Finite Group Databasebeta

← #14960204

Subgroups — #14960204

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076869C211yesmaximal, characteristic, complemented
2#13076804C213yesmaximal, complemented
3#13076696C213yesmaximal, complemented
4#13076693C216yesmaximal, complemented
5#13076613C211yesmaximal, characteristic, complemented
6#13076611C212yesmaximal, complemented
7#13071903C216yesmaximal, complemented
8#13071900C213yesmaximal, complemented
9#13071831C213yesmaximal, complemented
10C4×#67006C212yesmaximal, complemented
11C4×C11×#120C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic, complemented
14C2×C11×#120C2211yescharacteristic
15C2×C4×D4×C11C2213yes—
16C2×#67006C2212yes—
17C2×C4×C22⋊D11C2216yes—
18C2×C4×Dic22C2213yescomplemented
19C11×#386C2213yes—
20C11×#385C2213yes—
21C11×#379C2211yescharacteristic
22C4×C11×C22⋊C4C2213yes—
23#10622860C2212yes—
24#10622836C2216yes—
25#10622835C2216yes—
26#10622826C2216yes—
27#10622823C2216yes—
28C4×C22⋊Dic11C2216yes—
29C4×C22⋊Dic11C2213yescomplemented
30#10622604C2213yescomplemented
31#10622595C2216yescomplemented
32#10622592C2213yescomplemented
33#10622574C2216yes—
34#10622573C2213yes—
35#10622572C2216yes—
36#10622572C2216yescomplemented
37#10622566C2213yes—
38#10622566C2213yescomplemented
39#10622565C2216yes—
40#10622560C2213yes—
41#10622560C2216yes—
42#10622560C2213yes—
43#10622560C2213yescomplemented
44C4×(C2×D11)⋊C4C2216yescomplemented
45#10622545C2213yescomplemented
46#10622288C2216yescomplemented
47#10622286C2216yescomplemented
48#10622273C2216yescomplemented
49#10622271C2216yescomplemented
50C25×C11C2311yescharacteristic
51C22×D4×C11C2313yes—
52C23×C4×C11—46no—
53C23×C4×C11C2313yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2313yes—
56C22×C22⋊D11C2316yes—
57C22×C22⋊D11C2312yes—
58C2×#4339—46no—
59C22×D44C2311yescharacteristic
60C22×C4×D11C2312yes—
61C22×Dic22C2313yes—
62C22×Dic22C2311yescharacteristic
63C11×#120—24no—
64C4×D4×C11—46no—
65C2×C11×C4⋊C4C2313yes—
66C2×C11×C22⋊C4C2313yes—
67C2×C11×C22⋊C4C2313yes—
68C2×C11×C22⋊C4C2313yes—
69C2×C11×C22⋊C4C2313yes—
70C2×C42×C11C2313yes—
71#67006—28no—
72C2×C22⋊Dic11C2316yes—
73C2×C22⋊Dic11C2316yes—
74C2×C22⋊Dic11C2316yes—
75C2×C22⋊Dic11C2316yes—
76C4×C22⋊D11—412no—
77C2×(C2×D11)⋊C4C2316yes—
78C2×(C2×D11)⋊C4C2316yes—
79C2×(C2×D11)⋊C4C2316yes—
80C2×C4⋊Dic11C2313yes—
81C2×Dic11⋊C4C2316yes—
82C2×Dic11⋊C4C2316yes—
83C2×C4×Dic11C2316yes—
84C4×Dic22—46no—
85C11×#95C2316yes—
86C11⋊#95C2313yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2313yes—
93C11⋊#95C2313yes—
94C11⋊#95C2313yes—
95#36675—111nomaximal, Sylow
96C24×C11—43no—
97C24×C11—43no—
98C24×C11#4114yescomplemented
99C24×C11C2411yescharacteristic
100C24×C11C2413yes—
101C23×D11C2412yes—
102C2×D4×C11—26no—
103C2×D4×C11—43no—
104C2×D4×C11—43no—
105C22×C4×C11—212no—
106C22×C4×C11—26no—
107C22×C4×C11—26no—
108C22×C4×C11—43no—
109C22×C4×C11—46no—
110C22×C4×C11—416no—
111C22×C4×C11C2411yescharacteristic
112C22×C4×C11C2413yes—
113C22×C4×C11C2413yes—
114C22×C4×C11C2413yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—212no—
117C2×C22⋊D11—46no—
118C2×C22⋊D11—46no—
119C2×C22⋊D11—46no—
120C22×Dic11C2416yes—
121C22×Dic11C2416yes—
122C22×Dic11C2412yes—
123#4339—416no—
124C2×D44—43no—
125C2×C4×D11—212no—
126C2×Dic22—43no—
127C2×Dic22—46no—
128C2×Dic22—43no—
129C11×C4⋊C4—43no—
