Finite Group Databasebeta

← #14654531

Subgroups — #14654531

Order 2816.

632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078624C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3#13067179C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2535C211yesmaximal, characteristic
8C2×C11×#121—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#397—21no—
13C11×#392—21no—
14C11×#386—22no—
15C11×#382C2211yescharacteristic
16C11×#380—21no—
17#10622831—21no—
18#10622828—21no—
19#10622632—21no—
20C4×#4324—22no—
21#10622622—22no—
22#10622621—21no—
23#10622621—21no—
24#10622620—21no—
25#10622584—21no—
26#10622577—21no—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30D4⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622090—22no—
33C22×D4×C11—22no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C11×#121—42no—
39C11×#121—42no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—22no—
57#66979—21no—
58#66977—21no—
59#66977—21no—
60C2×#4318—21no—
61#66923—21no—
62#66922D411yescharacteristic, complemented
63#66922D411yescharacteristic, complemented
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×#95—22no—
67C11×#95—21no—
68C11×#95D412yes—
69#66896—22no—
70#66896—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66874—22no—
75#66872—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yescomplemented
82C4×C11⋊C8—21no—
83C4×C11⋊C8D412yescomplemented
84#10000—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—42no—
95C2×D4×C11—44no—
96C2×D4×C11—44no—
97C2×D4×C11—82no—
98C2×D4×C11SD1612yescomplemented
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—82no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C2×Dic22—21no—
115C2×Dic22—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—44no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—82no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C22⋊Dic11—41no—
133#4324—44no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11—41no—
141#4318—41no—
142#4318—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3101—111no—
147#3077—111no—
148#2535D1111yescharacteristic
149#1518—111no—
150#1486—111no—
151#1478—111no—
152#1286—111no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12011yescharacteristic
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—41no—
174D4×C11—88no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—82no—
186C2×C4×C11—82no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12711yescharacteristic
197C2×C4×C11C2×SD1611yescharacteristic
198C2×C4×C11#13511yescharacteristic
199C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C11#13711yescharacteristic
201C2×Dic11—41no—
202C2×Dic11—41no—
203Dic22—42no—
204Dic22—81no—
205C11⋊C8—42no—
206C11⋊C8—42no—
207C11⋊C8—81no—
208#533—111no—
209C2×#121—21no—
210C2×C4×D4C2×D1111yescharacteristic
211C2×C4×D4C2×D1111yescharacteristic
212#483—221no—
213#478—222no—
214#476—221no—
215#476—221no—
216#474—221no—
217#461—221no—
218#450—221no—
219C4×SD16—222no—
220#431—111no—
221#431—111no—
222#428—221no—
223#423—111no—
224#418—221no—
225#397—21no—
226#392—21no—
227#386—22no—
228#382C2×D1111yescharacteristic
229#380—21no—
230#328—222no—
231D4⋊C8—222no—
232D4⋊C8—222no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—81no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11#39211yescharacteristic
248C22×C11#45011yescharacteristic
249C22×C11#45211yescharacteristic
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#44811yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#46511yescharacteristic
260C4×C11#46811yescharacteristic
261Dic11—81no—
262Dic11—81no—
263C22×D4—22no—
264C22×D4C22⋊D1111yescharacteristic
265C22×D4C22⋊D1111yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C2×SD16—222no—
269C2×M16—221no—
270C4⋊Q8—111no—
271C4⋊Q8—111no—
272#125—221no—
273C22⋊Q8—221no—
274C22⋊Q8—221no—
275#121—42no—
276#121—42no—
277C4×Q8—221no—
278C4×Q8—221no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287#117—221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C22⋊C4—22no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42C22×D1111yescharacteristic
296#107—222no—
297#106—222no—
298#106—222no—
299C4⋊C8—112no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302C4⋊C8—221no—
303#103—222no—
304#102—222no—
305#102—222no—
306#102—222no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309C4×C8—112no—
310C4×C8—221no—
311#95—22no—
312#95—21no—
313#95C22⋊D1112yes—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—82no—
317C2×C11—82no—
318C2×C11#200011yescharacteristic
319C2×C11#200811yescharacteristic
320C2×C11#201011yescharacteristic
321C24—21no—
322C24—21no—
323C2×Q8—221no—
324C2×Q8—221no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4—82no—
336C2×D4#432412yescomplemented
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—82no—
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352SD16—444no—
353M16—441no—
354M16—441no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—441no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C22⋊C4—44no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—82no—
376C22⋊C4—441no—
377C42—441no—
378C42D4×D1111yescharacteristic
379C42D4×D1111yescharacteristic
380C42D4×D1111yescharacteristic
381C42#434111yescharacteristic
382C11#1000011yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—41no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23#6700611yescharacteristic
396Q8—442no—
397Q8—881no—
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4#6698511yescharacteristic
426C2×C4C2×#432411yescharacteristic
427C2×C4#6699011yescharacteristic
428C2×C4#6699011yescharacteristic
429C2×C4#6699111yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4#6699211yescharacteristic
432C2×C4#6699311yescharacteristic
433C2×C4#6700311yescharacteristic
434C2×C4#6700411yescharacteristic
435C8—442no—
436C8—442no—
437C8—881no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—44no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1062283111yescharacteristic
453C22#1062283611yescharacteristic
454C22#1062285211yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—881no—
463C4—881no—
464C4#1062265011yescharacteristic
465C4#1062265311yescharacteristic
466C4#1062265411yescharacteristic
467C4#1062265511yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—82no—
472C2#1306961911yescharacteristic
473C2#1306966911yescharacteristic
474C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2535C2
socleC22×C11#392
hypercenter#2535D11
hypocenterC11#10000
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #13078624C2semidirect
2. #13078413C2semidirect
3. #13067179C2semidirect
4. #13067041C2semidirect
5. #13067007C2semidirect
6. #13066474C2semidirect
62. #66922D4semidirect
63. #66922D4semidirect
81. C4⋊(C11⋊C8)D4semidirect
83. C4×C11⋊C8D4semidirect
98. C2×D4×C11SD16semidirect
336. C2×D4#4324semidirect
382. C11#10000semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130784132
#130671792
#130670412
#130670072
#130664742
C11×#25352
#1000011