Finite Group Databasebeta

← #14656155

Subgroups — #14656155

Order 2816.

590 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079746C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13073789C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067112C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622834—21no—
15#10622825—22no—
16#10622632—21no—
17#10622629—22no—
18#10622628—21no—
19#10622590—21no—
20#10622579—21no—
21#10622560—22no—
22C4×C4⋊Dic11C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622455—22no—
25#10622348—22no—
26#10622307—21no—
27#10622293—21no—
28C11×D4⋊C8—22no—
29#10622120—22no—
30#10622108—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×#4339—21no—
34C22×Dic22—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11—24no—
43C2×#4324—22no—
44#66985—42no—
45#66985—42no—
46C2×#4323—22no—
47#66983—21no—
48#66983—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D412yes—
52C2×C4×Dic11—21no—
53C2×#4318—21no—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D411yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11⋊#95—24no—
70C11⋊#95D412yes—
71#66885—24no—
72#66881—24no—
73#66874—22no—
74#66873—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77#10241—111nomaximal, Sylow
78C24×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11SD1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—44no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98#4339—41no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—82no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—84no—
118#4324—44no—
119#4323—44no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—42no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—22no—
134#3227—111no—
135#3036—111no—
136#2563—111no—
137#1549—111no—
138#1502—111no—
139#1478D1111yescharacteristic, complemented
140#1303—111no—
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147C22×D11—41no—
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C22⋊D11—81no—
169C22⋊D11—81no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—44no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176D44—41no—
177D44—41no—
178D44—42no—
179D44—81no—
180C4×D11—81no—
181C4×D11—81no—
182Dic22—41no—
183Dic22—41no—
184Dic22—82no—
185Dic22—82no—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—42no—
189C2×AGL(1,ℤ/8)—221no—
190#532—111no—
191C2×C4⋊Q8—111no—
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#431C2×D1111yescharacteristic
201#431C2×D1111yescharacteristic
202#423—111no—
203#417—221no—
204#393—222no—
205#390—221no—
206#382—221no—
207#380—222no—
208C4×C4⋊C4—111no—
209#332—222no—
210#327—222no—
211D4⋊C8—22no—
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—81no—
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#45412yes—
232C4×C11#46511yescharacteristic
233C4×C11#46811yescharacteristic
234Dic11—82no—
235Dic11—81no—
236Dic11—82no—
237C2×#41—221no—
238C22×Q8—221no—
239C22×D4D4411yescharacteristic
240C23×C4—21no—
241AGL(1,ℤ/8)—442no—
242AGL(1,ℤ/8)—442no—
243C2×SD16—222no—
244C2×D8—222no—
245C2×M16—221no—
246C4⋊Q8—111no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
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—112no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4D4411yescharacteristic
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—222no—
275#102—222no—
276#102—224no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C4×C8—21no—
280C4×C8—21no—
281#95—112no—
282#95—224no—
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—221no—
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—221no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—441no—
308C2×D4#431412yes—
309C22×C4—21no—
310C22×C4—44no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—441no—
316C22×C4C2×D4411yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319SD16—444no—
320D8—444no—
321M16—441no—
322M16—441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—222no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—442no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—884no—
340C42—441no—
341C42—441no—
342C42#433911yescharacteristic
343C42D4×D1111yescharacteristic
344C42D4×D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#1024111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—441no—
353C23#6693511yescharacteristic
354Q8—441no—
355Q8—441no—
356Q8—882no—
357Q8—882no—
358D4—22no—
359D4—22no—
360D4—41no—
361D4—41no—
362D4—442no—
363D4—441no—
364D4—441no—
365D4—881no—
366D4—881no—
367D4—881no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—442no—
375C2×C4—444no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4#6693511yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6693711yescharacteristic
385C2×C4C2×#431411yescharacteristic
386C2×C4#6695711yescharacteristic
387C2×C4#6696111yescharacteristic
388C2×C4#6696211yescharacteristic
389C2×C4#6698311yescharacteristic
390C2×C4#6699011yescharacteristic
391C2×C4#6699311yescharacteristic
392C8—42no—
393C8—81no—
394C8—442no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22#1062234711yescharacteristic
406C22#1062235111yescharacteristic
407C22#1062257311yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—882no—
413C4—881no—
414C4—882no—
415C4#1062234411yescharacteristic
416C4#1062234611yescharacteristic
417C4#1062272711yescharacteristic
418C4#1062274711yescharacteristic
419C4#1062281412yes—
420C2—21no—
421C2—21no—
422C2—82no—
423C2—1761no—
424C2#1306962111yescharacteristic
425C2#1306963911yescharacteristic
426C2#1306967011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#1478D11
hypocenterC11#10241
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #13079746C2semidirect
3. #13073789C2semidirect
4. #13067300C2semidirect
5. #13067112C2semidirect
6. #13066518C2semidirect
7. C11×#1478C2semidirect
139. #1478D11semidirect
346. C11#10241semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130780802
#130737892
#130673002
#130671122
#130665182
C11×#14782
#1024111