Finite Group Databasebeta

← #13075992

Subgroups — #13075992

Order 1408.

520 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#386C211yesmaximal, characteristic, complemented
2#10622836C211yesmaximal, characteristic
3#10622833C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic, complemented
5#10622824C211yesmaximal, characteristic, complemented
6#10622571C211yesmaximal, characteristic, complemented
7#10622569C211yesmaximal, characteristic, complemented
8#10622569C211yesmaximal, characteristic, complemented
9#10622560C211yesmaximal, characteristic, complemented
10#10622560C211yesmaximal, characteristic, complemented
11#10622556C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622277C211yesmaximal, characteristic, complemented
14C11⋊#401C211yesmaximal, characteristic, complemented
15C11⋊#401C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×Dic22C2211yescharacteristic
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×C22⋊Dic11C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
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
54C2×D4×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
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—41no—
70C2×C22⋊D11—41no—
71C22×Dic11—22no—
72C22×Dic11—41no—
73C22×Dic11—41no—
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C2×C4×D11—22no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—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—
94C22⋊Dic11—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99#2760—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#4112yes—
113C23×C11#4112yes—
114C23×C11C2411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11#4112yes—
122D4×C11—44no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—44no—
139C22⋊D11—44no—
140C22⋊D11—44no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—44no—
163C4×D11—44no—
164Dic22—44no—
165#401—111no—
166#401—111no—
167#393—111no—
168#393—111no—
169#393—111no—
170#392—111no—
171#386—111no—
172#386—111no—
173#386—111no—
174#386—111no—
175#386—111no—
176#386D1111yescharacteristic, complemented
177#381—111no—
178#381—111no—
179#381—111no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C2×#4111yescharacteristic
195C22×C11C2×#4111yescharacteristic
196C22×C11C2×#4111yescharacteristic
197C22×C11H(5,𝔽2)11yescharacteristic
198C22×C11H(5,𝔽2)11yescharacteristic
199C22×C11H(5,𝔽2)11yescharacteristic
200C22×C11H(5,𝔽2)11yescharacteristic
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219Dic11—41no—
220C22×Q8—111no—
221C22×D4—111no—
222C22×D4—111no—
223C22×D4C2×D1111yescharacteristic
224C23×C4—111no—
225C23×C4—111no—
226C23×C4C2×D1111yescharacteristic
227C2×C22⋊C4—111no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4C2×D1111yescharacteristic
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C22⋊C4C2×D1111yescharacteristic
239#95—111no—
240#95—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95—111no—
250#95—111no—
251#95—111no—
252#95—111no—
253#95C2×D1111yescharacteristic
254#95C2×D1111yescharacteristic
255C2×C11—42no—
256C2×C11—42no—
257C2×C11#53811yescharacteristic
258C2×C11#53811yescharacteristic
259C2×C11#53811yescharacteristic
260C2×C11#55111yescharacteristic
261C2×C11#55111yescharacteristic
262C2×C11#55111yescharacteristic
263C2×C11#56011yescharacteristic
264D11—42no—
265C24—111no—
266C24C22×D1111yescharacteristic
267C24C22×D1111yescharacteristic
268C2×Q8—441no—
269C2×Q8—441no—
270C2×Q8—441no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—222no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—441no—
279C2×D4—441no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4C22×D1111yescharacteristic
297C22×C4C22×D1111yescharacteristic
298C22×C4C22×D1111yescharacteristic
299C22×C4C22×D1111yescharacteristic
300C22×C4C22×D1111yescharacteristic
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C22⋊C4—441no—
313C11#276011yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—112no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23#433912yes—
334C23#434112yes—
335C23C23×D1111yescharacteristic
336Q8—444no—
337D4—44no—
338D4—444no—
339D4—444no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—444no—
378C2×C4—444no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—222no—
394C22—222no—
395C22—222no—
396C22—441no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22C2×#433911yescharacteristic
401C22C2×#434111yescharacteristic
402C22#6703711yescharacteristic
403C22#6703711yescharacteristic
404C22#6703711yescharacteristic
405C22#41×D1111yescharacteristic
406C22#6704211yescharacteristic
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—441no—
413C4—441no—
414C4—441no—
415C4—441no—
416C4—441no—
417C4—441no—
418C4—441no—
419C2—42no—
420C2—42no—
421C2—442no—
422C2#1062302611yescharacteristic
423C2#1062308711yescharacteristic
424C2#1062309111yescharacteristic
425C2#1062312411yescharacteristic
426C2#1062314411yescharacteristic
427C2#1062315111yescharacteristic
428C2#1062318911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radical#10622836C2
hypercenter#386D11
hypocenterC11#2760
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C11×#386C2semidirect
3. #10622833C2semidirect
4. #10622826C2semidirect
5. #10622824C2semidirect
6. #10622571C2semidirect
7. #10622569C2semidirect
8. #10622569C2semidirect
9. #10622560C2semidirect
10. #10622560C2semidirect
11. #10622556C2semidirect
12. #10622286C2semidirect
13. #10622277C2semidirect
14. C11⋊#401C2semidirect
15. C11⋊#401C2semidirect
176. #386D11semidirect
313. C11#2760semidirect

Maximal subgroups

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

subgroupindex
C11×#3862
#106228362
#106228332
#106228262
#106228242
#106225712
#106225692
#106225602
#106225562
#106222862
#106222772
C11⋊#4012
#276011