Finite Group Databasebeta

← #14737293

Subgroups — #14737293

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079746C211yesmaximal, characteristic
3#13079163C211yesmaximal, characteristic, complemented
4#13077359C211yesmaximal, characteristic
5#13068138C212yesmaximal, complemented
6#13068114C212yesmaximal, complemented
7#13068014C212yesmaximal, complemented
8#13067990C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622119C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66954—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622723—21no—
19#10622697C2212yes—
20#10622696C2212yes—
21#10622692C2212yes—
22#10622691C2212yes—
23#10622678—22no—
24#10622661—22no—
25#10622640—21no—
26#10622633—21no—
27#10622608—21no—
28#10622608—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622455C2212yes—
32#10622455C2212yes—
33#10622451C2212yes—
34#10622449—22no—
35#10622447C2212yes—
36#10622348—22no—
37#10622307—21no—
38#10622293—21no—
39C11×#333C2211yescharacteristic
40C11×#333C2211yescharacteristic
41C11×#332C2211yescharacteristic
42C11×#332C2211yescharacteristic
43#10622119C2212yes—
44#10622119C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47C2×#4339—21no—
48C22×Dic22—21no—
49C22×C8×C11—21no—
50C11×C4⋊Q8C2311yescharacteristic
51C11×C4⋊Q8C2311yescharacteristic
52C11×#125—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C11×#117—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4325—22no—
60#66983—21no—
61#66983D412yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×#4318D411yescharacteristic
65C2×#4318D411yescharacteristic
66C22×C11⋊C8—21no—
67#66954—44no—
68C2×#4313—22no—
69C2×C8×D11—22no—
70#66928—21no—
71#66927D411yescharacteristic
72C4×D44—21no—
73C4×D44C2312yes—
74#66922—21no—
75#66922—21no—
76#66922—21no—
77#66922D411yescharacteristic
78#66922C2312yes—
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×C4⋊C8C2311yescharacteristic
84C11×C22⋊C8—21no—
85C4×C8×C11—21no—
86#66899—22no—
87#66885—22no—
88#66885—22no—
89(C2×D11)⋊C8—22no—
90(C2×D11)⋊C8—22no—
91#66881—22no—
92#66881—22no—
93#66873—22no—
94#66872—22no—
95#66872—22no—
96#66872—22no—
97#66871—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103#19233—111nomaximal, Sylow
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—22no—
110C22×Dic11—41no—
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C2×D412yes—
116C2×C4×D11—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—82no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—42no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4325—82no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146C4⋊Dic11C2×D412yes—
147#4318—22no—
148#4318SD1614yescomplemented
149C2×C11⋊C8—22no—
150C2×C11⋊C8—81no—
151C2×C11⋊C8C2×D412yes—
152C2×C11⋊C8C2×D412yes—
153#4313—44no—
154C8×D11—44no—
155#3246—111no—
156#3227—111no—
157#3165—111no—
158#2935—111no—
159#1695—112no—
160#1691—112no—
161#1675—112no—
162#1671—112no—
163#1565—111no—
164#1542D1111yescharacteristic, complemented
165C2×#333—111no—
166C23×C11#12111yescharacteristic
167C22×D11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—81no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11C2×SD1612yes—
180C2×C4×C11#13712yes—
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C22⋊D11—44no—
185C2×Dic11—22no—
186C2×Dic11—42no—
187C2×Dic11—82no—
188D44—22no—
189D44—22no—
190D44—42no—
191D44—81no—
192C4×D11—42no—
193C4×D11—42no—
194Dic22—42no—
195Dic22—82no—
196Dic22—82no—
197C8×C11—41no—
198C8×C11—41no—
199C8×C11—41no—
200C8×C11—41no—
201C11⋊C8—22no—
202C11⋊C8—42no—
203C11⋊C8C2×SD1614yes—
204C2×#131—221no—
205#533C2×D1111yescharacteristic
206#532—111no—
207C2×C4⋊Q8—111no—
208#501—222no—
209#500—112no—
210#498—112no—
211#498—221no—
212#486—221no—
213#481—222no—
214#476—112no—
215#476—112no—
216#476—112no—
217#475—221no—
218#465—222no—
219#461—112no—
220#460—221no—
221#436—112no—
222#435—222no—
223C8×D4—112no—
224#431C2×D1111yescharacteristic
225#428—221no—
226#428—221no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8C2×D1111yescharacteristic
229#408—221no—
230C4×M16—111no—
231#335—112no—
232#334—112no—
233#333—112no—
234#333—112no—
235#333C2×D1111yescharacteristic
