Finite Group Databasebeta

← #14656154

Subgroups — #14656154

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#13079744C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2563C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66985—21no—
11#10623008C2211yescharacteristic
12C11×#393—22no—
13C11×#390—21no—
14C11×#382—21no—
15C11×#380—22no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622701—21no—
18#10622697—22no—
19#10622692—21no—
20#10622632—21no—
21#10622629—22no—
22#10622628—21no—
23#10622581—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29D4⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D412yes—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—24no—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—22no—
52#66985—42no—
53#66985—42no—
54C2×#4323—22no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×#95—24no—
64C11×#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66874—22no—
68#66873—22no—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10241—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11SD1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98#4339—41no—
99#4339—41no—
100#4339—41no—
101#4339—41no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—84no—
117C42×C11—41no—
118C42×C11—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#4324—44no—
124#4323—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3227—111no—
135#3036—111no—
136#2563D1111yescharacteristic, complemented
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#12011yescharacteristic
147C22×D11—41no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12711yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11#13511yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C22⋊D11—81no—
176C22⋊D11—81no—
177C2×Dic11—41no—
178D44—41no—
179D44—41no—
180D44—42no—
181D44—81no—
182C4×D11—81no—
183C4×D11—81no—
184Dic22—41no—
185Dic22—41no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C11⋊C8—81no—
189C2×AGL(1,ℤ/8)—221no—
190#532—111no—
191C2×C4⋊Q8C2×D1111yescharacteristic
192C2×C4×D4C2×D1111yescharacteristic
193#498—221no—
194#486—221no—
195#481—222no—
196#476—222no—
197#463—222no—
198#461—221no—
199#459—221no—
200#431—111no—
201#431—111no—
202#423—111no—
203#417—221no—
204#393—22no—
205#390—21no—
206#382—21no—
207#380—22no—
208C4×C4⋊C4C2×D1111yescharacteristic
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#39211yescharacteristic
220C22×C11#44811yescharacteristic
221C22×C11#44911yescharacteristic
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—82no—
229C4×C11—81no—
230C4×C11—82no—
231C4×C11#45011yescharacteristic
232C4×C11#45211yescharacteristic
233C4×C11#45412yes—
234C4×C11#46511yescharacteristic
235C4×C11#46811yescharacteristic
236Dic11—81no—
237C2×#41—221no—
238C22×Q8—21no—
239C22×D4C22⋊D1111yescharacteristic
240C23×C4—21no—
241AGL(1,ℤ/8)—442no—
242AGL(1,ℤ/8)—442no—
243C2×SD16—222no—
244C2×D8—222no—
245C2×M16—221no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—111no—
251#127—111no—
252#124—221no—
253#121—221no—
254#121—221no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—221no—
260C4×D4—221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C22⋊D1111yescharacteristic
264C2×C4⋊C4C22⋊D1112yes—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—24no—
267C2×C42—21no—
268C2×C42C22×D1111yescharacteristic
269#106—224no—
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274#103—222no—
275#102—222no—
276#102—224no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C4×C8—221no—
280C4×C8—221no—
281#95—24no—
282#95C22⋊D1112yes—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—82no—
286C2×C11#200011yescharacteristic
287C2×C11#200311yescharacteristic
288C2×C11#200811yescharacteristic
289D11—161no—
290C24—21no—
291#41—441no—
292#41—441no—
293#41—441no—
294#41—441no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—82no—
298C2×Q8—221no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—441no—
308C2×D4#432512yes—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—44no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—441no—
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—444no—
320D8—444no—
321M16—441no—
322M16—441no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—441no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—84no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C42—41no—
341C42—41no—
342C42D4×D1111yescharacteristic
343C42D4×D1111yescharacteristic
344C42D4×D1111yescharacteristic
345C42#434111yescharacteristic
346C11#1024111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—441no—
353C23#6700611yescharacteristic
354Q8—82no—
355Q8—82no—
356Q8—441no—
357Q8—441no—
358D4—22no—
359D4—22no—
360D4—41no—
361D4—41no—
362D4—441no—
363D4—441no—
364D4—442no—
365D4—881no—
366D4—881no—
367D4—881no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4#6699011yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4#6699211yescharacteristic
387C2×C4#6699311yescharacteristic
388C2×C4C2×#432511yescharacteristic
389C2×C4#6699511yescharacteristic
390C2×C4#6700211yescharacteristic
391C2×C4#6700311yescharacteristic
392C8—442no—
393C8—442no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22#1062283611yescharacteristic
406C22#1062284011yescharacteristic
407C22#1062285111yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—82no—
414C4—881no—
415C4#1062265911yescharacteristic
416C4#1062266011yescharacteristic
417C4#1062266111yescharacteristic
418C4#1062266211yescharacteristic
419C4#1062267512yes—
420C2—21no—
421C2—21no—
422C2—82no—
423C2—1761no—
424C2#1306961711yescharacteristic
425C2#1306963811yescharacteristic
426C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2563C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#2563D11
hypocenterC11#10241
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
3. #13067301C2semidirect
4. #13067110C2semidirect
5. #13067007C2semidirect
6. #13066519C2semidirect
7. C11×#2563C2semidirect
136. #2563D11semidirect
346. C11#10241semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780802
#130673012
#130671102
#130670072
#130665192
C11×#25632
#1024111