Finite Group Databasebeta

← #14737192

Subgroups — #14737192

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079592C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068131C211yesmaximal, characteristic, complemented
4#13068126C211yesmaximal, characteristic, complemented
5#13068097C211yesmaximal, characteristic, complemented
6#13068092C211yesmaximal, characteristic, complemented
7#13068057C212yesmaximal, complemented
8#13068050C212yesmaximal, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067321C212yesmaximal, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#486C2212yes—
17C11×#466—21no—
18C11×#466—21no—
19C4×C11×D8—21no—
20C4×C11×D8—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622852—22no—
23#10622851—22no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622703C2212yes—
27#10622696C2212yes—
28#10622688C2212yes—
29#10622685C2212yes—
30#10622672—22no—
31#10622669—22no—
32#10622539C2211yescharacteristic
33#10622538C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×#41—22no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8C2312yes—
53C11×#127C2312yes—
54C11×#124—22no—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326—22no—
61C2×#4325—22no—
62C2×#4324—22no—
63C2×#4323—22no—
64#66983D411yescharacteristic
65#66982—21no—
66C4×C22⋊D11—21no—
67#66977D411yescharacteristic
68C2×#4313—21no—
69C2×C8×D11—21no—
70#66929—21no—
71#66928D411yescharacteristic
72C4×D44C2311yescharacteristic
73#66925—21no—
74#66923D411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×#107—21no—
77C11×#107—21no—
78C11×#102—22no—
79C11×#102—22no—
80C4×C8×C11D411yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11C2311yescharacteristic
83C4×C8×C11C2311yescharacteristic
84#66899—22no—
85#66899—22no—
86#66896—22no—
87#66896—22no—
88C22⋊(C11⋊C8)—21no—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—21no—
91(C2×D11)⋊C8—21no—
92#66879—21no—
93Dic11⋊C8—21no—
94Dic11⋊C8—21no—
95C8×Dic11—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—21no—
101C4×C11⋊C8—22no—
102#19225—111nomaximal, Sylow
103C11×#41—82no—
104C11×#41—82no—
105C2×Q8×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—21no—
115C2×D44C2×D411yescharacteristic
116C2×C4×D11—21no—
117C2×Dic22C2×D411yescharacteristic
118C11×D8—42no—
119C11×D8—42no—
120C2×C8×C11—22no—
121C2×C8×C11—41no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C22⋊Dic11—21no—
135#4326—82no—
136#4325—82no—
137#4324—82no—
138#4323—82no—
139(C2×D11)⋊C4—21no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143C4⋊Dic11C2×D411yescharacteristic
144C4⋊Dic11C2×D411yescharacteristic
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149C4×Dic11—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154#4313—42no—
155C8×D11—42no—
156#3212—112no—
157#3169D1111yescharacteristic, complemented
158#2966—111no—
159#1694—111no—
160#1693—111no—
161#1688—111no—
162#1687—111no—
163#1682—112no—
164#1681—112no—
165#1564—111no—
166#1553—112no—
167C23×C11—42no—
168C23×C11#12111yescharacteristic
169C22×D11—21no—
170Q8×C11—42no—
171Q8×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—82no—
177D4×C11—84no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—84no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C22⋊D11—42no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194D44—22no—
195C4×D11—41no—
196C4×D11—41no—
197Dic22—22no—
198C8×C11—21no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11#13512yes—
202C11⋊C8—41no—
203C11⋊C8—41no—
204C11⋊C8—42no—
205C11⋊C8—42no—
206#532C2×D1112yes—
207#529—111no—
208#500C2×D1111yescharacteristic
209#495—222no—
210#493C2×D1111yescharacteristic
211#488—222no—
212#486C2×D1112yes—
213#466—21no—
214#466—21no—
215#462—112no—
216#461—112no—
217#460—112no—
218#459—112no—
219#452—222no—
220#449—222no—
221#446—111no—
222C8×Q8—111no—
223C4×D8—21no—
224C4×D8—21no—
225#436—111no—
226#435—221no—
227C8×D4—111no—
228C8×D4—221no—
229#433—221no—
230#432—111no—
231#431—112no—
232#405—221no—
233C2×C4×C8C2×D1111yescharacteristic
234#335—112no—
235#334—111no—
236#334—111no—
237#332—112no—
238#332—112no—
239#331—112no—
