Finite Group Databasebeta

← #14656151

Subgroups — #14656151

Order 2816.

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

normal subgroups only

This group has 590 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#13079741C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#463—22no—
13C11×#461—21no—
14C11×#459—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17#10622834—21no—
18#10622825—22no—
19#10622692—21no—
20#10622683—21no—
21#10622647—22no—
22#10622621—22no—
23#10622590—21no—
24#10622560—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29D4⋊(C11⋊C8)—22no—
30#10622124—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D412yes—
58C2×C4×Dic11—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—22no—
66C11×#102—22no—
67#66896—24no—
68C11⋊#95—24no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10241—111nomaximal, Sylow
78C24×C11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×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—41no—
93C2×D4×C11SD1612yes—
94C22×C4×C11—21no—
95C22×C4×C11—44no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—22no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—82no—
107C11×SD16—44no—
108C11×D8—44no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C22⋊Dic11—84no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—42no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3227—111no—
135#3036D1111yescharacteristic
136#2563—111no—
137#1549—111no—
138#1502—111no—
139#1478—111no—
140#1303—111no—
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11#12011yescharacteristic
148Q8×C11—41no—
149Q8×C11—41no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—42no—
156D4×C11—41no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×SD1611yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—44no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184Dic22—82no—
185Dic22—82no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—81no—
189C2×AGL(1,ℤ/8)—21no—
190#532C2×D1111yescharacteristic
191C2×C4⋊Q8—111no—
192C2×C4×D4C2×D1111yescharacteristic
193#498—221no—
194#486—221no—
195#481—222no—
196#476—222no—
197#463—22no—
198#461—21no—
199#459—21no—
200#431—111no—
201#431—111no—
202#423C2×D1111yescharacteristic
203#417—21no—
204#393—222no—
205#390—221no—
206#382—221no—
207#380—222no—
208C4×C4⋊C4—111no—
209#332—222no—
210#327—222no—
211D4⋊C8—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39211yescharacteristic
223C22×C11#44811yescharacteristic
224C22×C11#44911yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#45412yes—
233C4×C11#46511yescharacteristic
234C4×C11#46811yescharacteristic
235Dic11—82no—
236Dic11—82no—
237C2×#41—21no—
238C22×Q8—221no—
239C22×D4C22⋊D1111yescharacteristic
240C23×C4—21no—
241AGL(1,ℤ/8)—42no—
242AGL(1,ℤ/8)—42no—
243C2×SD16—22no—
244C2×D8—22no—
245C2×M16—21no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8C22⋊D1111yescharacteristic
251#127C22⋊D1111yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4C22⋊D1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—224no—
267C2×C42—221no—
268C2×C42C22×D1111yescharacteristic
269#106—224no—
270C4⋊C8—21no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8C22⋊D1112yes—
274#103—22no—
275#102—22no—
276#102—224no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C4×C8—221no—
280C4×C8—221no—
281#95—112no—
282#95—224no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—82no—
286C2×C11—161no—
287C2×C11#200011yescharacteristic
288C2×C11#200311yescharacteristic
289C2×C11#200811yescharacteristic
290C24—21no—
291#41—41no—
292#41—41no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—882no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4#432412yes—
309C22×C4—21no—
310C22×C4—44no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—44no—
320D8—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—442no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—884no—
340C42—441no—
341C42—441no—
342C42D4×D1111yescharacteristic
343C42#434111yescharacteristic
344C42C2×C22⋊D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#1024111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23#6699011yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—882no—
357Q8—882no—
358D4—22no—
359D4—22no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—442no—
378C2×C4—444no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6698511yescharacteristic
383C2×C4C2×#432411yescharacteristic
384C2×C4#6699011yescharacteristic
385C2×C4#6699111yescharacteristic
386C2×C4#6699211yescharacteristic
387C2×C4#6699211yescharacteristic
388C2×C4#6699311yescharacteristic
389C2×C4#6700311yescharacteristic
390C2×C4#6700411yescharacteristic
391C2×C4#6700611yescharacteristic
392C8—42no—
393C8—442no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1062265011yescharacteristic
406C22#1062265311yescharacteristic
407C22#1062283611yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—882no—
414C4—882no—
415C4#1062265411yescharacteristic
416C4#1062265511yescharacteristic
417C4#1062281412yes—
418C4#1062283111yescharacteristic
419C4#1062285211yescharacteristic
420C2—21no—
421C2—21no—
422C2—82no—
423C2—161no—
424C2#1306961911yescharacteristic
425C2#1306963511yescharacteristic
426C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10241
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. #13079741C2semidirect
2. #13073789C2semidirect
3. #13067302C2semidirect
4. #13067111C2semidirect
5. #13067007C2semidirect
6. #13066517C2semidirect
346. C11#10241semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130737892
#130673022
#130671112
#130670072
#130665172
C11×#30362
#1024111