130C11×C22⋊C4—26no—
131C11×C22⋊C4—43no—
132C11×C22⋊C4—43no—
133C11×C22⋊C4—43no—
134C42×C11—26no—
135C22⋊Dic11—212no—
136C22⋊Dic11—46no—
137C22⋊Dic11—46no—
138C22⋊Dic11—46no—
139(C2×D11)⋊C4—46no—
140(C2×D11)⋊C4—46no—
141(C2×D11)⋊C4—46no—
142C4⋊Dic11—43no—
143Dic11⋊C4—46no—
144Dic11⋊C4—46no—
145C4×Dic11—212no—
146#2840—111no—
147#2835—113no—
148#2824—116no—
149#2824—113no—
150#2812—111no—
151#2812—112no—
152#2398—116no—
153#2398—113no—
154#2388—113no—
155C4×#120—112no—
156C4×#120D1111yescharacteristic, complemented
157C23×C11—26no—
158C23×C11—23no—
159C23×C11—26no—
160C23×C11—23no—
161C23×C11—21no—
162C23×C11—23no—
163C23×C11—23no—
164C23×C11—412no—
165C23×C11—44no—
166C23×C11—412no—
167C23×C11C2×#4116yes—
168C23×C11C2511yescharacteristic
169C22×D11—22no—
170C22×D11—26no—
171C22×D11—26no—
172D4×C11—412no—
173C2×C4×C11—23no—
174C2×C4×C11—23no—
175C2×C4×C11—26no—
176C2×C4×C11—23no—
177C2×C4×C11—23no—
178C2×C4×C11—23no—
179C2×C4×C11—23no—
180C2×C4×C11—26no—
181C2×C4×C11—412no—
182C2×C4×C11—44no—
183C2×C4×C11—412no—
184C2×C4×C11H(5,𝔽2)16yes—
185C22⋊D11—424no—
186C22⋊D11—48no—
187C2×Dic11—26no—
188C2×Dic11—26no—
189C2×Dic11—26no—
190C2×Dic11—26no—
191C2×Dic11—26no—
192C2×Dic11—26no—
193C2×Dic11—26no—
194D44—44no—
195C4×D11—48no—
196Dic22—412no—
197Dic22—44no—
198C22×#41—111no—
199C24×C4C2×D1111yescharacteristic
200C2×#120—112no—
201C2×#120C2×D1111yescharacteristic
202C2×C4×Q8—113no—
203C2×C4×D4—116no—
204C2×C4×D4C2×D1113yes—
205#400—116no—
206#400—116no—
207#400—116no—
208#397—113no—
209#397—116no—
210#397—113no—
211#397—116no—
212#395—113no—
213#394—116no—
214#394—113no—
215#394—116no—
216#394—116no—
217#394—116no—
218#393—113no—
219#393—116no—
220#393—113no—
221#393—113no—
222#393—116no—
223#392—116no—
224#392—113no—
225#386—116no—
226#386C2×D1113yes—
227#385—116no—
228#385C2×D1113yes—
229#379—112no—
230#379C2×D1111yescharacteristic
231C4×C22⋊C4—113no—
232C4×C22⋊C4—116no—
233C4×C22⋊C4—116no—
234C4×C22⋊C4C2×D1113yes—
235#376—113no—
236C22×C11—26no—
237C22×C11—212no—
238C22×C11—416no—
239C22×C11—43no—
240C22×C11—46no—
241C22×C11—43no—
242C22×C11—43no—
243C22×C11—41no—
244C22×C11—43no—
245C22×C11C22×#4111yescharacteristic
246C22×C11C2×H(5,𝔽2)13yes—
247C22×C11#58513yes—
248C2×D11—46no—
249C2×D11—42no—
250C2×D11—46no—
251C4×C11—43no—
252C4×C11—43no—
253C4×C11—41no—
254C4×C11—43no—
255C4×C11H(3,𝔽4)14yes—
256Dic11—46no—
257Dic11—42no—
258Dic11—46no—
259C25C22×D1111yescharacteristic
260C2×#41—446no—
261C22×Q8—113no—
262C22×Q8—111no—
263C22×D4—116no—
264C22×D4—112no—
265C22×D4—111no—
266C22×D4C22×D1113yes—
267C23×C4—46no—
268C23×C4—112no—
269C23×C4C22×D1113yes—
270C23×C4C22×D1111yescharacteristic
271C23×C4C22×D1113yes—
272#120—24no—
273#120—228no—
274C4×Q8—446no—
275C4×D4—46no—
276C4×D4—4412no—
277C2×C4⋊C4—116no—
278C2×C4⋊C4—116no—
279C2×C4⋊C4—113no—
280C2×C4⋊C4C22×D1113yes—
281C2×C22⋊C4—116no—
282C2×C22⋊C4—116no—
283C2×C22⋊C4—116no—
284C2×C22⋊C4—116no—
285C2×C22⋊C4—116no—
286C2×C22⋊C4—116no—
287C2×C22⋊C4—116no—
288C2×C22⋊C4C22×D1113yes—
289C2×C22⋊C4C22×D1113yes—
290C2×C22⋊C4C22×D1113yes—
291C2×C22⋊C4C22×D1113yes—
292C2×C42—116no—
293C2×C42C22×D1113yes—
294#95—113no—
295#95—116no—
296#95—113no—
297#95—116no—
298#95—116no—
299#95—113no—
300#95—116no—
301#95—113no—
302#95—116no—
303#95C22×D1116yes—
304C2×C11—46no—
305C2×C11—81no—