240#331—112no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C2×#12111yescharacteristic
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—82no—
256C4×C11C2×#13511yescharacteristic
257C4×C11#57511yescharacteristic
258C4×C11#57612yes—
259Dic11—41no—
260Dic11—41no—
261Dic11—41no—
262C2×#41—22no—
263C2×Q16—222no—
264C2×SD16—222no—
265C2×SD16—222no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—222no—
269C2×M16—221no—
270C22×C8—221no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22⋊D1111yescharacteristic
273C4⋊Q8C22×D1112yes—
274#127C22×D1112yes—
275#126—221no—
276#125—111no—
277#124—22no—
278#124—111no—
279#123—221no—
280C22⋊Q8—111no—
281#121—22no—
282#121—22no—
283#121—111no—
284C4×Q8—111no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—111no—
288C4×D4—221no—
289#117—221no—
290C2×C42C22×D1111yescharacteristic
291#107—21no—
292#107—21no—
293C4⋊C8—111no—
294C4⋊C8—111no—
295C4⋊C8—112no—
296C4⋊C8—112no—
297C4⋊C8—221no—
298C4⋊C8—221no—
299#103—222no—
300#103—222no—
301#102—22no—
302#102—22no—
303#102—222no—
304#102—222no—
305C22⋊C8—222no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309#97—221no—
310#97—221no—
311C4×C8—221no—
312C4×C8—222no—
313C4×C8C22⋊D1111yescharacteristic
314C4×C8C22⋊D1111yescharacteristic
315C4×C8C22×D1111yescharacteristic
316C4×C8C22×D1111yescharacteristic
317C2×C11—41no—
318C2×C11—162no—
319C2×C11#303511yescharacteristic
320C2×C11#305811yescharacteristic
321C2×C11#306711yescharacteristic
322D11—81no—
323#41—82no—
324#41—82no—
325C2×Q8—22no—
326C2×Q8—111no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—42no—
331C2×D4—111no—
332C2×D4—221no—
333C22×C4—42no—
334C22×C4—221no—
335C22×C4D4×D1111yescharacteristic
336C22×C4#434111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338Q16—882no—
339SD16—882no—
340SD16—882no—
341D8—42no—
342D8—42no—
343D8—882no—
344M16—442no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—221no—
350C2×C8—221no—
351C2×C8—442no—
352C2×C8C2×C22⋊D1111yescharacteristic
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C2×C22⋊D1111yescharacteristic
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—111no—
359C4⋊C4—111no—
360C4⋊C4—221no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—221no—
367C22⋊C4—221no—
368C22⋊C4—221no—
369C22⋊C4—221no—
370C22⋊C4—221no—
371C42—221no—
372C42D4×D1111yescharacteristic
373C42#434111yescharacteristic
374C42C2×C22⋊D1111yescharacteristic
375C42C23×D1111yescharacteristic
376C11#1922511yescharacteristic, complemented, Sylow
377C23—42no—
378C23—221no—
379C23#6699111yescharacteristic
380Q8—42no—
381Q8—42no—
382Q8—222no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—84no—
389D4—222no—
390D4—442no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—84no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4#6699111yescharacteristic
403C2×C4#6699111yescharacteristic
404C2×C4#6699111yescharacteristic
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4C2×#434111yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—21no—
409C8—21no—
410C8—21no—
411C8—442no—
412C8—442no—
413C8—441no—
414C8—441no—
415C8#6700312yes—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22C2×#6699111yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—82no—
431C4—441no—
432C4—441no—
433C4—441no—
434C4#1062328812yes—
435C4C2×#6700311yescharacteristic
436C4#1062335311yescharacteristic
437C2—41no—
438C2—162no—
439C2—881no—
440C2#1307806511yescharacteristic
441C2#1307826011yescharacteristic
442C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19225
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079592C2semidirect
2. #13077591C2semidirect
3. #13068131C2semidirect
4. #13068126C2semidirect
5. #13068097C2semidirect
6. #13068092C2semidirect
7. #13068057C2semidirect
8. #13068050C2semidirect
9. #13067364C2semidirect
10. #13067321C2semidirect
11. C11×#3169C2semidirect
157. #3169D11semidirect
376. C11#19225semidirect

Maximal subgroups

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

subgroupindex
#130795922
#130775912
#130681312
#130681262
#130680972
#130680922
#130680572
#130680502
#130673642
#130673212
C11×#31692
#1922511