Finite Group Databasebeta

← #14739239

Subgroups — #14739239

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic
4#13068032C212yesmaximal, complemented
5#13068025C212yesmaximal, complemented
6#13067998C212yesmaximal, complemented
7#13067991C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10C2×#10622119C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C8×Q8×C11C2212yes—
17C8×D4×C11—22no—
18C8×D4×C11C2212yes—
19C11×#431—21no—
20C11×#431C2211yescharacteristic
21C2×C11×C4⋊C8—21no—
22C2×C11×C4⋊C8C2211yescharacteristic
23#10622845—21no—
24#10622644C2211yescharacteristic
25#10622641—21no—
26#10622640C2211yescharacteristic
27#10622634C2212yes—
28#10622633—21no—
29#10622632C2211yescharacteristic
30#10622629—21no—
31#10622628C2211yescharacteristic
32#10622621C2212yes—
33#10622620—21no—
34#10622615—21no—
35#10622608—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622455—21no—
39#10622455—21no—
40#10622348—22no—
41#10622307C2212yes—
42#10622293C2212yes—
43#10622124C2212yes—
44#10622123C2212yes—
45#10622119C2212yes—
46#10622119C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×C11×#41D411yescharacteristic
50C2×#4339—21no—
51C22×Dic22—21no—
52C22×C8×C11—21no—
53C22×C8×C11—22no—
54C4×Q8×C11D411yescharacteristic
55C4×Q8×C11C2311yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#67003—44no—
65C2×#4326—21no—
66C2×#4325—21no—
67C2×#4324—21no—
68C2×#4323—21no—
69#66983—21no—
70#66983—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×#4318—21no—
74C22×C11⋊C8—21no—
75#66928—21no—
76#66927C2311yescharacteristic
77C4×D44—21no—
78C4×D44—21no—
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922C2312yes—
83#66922C2311yescharacteristic
84C11×C4⋊C8—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8C2312yes—
89C11×C22⋊C8—22no—
90C11×C22⋊C8D412yes—
91C4×C8×C11—22no—
92C4×C8×C11C2312yes—
93#66899—22no—
94#66896—22no—
95#66885—22no—
96#66885—22no—
97#66881—22no—
98#66881—22no—
99#66874—21no—
100#66874—21no—
101#66873—21no—
102#66873—21no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19414—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41SD1614yes—
113C2×Q8×C11C2×D411yescharacteristic
114C2×D4×C11—21no—
115C2×D4×C11C2×D411yescharacteristic
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124#4339—42no—
125#4339—42no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—41no—
133C2×Dic22—82no—
134C2×C8×C11—22no—
135C2×C8×C11—81no—
136C2×C8×C11—82no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C2×D411yescharacteristic
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C22⋊C4—21no—
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153#4326—42no—
154#4325—42no—
155#4324—42no—
156#4323—42no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—22no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—42no—
170#3227—111no—
171#3079—111no—
172#3035—111no—
173#2988D1111yescharacteristic, complemented
174#1678—112no—
175#1677—112no—
176#1672—112no—
177#1671—112no—
178#1570—111no—
179#1547—111no—
180C2×#333—111no—
181C23×C11—21no—
182C23×C11#12111yescharacteristic
183C22×D11—41no—
184Q8×C11—21no—
185Q8×C11C2×SD1612yes—
186D4×C11—24no—
187D4×C11—21no—
188D4×C11C2×SD1612yes—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—81no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C22⋊D11—82no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—82no—
211D44—41no—
212D44—41no—
213D44—41no—
214D44—41no—
215D44—81no—
216C4×D11—82no—
217Dic22—41no—
218Dic22—41no—
219Dic22—82no—
220Dic22—82no—
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—42no—
224C11⋊C8—41no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C2×#135—221no—
228#532—111no—
229C2×C4⋊Q8—111no—
230C4×#41C2×D1111yescharacteristic
231#498—112no—
232#486—112no—
233#481—222no—
234#477—112no—
235#476—112no—
236#476—221no—
237#476—221no—
238#475—221no—
239#474—221no—
240#464—221no—
241#463—221no—
242#462—111no—
243#461—111no—
244#460—111no—
245#459—111no—
246C8×Q8C2×D1112yes—
247C8×D4—22no—
248C8×D4C2×D1112yes—
249#431—21no—
250#431C2×D1111yescharacteristic
251#428—221no—
252#423—111no—
253C2×C4⋊C8—21no—
254C2×C4⋊C8—111no—
255C2×C4⋊C8C2×D1111yescharacteristic
256#417—221no—
257#416—221no—
258#334—112no—
259#334—112no—
260#333—112no—
261#333—112no—
262#332—112no—
