Finite Group Databasebeta

← #14654515

Subgroups — #14654515

Order 2816.

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

normal subgroups only

This group has 602 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#13078643C211yesmaximal, characteristic, complemented
2#13073970C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic, complemented
4#13067044C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#463—22no—
13C11×#461—21no—
14C11×#459—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17#10622834—21no—
18#10622823—22no—
19#10622707—21no—
20#10622688—21no—
21#10622653—21no—
22#10622647—21no—
23C4×#4324—22no—
24#10622586—21no—
25#10622562—21no—
26#10622560—21no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622175—22no—
31D4⋊(C11⋊C8)—22no—
32#10622122—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C22×Dic22D411yescharacteristic
37C11×AGL(1,ℤ/8)—42no—
38C11×AGL(1,ℤ/8)—42no—
39C2×C11×SD16—22no—
40C2×C11×D8—22no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×#4324—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×#103—22no—
71C11×#102—22no—
72#66896—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95D412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78#66874—22no—
79#66872—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8D412yes—
84#9998—111nomaximal, Sylow
85C24×C11—21no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C2×D4×C11SD1612yescomplemented
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—42no—
115C11×SD16—44no—
116C11×D8—44no—
117C11×M16—41no—
118C11×M16—41no—
119C2×C8×C11—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C22⋊Dic11—44no—
133C22⋊Dic11—82no—
134#4324—44no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—82no—
142C4×Dic11—41no—
143C4×Dic11—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3103—111no—
147#3036D1111yescharacteristic
148#2580—111no—
149#1517—111no—
150#1487—111no—
151#1478—111no—
152#1286—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11#12011yescharacteristic
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—42no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—81no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12711yescharacteristic
187C2×C4×C11C2×SD1611yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11#13711yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200Dic22—22no—
201Dic22—22no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—42no—
205C11⋊C8—42no—
206C11⋊C8—81no—
207C2×AGL(1,ℤ/8)—21no—
208#532C2×D1111yescharacteristic
209C2×C4×Q8—111no—
210C2×C4×D4C2×D1111yescharacteristic
211#481—221no—
212#475—221no—
213#463—22no—
214#461—21no—
215#460—221no—
216#459—21no—
217#448—221no—
218C4×SD16—222no—
219#431—111no—
220#431—111no—
221#423C2×D1111yescharacteristic
222#417—21no—
223#399—221no—
224#393—221no—
225#390—221no—
226#389—221no—
227#385—222no—
228#382—111no—
229#327—222no—
230Q8⋊C8—222no—
231D4⋊C8—222no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—44no—
235C22×C11—42no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11#39211yescharacteristic
243C22×C11#44811yescharacteristic
244C22×C11#44911yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11#45011yescharacteristic
252C4×C11#45211yescharacteristic
253C4×C11#46511yescharacteristic
254C4×C11#46811yescharacteristic
255Dic11—42no—
256Dic11—82no—
257Dic11—81no—
258C2×#41—21no—
259C22×Q8—111no—
260C22×D4C22⋊D1111yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—42no—
263AGL(1,ℤ/8)—42no—
264C2×SD16—22no—
265C2×SD16—222no—
266C2×D8—22no—
267C2×M16—21no—
268C4⋊Q8C22⋊D1111yescharacteristic
269#127C22⋊D1111yescharacteristic
270#124—21no—
271#121—21no—
272#121—21no—
273C4×Q8—221no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×Q8—221no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4C22⋊D1111yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4—222no—
291C2×C42—221no—
292C2×C42C22×D1111yescharacteristic
293#106—222no—
294C4⋊C8—21no—
295C4⋊C8—221no—
296C4⋊C8—221no—
297C4⋊C8C22⋊D1112yes—
298#103—22no—
299#103—222no—
300#102—22no—
301#102—222no—
302C22⋊C8—221no—
303C22⋊C8—221no—
304C4×C8—112no—
305C4×C8—221no—
306#95—112no—
307#95—222no—
308#95—221no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—82no—
312C2×C11—161no—
313C2×C11#200011yescharacteristic
314C2×C11#200811yescharacteristic
315C2×C11#201011yescharacteristic
316C24—21no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321C2×Q8—21no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×Q8—442no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C2×D4#432412yescomplemented
335C22×C4—21no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—82no—
340C22×C4—221no—
341C22×C4—222no—
342C22×C4—221no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346SD16—44no—
347SD16—444no—
348D8—44no—
349M16—41no—
350M16—41no—
351C2×C8—22no—
352C2×C8—222no—
353C2×C8—441no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—882no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—444no—
370C22⋊C4—882no—
371C42—441no—
372C42—441no—
373C42D4×D1111yescharacteristic
374C42#434111yescharacteristic
375C42C2×C22⋊D1111yescharacteristic
376C42C2×C22⋊D1111yescharacteristic
377C11#999811yescharacteristic, complemented, Sylow
378C23—22no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23#6699011yescharacteristic
385Q8—41no—
386Q8—41no—
387Q8—222no—
388Q8—222no—
389Q8—441no—
390Q8—441no—
391D4—22no—
392D4—22no—
393D4—42no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—81no—
399D4—81no—
400D4—81no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—222no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4#6698511yescharacteristic
420C2×C4C2×#432411yescharacteristic
421C2×C4#6699011yescharacteristic
422C2×C4#6699111yescharacteristic
423C2×C4#6699211yescharacteristic
424C2×C4#6699211yescharacteristic
425C2×C4#6699311yescharacteristic
426C2×C4#6700311yescharacteristic
427C2×C4#6700411yescharacteristic
428C2×C4#6700611yescharacteristic
429C8—42no—
430C8—442no—
431C8—881no—
432C22—21no—
433C22—21no—
434C22—44no—
435C22—42no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22#1062265011yescharacteristic
443C22#1062265311yescharacteristic
444C22#1062283611yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—81no—
451C4—442no—
452C4—882no—
453C4—881no—
454C4#1062265411yescharacteristic
455C4#1062265511yescharacteristic
456C4#1062283111yescharacteristic
457C4#1062285211yescharacteristic
458C2—21no—
459C2—21no—
460C2—82no—
461C2—161no—
462C2#1306961911yescharacteristic
463C2#1306966711yescharacteristic
464C2#1306968011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#9998
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13078643C2semidirect
2. #13073970C2semidirect
3. #13067176C2semidirect
4. #13067044C2semidirect
5. #13067007C2semidirect
6. #13066476C2semidirect
100. C2×D4×C11SD16semidirect
334. C2×D4#4324semidirect
377. C11#9998semidirect

Maximal subgroups

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

subgroupindex
#130786432
#130739702
#130671762
#130670442
#130670072
#130664762
C11×#30362
#999811