Finite Group Databasebeta

← #14737613

Subgroups — #14737613

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic, complemented
3C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068062C212yesmaximal, complemented
5#13068058C212yesmaximal, complemented
6#13068008C212yesmaximal, complemented
7#13067974C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3037C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C11×#532C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66995—21no—
16#10623008C2211yescharacteristic
17C11×#464—22no—
18C11×#462C2212yes—
19C11×#460C2212yes—
20C11×#423C2211yescharacteristic
21C11×#417—21no—
22#10622701C2211yescharacteristic
23#10622691C2211yescharacteristic
24#10622686C2211yescharacteristic
25#10622683C2211yescharacteristic
26#10622651—21no—
27#10622651—21no—
28#10622644C2212yes—
29#10622641—22no—
30#10622640C2212yes—
31Q8×C11⋊C8—21no—
32Q8×C11⋊C8—21no—
33Q8×C11⋊C8C2212yes—
34Q8×C11⋊C8C2212yes—
35C4×#4323—21no—
36C4×#4323—21no—
37#10622579—21no—
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8—21no—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622182C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622117C2212yes—
48#10622117C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C2×#4339—21no—
52C11×#137—44no—
53C2×C11×Q16—22no—
54C2×C11×SD16—22no—
55C2×C11×M16—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11D412yes—
64C4×Q8×C11C2312yes—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4326—22no—
72#66995—44no—
73C2×#4325—22no—
74C2×#4323—21no—
75C2×#4323—21no—
76#66983—21no—
77#66983—21no—
78C2×#4318—21no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8D411yescharacteristic
82#66928—21no—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×#103—22no—
90C11×#102—22no—
91#66896—21no—
92#66896—21no—
93#66874—22no—
94#66873—22no—
95#66873—21no—
96#66873—21no—
97#66871—21no—
98#66871—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—22no—
106C4×C11⋊C8—22no—
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111#19261—111nomaximal, Sylow
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11D814yescomplemented
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C2×C22⋊D11—41no—
130#4339—42no—
131#4339—42no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×Q16—44no—
138C11×SD16—44no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4326—44no—
156#4325—44no—
157#4323—42no—
158#4323—42no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—41no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173#3169—111no—
174#3037—111no—
175#3037D1111yescharacteristic, complemented
176C2×C8×Q8—111no—
177#1682—112no—
178#1682—112no—
179#1674—112no—
180#1668—112no—
181#1567—111no—
182#1547—111no—
183#1547—111no—
184C23×C11—41no—
185C23×C11#12111yescharacteristic
186C22×D11—41no—
187Q8×C11—22no—
188Q8×C11—24no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11C2×D814yes—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—81no—
197D4×C11—82no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—82no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11C2×D812yes—
211C2×C4×C11#13512yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—82no—
216C2×Dic11—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—81no—
222C4×D11—82no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—42no—
226C11⋊C8—21no—
227C11⋊C8—21no—
228C11⋊C8—21no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C11⋊C8#13712yescomplemented
232C2×#137—21no—
233C2×#137—221no—
234#532—111no—
235#532C2×D1111yescharacteristic
236C2×C4×Q8C2×D1111yescharacteristic
237#500—111no—
238#493—111no—
239#486—111no—
240#486—111no—
241#466—221no—
242#466—221no—
243#464—22no—
244#464—222no—
245#462—112no—
246#462C2×D1112yes—
247#460—112no—
248#460C2×D1112yes—
249C8×Q8—112no—
250C8×Q8—112no—
251C8×Q8—221no—
252C8×Q8—221no—
253C4×D8—221no—
254C4×D8—221no—
255#423—111no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258C2×C4⋊C8—221no—
259#417—21no—
260#417—221no—
261C2×C4×C8—111no—
262C2×C4×C8—221no—
263#335—112no—
264#335—112no—
265#332—112no—
266#332—112no—
267#331—112no—
