Finite Group Databasebeta

← #13076702

Subgroups — #13076702

Order 1408.

522 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#386C211yesmaximal, characteristic, complemented
2#10622836C211yesmaximal, characteristic, complemented
3#10622836C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic, complemented
5#10622826C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622572C211yesmaximal, characteristic, complemented
10#10622565C211yesmaximal, characteristic, complemented
11#10622561C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622287C211yesmaximal, characteristic, complemented
14#10622285C211yesmaximal, characteristic, complemented
15C11⋊#401C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C24×C11C2311yescharacteristic
53C23×D11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105#2825—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11#4112yes—
120C23×C11C2411yescharacteristic
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
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—
135D4×C11—44no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
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—44no—
152C22⋊D11—44no—
153C22⋊D11—44no—
154C22⋊D11—44no—
155C22⋊D11—44no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
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—
174D44—44no—
175#401—111no—
176#397—111no—
177#397—111no—
178#397—111no—
179#396—111no—
180#394—111no—
181#394—111no—
182#394—111no—
183#392—111no—
184#392—111no—
185#392—111no—
186#392—111no—
187#386—111no—
188#386—111no—
189#386D1111yescharacteristic, complemented
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11C2×#4111yescharacteristic
205C22×C11H(5,𝔽2)11yescharacteristic
206C22×C11H(5,𝔽2)11yescharacteristic
207C22×C11H(5,𝔽2)11yescharacteristic
208C22×C11H(5,𝔽2)11yescharacteristic
209C22×C11H(5,𝔽2)11yescharacteristic
210C22×C11H(5,𝔽2)11yescharacteristic
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—41no—
230Dic11—41no—
231Dic11—41no—
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235Dic11—41no—
236C22×D4—111no—
237C22×D4—111no—
238C22×D4—111no—
239C22×D4—111no—
240C22×D4—111no—
241C22×D4C2×D1111yescharacteristic
242C23×C4C2×D1111yescharacteristic
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—111no—
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—111no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4C2×D1111yescharacteristic
259C2×C22⋊C4C2×D1111yescharacteristic
260C2×C22⋊C4C2×D1111yescharacteristic
261#95—111no—
262#95—111no—
263#95—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95—111no—
269#95C2×D1111yescharacteristic
270#95C2×D1111yescharacteristic
271C2×C11—42no—
272C2×C11—81no—
273C2×C11#53811yescharacteristic
274C2×C11#53811yescharacteristic
275C2×C11#53811yescharacteristic
276C2×C11#56011yescharacteristic
277C2×C11#56011yescharacteristic
278C2×C11#56011yescharacteristic
279C2×C11#56011yescharacteristic
280D11—81no—
281D11—81no—
282C24—111no—
283C24—111no—
284C24C22×D1111yescharacteristic
285C24C22×D1111yescharacteristic
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4C22×D1111yescharacteristic
314C22×C4C22×D1111yescharacteristic
315C22×C4C22×D1111yescharacteristic
316C22×C4C22×D1111yescharacteristic
317C22×C4C22×D1111yescharacteristic
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C11#282511yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23#433912yes—
365C23C23×D1111yescharacteristic
366D4—44no—
367D4—444no—
368D4—444no—
369D4—444no—
370D4—444no—
371D4—444no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—44no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22—441no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22C2×#433911yescharacteristic
435C22#6703711yescharacteristic
436C22#6703711yescharacteristic
437C22#6703711yescharacteristic
438C22#6703711yescharacteristic
439C22#6704211yescharacteristic
440C22#6704211yescharacteristic
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—441no—
447C4—441no—
448C4—441no—
449C4—441no—
450C4—441no—
451C4—441no—
452C2—42no—
453C2—81no—
454C2—881no—
455C2—881no—
456C2#1062302511yescharacteristic
457C2#1062309111yescharacteristic
458C2#1062309111yescharacteristic
459C2#1062312611yescharacteristic
460C2#1062315111yescharacteristic
461C2#1062315111yescharacteristic
462C2#1062319711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2825
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C11×#386C2semidirect
2. #10622836C2semidirect
3. #10622836C2semidirect
4. #10622826C2semidirect
5. #10622826C2semidirect
6. #10622574C2semidirect
7. #10622573C2semidirect
8. #10622573C2semidirect
9. #10622572C2semidirect
10. #10622565C2semidirect
11. #10622561C2semidirect
12. #10622288C2semidirect
13. #10622287C2semidirect
14. #10622285C2semidirect
15. C11⋊#401C2semidirect
189. #386D11semidirect
336. C11#2825semidirect

Maximal subgroups

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

subgroupindex
C11×#3862
#106228362
#106228262
#106225742
#106225732
#106225722
#106225652
#106225612
#106222882
#106222872
#106222852
C11⋊#4012
#282511