Finite Group Databasebeta

← #14736519

Subgroups — #14736519

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2#13078676C212yesmaximal, complemented
3#13068156C212yesmaximal, complemented
4#13068149C212yesmaximal, complemented
5#13068144C211yesmaximal, characteristic, complemented
6#13068139C211yesmaximal, characteristic, complemented
7#13068100C211yesmaximal, characteristic, complemented
8#13068095C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067276C212yesmaximal, complemented
11C11×#2965C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623008C2212yes—
14C11×#446C2211yescharacteristic
15C11×#446C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#436C2211yescharacteristic
18C11×#435—21no—
19C11×#435—21no—
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C4×C11×M16—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622851—22no—
25#10622728—21no—
26#10622728—21no—
27#10622640C2212yes—
28C4×#4325—22no—
29#10622634C2212yes—
30#10622628C2212yes—
31C4×#4323—22no—
32#10622621C2212yes—
33#10622616—22no—
34#10622538C2212yes—
35#10622308C2211yescharacteristic
36#10622307C2212yes—
37C4×D88—21no—
38C4×D88—21no—
39#10622295C2211yescharacteristic
40#10622123C2212yes—
41#10622123C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×#41D411yescharacteristic
48C2×#4339—22no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C4×Q8×C11D411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11D411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4323—22no—
65#66983—22no—
66#66983—22no—
67C2×D88—21no—
68C2×D88—21no—
69#66928—22no—
70#66927C2312yes—
71C4×D44—22no—
72C4×D44—22no—
73#66922C2312yes—
74C11×C4⋊C8—21no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2311yescharacteristic
77C11×C4⋊C8C2311yescharacteristic
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×#97—21no—
82C11×#97—21no—
83C4×C8×C11—21no—
84C4×C8×C11D411yescharacteristic
85C4×C8×C11D411yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88#66899—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—22no—
91#66885—22no—
92#66885—22no—
93#66882—21no—
94#66882—21no—
95#66873—22no—
96#66873—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19160—111nomaximal, Sylow
103C11×#41—42no—
104C2×Q8×C11C2×D411yescharacteristic
105C2×D4×C11—21no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—42no—
114#4339—84no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×C4×D11—42no—
119C2×Dic22—22no—
120C11×M16—42no—
121C11×M16—42no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—41no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4C2×D411yescharacteristic
133C11×C4⋊C4C2×D411yescharacteristic
134C11×C22⋊C4—21no—
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4325—44no—
145#4323—44no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152D88—42no—
153D88—42no—
154#3169—111no—
155#3106—112no—
156#2965D1111yescharacteristic, complemented
157#1698—112no—
158#1697—112no—
159#1696—111no—
160#1695—111no—
161#1688—111no—
162#1687—111no—
163#1564—111no—
164#1543—112no—
165C23×C11—21no—
166C23×C11#12111yescharacteristic
167C22×D11—42no—
168Q8×C11—22no—
169D4×C11—22no—
170D4×C11—42no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C22⋊D11—84no—
189C2×Dic11—42no—
190D44—42no—
191D44—42no—
192D44—42no—
193D44—42no—
194D44—82no—
195C4×D11—84no—
196Dic22—82no—
197C8×C11—21no—
198C8×C11—21no—
199C8×C11—21no—
200C8×C11—41no—
201C8×C11—41no—
202C8×C11#13512yes—
203C11⋊C8—42no—
204C11⋊C8—42no—
205#532—112no—
206C4×#41C2×D1111yescharacteristic
207#500—111no—
208#493—111no—
209#486—112no—
210#482—222no—
211#477—112no—
212#476—112no—
213#466—221no—
214#466—221no—
215#460—112no—
216#459—112no—
217#449—222no—
218#446C2×D1111yescharacteristic
219#446C2×D1111yescharacteristic
220C4×SD16—222no—
221C4×D8—222no—
222C4×D8—221no—
223C4×D8—221no—
224#436C2×D1111yescharacteristic
225#436C2×D1111yescharacteristic
226#435—21no—
227#435—21no—
228#431—21no—
229#431—112no—
230#431C2×D1111yescharacteristic
231C4×M16—21no—
232C2×C4×C8C2×D1111yescharacteristic
233#335—112no—
234#334—111no—
235#334—111no—
236#333—112no—
237#333—112no—
238#331—112no—
239#331—112no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11C2×#12111yescharacteristic
