Finite Group Databasebeta

← #13072033

Subgroups — #13072033

Order 1408.

704 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66946C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66925C211yesmaximal, characteristic, complemented
5C11×#388C211yesmaximal, characteristic, complemented
6#10622603C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622570C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622285C211yesmaximal, characteristic, complemented
13#10622284C211yesmaximal, characteristic, complemented
14#10622280C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C42×C11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×C4⋊Dic11C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×C4×Dic11C2211yescharacteristic
46C2×C4×Dic11C2211yescharacteristic
47#66946—24no—
48#66937—24no—
49#66937—24no—
50#66925—24no—
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—22no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11D414yescomplemented
94C11×C4⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C42×C11—22no—
99C22⋊Dic11—41no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—41no—
114Dic11⋊C4D414yescomplemented
115C4×Dic11—22no—
116C4×Dic11—22no—
117#2414—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11C2×D412yes—
146C22×D11#4112yes—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11C2×D412yes—
163C2×C4×C11C2×D412yes—
164C2×C4×C11#4112yes—
165C22⋊D11—44no—
166C22⋊D11—44no—
167C22⋊D11—44no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11C2×D412yes—
180C2×Dic11C2×D412yes—
181C2×Dic11C2×D412yes—
182C2×Dic11#4112yes—
183D44—28no—
184D44—44no—
185D44—44no—
186C4×D11—28no—
187C4×D11—44no—
188C2×#121—111no—
189C2×#121—111no—
190C2×C4×D4—111no—
191C2×#117—111no—
192#394—111no—
193#394—111no—
194#392—111no—
195#392—111no—
196#390—111no—
197#390—111no—
198#390—111no—
199#389—111no—
200#388—111no—
201#388D1111yescharacteristic, complemented
202#380—111no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11C22×D411yescharacteristic
211C22×C11C22×D411yescharacteristic
212C22×C11C2×#4111yescharacteristic
213C22×C11C2×#4111yescharacteristic
214C22×C11C2×#4111yescharacteristic
215C22×C11H(5,𝔽2)11yescharacteristic
216C22×C11H(5,𝔽2)11yescharacteristic
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C4×C11—22no—
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—41no—
244Dic11—22no—
245Dic11—41no—
246Dic11—41no—
247Dic11—41no—
248Dic11#12114yes—
249C22×D4—111no—
250C22×D4—111no—
251C22×D4—111no—
252C22×D4—111no—
253C22×D4—111no—
254C22×D4—111no—
255C23×C4—111no—
256C23×C4—111no—
257#121—224no—
258#121—224no—
259C4×D4—224no—
260#117—224no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4C2×D1111yescharacteristic
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4C2×D1111yescharacteristic
279C2×C22⋊C4C2×D1111yescharacteristic
280C2×C22⋊C4C2×D1111yescharacteristic
281C2×C42—111no—
282C2×C42—111no—
283C2×C42C2×D1111yescharacteristic
284#95—111no—
285#95—111no—
286#95C2×D1111yescharacteristic
287#95C2×D1111yescharacteristic
288C2×C11—81no—
289C2×C11C2×#12111yescharacteristic
290C2×C11#52511yescharacteristic
291C2×C11#53511yescharacteristic
292C2×C11#54611yescharacteristic
293C2×C11#55011yescharacteristic
294C2×C11#55311yescharacteristic
295C2×C11#55511yescharacteristic
296D11—42no—
297D11—42no—
298D11—81no—
299C24—111no—
300C24—111no—
301C24—111no—
302C24C22×D1111yescharacteristic
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—222no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—222no—
312C2×D4—222no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—114no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—222no—
331C22×C4—222no—
332C22×C4C22×D1111yescharacteristic
333C22×C4C22×D1111yescharacteristic
334C22×C4C22×D1111yescharacteristic
335C22×C4C22×D1111yescharacteristic
336C22×C4C22×D1111yescharacteristic
337C22×C4C22×D1111yescharacteristic
338C4⋊C4—22no—
339C4⋊C4—114no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—222no—
348C22⋊C4—222no—
349C22⋊C4—222no—
350C22⋊C4—222no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C22⋊C4—222no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—22no—
359C42—222no—
360C42—222no—
361C11#241411yescharacteristic, complemented, Sylow
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—112no—
370C23—112no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23C23×D1111yescharacteristic
391D4—228no—
392D4—444no—
393D4—444no—
394D4—444no—
395D4—444no—
396D4—444no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—112no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—112no—
416C2×C4—228no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—444no—
429C2×C4#433912yes—
430C2×C4D4×D1112yes—
431C2×C4D4×D1112yes—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22—441no—
456C22—441no—
457C22—441no—
458C22—441no—
459C22—441no—
460C22C2×#433911yescharacteristic
461C22C2×D4×D1111yescharacteristic
462C22C2×D4×D1111yescharacteristic
463C22#41×D1111yescharacteristic
464C22#41×D1111yescharacteristic
465C22#6704211yescharacteristic
466C22#6704211yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—114no—
474C4—222no—
475C4—441no—
476C4—441no—
477C4—441no—
478C2—81no—
479C2—442no—
480C2—442no—
481C2—881no—
482C2#1062306311yescharacteristic
483C2#1062307811yescharacteristic
484C2#1062308411yescharacteristic
485C2D11×#12111yescharacteristic
486C2#1062318511yescharacteristic
487C2#1062320511yescharacteristic
488C2#1062324011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
hypercenter#388D11
hypocenterC11#2414
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66946C2semidirect
2. C2×#66937C2semidirect
3. C2×#66937C2semidirect
4. C2×#66925C2semidirect
5. C11×#388C2semidirect
6. #10622603C2semidirect
7. #10622574C2semidirect
8. #10622573C2semidirect
9. #10622570C2semidirect
10. #10622570C2semidirect
11. #10622552C2semidirect
12. #10622285C2semidirect
13. #10622284C2semidirect
14. #10622280C2semidirect
15. #10622260C2semidirect
93. C2×C4×D11D4semidirect
114. Dic11⋊C4D4semidirect
201. #388D11semidirect
361. C11#2414semidirect

Maximal subgroups

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

subgroupindex
C2×#669462
C2×#669372
C2×#669252
C11×#3882
#106226032
#106225742
#106225732
#106225702
#106225522
#106222852
#106222842
#106222802
#106222602
#241411