Finite Group Databasebeta

← #13075895

Subgroups — #13075895

Order 1408.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#392C211yesmaximal, characteristic
2#10622835C211yesmaximal, characteristic, complemented
3#10622835C211yesmaximal, characteristic, complemented
4#10622835C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622833C211yesmaximal, characteristic, complemented
7#10622833C211yesmaximal, characteristic, complemented
8#10622565C211yesmaximal, characteristic, complemented
9#10622564C211yesmaximal, characteristic, complemented
10#10622559C211yesmaximal, characteristic, complemented
11#10622558C211yesmaximal, characteristic, complemented
12#10622557C211yesmaximal, characteristic, complemented
13#10622557C211yesmaximal, characteristic, complemented
14#10622273C211yesmaximal, characteristic, complemented
15#10622263C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C24×C11C2311yescharacteristic
53C24×C11C2311yescharacteristic
54C2×D4×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—41no—
68C22×Dic11—41no—
69C22×Dic11—41no—
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C11×C22⋊C4—22no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C22⋊Dic11—22no—
82C22⋊Dic11—22no—
83C22⋊Dic11—22no—
84C22⋊Dic11—22no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88C22⋊Dic11—41no—
89C22⋊Dic11—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—22no—
98C4×Dic11—41no—
99#2753—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—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11#4112yes—
121C23×C11C2411yescharacteristic
122D4×C11—44no—
123D4×C11—44no—
124D4×C11—44no—
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#4112yes—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
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—44no—
161C2×Dic11#4112yes—
162#400—111no—
163#397—111no—
164#394—111no—
165#394—111no—
166#394—111no—
167#392D1111yescharacteristic
168#390—111no—
169#388—111no—
170#388—111no—
171#388—111no—
172#388—111no—
173#386—111no—
174#386—111no—
175#385—111no—
176#382—111no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
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×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11C2×#4111yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C22×C11C2×#4111yescharacteristic
201C22×C11H(5,𝔽2)11yescharacteristic
202C22×C11H(5,𝔽2)11yescharacteristic
203C22×C11H(5,𝔽2)11yescharacteristic
204C22×C11H(5,𝔽2)11yescharacteristic
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209Dic11—22no—
210Dic11—41no—
211Dic11—41no—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216Dic11—41no—
217C22×D4C2×D1111yescharacteristic
218C22×D4C2×D1111yescharacteristic
219C22×D4C2×D1111yescharacteristic
220C23×C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C22⋊C4—111no—
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⋊C4—111no—
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C22⋊C4C2×D1111yescharacteristic
239C2×C22⋊C4C2×D1111yescharacteristic
240C2×C42—111no—
241C2×C42—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#95C2×D1111yescharacteristic
252C2×C11—42no—
253C2×C11—81no—
254C2×C11—81no—
255C2×C11#53811yescharacteristic
256C2×C11#54011yescharacteristic
257C2×C11#54011yescharacteristic
258C2×C11#55111yescharacteristic
259C2×C11#55311yescharacteristic
260C2×C11#55311yescharacteristic
261C2×C11H(3,𝔽4)11yescharacteristic
262C24C22×D1111yescharacteristic
263C24C22×D1111yescharacteristic
264C24C22×D1111yescharacteristic
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—222no—
309C42—441no—
310C11#275311yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
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—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23#434112yes—
332C23C23×D1111yescharacteristic
333D4—44no—
334D4—44no—
335D4—44no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—112no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
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—444no—
372C2×C4#434112yes—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22C2×#434111yescharacteristic
395C22C2×#434111yescharacteristic
396C22#6703711yescharacteristic
397C22#6703711yescharacteristic
398C22#6703711yescharacteristic
399C22#6703711yescharacteristic
400C22#41×D1111yescharacteristic
401C4—22no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—222no—
406C4—441no—
407C4—441no—
408C4—441no—
409C4—441no—
410C4—441no—
411C4—441no—
412C4—441no—
413C2—42no—
414C2—81no—
415C2—81no—
416C2#1062311811yescharacteristic
417C2#1062312411yescharacteristic
418C2#1062312511yescharacteristic
419C2#1062313211yescharacteristic
420C2#1062314511yescharacteristic
421C2#1062314611yescharacteristic
422C2#1062325011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC11×#392C2
hypercenter#392D11
hypocenterC11#2753
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
2. #10622835C2semidirect
3. #10622835C2semidirect
4. #10622835C2semidirect
5. #10622834C2semidirect
6. #10622833C2semidirect
7. #10622833C2semidirect
8. #10622565C2semidirect
9. #10622564C2semidirect
10. #10622559C2semidirect
11. #10622558C2semidirect
12. #10622557C2semidirect
13. #10622557C2semidirect
14. #10622273C2semidirect
15. #10622263C2semidirect
310. C11#2753semidirect

Maximal subgroups

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

subgroupindex
C11×#3922
#106228352
#106228342
#106228332
#106225652
#106225642
#106225592
#106225582
#106225572
#106222732
#106222632
#275311