247C2×D11—82no—
248C2×D11—82no—
249C2×D11—82no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—41no—
254C4×C11—41no—
255C4×C11—41no—
256C4×C11#47212yes—
257C4×C11C2×#13511yescharacteristic
258C4×C11#57512yes—
259C4×C11#57511yescharacteristic
260Dic11—82no—
261C2×#41—222no—
262C2×#41D4411yescharacteristic
263C2×SD16—222no—
264C2×D8—222no—
265C2×D8—221no—
266C2×D8—221no—
267C2×M16—21no—
268C2×M16—21no—
269C22×C8C22⋊D1111yescharacteristic
270C22×C8C22⋊D1111yescharacteristic
271C4⋊Q8—112no—
272#127—112no—
273#124—222no—
274#121—222no—
275#121—222no—
276C4×Q8D4411yescharacteristic
277C4×Q8C22×D1111yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—222no—
281C4×D4—222no—
282C4×D4D4411yescharacteristic
283C4×D4C22×D1111yescharacteristic
284#117—21no—
285#117D4411yescharacteristic
286C2×C42—21no—
287C2×C42C22×D1111yescharacteristic
288#107—221no—
289#107—221no—
290#107—222no—
291#106—222no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—112no—
295C4⋊C8—112no—
296C4⋊C8C22×D1111yescharacteristic
297C4⋊C8C22×D1111yescharacteristic
298#103—222no—
299#102—222no—
300#102—222no—
301#102—222no—
302#102—222no—
303#102—222no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—222no—
308#97—21no—
309#97—21no—
310C4×C8—21no—
311C4×C8—222no—
312C4×C8C22⋊D1111yescharacteristic
313C4×C8C22⋊D1111yescharacteristic
314C4×C8C22×D1111yescharacteristic
315C4×C8C22×D1111yescharacteristic
316C2×C11—41no—
317C2×C11—81no—
318C2×C11#303511yescharacteristic
319C2×C11#305411yescharacteristic
320C2×C11C2×#47211yescharacteristic
321D11—162no—
322#41—42no—
323#41—884no—
324C2×Q8—222no—
325C2×Q8C2×D4411yescharacteristic
326C2×D4—21no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—442no—
331C2×D4C2×D4411yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—442no—
336C22×C4C2×D4411yescharacteristic
337C22×C4#433911yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339SD16—444no—
340D8—442no—
341D8—444no—
342D8—442no—
343M16—42no—
344M16—42no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—41no—
349C2×C8—222no—
350C2×C8—222no—
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C2×C22⋊D1111yescharacteristic
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—222no—
358C4⋊C4—222no—
359C4⋊C4C2×D4411yescharacteristic
360C4⋊C4C2×D4411yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—442no—
365C22⋊C4—442no—
366C42—21no—
367C42—21no—
368C42—21no—
369C42C2×D4411yescharacteristic
370C42#433911yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C42C23×D1111yescharacteristic
373C11#1916011yescharacteristic, complemented, Sylow
374C23—21no—
375C23—442no—
376C23#6698311yescharacteristic
377Q8—22no—
378Q8—882no—
379D4—22no—
380D4—42no—
381D4—442no—
382D4—442no—
383D4—442no—
384D4—442no—
385D4—882no—
386D4—884no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—442no—
399C2×C4—884no—
400C2×C4#6698311yescharacteristic
401C2×C4#6698311yescharacteristic
402C2×C4#6698311yescharacteristic
403C2×C4C22×D4411yescharacteristic
404C2×C4C2×#433911yescharacteristic
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—41no—
410C8—41no—
411C8—442no—
412C8—442no—
413C8#6700312yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—882no—
421C22—882no—
422C22—882no—
423C22C2×#6698311yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—882no—
431C4#1062275512yes—
432C4#1062327912yes—
433C4C2×#6700311yescharacteristic
434C4#1062335311yescharacteristic
435C2—41no—
436C2—81no—
437C2—1762no—
438C2#1307807111yescharacteristic
439C2#1307822511yescharacteristic
440C2C2×#1062275511yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C2×#121
hypercenter#2965D11
hypocenterC11#19160
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13078676C2semidirect
3. #13068156C2semidirect
4. #13068149C2semidirect
5. #13068144C2semidirect
6. #13068139C2semidirect
7. #13068100C2semidirect
8. #13068095C2semidirect
9. #13067364C2semidirect
10. #13067276C2semidirect
11. C11×#2965C2semidirect
156. #2965D11semidirect
373. C11#19160semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130786762
#130681562
#130681492
#130681442
#130681392
#130681002
#130680952
#130673642
#130672762
C11×#29652
#1916011