Finite Group Databasebeta

← #13073713

Subgroups — #13073713

Order 1408.

582 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×#66936C211yesmaximal, characteristic, complemented
3#10622844C211yesmaximal, characteristic, complemented
4#10622843C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic
6#10622833C211yesmaximal, characteristic, complemented
7#10622571C211yesmaximal, characteristic, complemented
8#10622570C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622566C211yesmaximal, characteristic, complemented
11#10622565C211yesmaximal, characteristic, complemented
12#10622558C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15#10622546C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C11×#124—24no—
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C42×C11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×C4⋊Dic11C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42#66936—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
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—41no—
73C22×Dic11—22no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—41no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4D414yescomplemented
90C42×C11—22no—
91C22⋊Dic11—22no—
92C22⋊Dic11—22no—
93C22⋊Dic11—22no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103C4×Dic11—41no—
104C4×Dic11—41no—
105#2557—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×C11C2×D412yes—
120C23×C11C2411yescharacteristic
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11#4112yes—
128Q8×C11—44no—
129D4×C11—44no—
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—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11C2×D412yes—
143C2×C4×C11C2×D412yes—
144C2×C4×C11#4112yes—
145C22⋊D11—44no—
146C22⋊D11—44no—
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—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—44no—
167C2×Dic11#4112yes—
168C2×Dic11#4112yes—
169C4×D11—44no—
170C2×#124D1111yescharacteristic, complemented
171C2×#123—111no—
172#397—111no—
173#397—111no—
174#393—111no—
175#392—111no—
176#391—111no—
177#390—111no—
178#388—111no—
179#387—111no—
180#386—111no—
181#386—111no—
182#386—111no—
183C4×C22⋊C4—111no—
184C4×C22⋊C4—111no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
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×C11—41no—
199C22×C11C22×D411yescharacteristic
200C22×C11C2×#4111yescharacteristic
201C22×C11C2×#4111yescharacteristic
202C22×C11C2×#4111yescharacteristic
203C22×C11C2×#4111yescharacteristic
204C22×C11H(5,𝔽2)11yescharacteristic
205C22×C11H(5,𝔽2)11yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11—41no—
218Dic11—22no—
219Dic11—22no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224Dic11—41no—
225C22×Q8C2×D1111yescharacteristic
226C22×D4—111no—
227C22×D4—111no—
228C22×D4C2×D1111yescharacteristic
229C23×C4—111no—
230C23×C4—111no—
231#124—24no—
232#123—224no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4C2×D1111yescharacteristic
246C2×C22⋊C4C2×D1111yescharacteristic
247C2×C22⋊C4C2×D1111yescharacteristic
248C2×C22⋊C4C2×D1111yescharacteristic
249C2×C42—111no—
250C2×C42—111no—
251C2×C42C2×D1111yescharacteristic
252#95—111no—
253#95—111no—
254#95—111no—
255#95—111no—
256#95—111no—
257#95—111no—
258#95—111no—
259#95—111no—
260#95—111no—
261#95—111no—
262C2×C11—42no—
263C2×C11—81no—
264C2×C11#52911yescharacteristic
265C2×C11#53211yescharacteristic
266C2×C11#53811yescharacteristic
267C2×C11#54611yescharacteristic
268C2×C11#54611yescharacteristic
269C2×C11#55111yescharacteristic
270C2×C11#55911yescharacteristic
271D11—42no—
272C24—111no—
273C24C22×D1111yescharacteristic
274C24C22×D1111yescharacteristic
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—222no—
282C2×D4—222no—
283C2×D4—222no—
284C2×D4—222no—
285C2×D4—441no—
286C2×D4—441no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4C22×D1111yescharacteristic
301C22×C4C22×D1111yescharacteristic
302C22×C4C22×D1111yescharacteristic
303C22×C4C22×D1111yescharacteristic
304C22×C4C22×D1111yescharacteristic
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—222no—
312C22⋊C4—222no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4C22⋊D1114yescomplemented
321C42—22no—
322C42—441no—
323C42—441no—
324C11#255711yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—112no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—221no—
345C23C2×C22⋊D1112yes—
346C23C23×D1111yescharacteristic
347Q8—44no—
348D4—44no—
349D4—444no—
350D4—444no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—112no—
364C2×C4—112no—
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—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—444no—
385C2×C4—444no—
386C2×C4#434112yes—
387C2×C4C2×C22⋊D1112yes—
388C2×C4C2×C22⋊D1112yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—441no—
410C22C2×#434111yescharacteristic
411C22#6703711yescharacteristic
412C22#41×D1111yescharacteristic
413C22#41×D1111yescharacteristic
414C22#41×D1111yescharacteristic
415C22#6704211yescharacteristic
416C22C22×C22⋊D1111yescharacteristic
417C4—22no—
418C4—22no—
419C4—22no—
420C4—41no—
421C4—41no—
422C4—222no—
423C4—222no—
424C4—441no—
425C4—441no—
426C4—441no—
427C4—441no—
428C4—441no—
429C2—42no—
430C2—81no—
431C2—442no—
432C2#1062320911yescharacteristic
433C2#1062321011yescharacteristic
434C2#1062321111yescharacteristic
435C2#1062321211yescharacteristic
436C2#1062333711yescharacteristic
437C2#1062336011yescharacteristic
438C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radical#10622836C2
hypercenterC2×#124D11
hypocenterC11#2557
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66936C2semidirect
3. #10622844C2semidirect
4. #10622843C2semidirect
6. #10622833C2semidirect
7. #10622571C2semidirect
8. #10622570C2semidirect
9. #10622569C2semidirect
10. #10622566C2semidirect
11. #10622565C2semidirect
12. #10622558C2semidirect
13. C22⋊C4×Dic11C2semidirect
14. C4×(C2×D11)⋊C4C2semidirect
15. #10622546C2semidirect
89. C11×C22⋊C4D4semidirect
170. C2×#124D11semidirect
320. C22⋊C4C22⋊D11semidirect
324. C11#2557semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669362
#106228442
#106228432
#106228362
#106228332
#106225712
#106225702
#106225692
#106225662
#106225652
#106225582
C22⋊C4×Dic112
C4×(C2×D11)⋊C42
#106225462
#255711