Finite Group Databasebeta

← #13075047

Subgroups — #13075047

Order 1408.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic, complemented
4#10622836C211yesmaximal, characteristic, complemented
5#10622826C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622565C211yesmaximal, characteristic, complemented
11#10622565C211yesmaximal, characteristic, complemented
12#10622281C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622277C211yesmaximal, characteristic, complemented
15#10622273C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32#66991—24no—
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×C4⋊Dic11C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42#66937—24no—
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11D414yescomplemented
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—41no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—22no—
109Dic11⋊C4—22no—
110Dic11⋊C4—41no—
111#2688—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2×D412yes—
126C23×C11C2411yescharacteristic
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×D11C2×D412yes—
140C22×D11#4112yes—
141D4×C11—44no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
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—44no—
157C2×C4×C11#4112yes—
158C22⋊D11—44no—
159C22⋊D11—44no—
160C22⋊D11—44no—
161C22⋊D11—44no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
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—
180D44—44no—
181C4×D11—44no—
182C4×D11—44no—
183C2×#121—111no—
184C2×#121—111no—
185#400—111no—
186#397—111no—
187#397—111no—
188#394—111no—
189#392—111no—
190#392—111no—
191#386—111no—
192#386—111no—
193#386—111no—
194#386—111no—
195#386D1111yescharacteristic, complemented
196#385—111no—
197#381—111no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11C22×D411yescharacteristic
213C22×C11C2×#4111yescharacteristic
214C22×C11C2×#4111yescharacteristic
215C22×C11H(5,𝔽2)11yescharacteristic
216C22×C11H(5,𝔽2)11yescharacteristic
217C22×C11H(5,𝔽2)11yescharacteristic
218C22×C11H(5,𝔽2)11yescharacteristic
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C4×C11—22no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—41no—
238Dic11—22no—
239Dic11—41no—
240Dic11—41no—
241Dic11—41no—
242Dic11—41no—
243Dic11—41no—
244C22×D4—111no—
245C22×D4—111no—
246C22×D4—111no—
247C22×D4—111no—
248C22×D4—111no—
249C22×D4C2×D1111yescharacteristic
250C23×C4—111no—
251C23×C4—111no—
252C23×C4C2×D1111yescharacteristic
253#121—224no—
254#121—224no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4C2×D1111yescharacteristic
269C2×C22⋊C4C2×D1111yescharacteristic
270C2×C22⋊C4C2×D1111yescharacteristic
271#95—111no—
272#95—111no—
273#95—111no—
274#95—111no—
275#95—111no—
276#95—111no—
277#95—111no—
278#95—111no—
279#95C2×D1111yescharacteristic
280#95C2×D1111yescharacteristic
281C2×C11—42no—
282C2×C11—81no—
283C2×C11#53411yescharacteristic
284C2×C11#53811yescharacteristic
285C2×C11#54011yescharacteristic
286C2×C11#54611yescharacteristic
287C2×C11#54611yescharacteristic
288C2×C11#55311yescharacteristic
289C2×C11#56011yescharacteristic
290D11—42no—
291D11—42no—
292C24—111no—
293C24—111no—
294C24C22×D1111yescharacteristic
295C24C22×D1111yescharacteristic
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—114no—
300C2×D4—222no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—222no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4C22×D1111yescharacteristic
330C22×C4C22×D1111yescharacteristic
331C22×C4C22×D1111yescharacteristic
332C22×C4C22×D1111yescharacteristic
333C22×C4C22×D1111yescharacteristic
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—441no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C11#268811yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—112no—
365C23—112no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23D4×D1112yes—
379C23C23×D1111yescharacteristic
380D4—44no—
381D4—444no—
382D4—444no—
383D4—444no—
384D4—444no—
385D4—444no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—44no—
401C2×C4—112no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—444no—
420C2×C4—444no—
421C2×C4#433912yes—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22C2×#433911yescharacteristic
451C22C2×D4×D1111yescharacteristic
452C22#6703711yescharacteristic
453C22#6703711yescharacteristic
454C22#6703711yescharacteristic
455C22#41×D1111yescharacteristic
456C22#6704211yescharacteristic
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—222no—
463C4—441no—
464C4—441no—
465C4—441no—
466C4—441no—
467C4—441no—
468C2—42no—
469C2—81no—
470C2—442no—
471C2—442no—
472C2#1062302111yescharacteristic
473C2#1062308911yescharacteristic
474C2#1062309311yescharacteristic
475C2#1062312611yescharacteristic
476C2#1062313611yescharacteristic
477C2#1062314111yescharacteristic
478C2#1062318811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2688
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. C2×#66937C2semidirect
3. C11×#386C2semidirect
4. #10622836C2semidirect
5. #10622826C2semidirect
6. #10622826C2semidirect
7. #10622573C2semidirect
8. #10622572C2semidirect
9. #10622569C2semidirect
10. #10622565C2semidirect
11. #10622565C2semidirect
12. #10622281C2semidirect
13. #10622278C2semidirect
14. #10622277C2semidirect
15. #10622273C2semidirect
79. C2×C22⋊D11D4semidirect
195. #386D11semidirect
350. C11#2688semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669372
C11×#3862
#106228362
#106228262
#106225732
#106225722
#106225692
#106225652
#106222812
#106222782
#106222772
#106222732
#268811