268#331—112no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#46612yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—24no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11#46612yes—
286C4×C11C22×D811yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11C2×#13711yescharacteristic
289C4×C11#57511yescharacteristic
290Dic11—81no—
291C2×#41—21no—
292C2×#41—221no—
293C22×Q8C22⋊D1111yescharacteristic
294#137—44no—
295#137—444no—
296C2×Q16—22no—
297C2×Q16—222no—
298C2×SD16—22no—
299C2×SD16—222no—
300C2×D8—221no—
301C2×D8—221no—
302C2×M16—21no—
303C2×M16—221no—
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—221no—
307C4⋊Q8—111no—
308C4⋊Q8C22×D1111yescharacteristic
309#127—111no—
310#127C22×D1111yescharacteristic
311#124—21no—
312#124—221no—
313#121—21no—
314#121—21no—
315#121—221no—
316#121—221no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8C22⋊D1112yes—
320C4×Q8C22×D1112yes—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—221no—
324C4×D4—221no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C42—21no—
328C2×C42C22×D1111yescharacteristic
329#107—221no—
330#107—221no—
331C4⋊C8—21no—
332C4⋊C8—112no—
333C4⋊C8—112no—
334C4⋊C8—222no—
335C4⋊C8—222no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22×D1112yes—
339#103—22no—
340#103—222no—
341#102—22no—
342#102—221no—
343#102—221no—
344#102—221no—
345#102—221no—
346#102—222no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8—222no—
352C4×C8—222no—
353C2×C11—22no—
354C2×C11—161no—
355C2×C11#303711yescharacteristic
356C2×C11C2×#46611yescharacteristic
357C2×C11#306711yescharacteristic
358D11—161no—
359#41—42no—
360#41—42no—
361#41—442no—
362#41—442no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—21no—
366C2×Q8—221no—
367C2×Q8#432314yescomplemented
368C2×Q8C2×C22⋊D1112yes—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—441no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—441no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384Q16—44no—
385Q16—444no—
386SD16—44no—
387SD16—444no—
388D8—442no—
389D8—442no—
390M16—42no—
391M16—442no—
392C2×C8—22no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—441no—
401C2×C8—442no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4C2×C22⋊D1112yes—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C42—22no—
415C42—22no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1926111yescharacteristic, complemented, Sylow
421C23—41no—
422C23—441no—
423C23#6699211yescharacteristic
424Q8—22no—
425Q8—24no—
426Q8—41no—
427Q8—41no—
428Q8—441no—
429Q8—441no—
430Q8C2×#432314yes—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—81no—
436D4—82no—
437D4—441no—
438D4—441no—
439D4—441no—
440D4—441no—
441D4—881no—
442D4—882no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—441no—
453C2×C4—882no—
454C2×C4C2×#432312yes—
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4#6700312yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—42no—
463C8—112no—
464C8—221no—
465C8—221no—
466C8—221no—
467C8—442no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22#1062265112yes—
478C22C2×#6699211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—24no—
483C4—42no—
484C4—81no—
485C4—881no—
486C4#1062265112yes—
487C4D11×#13711yescharacteristic
488C4#1062330811yescharacteristic
489C4C22×#432311yescharacteristic
490C4C2×#6700311yescharacteristic
491C2—22no—
492C2—161no—
493C2—1761no—
494C2#1307808511yescharacteristic
495C2C2×#1062265111yescharacteristic
496C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3037C2
socleC22×C11C2×#121
prime radical#13079191C2
hypercenter#3037D11
hypocenterC11#19261
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. C2×Q8×C11⋊C8C2semidirect
4. #13068062C2semidirect
5. #13068058C2semidirect
6. #13068008C2semidirect
7. #13067974C2semidirect
8. #13067374C2semidirect
9. #13067294C2semidirect
10. #13067293C2semidirect
11. C11×#3037C2semidirect
117. C2×Q8×C11D8semidirect
175. #3037D11semidirect
231. C11⋊C8#137semidirect
367. C2×Q8#4323semidirect
420. C11#19261semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130780882
C2×Q8×C11⋊C82
#130680622
#130680582
#130680082
#130679742
#130673742
#130672942
#130672932
C11×#30372
#1926111