Finite Group Databasebeta

← #14645713

Subgroups — #14645713

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic
2#13069564C211yesmaximal, characteristic, complemented
3#13067307C211yesmaximal, characteristic, complemented
4#13067302C211yesmaximal, characteristic, complemented
5#13067114C211yesmaximal, characteristic, complemented
6#13067003C211yesmaximal, characteristic
7C11×#1806C211yesmaximal, characteristic
8C4×C11×#41C2211yescharacteristic
9#10623358—21no—
10#10623101C412yescomplemented
11Q8×Dic22—21no—
12#10623074—21no—
13#10623074—22no—
14D4×Dic22—22no—
15D4×Dic22C412yescomplemented
16#10623050—21no—
17#10623050—22no—
18#10623001—21no—
19#10623001C2211yescharacteristic
20C2×#66922—21no—
21C2×#66922C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#104—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C11×#339—21no—
28Q8⋊(C11⋊C8)—21no—
29D4⋊(C11⋊C8)—21no—
30#10622167—22no—
31#10622124—22no—
32#10622124—21no—
33#10622119—21no—
34#10622090—22no—
35C2×C11×#41D411yescharacteristic
36C22×Dic22—21no—
37C22×Dic22—22no—
38C2×C11×M16—21no—
39C4×Q8×C11C2×C411yescharacteristic
40C4×Q8×C11D411yescharacteristic
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11C2×C411yescharacteristic
44C4×D4×C11D411yescharacteristic
45C11×#117—21no—
46C11×#117D411yescharacteristic
47C2×C11×C4⋊C4—21no—
48C2×C42×C11—21no—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51Q8×Dic11—22no—
52D4×Dic11—24no—
53D4×Dic11—22no—
54#66979—22no—
55#66979—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D412yes—
60#66977—22no—
61#66977—21no—
62#66977—22no—
63#66977D412yes—
64C22×C11⋊C8—21no—
65#66943—22no—
66#66943—24no—
67#66941—24no—
68#66941—22no—
69#66931—24no—
70#66931—24no—
71#66931—24no—
72#66923—22no—
73#66923—21no—
74#66922—22no—
75#66922—22no—
76#66922—22no—
77#66922—21no—
78#66922—21no—
79#66922C2×C412yes—
80#66922D411yescharacteristic
81#66922D412yes—
82#66922D411yescharacteristic
83C4×Dic22—22no—
84C4×Dic22—21no—
85C4×Dic22—22no—
86C4×Dic22C2×C412yes—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×#104—42no—
90C11×#95—21no—
91C22⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4×C11⋊C8—21no—
96#8424—111nomaximal, Sylow
97C11×#41—21no—
98C11×#41—21no—
99C11×#41SD1612yes—
100C11×#41Q1612yes—
101C2×Q8×C11C22⋊C411yescharacteristic
102C2×D4×C11—21no—
103C2×D4×C11C22⋊C411yescharacteristic
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—22no—
113C2×Dic22—24no—
114C2×Dic22—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—82no—
118C2×Dic22—84no—
119C2×Dic22C22⋊C412yes—
120C11×M16—41no—
121C11×M16—41no—
122C2×C8×C11—41no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4C22⋊C411yescharacteristic
128C11×C4⋊C4C22⋊C411yescharacteristic
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—41no—
136C42×C11—41no—
137C42×C11C22×C411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C22⋊Dic11—24no—
142C22⋊Dic11—22no—
143C4⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11C22⋊C412yes—
152C4⋊Dic11C22⋊C414yes—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—22no—
156Dic11⋊C4—22no—
157C4×Dic11—24no—
158C4×Dic11—22no—
159C2×C11⋊C8—42no—
160C2×C11⋊C8—41no—
161C2×C11⋊C8—41no—
162#3503—111no—
163#1987—111no—
164#1806D1111yescharacteristic
165#1550—111no—
166#1549—111no—
167#1503—111no—
168#1477—111no—
169C23×C11—21no—
170C23×C11#12011yescharacteristic
171Q8×C11—21no—
172Q8×C11#10312yes—
173D4×C11—22no—
174D4×C11—22no—
175D4×C11—21no—
176D4×C11#10312yes—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11C2×C22⋊C411yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11C2×SD1611yescharacteristic
198C2×C4×C11C2×Q1611yescharacteristic
199C2×C4×C11#13711yescharacteristic
200C2×C4×C11#13711yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—82no—
205C2×Dic11—84no—
206Dic22—44no—
207Dic22—41no—
208Dic22—41no—
209Dic22—42no—
210Dic22—82no—
211Dic22—84no—
212C8×C11—81no—
213C11⋊C8—81no—
214C11⋊C8—81no—
215Q82—221no—
216#557—112no—
217#554—222no—
218#554—221no—
219D4×Q8—112no—
220D4×Q8—222no—
221#544—222no—
222#544—221no—
223#533—111no—
224#533—221no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8—221no—
227#520—221no—
228C4×#41C2×D1111yescharacteristic
229#431—111no—
230#423C2×D1111yescharacteristic
231C2×C4⋊C8—111no—
232C2×#104—21no—
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—222no—
235#339—21no—
236#333—221no—
237#332—222no—
238#332—221no—
239#328—222no—
240Q8⋊C8—221no—
241D4⋊C8—221no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—22no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11#37911yescharacteristic
248C22×C11#44811yescharacteristic
