Finite Group Databasebeta

← #13072224

Subgroups — #13072224

Order 1408.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4341C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66983C211yesmaximal, characteristic, complemented
4C2×#66939C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6C2×C11⋊#95C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622571C211yesmaximal, characteristic, complemented
10#10622571C211yesmaximal, characteristic, complemented
11#10622563C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622281C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622269C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C23×Dic11C2211yescharacteristic
24C23×Dic11C2211yescharacteristic
25C2×#4341—24no—
26C2×#4341—24no—
27C2×#4341—24no—
28C22×D44C2211yescharacteristic
29C22×C4×D11C2211yescharacteristic
30C22×Dic22C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35#66992—24no—
36#66983—24no—
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊Dic11C2211yescharacteristic
46C2×C4⋊Dic11C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48#66939—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11D414yescomplemented
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11D414yescomplemented
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—41no—
92C22×Dic11D414yescomplemented
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99#4341—232no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—41no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×Dic22—22no—
107C2×Dic22—22no—
108C2×Dic22—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C22⋊Dic11—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123Dic11⋊C4—22no—
124#2430—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11C2×D412yes—
136C23×C11C2×D412yes—
137C23×C11C2×D412yes—
138C23×C11C2×D412yes—
139C23×C11C2411yescharacteristic
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11C2×D412yes—
154D4×C11—28no—
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×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—44no—
169C2×C4×C11C2×D412yes—
170C2×C4×C11#4112yescomplemented
171C22⋊D11—28no—
172C22⋊D11—28no—
173C22⋊D11—44no—
174C22⋊D11—44no—
175C2×Dic11—28no—
176C2×Dic11—28no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—44no—
192C2×Dic11C2×D412yes—
193C2×Dic11C2×D412yes—
194C2×Dic11C2×D412yes—
195C2×Dic11#4112yescomplemented
196D44—44no—
197C4×D11—28no—
198Dic22—28no—
199C22×#41—111no—
200C2×#123—111no—
201C2×#121—111no—
202C2×#121—111no—
203#395—111no—
204#394—111no—
205#393—111no—
206#392—111no—
207#386—111no—
208#386—111no—
209#386—111no—
210#386D1111yescharacteristic, complemented
211#385—111no—
212#385—111no—
213C2×#95—111no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11#12014yes—
228C22×C11C22×D411yescharacteristic
229C22×C11C22×D411yescharacteristic
230C22×C11C22×D411yescharacteristic
231C22×C11C2×#4111yescharacteristic
232C22×C11C2×#4111yescharacteristic
233C22×C11H(5,𝔽2)11yescharacteristic
234C22×C112−1+411yescharacteristic
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C2×D11—41no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—41no—
252C4×C11—41no—
253C4×C11—41no—
254Dic11—22no—
255Dic11—22no—
256Dic11—22no—
257Dic11—22no—
258Dic11—41no—
259Dic11—41no—
260C2×#41—224no—
261C2×#41—224no—
262C2×#41—224no—
263C22×Q8—111no—
264C22×D4—111no—
265C22×D4—111no—
266C22×D4—111no—
267C22×D4—111no—
268C22×D4—111no—
269C22×D4C2×D1111yescharacteristic
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—111no—
274C23×C4C2×D1111yescharacteristic
275#123—224no—
276#121—224no—
277#121—224no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4C2×D1111yescharacteristic
291C2×C22⋊C4C2×D1111yescharacteristic
292C2×C22⋊C4C2×D1111yescharacteristic
293#95—111no—
294#95—111no—
295#95—111no—
296#95—111no—
297#95—111no—
298#95—111no—
299#95C2×D1111yescharacteristic
300#95C2×D1111yescharacteristic
301C2×C11—24no—
302C2×C11—42no—
303C2×C11C2×#12011yescharacteristic
304C2×C11#53211yescharacteristic
305C2×C11#53711yescharacteristic
306C2×C11#54611yescharacteristic
307C2×C11#54611yescharacteristic
308C2×C11#54711yescharacteristic
309C2×C11#54711yescharacteristic
310D11—42no—
311D11—81no—
312C24—111no—
313C24—111no—
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316#41—2232no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×Q8—222no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—114no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4D4414yescomplemented
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—41no—
341C22×C4—114no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—441no—
359C22×C4C22×D1111yescharacteristic
360C22×C4C22×D1111yescharacteristic
361C22×C4C22×D1111yescharacteristic
362C22×C4C22×D1111yescharacteristic
363C22×C4C22×D1111yescharacteristic
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—41no—
371C22⋊C4—222no—
372C22⋊C4—222no—
373C22⋊C4—222no—
374C22⋊C4—222no—
375C22⋊C4—222no—
376C22⋊C4—222no—
377C22⋊C4—222no—
378C22⋊C4—441no—
379C11#243011yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—112no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23C2×D4412yes—
405C23C2×D4412yes—
406C23D4×D1112yes—
407C23D4×D1112yes—
408C23C23×D1111yescharacteristic
409Q8—228no—
410D4—28no—
411D4—228no—
412D4—228no—
413D4—444no—
414D4—444no—
415D4—444no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—112no—
431C2×C4—112no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—228no—
435C2×C4—228no—
436C2×C4—228no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—444no—
452C2×C4C2×D4412yes—
453C2×C4#434112yescomplemented
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—222no—
468C22—222no—
469C22—222no—
470C22—441no—
471C22—441no—
472C22—441no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22—441no—
481C22#6693514yes—
482C22C22×D4411yescharacteristic
483C22C2×D4×D1111yescharacteristic
484C22C2×D4×D1111yescharacteristic
485C22C2×#434111yescharacteristic
486C22#6703711yescharacteristic
487C22#41×D1111yescharacteristic
488C22#6704311yescharacteristic
489C4—22no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—222no—
495C4—222no—
496C4—222no—
497C4—222no—
498C4—441no—
499C4—441no—
500C2—24no—
501C2—42no—
502C2—442no—
503C2—881no—
504C2C2×#6693511yescharacteristic
505C2#1062308511yescharacteristic
506C2#1062308611yescharacteristic
507C2#1062312211yescharacteristic
508C2#1062312711yescharacteristic
509C2#1062312811yescharacteristic
510C2#1062318611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#4341C2semidirect
2. C2×#66992C2semidirect
3. C2×#66983C2semidirect
4. C2×#66939C2semidirect
5. C11×#386C2semidirect
6. C2×C11⋊#95C2semidirect
7. #10622574C2semidirect
8. #10622573C2semidirect
9. #10622571C2semidirect
10. #10622571C2semidirect
11. #10622563C2semidirect
12. #10622286C2semidirect
13. #10622281C2semidirect
14. #10622278C2semidirect
15. #10622269C2semidirect
63. C2×D4×C11D4semidirect
83. C2×C22⋊D11D4semidirect
92. C22×Dic11D4semidirect
170. C2×C4×C11#41semidirect
195. C2×Dic11#41semidirect
210. #386D11semidirect
337. C2×D4D44semidirect
379. C11#2430semidirect
453. C2×C4#4341semidirect

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×#669832
C2×#669392
C11×#3862
C2×C11⋊#952
#106225742
#106225732
#106225712
#106225632
#106222862
#106222812
#106222782
#106222692
#243011