Finite Group Databasebeta

← #14654528

Subgroups — #14654528

Order 2816.

632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078409C211yesmaximal, characteristic, complemented
2#13073517C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#3101C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66983—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#483—21no—
13C11×#476—21no—
14C11×#461—21no—
15C11×#450—21no—
16C4×C11×SD16—22no—
17C11×#431C2211yescharacteristic
18#10622836—21no—
19#10622825—21no—
20#10622700—21no—
21#10622697—21no—
22#10622679—22no—
23#10622614—21no—
24#10622608—21no—
25#10622606—21no—
26#10622569—22no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622176—22no—
31D4⋊(C11⋊C8)—22no—
32#10622097—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C22×C22⋊D11—22no—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C2×C11×SD16—22no—
39C11×C4⋊Q8D411yescharacteristic, complemented
40C11×C4⋊Q8D411yescharacteristic, complemented
41C11×#125—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C11×#117—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55#66983—42no—
56#66983—42no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×#4318—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C11×#106—22no—
67C11×C4⋊C8—21no—
68C11×#103—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C4×C8×C11D412yescomplemented
72C11⋊#95—22no—
73C11⋊#95—21no—
74C11⋊#95D412yes—
75C22⋊(C11⋊C8)—21no—
76#66873—22no—
77#66873—22no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yescomplemented
83C4×C11⋊C8—21no—
84#10000—111nomaximal, Sylow
85C24×C11—21no—
86C23×D11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—42no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—44no—
103C2×C22⋊D11—44no—
104C2×C22⋊D11—82no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44SD1612yescomplemented
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—82no—
116C11×SD16—44no—
117C2×C8×C11—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C22⋊Dic11—82no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142#4318—41no—
143#4318—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3101D1111yescharacteristic, complemented
147#3077—111no—
148#2535—111no—
149#1518—111no—
150#1486—111no—
151#1478—111no—
152#1286—111no—
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11#12011yescharacteristic
161C22×D11—22no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166Q8×C11—42no—
167Q8×C11—81no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11C2×SD1611yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11#13711yescharacteristic
193C22⋊D11—88no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199D44—22no—
200D44—22no—
201D44—41no—
202D44—41no—
203C4×D11—82no—
204C4×D11—82no—
205C8×C11—42no—
206C11⋊C8—42no—
207C11⋊C8—81no—
208#533C2×D1111yescharacteristic
209C2×#121—221no—
210C2×C4×D4—111no—
211C2×C4×D4C2×D1111yescharacteristic
212#483—21no—
213#478—222no—
214#476—21no—
215#476—221no—
216#474—221no—
217#461—21no—
218#450—21no—
219C4×SD16—22no—
220#431—111no—
221#431C2×D1111yescharacteristic
222#428—221no—
223#423—111no—
224#418—221no—
225#397—221no—
226#392—221no—
227#386—222no—
228#382—111no—
229#380—221no—
230#328—222no—
231D4⋊C8—222no—
232D4⋊C8—222no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11#39211yescharacteristic
243C22×C11#45011yescharacteristic
244C22×C11#45211yescharacteristic
245C2×D11—44no—
246C2×D11—42no—
247C2×D11—82no—
248C2×D11—81no—
249C2×D11—81no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#44811yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#46511yescharacteristic
260C4×C11#46811yescharacteristic
261Dic11—82no—
262Dic11—81no—
263C22×D4—111no—
264C22×D4—222no—
265C22×D4C22⋊D1111yescharacteristic
266C23×C4—21no—
267C23×C4—221no—
268C2×SD16—22no—
269C2×M16—221no—
270C4⋊Q8C22⋊D1111yescharacteristic, complemented
271C4⋊Q8C22⋊D1111yescharacteristic, complemented
272#125—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—442no—
276#121—442no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—221no—
284C4×D4—221no—
285C4×D4—221no—
286C4×D4—221no—
287#117—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42C22×D1111yescharacteristic
296#107—222no—
297#106—22no—
298#106—222no—
299C4⋊C8—21no—
300C4⋊C8—112no—
301C4⋊C8—221no—
302C4⋊C8—221no—
303#103—22no—
304#102—22no—
305#102—222no—
306#102—222no—
307C22⋊C8—21no—
308C22⋊C8—221no—
309C4×C8—221no—
310C4×C8C22⋊D1112yescomplemented
311#95—112no—
312#95—222no—
313#95—221no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—82no—
317C2×C11#200011yescharacteristic
318C2×C11#200811yescharacteristic
319C2×C11#201011yescharacteristic
320D11—82no—
321C24—21no—
322C24—221no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—42no—
328C2×D4—112no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—444no—
335C2×D4—444no—
336C2×D4—882no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352SD16—44no—
353M16—441no—
354M16—441no—
355C2×C8—22no—
356C2×C8—222no—
357C2×C8—441no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—444no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—882no—
377C42—41no—
378C42D4×D1111yescharacteristic
379C42#434111yescharacteristic
380C42C2×C22⋊D1111yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C11#1000011yescharacteristic, complemented, Sylow
383C23—22no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—222no—
391C23—442no—
392C23—442no—
393C23—441no—
394C23—441no—
395C23#6699011yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—22no—
399D4—22no—
400D4—41no—
401D4—41no—
402D4—222no—
403D4—222no—
404D4—441no—
405D4—441no—
406D4—888no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—882no—
424C2×C4—882no—
425C2×C4SD16×D1111yescharacteristic
426C2×C4#6696711yescharacteristic
427C2×C4#6696811yescharacteristic
428C2×C4#6696911yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6699111yescharacteristic
431C2×C4#6699211yescharacteristic
432C2×C4#6699211yescharacteristic
433C2×C4#6699311yescharacteristic
434C2×C4#6700611yescharacteristic
435C8—42no—
436C8—442no—
437C8—881no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—444no—
448C22—442no—
449C22—882no—
450C22—881no—
451C22—881no—
452C22#1062278211yescharacteristic
453C22#1062278611yescharacteristic
454C22#1062283611yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—882no—
463C4—881no—
464C4#1062278311yescharacteristic
465C4#1062278411yescharacteristic
466C4#1062278511yescharacteristic
467C4#1062278711yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—882no—
472C2#1306961611yescharacteristic
473C2#1306966611yescharacteristic
474C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3101C2
socleC22×C11#392
prime radical#13073517C2
hypercenter#3101D11
hypocenterC11#10000
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13067180C2semidirect
4. #13067041C2semidirect
5. #13067008C2semidirect
6. #13066475C2semidirect
7. C11×#3101C2semidirect
39. C11×C4⋊Q8D4semidirect
40. C11×C4⋊Q8D4semidirect
71. C4×C8×C11D4semidirect
82. C4⋊(C11⋊C8)D4semidirect
112. C2×D44SD16semidirect
146. #3101D11semidirect
270. C4⋊Q8C22⋊D11semidirect
271. C4⋊Q8C22⋊D11semidirect
310. C4×C8C22⋊D11semidirect
382. C11#10000semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130735172
#130671802
#130670412
#130670082
#130664752
C11×#31012
#1000011