249C22×C11#45111yescharacteristic
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—22no—
254C4×C11—41no—
255C4×C11—41no—
256C4×C11—82no—
257C4×C11C2×#10311yescharacteristic
258C4×C11#41911yescharacteristic
259C4×C11#44811yescharacteristic
260C4×C11#45111yescharacteristic
261C4×C11#45411yescharacteristic
262C4×C11#45611yescharacteristic
263Dic11—42no—
264Dic11—44no—
265Dic11—42no—
266C2×#41C22⋊D1111yescharacteristic
267C22×Q8—222no—
268C22×Q8—221no—
269C2×M16—21no—
270C22×C8—221no—
271C4⋊Q8—112no—
272C4⋊Q8—112no—
273C4⋊Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8—222no—
276C4⋊Q8—222no—
277C4⋊Q8—222no—
278C4⋊Q8—224no—
279C4⋊Q8—222no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282#125—222no—
283#125—224no—
284#125—222no—
285#125—221no—
286C22⋊Q8—112no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289C22⋊Q8—224no—
290C22⋊Q8—222no—
291C22⋊Q8—222no—
292C22⋊Q8—221no—
293C4×Q8—112no—
294C4×Q8—222no—
295C4×Q8—222no—
296C4×Q8—222no—
297C4×Q8—221no—
298C4×Q8C4×D1111yescharacteristic
299C4×Q8D4411yescharacteristic
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—224no—
303C4×D4—222no—
304C4×D4C4×D1111yescharacteristic
305C4×D4D4411yescharacteristic
306#117—21no—
307#117—222no—
308#117—221no—
309#117C22⋊D1111yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42C22×D1111yescharacteristic
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8—221no—
321C4⋊C8—221no—
322C4⋊C8—221no—
323#104—42no—
324C22⋊C8—221no—
325C4×C8—221no—
326#95—21no—
327C2×C11—21no—
328C2×C11—21no—
329C2×C11—42no—
330C2×C11#178711yescharacteristic
331C2×C11#179311yescharacteristic
332C2×C11#179511yescharacteristic
333#41—21no—
334#41—21no—
335#41#432412yes—
336#41#432612yes—
337C2×Q8—112no—
338C2×Q8—224no—
339C2×Q8—222no—
340C2×Q8—221no—
341C2×Q8—222no—
342C2×Q8—882no—
343C2×Q8—884no—
344C2×Q8(C2×D11)⋊C411yescharacteristic
345C2×D4—21no—
346C2×D4(C2×D11)⋊C411yescharacteristic
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—224no—
352C22×C4—222no—
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356M16—41no—
357M16—41no—
358C2×C8—41no—
359C2×C8—442no—
360C2×C8—441no—
361C2×C8—441no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—114no—
367C4⋊C4—112no—
368C4⋊C4—224no—
369C4⋊C4—224no—
370C4⋊C4—224no—
371C4⋊C4—224no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4(C2×D11)⋊C411yescharacteristic
381C4⋊C4(C2×D11)⋊C411yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—224no—
386C22⋊C4—222no—
387C42—21no—
388C42—21no—
389C42—21no—
390C42—41no—
391C42—41no—
392C42—224no—
393C42—222no—
394C42C2×C4×D1111yescharacteristic
395C42C2×D4411yescharacteristic
396C42D4×D1111yescharacteristic
397C42D4×D1111yescharacteristic
398C11#842411yescharacteristic, complemented, Sylow
399C23—21no—
400C23#6699011yescharacteristic
401Q8—21no—
402Q8—442no—
403Q8—444no—
404Q8—441no—
405Q8—441no—
406Q8—882no—
407Q8—884no—
408Q8#6687412yes—
409D4—22no—
410D4—22no—
411D4—21no—
412D4#6687412yes—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—222no—
428C2×C4—224no—
429C2×C4—222no—
430C2×C4—882no—
431C2×C4—884no—
432C2×C4C22⋊C4×D1111yescharacteristic
433C2×C4C22⋊C4×D1111yescharacteristic
434C2×C4#6693511yescharacteristic
435C2×C4#6693511yescharacteristic
436C2×C4C2×(C2×D11)⋊C411yescharacteristic
437C2×C4C2×#432411yescharacteristic
438C2×C4#6699011yescharacteristic
439C2×C4C2×#432611yescharacteristic
440C2×C4#6700411yescharacteristic
441C2×C4#6700411yescharacteristic
442C8—81no—
443C8—881no—
444C8—881no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22#1062256811yescharacteristic
451C22#1062265311yescharacteristic
452C22#1062266311yescharacteristic
453C4—22no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—41no—
458C4—41no—
459C4—82no—
460C4—442no—
461C4—444no—
462C4—442no—
463C4#1062243911yescharacteristic
464C4#1062244011yescharacteristic
465C4C2×#6687411yescharacteristic
466C4#1062261711yescharacteristic
467C4#1062265311yescharacteristic
468C4#1062266311yescharacteristic
469C2—21no—
470C2—21no—
471C2—42no—
472C2#1306855011yescharacteristic
473C2#1306857611yescharacteristic
474C2#1306858511yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1806C2
socleC22×C11#379
prime radicalC2×C11×#41D4
cosocleC2×C42×C11C23
hypercenter#1806D11
hypocenterC11#8424
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #13069564C2semidirect
3. #13067307C2semidirect
4. #13067302C2semidirect
5. #13067114C2semidirect
10. #10623101C4semidirect
15. D4×Dic22C4semidirect
398. C11#8424semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130695642
#130673072
#130673022
#130671142
#130670032
C11×#18062
#842411