Finite Group Databasebeta

← #14643080

Subgroups — #14643080

Order 2816.

494 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 81 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#13075641C211yesmaximal, characteristic
2#13070153C211yesmaximal, characteristic, complemented
3#13070149C211yesmaximal, characteristic, complemented
4#13070148C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic, complemented
8C2×#66938—21no—
9C11×#390C2211yescharacteristic
10#10622836—21no—
11C2×#66896—21no—
12C2×#66885—21no—
13C2×#66882—21no—
14C2×#66881—21no—
15C2×#66880—21no—
16#10622603—21no—
17C2×#66872—21no—
18#10622574—21no—
19#10622573—21no—
20#10622564—21no—
21#10622552C2211yescharacteristic
22#10622548C2211yescharacteristic
23#10622542C2211yescharacteristic
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44D411yescharacteristic
31C22×Dic22D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51#66938—42no—
52#66938—42no—
53#66896—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66885—42no—
58#66882—42no—
59#66881—42no—
60#66880—42no—
61#66872—42no—
62#7830—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—81no—
75C2×C22⋊D11—81no—
76C2×C22⋊D11—81no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—41no—
86C2×D44—41no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22SD1612yes—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C22⋊Dic11—42no—
104C22⋊Dic11—81no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—81no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4×Dic11—42no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#2733—111no—
124#2095—111no—
125#2094—111no—
126#2094—111no—
127#1272—111no—
128#1270—111no—
129#1270D1111yescharacteristic, complemented
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11#12011yescharacteristic
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145D4×C11—42no—
146D4×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11C2×SD1611yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C22⋊D11—84no—
163C22⋊D11—84no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176D44—42no—
177D44—81no—
178Dic22—42no—
179Dic22—81no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C2×#124—221no—
184C2×#107—221no—
185C2×#106—221no—
186C2×#106—221no—
187C2×#103—221no—
188C2×#102—221no—
189C2×#102—221no—
190#394—221no—
191#392—221no—
192#392—221no—
193#391—111no—
194#390—111no—
195#390C2×D1111yescharacteristic
196#388—221no—
197#388—221no—
198#384—111no—
199#336—111no—
200#336C2×D1111yescharacteristic
201#336C2×D1111yescharacteristic
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#45011yescharacteristic
210C22×C11#45211yescharacteristic
211C22×C11#45211yescharacteristic
212C22×C11#45311yescharacteristic
213C22×C11#45311yescharacteristic
214C22×C11#45311yescharacteristic
215C22×C11#45811yescharacteristic
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—81no—
230Dic11—42no—
231Dic11—81no—
232Dic11—81no—
233Dic11—161no—
234C22×Q8—111no—
235C22×D4—111no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4D4411yescharacteristic
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—221no—
242#124—442no—
243#124—442no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4D4411yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260#107—442no—
261#106—442no—
262#106—442no—
263#103—442no—
264#102—442no—
265#102—442no—
266#95—221no—
267#95—221no—
268#95—221no—
269C2×C11—161no—
270C2×C11#161311yescharacteristic
271C2×C11#161811yescharacteristic
272C2×C11#161811yescharacteristic
273C2×C11#163111yescharacteristic
274C2×C11#163111yescharacteristic
275C2×C11#163411yescharacteristic
276C2×C11#165511yescharacteristic
277D11—161no—
278C24—21no—
279C24—221no—
280C2×Q8—112no—
281C2×Q8—221no—
282C2×Q8—441no—
283C2×Q8—441no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—442no—
293C2×D4—881no—
294C2×D4—881no—
295C2×D4—881no—
296C2×D4—881no—
297C2×D4—881no—
298C22×C4—21no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—441no—
303C22×C4C2×D4411yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—441no—
314C2×C8—441no—
315C4⋊C4—41no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—881no—
335C22⋊C4—881no—
336C42—41no—
337C42—442no—
338C11#783011yescharacteristic, complemented, Sylow
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23#6693511yescharacteristic
354Q8—442no—
355Q8—881no—
356D4—42no—
357D4—81no—
358D4—442no—
359D4—881no—
360D4—884no—
361D4—884no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4#6695711yescharacteristic
384C2×C4#6696211yescharacteristic
385C2×C4#6696411yescharacteristic
386C2×C4#6696511yescharacteristic
387C2×C4SD16×D1111yescharacteristic
388C2×C4#6696811yescharacteristic
389C8—42no—
390C8—42no—
391C8—442no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—881no—
400C22—881no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22#1062234611yescharacteristic
407C22#1062235511yescharacteristic
408C22#1062236011yescharacteristic
409C22#1062238911yescharacteristic
410C22#1062239611yescharacteristic
411C22#1062243511yescharacteristic
412C22#1062243511yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—442no—
421C4—881no—
422C4—881no—
423C4—1761no—
424C2—161no—
425C2—1761no—
426C2#1306763711yescharacteristic
427C2#1306766511yescharacteristic
428C2#1306766611yescharacteristic
429C2#1306774411yescharacteristic
430C2#1306774611yescharacteristic
431C2#1306776311yescharacteristic
432C2#1306790611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radical#13075641C2
hypercenter#1270D11
hypocenterC11#7830
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070153C2semidirect
3. #13070149C2semidirect
4. #13070148C2semidirect
5. #13066441C2semidirect
6. #13066436C2semidirect
7. C11×#1270C2semidirect
129. #1270D11semidirect
338. C11#7830semidirect

Maximal subgroups

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

subgroupindex
#130756412
#130701532
#130701492
#130701482
#130664412
#130664362
C11×#12702
#783011