306C2×C11#345913yes—
307C2×C11C2×H(3,𝔽4)11yescharacteristic
308C2×C11#352913yes—
309D11—82no—
310C24—43no—
311C24—43no—
312C24—112no—
313C24#433914yescomplemented
314C24C23×D1111yescharacteristic
315C24C23×D1113yes—
316#41—4416no—
317C2×Q8—443no—
318C2×Q8—443no—
319C2×Q8—446no—
320C2×D4—26no—
321C2×D4—43no—
322C2×D4—43no—
323C2×D4—2212no—
324C2×D4—443no—
325C2×D4—446no—
326C2×D4—446no—
327C2×D4—446no—
328C22×C4—26no—
329C22×C4—26no—
330C22×C4—212no—
331C22×C4—46no—
332C22×C4—43no—
333C22×C4—416no—
334C22×C4—116no—
335C22×C4—116no—
336C22×C4—112no—
337C22×C4—2212no—
338C22×C4C23×D1111yescharacteristic
339C22×C4C23×D1113yes—
340C22×C4C23×D1113yes—
341C22×C4C23×D1113yes—
342C22×C4C23×D1111yescharacteristic
343C4⋊C4—43no—
344C4⋊C4—446no—
345C4⋊C4—446no—
346C4⋊C4—443no—
347C22⋊C4—26no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—43no—
351C22⋊C4—2212no—
352C22⋊C4—446no—
353C22⋊C4—446no—
354C22⋊C4—446no—
355C22⋊C4—446no—
356C22⋊C4—446no—
357C22⋊C4—446no—
358C42—26no—
359C42—2212no—
360C11#3667511yescharacteristic, complemented, Sylow
361C23—23no—
362C23—26no—
363C23—23no—
364C23—26no—
365C23—21no—
366C23—23no—
367C23—23no—
368C23—412no—
369C23—44no—
370C23—412no—
371C23—222no—
372C23—226no—
373C23—226no—
374C23C2×#433916yes—
375C23C24×D1111yescharacteristic
376Q8—444no—
377Q8—4412no—
378D4—412no—
379D4—444no—
380D4—4424no—
381D4—448no—
382C2×C4—23no—
383C2×C4—23no—
384C2×C4—23no—
385C2×C4—23no—
386C2×C4—23no—
387C2×C4—26no—
388C2×C4—26no—
389C2×C4—23no—
390C2×C4—412no—
391C2×C4—412no—
392C2×C4—44no—
393C2×C4—226no—
394C2×C4—226no—
395C2×C4—226no—
396C2×C4—226no—
397C2×C4—226no—
398C2×C4—226no—
399C2×C4—226no—
400C2×C4—448no—
401C2×C4#6703716yes—
402C22—26no—
403C22—212no—
404C22—416no—
405C22—43no—
406C22—43no—
407C22—46no—
408C22—41no—
409C22—43no—
410C22—43no—
411C22—442no—
412C22—446no—
413C22—446no—
414C22C22×#433911yescharacteristic
415C22C2×#6703713yes—
416C22#1062345313yes—
417C4—43no—
418C4—41no—
419C4—43no—
420C4—43no—
421C4—442no—
422C4—446no—
423C4—446no—
424C4#1062312514yes—
425C2—46no—
426C2—81no—
427C2—882no—
428C2#1308202513yes—
429C2C2×#1062312511yescharacteristic
430C2#1308275413yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
hypercenterC4×#120D11
hypocenterC11#36675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. #13076869C2semidirect
2. #13076804C2semidirect
3. #13076696C2semidirect
4. #13076693C2semidirect
5. #13076613C2semidirect
6. #13076611C2semidirect
7. #13071903C2semidirect
8. #13071900C2semidirect
9. #13071831C2semidirect
10. C4×#67006C2semidirect
11. C4×C11×#120C2semidirect
13. C22×#4339C22semidirect
18. C2×C4×Dic22C22semidirect
29. C4×C22⋊Dic11C22semidirect
30. #10622604C22semidirect
31. #10622595C22semidirect
32. #10622592C22semidirect
36. #10622572C22semidirect
38. #10622566C22semidirect
43. #10622560C22semidirect
44. C4×(C2×D11)⋊C4C22semidirect
45. #10622545C22semidirect
46. #10622288C22semidirect
47. #10622286C22semidirect
48. #10622273C22semidirect
49. #10622271C22semidirect
98. C24×C11#41semidirect
156. C4×#120D11semidirect
313. C24#4339semidirect
360. C11#36675semidirect

Maximal subgroups

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

subgroupindex
#130768692
#130768042
#130766962
#130766932
#130766132
#130766112
#130719032
#130719002
#130718312
C4×#670062
C4×C11×#1202
#3667511