Finite Group Databasebeta

← #13074880

Subgroups — #13074880

Order 1408.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66993C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66983C211yesmaximal, characteristic, complemented
4C2×#66939C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622571C211yesmaximal, characteristic, complemented
12#10622285C211yesmaximal, characteristic, complemented
13#10622284C211yesmaximal, characteristic, complemented
14#10622283C211yesmaximal, characteristic, complemented
15#10622266C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C23×Dic11C2211yescharacteristic
25C22×D44C2211yescharacteristic
26C22×D44C2211yescharacteristic
27C22×D44C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32#66993—24no—
33#66992—24no—
34#66983—24no—
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
47C2×C4×Dic11C2211yescharacteristic
48#66939—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11D414yescomplemented
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C2×C22⋊D11—22no—
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⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—41no—
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11D414yescomplemented
121Dic11⋊C4—22no—
122C4×Dic11—22no—
123#2673—111nomaximal, Sylow
124C23×C11—21no—
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×C11—21no—
136C23×C11C2×D412yes—
137C23×C11C2×D412yes—
138C23×C11C2411yescharacteristic
139C22×D11—21no—
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×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160D4×C11—44no—
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—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—44no—
175C2×C4×C11C2×D412yes—
176C2×C4×C11C2×D412yes—
177C22⋊D11—44no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C22⋊D11—44no—
181C22⋊D11—44no—
182C22⋊D11—44no—
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—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—44no—
196C2×Dic11C2×D412yes—
197C2×Dic11C2×D412yes—
198C2×Dic11#4112yes—
199D44—44no—
200D44—44no—
201D44—44no—
202C2×#127—111no—
203C2×#123—111no—
204C2×#121—111no—
205C2×#121—111no—
206#394—111no—
207#394—111no—
208#392—111no—
209#392—111no—
210#392—111no—
211#392—111no—
212#388—111no—
213#387—111no—
214#386—111no—
215#386—111no—
216#386D1111yescharacteristic, complemented
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—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11C22×D411yescharacteristic
232C22×C11C22×D411yescharacteristic
233C22×C11C2×#4111yescharacteristic
234C22×C11H(5,𝔽2)11yescharacteristic
235C22×C11H(5,𝔽2)11yescharacteristic
236C22×C11H(5,𝔽2)11yescharacteristic
237C22×C11H(5,𝔽2)11yescharacteristic
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—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—41no—
262C4×C11—41no—
263C4×C11—41no—
264Dic11—22no—
265Dic11—22no—
266Dic11—22no—
267Dic11—41no—
268Dic11—41no—
269C22×D4—111no—
270C22×D4—111no—
271C22×D4—111no—
272C22×D4—111no—
273C22×D4—111no—
274C22×D4—111no—
275C22×D4—111no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4C2×D1111yescharacteristic
279C23×C4—111no—
280C23×C4C2×D1111yescharacteristic
281#127—224no—
282#123—224no—
283#121—224no—
284#121—224no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—111no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4C2×D1111yescharacteristic
299C2×C22⋊C4C2×D1111yescharacteristic
300C2×C22⋊C4C2×D1111yescharacteristic
301C2×C42—111no—
302#95—111no—
303#95—111no—
304#95—111no—
305#95—111no—
306#95C2×D1111yescharacteristic
307#95C2×D1111yescharacteristic
308C2×C11—42no—
309C2×C11—42no—
310C2×C11#53411yescharacteristic
311C2×C11#53511yescharacteristic
312C2×C11#54011yescharacteristic
313C2×C11D4211yescharacteristic
314C2×C11#54611yescharacteristic
315C2×C11#55011yescharacteristic
316C2×C11#56011yescharacteristic
317D11—81no—
318D11—81no—
319D11—81no—
320C24—111no—
321C24—111no—
322C24—111no—
323C24C22×D1111yescharacteristic
324C24C22×D1111yescharacteristic
325C2×D4—41no—
326C2×D4—41no—
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—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—222no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4D4414yescomplemented
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—441no—
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C22×C4C22×D1111yescharacteristic
371C4⋊C4—114no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—222no—
388C11#267311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23—221no—
415C23—221no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23C2×D4412yes—
423C23C2×D4412yes—
424C23C23×D1111yescharacteristic
425D4—44no—
426D4—444no—
427D4—444no—
428D4—444no—
429D4—444no—
430D4—444no—
431D4—444no—
432D4—444no—
433D4—444no—
434D4—444no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—44no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—444no—
465C2×C4C2×D4412yes—
466C2×C4D4×D1112yes—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—441no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22—441no—
497C22—441no—
498C22—441no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22C22×D4411yescharacteristic
503C22C2×D4×D1111yescharacteristic
504C22#6703711yescharacteristic
505C22#6703711yescharacteristic
506C22#6703711yescharacteristic
507C22#41×D1111yescharacteristic
508C22#6704211yescharacteristic
509C4—22no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—222no—
515C4—222no—
516C4—222no—
517C4—441no—
518C4—441no—
519C2—42no—
520C2—42no—
521C2—881no—
522C2—881no—
523C2—881no—
524C2#1062302411yescharacteristic
525C2D4×D4411yescharacteristic
526C2#1062308511yescharacteristic
527C2#1062312311yescharacteristic
528C2#1062313011yescharacteristic
529C2#1062315111yescharacteristic
530C2#1062319411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2673
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66992C2semidirect
3. C2×#66983C2semidirect
4. C2×#66939C2semidirect
5. C11×#386C2semidirect
6. #10622826C2semidirect
7. #10622574C2semidirect
8. #10622573C2semidirect
9. #10622573C2semidirect
10. #10622573C2semidirect
11. #10622571C2semidirect
12. #10622285C2semidirect
13. #10622284C2semidirect
14. #10622283C2semidirect
15. #10622266C2semidirect
62. C2×D4×C11D4semidirect
120. C4⋊Dic11D4semidirect
216. #386D11semidirect
354. C2×D4D44semidirect
388. C11#2673semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669922
C2×#669832
C2×#669392
C11×#3862
#106228262
#106225742
#106225732
#106225712
#106222852
#106222842
#106222832
#106222662
#267311