C2×C4×C22⋊D11C2semidirect
6. C2×#66948C2semidirect
7. #10622605C2semidirect
8. #10622601C2semidirect
9. C4⋊C4×Dic11C2semidirect
10. #10622573C2semidirect
11. #10622570C2semidirect
74. C11×C4⋊C4D4semidirect
83. C4⋊Dic11D4semidirect
87. C4×Dic11D4semidirect
144. C2×C22⋊Q8D11semidirect
264. C4⋊C4C22⋊D11semidirect
275. C11#2540semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#670002
C2×#669992
C2×#669832
C2×C4×C22⋊D112
C2×#669482
#106226052
#106226012
C4⋊C4×Dic112
#106225732
#106225702
#254011