236#333C2×D1111yescharacteristic
237#332C2×D1111yescharacteristic
238#332C2×D1111yescharacteristic
239C22×C11—21no—
240C22×C11—21no—
241C22×C11#46112yes—
242C22×C11C2×#12111yescharacteristic
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11#46112yes—
252C4×C11C22×SD1611yescharacteristic
253C4×C11C2×#13711yescharacteristic
254C4×C11#57711yescharacteristic
255C4×C11#57811yescharacteristic
256Dic11—42no—
257Dic11—82no—
258C2×#41—221no—
259C22×Q8—221no—
260C2×SD16—222no—
261#131—444no—
262C2×M16—111no—
263C2×M16—111no—
264C2×M16—222no—
265C22×C8—21no—
266C22×C8—222no—
267C22×C8—221no—
268C4⋊Q8—111no—
269C4⋊Q8—112no—
270C4⋊Q8—221no—
271C4⋊Q8—221no—
272C4⋊Q8—221no—
273C4⋊Q8C22×D1111yescharacteristic
274C4⋊Q8C22×D1111yescharacteristic
275#127—111no—
276#125—21no—
277#124—221no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280#121—112no—
281#121—221no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—112no—
285C4×D4—221no—
286#117—21no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C42C22×D1111yescharacteristic
290#107—222no—
291#107—222no—
292#106—222no—
293#106—222no—
294#106—222no—
295#106—222no—
296#106—222no—
297C4⋊C8—21no—
298C4⋊C8—112no—
299C4⋊C8—221no—
300C4⋊C8C22×D1111yescharacteristic
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303C4⋊C8C22×D1111yescharacteristic
304#103—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—21no—
309C22⋊C8—222no—
310C22⋊C8—222no—
311#97—112no—
312C4×C8—21no—
313C4×C8—112no—
314C2×C11—22no—
315C2×C11C2×#46111yescharacteristic
316C2×C11#306311yescharacteristic
317C2×C11#306811yescharacteristic
318D11—82no—
319#41—442no—
320#41—442no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—441no—
326C2×Q8—882no—
327C2×D4—112no—
328C2×D4—222no—
329C2×D4—221no—
330C2×D4—221no—
331C22×C4—222no—
332C22×C4—441no—
333C22×C4#433911yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336SD16—882no—
337M16—114no—
338M16—222no—
339M16—444no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—42no—
345C2×C8—112no—
346C2×C8—112no—
347C2×C8—222no—
348C2×C8—444no—
349C2×C8—881no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—112no—
357C4⋊C4—221no—
358C4⋊C4—222no—
359C4⋊C4—222no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C22⋊C4—41no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C42—41no—
366C42#433911yescharacteristic
367C42D4×D1111yescharacteristic
368C42D4×D1111yescharacteristic
369C42C23×D1111yescharacteristic
370C11#1923311yescharacteristic, complemented, Sylow
371C23—222no—
372C23#6693711yescharacteristic
373Q8—41no—
374Q8—41no—
375Q8—81no—
376Q8—442no—
377Q8—882no—
378Q8—882no—
379D4—222no—
380D4—222no—
381D4—444no—
382D4—442no—
383D4—881no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—222no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—882no—
394C2×C4#6693711yescharacteristic
395C2×C4#6693711yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4SD16×D1112yes—
398C2×C4#6697112yes—
399C2×C4C2×#433911yescharacteristic
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×D4×D1111yescharacteristic
402C8—41no—
403C8—41no—
404C8—41no—
405C8—41no—
406C8—114no—
407C8—222no—
408C8—442no—
409C22—21no—
410C22—21no—
411C22—442no—
412C22—442no—
413C22—442no—
414C22#1062243112yes—
415C22C2×#6693711yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—81no—
421C4—442no—
422C4—882no—
423C4#1062243112yes—
424C4C2×SD16×D1111yescharacteristic
425C4C2×#6697111yescharacteristic
426C4#1062330111yescharacteristic
427C4#1062330211yescharacteristic
428C2—22no—
429C2—882no—
430C2C2×#1062243111yescharacteristic
431C2#1307831011yescharacteristic
432C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1542D11
hypocenterC11#19233
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #13079163C2semidirect
5. #13068138C2semidirect
6. #13068114C2semidirect
7. #13068014C2semidirect
8. #13067990C2semidirect
9. #13067369C2semidirect
10. C2×#10622119C2semidirect
11. C11×#1542C2semidirect
148. #4318SD16semidirect
164. #1542D11semidirect
370. C11#19233semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797462
#130791632
#130773592
#130681382
#130681142
#130680142
#130679902
#130673692
C2×#106221192
C11×#15422
#1923311