Finite Group Databasebeta

← #14666069

Subgroups — #14666069

Order 2816.

456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069867C211yesmaximal, characteristic, complemented
2#13067567C211yesmaximal, characteristic, complemented
3#13067533C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2824C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#400—21no—
10C11×#397—21no—
11C11×#394—21no—
12C11×#394—21no—
13C11×#393—21no—
14C11×#393C2211yescharacteristic
15C11×#392C2211yescharacteristic
16C11×#386—21no—
17C11×#385C2211yescharacteristic
18#10622840—21no—
19#10622830—21no—
20#10622826—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C22×C22⋊D11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×#4325—41no—
44C2×#4323—41no—
45#66983—21no—
46#66983—21no—
47C2×(C2×D11)⋊C4—41no—
48#66939—41no—
49#66935—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57#66899—41no—
58#66896—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66870—42no—
63#12136—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—81no—
73C2×D4×C11—81no—
74C2×D4×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—81no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92C2×D44—21no—
93C2×D44—21no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—81no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107#4325—82no—
108#4323—82no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—82no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2824D1111yescharacteristic, complemented
117#2044—111no—
118#1601—111no—
119#1595—111no—
120#1351—111no—
121#1343—111no—
122#1326—111no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11#12011yescharacteristic
135C23×C11#13511yescharacteristic
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—81no—
141C22×D11—81no—
142Q8×C11—42no—
143Q8×C11—81no—
144D4×C11—42no—
145D4×C11—81no—
146D4×C11—82no—
147D4×C11—82no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C22⋊D11—81no—
170C22⋊D11—81no—
171C22⋊D11—81no—
172C22⋊D11—81no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—81no—
180D44—81no—
181C11⋊C8—81no—
182C11⋊C8—81no—
183#534—111no—
184#448—221no—
185#447—221no—
186C2×#99—221no—
187#400—21no—
188#397—21no—
189#394—21no—
190#394—21no—
191#393—21no—
192#393C2×D1111yescharacteristic
193#392C2×D1111yescharacteristic
194#386—21no—
195#386—221no—
196#385C2×D1111yescharacteristic
197#342—111no—
198#327—221no—
199#327—221no—
200#323—111no—
201#323—111no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#44911yescharacteristic
219C22×C11#45411yescharacteristic
220C22×C11B(4,𝔽2)11yescharacteristic
221C2×D11—82no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—161no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233Dic11—81no—
234Dic11—161no—
235C22×Q8C22⋊D1111yescharacteristic
236C22×D4—21no—
237C22×D4—221no—
238C22×D4C22⋊D1111yescharacteristic
239C23×C4C22⋊D1111yescharacteristic
240C2×SD16—441no—
241C2×D8—441no—
242#123—441no—
243#121—221no—
244#121—221no—
245#120—441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—441no—
256C2×C22⋊C4C22⋊D1111yescharacteristic
257C2×C22⋊C4C22×D1111yescharacteristic
258#103—441no—
259#102—441no—
260#99—442no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—441no—
269#95C22⋊D1111yescharacteristic
270#95C22⋊D1111yescharacteristic
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11—161no—
276C2×C11#159711yescharacteristic
277C2×C11#219911yescharacteristic
278C2×C11#220011yescharacteristic
279D11—161no—
280C24—21no—
281C24—221no—
282C24C2×C22⋊D1111yescharacteristic
283C2×Q8—41no—
284C2×Q8—81no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—81no—
289C2×D4—81no—
290C2×D4—81no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—81no—
306C22×C4—221no—
307C22×C4—441no—
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310SD16—882no—
311D8—882no—
312C2×C8—441no—
313C2×C8—441no—
314C4⋊C4—81no—
315C4⋊C4—81no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—41no—
321C22⋊C4—81no—
322C22⋊C4—81no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—882no—
332C11#1213611yescharacteristic, complemented, Sylow
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—881no—
348C23—881no—
349C23#6700211yescharacteristic
350C23#6700311yescharacteristic
351C23#6700611yescharacteristic
352Q8—42no—
353Q8—81no—
354D4—42no—
355D4—81no—
356D4—82no—
357D4—82no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362D4—881no—
363D4—881no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C8—881no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—882no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—1761no—
414C22#1062285111yescharacteristic
415C22#1062285711yescharacteristic
416C22#1062285811yescharacteristic
417C4—41no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—881no—
425C4—1761no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—161no—
431C2—1761no—
432C2#1306754511yescharacteristic
433C2#1307061711yescharacteristic
434C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2824C2
socleC22×C11B(4,𝔽2)
prime radical#13067533C2
hypercenter#2824D11
hypocenterC11#12136
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2824

Complements

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

NH ≅ G/Ntype
1. #13069867C2semidirect
2. #13067567C2semidirect
4. #13066637C2semidirect
5. #13066613C2semidirect
6. #13066564C2semidirect
7. C11×#2824C2semidirect
116. #2824D11semidirect
332. C11#12136semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130675672
#130675332
#130666372
#130666132
#130665642
C11×#28242
#1213611