Finite Group Databasebeta

← #14666463

Subgroups — #14666463

Order 2816.

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

normal subgroups only

This group has 474 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#13069657C211yesmaximal, characteristic, complemented
2#13067652C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic, complemented
4#13066643C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#2828C211yesmaximal, characteristic, complemented
8C2×#66985—21no—
9#10623041C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C11×#397—21no—
12C11×#394—21no—
13C11×#394—21no—
14C11×#394C2211yescharacteristic
15C11×#392—21no—
16C11×#392—21no—
17C11×#390C2211yescharacteristic
18C11×#388—21no—
19#10622830—21no—
20#10622581—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C2×#4339—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11D411yescharacteristic
44C2×#4324—41no—
45#66985—42no—
46#66985—42no—
47C2×#4323—41no—
48C2×#4323—41no—
49#66983—21no—
50#66983—21no—
51C2×#4318—21no—
52#66950—41no—
53#66948—41no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59#66896—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#66869—42no—
65#12198—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—81no—
74C2×D4×C11—81no—
75C2×D4×C11—81no—
76C2×D4×C11—81no—
77C2×D4×C11—81no—
78C2×D4×C11—81no—
79C2×D4×C11—81no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88#4339—41no—
89#4339—41no—
90#4339—41no—
91#4339—41no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—81no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C42×C11—41no—
110#4324—44no—
111#4323—44no—
112#4323—82no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117#4318—22no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122#2828D1111yescharacteristic, complemented
123#2006—111no—
124#1616—111no—
125#1598—111no—
126#1353—111no—
127#1345—111no—
128#1318—111no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11#12011yescharacteristic
144C22×D11—41no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—84no—
150D4×C11—84no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
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—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C22⋊D11—81no—
172C22⋊D11—81no—
173C2×Dic11—41no—
174D44—41no—
175D44—41no—
176D44—81no—
177D44—81no—
178C4×D11—81no—
179C4×D11—81no—
180Dic22—41no—
181Dic22—41no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C11⋊C8—81no—
185C2×AGL(1,ℤ/8)—221no—
186#537—111no—
187#481—221no—
188#447—221no—
189C2×#104—221no—
190#400C2×D1111yescharacteristic
191#397—21no—
192#394—21no—
193#394—21no—
194#394C2×D1111yescharacteristic
195#392—21no—
196#392—21no—
197#390C2×D1111yescharacteristic
198#388—21no—
199#343—111no—
200#327—221no—
201#327—221no—
202#324—111no—
203#324—111no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
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—81no—
219C22×C11—81no—
220C22×C11#44911yescharacteristic
221C22×C11#45311yescharacteristic
222C22×C11B(4,𝔽2)11yescharacteristic
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234Dic11—81no—
235C2×#41—221no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C22⋊D1111yescharacteristic
239C22×D4C22⋊D1111yescharacteristic
240AGL(1,ℤ/8)—442no—
241AGL(1,ℤ/8)—442no—
242C2×SD16—441no—
243C2×D8—441no—
244C2×D8—441no—
245C2×M16—221no—
246C22⋊Q8—441no—
247#121—221no—
248#121—221no—
249#121—441no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C4⋊C4C22×D1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42C22⋊D1111yescharacteristic
262#106—441no—
263#104—442no—
264#102—441no—
265#102—441no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95C22⋊D1111yescharacteristic
272#95C22⋊D1111yescharacteristic
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—161no—
276C2×C11—161no—
277C2×C11#160011yescharacteristic
278C2×C11#220011yescharacteristic
279C2×C11#220211yescharacteristic
280D11—161no—
281C24—21no—
282C24—21no—
283#41—441no—
284#41—441no—
285#41—441no—
286#41—441no—
287C2×Q8—221no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—441no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—441no—
309C22×C4C2×C22⋊D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—444no—
313D8—444no—
314D8—882no—
315M16—222no—
316M16—441no—
317C2×C8—441no—
318C2×C8—441no—
319C2×C8—441no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C42—41no—
337C11#1219811yescharacteristic, complemented, Sylow
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—441no—
353C23#6700611yescharacteristic
354Q8—441no—
355Q8—441no—
356D4—42no—
357D4—42no—
358D4—81no—
359D4—81no—
360D4—84no—
361D4—84no—
362D4—441no—
363D4—441no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—441no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4#6700211yescharacteristic
390C2×C4#6700311yescharacteristic
391C8—442no—
392C8—881no—
393C8—881no—
394C22—21no—
395C22—21no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22#1062285111yescharacteristic
414C22#1062285411yescharacteristic
415C22#1062285711yescharacteristic
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—881no—
425C2—21no—
426C2—21no—
427C2—161no—
428C2—161no—
429C2—1761no—
430C2#1306756211yescharacteristic
431C2#1307062311yescharacteristic
432C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2828C2
socleC22×C11B(4,𝔽2)
hypercenter#2828D11
hypocenterC11#12198
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2828

Complements

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

NH ≅ G/Ntype
1. #13069657C2semidirect
2. #13067652C2semidirect
3. #13067550C2semidirect
4. #13066643C2semidirect
5. #13066619C2semidirect
6. #13066548C2semidirect
7. C11×#2828C2semidirect
122. #2828D11semidirect
337. C11#12198semidirect

Maximal subgroups

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

subgroupindex
#130696572
#130676522
#130675502
#130666432
#130666192
#130665482
C11×#28282
#1219811