Finite Group Databasebeta

← #14656186

Subgroups — #14656186

Order 2816.

740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079554C211yesmaximal, characteristic, complemented
2#13073562C211yesmaximal, characteristic
3#13067285C211yesmaximal, characteristic, complemented
4#13067115C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66993—21no—
11C2×#66983—22no—
12C2×#66927C2211yescharacteristic
13C11×#478—22no—
14C11×#476—21no—
15C11×#474—21no—
16C11×#428—21no—
17C11×#423C2211yescharacteristic
18C11×#418—21no—
19#10622701—21no—
20#10622698—21no—
21#10622659—22no—
22#10622640—22no—
23#10622601—21no—
24#10622573—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622176—22no—
29D4⋊(C11⋊C8)—22no—
30#10622123—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×C22⋊D11—24no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44D412yes—
37C2×C11×M16—21no—
38C11×C4⋊Q8D411yescharacteristic, complemented
39C11×C4⋊Q8D411yescharacteristic, complemented
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C11×#117—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—24no—
54#66993—42no—
55#66993—42no—
56#66983—48no—
57C2×(C2×D11)⋊C4—24no—
58C2×C4⋊Dic11—21no—
59C2×C4×Dic11—21no—
60#66927—21no—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64C11×#107—22no—
65C11×#106—22no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yescomplemented
68C11×#102—22no—
69C11×#102—22no—
70C11⋊#95D412yes—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66873—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yescomplemented
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10246—111nomaximal, Sylow
79C24×C11—21no—
80C23×D11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11SD1612yescomplemented
89C22×C4×C11—21no—
90C22×C4×C11—44no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—48no—
97C2×C22⋊D11—48no—
98C2×C22⋊D11—84no—
99C22×Dic11—22no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—44no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—82no—
112C11×M16—41no—
113C11×M16—41no—
114C2×C8×C11—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#4325—84no—
132(C2×D11)⋊C4—48no—
133C4⋊Dic11—24no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3208—111no—
139#3077D1111yescharacteristic, complemented
140#2541—111no—
141#1545—111no—
142#1503—111no—
143#1478—111no—
144#1303—111no—
145C23×C11—22no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151C22×D11—44no—
152C22×D11—44no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156Q8×C11—42no—
157Q8×C11—81no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—41no—
161D4×C11—41no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11#13711yescharacteristic
180C22⋊D11—816no—
181C2×Dic11—24no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184D44—44no—
185D44—82no—
186D44—82no—
187D44—82no—
188D44—81no—
189D44—81no—
190D44—81no—
191D44—81no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—81no—
195#533C2×D1111yescharacteristic
196C2×#127—111no—
197C2×#127—221no—
198C2×#121—222no—
199C2×C4×D4C2×D1111yescharacteristic
200#492—221no—
201#486—221no—
202#478—22no—
203#476—21no—
204#474—21no—
205#460—222no—
206#450—222no—
207#431—111no—
208#431—111no—
209#428—21no—
210#423C2×D1111yescharacteristic
211#418—21no—
212#392—222no—
213#390—221no—
214C4×C4⋊C4—111no—
215#331—222no—
216#328—222no—
217D4⋊C8—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39211yescharacteristic
226C22×C11#45011yescharacteristic
227C22×C11#45211yescharacteristic
228C2×D11—84no—
229C2×D11—84no—
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11#44811yescharacteristic
240C4×C11#44911yescharacteristic
241C4×C11#45312yes—
242C4×C11#46511yescharacteristic
243C4×C11#46811yescharacteristic
244Dic11—44no—
245C22×D4—112no—
246C22×D4—224no—
247C22×D4—221no—
248C22×D4—221no—
249C22×D4C22⋊D1111yescharacteristic
250C23×C4—21no—
251C2×SD16—224no—
252C2×M16—21no—
253C4⋊Q8C22⋊D1111yescharacteristic, complemented
254C4⋊Q8C22⋊D1111yescharacteristic, complemented
255#127—221no—
256#127—221no—
257#127—221no—
258#127—221no—
259#127—442no—
260#127—442no—
261#125—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264#121—448no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271#117—21no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—224no—
276C2×C42—221no—
277C2×C42C22×D1111yescharacteristic
278#107—22no—
279#106—22no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8C22⋊D1112yescomplemented
284#102—22no—
285#102—22no—
286#102—224no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C4×C8—221no—
290C4×C8—221no—
291#95—112no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#200011yescharacteristic
296C2×C11#200211yescharacteristic
297C2×C11#200811yescharacteristic
298D11—162no—
299C24—21no—
300C24—222no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—444no—
311C2×D4—448no—
312C2×D4—448no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—882no—
322C2×D4—884no—
323C2×D4#432512yescomplemented
324C22×C4—21no—
325C22×C4—44no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—222no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—884no—
333M16—41no—
334M16—41no—
335C2×C8—22no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—224no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—448no—
351C42—41no—
352C42—441no—
353C42—441no—
354C42D4×D1111yescharacteristic
355C42#434111yescharacteristic
356C42C2×C22⋊D1111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C11#1024611yescharacteristic, complemented, Sylow
359C23—22no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—444no—
365C23—444no—
366C23—442no—
367C23—442no—
368C23—442no—
369C23#6699011yescharacteristic
370Q8—42no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—41no—
376D4—444no—
377D4—882no—
378D4—882no—
379D4—882no—
380D4—8816no—
381D4—881no—
382D4—881no—
383D4—881no—
384D4—881no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—224no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4#6699011yescharacteristic
397C2×C4#6699111yescharacteristic
398C2×C4#6699211yescharacteristic
399C2×C4#6699211yescharacteristic
400C2×C4#6699311yescharacteristic
401C2×C4C2×#432511yescharacteristic
402C2×C4#6699511yescharacteristic
403C2×C4#6700211yescharacteristic
404C2×C4#6700311yescharacteristic
405C2×C4#6700611yescharacteristic
406C8—42no—
407C8—442no—
408C8—881no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—884no—
417C22—884no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22#1062265911yescharacteristic
422C22#1062266011yescharacteristic
423C22#1062283611yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—81no—
430C4—444no—
431C4#1062266111yescharacteristic
432C4#1062266211yescharacteristic
433C4#1062281112yes—
434C4#1062284011yescharacteristic
435C4#1062285111yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—1762no—
440C2#1306961711yescharacteristic
441C2#1306962811yescharacteristic
442C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radical#13073562C2
hypercenter#3077D11
hypocenterC11#10246
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
3. #13067285C2semidirect
4. #13067115C2semidirect
5. #13067007C2semidirect
6. #13066517C2semidirect
7. C11×#3077C2semidirect
38. C11×C4⋊Q8D4semidirect
39. C11×C4⋊Q8D4semidirect
67. C11×C4⋊C8D4semidirect
75. C4⋊(C11⋊C8)D4semidirect
88. C2×D4×C11SD16semidirect
139. #3077D11semidirect
253. C4⋊Q8C22⋊D11semidirect
254. C4⋊Q8C22⋊D11semidirect
283. C4⋊C8C22⋊D11semidirect
323. C2×D4#4325semidirect
358. C11#10246semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130735622
#130672852
#130671152
#130670072
#130665172
C11×#30772
#1024611