Finite Group Databasebeta

← #14665992

Subgroups — #14665992

Order 2816.

542 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076881C211yesmaximal, characteristic, complemented
2#13069740C211yesmaximal, characteristic
3#13067636C211yesmaximal, characteristic, complemented
4#13066641C211yesmaximal, characteristic, complemented
5#13066640C211yesmaximal, characteristic, complemented
6#13066543C211yesmaximal, characteristic, complemented
7C11×#1613C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×#66990—21no—
10C11×#481—21no—
11C11×#399C2211yescharacteristic
12C2×#66898—21no—
13#10622647—21no—
14#10622607—21no—
15#10622607—21no—
16#10622607—21no—
17#10622568—21no—
18#10622568C2211yescharacteristic
19#10622562—21no—
20#10622562C2211yescharacteristic
21#10622289—21no—
22C11×#327—21no—
23C11×#323C2211yescharacteristic
24#10622175—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C24×D11D411yescharacteristic
28C22×D4×C11—21no—
29C22×C22⋊D11—41no—
30C11×#123—41no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#120—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic, complemented
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41#66990—42no—
42#66990—42no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—41no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic, complemented
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C11×#106—41no—
56C11×#102—41no—
57C11×C22⋊C8—21no—
58C11×#95D411yescharacteristic, complemented
59#66898—42no—
60#66896—41no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic, complemented
63C22⋊(C11⋊C8)—21no—
64#66872—41no—
65#12124—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—41no—
71C23×D11—41no—
72C23×D11—81no—
73C23×D11—81no—
74C23×D11SD1612yes—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—44no—
89C2×C22⋊D11—82no—
90C2×C22⋊D11—82no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—81no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C22⋊Dic11—22no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—81no—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112(C2×D11)⋊C4—81no—
113(C2×D11)⋊C4—81no—
114(C2×D11)⋊C4—81no—
115C4⋊Dic11—41no—
116C4⋊Dic11—81no—
117Dic11⋊C4—81no—
118Dic11⋊C4—81no—
119Dic11⋊C4—81no—
120C2×C11⋊C8—41no—
121#2842—111no—
122#2021—111no—
123#1613—111no—
124#1613D1111yescharacteristic, complemented
125#1352—111no—
126#1352—111no—
127#1316—111no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11#12011yescharacteristic
138C23×C11C2×SD1611yescharacteristic
139C23×C11#13711yescharacteristic
140C22×D11—22no—
141C22×D11—42no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—82no—
151C22×D11—81no—
152C22×D11—82no—
153C22×D11—84no—
154C22×D11—81no—
155C22×D11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C22⋊D11—88no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C8×C11—81no—
189C11⋊C8—81no—
190#534C2×D1111yescharacteristic
191C2×#120—221no—
192#481—21no—
193#481—221no—
194C2×#99—221no—
195#399—111no—
196#399—221no—
197#399C2×D1111yescharacteristic
198#396—221no—
199#396—221no—
200#396—221no—
201#396—221no—
202#379—111no—
203#379—221no—
204#342—111no—
205#327—21no—
206#327—221no—
207#323—111no—
208#323C2×D1111yescharacteristic
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11—82no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—161no—
223C22×C11#44811yescharacteristic
224C22×C11#45311yescharacteristic
225C22×C11B(4,𝔽2)11yescharacteristic
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—44no—
229C2×D11—42no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—82no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—81no—
242Dic11—81no—
243Dic11—81no—
244Dic11—82no—
245Dic11—81no—
246C25—111no—
247C22×D4—21no—
248C22×D4—441no—
249#123—41no—
250#121—21no—
251#121—21no—
252#120—41no—
253#120—442no—
254#120—442no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
262C2×C22⋊C4—21no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—441no—
273C2×C22⋊C4C22×D1111yescharacteristic
274#106—41no—
275#106—441no—
276#102—41no—
277#102—441no—
278#99—442no—
279C22⋊C8—21no—
280C22⋊C8—221no—
281#95—111no—
282#95—221no—
283#95C22⋊D1111yescharacteristic, complemented
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11—161no—
289C2×C11#159611yescharacteristic
290C2×C11#220011yescharacteristic
291C2×C11#220011yescharacteristic
292D11—82no—
293C24—21no—
294C24—112no—
295C24—221no—
296C24—221no—
297C24—441no—
298C24—441no—
299C24—881no—
300C24—881no—
301C24D4×D1111yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—444no—
311C2×D4—882no—
312C2×D4—882no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—441no—
320C22×C4D4×D1111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322C2×C8—41no—
323C2×C8—441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—81no—
328C4⋊C4—441no—
329C4⋊C4—881no—
330C4⋊C4—881no—
331C4⋊C4—881no—
332C4⋊C4—881no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—81no—
337C22⋊C4—222no—
338C22⋊C4—444no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—881no—
342C22⋊C4—881no—
343C22⋊C4—881no—
344C22⋊C4—881no—
345C22⋊C4—881no—
346C22⋊C4—881no—
347C22⋊C4—881no—
348C11#1212411yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23—222no—
359C23—442no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—442no—
365C23—442no—
366C23—441no—
367C23—441no—
368C23—881no—
369C23—882no—
370C23—882no—
371C23—881no—
372C23—881no—
373C23—884no—
374C23SD16×D1111yescharacteristic
375C23#6696811yescharacteristic
376C23#6699011yescharacteristic
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—888no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—881no—
408C2×C4—881no—
409C8—81no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—82no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—161no—
425C22—442no—
426C22—442no—
427C22—444no—
428C22—442no—
429C22—881no—
430C22—881no—
431C22—882no—
432C22—882no—
433C22—882no—
434C22—881no—
435C22—881no—
436C22#1062264511yescharacteristic
437C22#1062278311yescharacteristic
438C22#1062281111yescharacteristic
439C4—41no—
440C4—41no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—881no—
445C4—881no—
446C4—882no—
447C4—881no—
448C2—21no—
449C2—21no—
450C2—41no—
451C2—41no—
452C2—161no—
453C2—882no—
454C2#1306753711yescharacteristic
455C2#1307062011yescharacteristic
456C2#1307062211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1613C2
socleC22×C11B(4,𝔽2)
prime radical#13069740C2
hypercenter#1613D11
hypocenterC11#12124
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1613

Complements

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

NH ≅ G/Ntype
1. #13076881C2semidirect
3. #13067636C2semidirect
4. #13066641C2semidirect
5. #13066640C2semidirect
6. #13066543C2semidirect
7. C11×#1613C2semidirect
35. C2×C11×C4⋊C4D4semidirect
51. C2×C4⋊Dic11D4semidirect
58. C11×#95D4semidirect
62. C11⋊#95D4semidirect
124. #1613D11semidirect
261. C2×C4⋊C4C22⋊D11semidirect
283. #95C22⋊D11semidirect
348. C11#12124semidirect

Maximal subgroups

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

subgroupindex
#130768812
#130697402
#130676362
#130666412
#130666402
#130665432
C11×#16132
#1212411