263#331—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11#46512yes—
270C22×C11C2×#12111yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11#46512yes—
281C4×C11C22×SD1611yescharacteristic
282C4×C11C2×#13511yescharacteristic
283C4×C11#57711yescharacteristic
284C4×C11#57811yescharacteristic
285Dic11—81no—
286Dic11—82no—
287C2×#41—221no—
288C2×#41D4411yescharacteristic
289C22×Q8—221no—
290#135—444no—
291C2×Q16—221no—
292C2×SD16—221no—
293C2×SD16—221no—
294C2×D8—221no—
295C2×M16—221no—
296C22×C8—21no—
297C22×C8—22no—
298C22×C8—221no—
299C4⋊Q8—112no—
300C4⋊Q8—111no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304#127—111no—
305#124—221no—
306#121—221no—
307#121—221no—
308C4×Q8D4411yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4D4411yescharacteristic
315C4×D4C22×D1111yescharacteristic
316#117—21no—
317#117D4411yescharacteristic
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C42—21no—
321C2×C42C22×D1111yescharacteristic
322#107—222no—
323#106—222no—
324#106—222no—
325#106—222no—
326C4⋊C8—22no—
327C4⋊C8—21no—
328C4⋊C8—112no—
329C4⋊C8—111no—
330C4⋊C8—111no—
331C4⋊C8—221no—
332C4⋊C8—221no—
333C4⋊C8C22⋊D1111yescharacteristic
334C4⋊C8C22⋊D1111yescharacteristic
335C4⋊C8C22×D1112yes—
336#103—222no—
337#103—221no—
338#103—221no—
339#102—222no—
340#102—222no—
341#102—222no—
342#102—221no—
343#102—221no—
344C22⋊C8—22no—
345C22⋊C8C22⋊D1112yes—
346C4×C8—22no—
347C4×C8C22×D1112yes—
348C2×C11—22no—
349C2×C11—42no—
350C2×C11#304611yescharacteristic
351C2×C11C2×#46511yescharacteristic
352C2×C11#306811yescharacteristic
353D11—161no—
354#41—22no—
355#41—442no—
356#41—442no—
357#41#431414yes—
358C2×Q8—221no—
359C2×Q8—222no—
360C2×Q8—441no—
361C2×Q8—882no—
362C2×Q8C2×D4411yescharacteristic
363C2×D4—21no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—441no—
368C2×D4C2×D4411yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4C2×D4411yescharacteristic
375C22×C4#433911yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—442no—
378SD16—442no—
379SD16—442no—
380D8—442no—
381M16—442no—
382C2×C8—22no—
383C2×C8—82no—
384C2×C8—81no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—442no—
389C2×C8C2×C22⋊D1112yes—
390C2×C8C2×C22⋊D1112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—222no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4C2×D4411yescharacteristic
400C4⋊C4C2×D4411yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42C2×D4411yescharacteristic
410C42#433911yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1941411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—441no—
416C23#6698311yescharacteristic
417Q8—21no—
418Q8—441no—
419Q8—441no—
420Q8—882no—
421Q8—882no—
422Q8C2×#431412yes—
423D4—24no—
424D4—21no—
425D4—441no—
426D4—441no—
427D4—441no—
428D4—441no—
429D4—881no—
430D4—882no—
431D4C2×#431412yes—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—81no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—882no—
445C2×C4—882no—
446C2×C4C2×#431412yes—
447C2×C4#6695712yes—
448C2×C4#6698311yescharacteristic
449C2×C4#6698311yescharacteristic
450C2×C4#6698311yescharacteristic
451C2×C4C22×D4411yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—22no—
455C8—22no—
456C8—42no—
457C8—441no—
458C8—441no—
459C8—442no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22#1062272712yes—
469C22C2×#6698311yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—882no—
477C4—881no—
478C4#1062272712yes—
479C4C22×#431411yescharacteristic
480C4C2×#6695711yescharacteristic
481C4#1062336711yescharacteristic
482C4#1062336911yescharacteristic
483C2—22no—
484C2—42no—
485C2—1761no—
486C2#1307816611yescharacteristic
487C2C2×#1062272711yescharacteristic
488C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#2988D11
hypocenterC11#19414
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079746C2semidirect
2. #13078431C2semidirect
4. #13068032C2semidirect
5. #13068025C2semidirect
6. #13067998C2semidirect
7. #13067991C2semidirect
8. #13067387C2semidirect
9. #13067291C2semidirect
10. C2×#10622119C2semidirect
11. C11×#2988C2semidirect
173. #2988D11semidirect
413. C11#19414semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130784312
#130780712
#130680322
#130680252
#130679982
#130679912
#130673872
#130672912
C2×#106221192
C11×#29882
#1941411