Finite Group Databasebeta

← #14657263

Subgroups — #14657263

Order 2816.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076668C211yesmaximal, characteristic
2#13069585C211yesmaximal, characteristic, complemented
3#13069432C211yesmaximal, characteristic
4#13068785C211yesmaximal, characteristic, complemented
5C2×#10622103C211yesmaximal, characteristic, complemented
6C2×#10622102C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic, complemented
8C2×#66928C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66885—21no—
14C2×#66880—21no—
15#10622607—21no—
16#10622607—21no—
17C2×#66872—21no—
18C2×#66871—21no—
19#10622548C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622290—21no—
22#10622287—21no—
23#10622285—21no—
24#10622269—21no—
25#10622189—21no—
26#10622189—21no—
27#10622103—22no—
28#10622102—22no—
29C22×D44D411yescharacteristic
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C22×C11⋊C8—21no—
52#66928—21no—
53#66928—21no—
54#66928—21no—
55#66928—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60C11×#97—21no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68#66885—42no—
69#66880—42no—
70#66872—42no—
71#66871—42no—
72#66867—21no—
73#66867D412yes—
74#10427—111nomaximal, Sylow
75C23×D11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—41no—
88C2×D44—41no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112(C2×D11)⋊C4—81no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—42no—
122C4⋊Dic11—81no—
123C4⋊Dic11—81no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131#2820—111no—
132#1992—111no—
133#1959—111no—
134#1847—111no—
135C2×#330—111no—
136C2×#329—111no—
137#1295D1111yescharacteristic, complemented
138C23×C11#12011yescharacteristic
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
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#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×C4×C11#12411yescharacteristic
164C2×Dic11—41no—
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—24no—
183C2×#125—111no—
184C2×#124—111no—
185C2×#107—221no—
186C2×#106—221no—
187C2×#103—221no—
188C2×#102—221no—
189C2×#97—111no—
190C2×#97C2×D1111yescharacteristic
191C2×#97C2×D1111yescharacteristic
192#399—221no—
193#397—221no—
194#396—221no—
195#396—221no—
196#395—221no—
197#394—221no—
198#384—111no—
199#382C2×D1111yescharacteristic
200#340—221no—
201#340—221no—
202#330—222no—
203#329—222no—
204C22×C11#39411yescharacteristic
205C22×C11#45311yescharacteristic
206C22×C11#45311yescharacteristic
207C22×C11#45411yescharacteristic
208C22×C11#45511yescharacteristic
209C22×C11#45611yescharacteristic
210C22×C11#45611yescharacteristic
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—81no—
226Dic11—81no—
227Dic11—81no—
228Dic11—81no—
229Dic11—161no—
230C22×Q8—111no—
231C22×D4—111no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—221no—
235#125—221no—
236#125—221no—
237#125—221no—
238#125—221no—
239#124—221no—
240#124—221no—
241#124—221no—
242#124—221no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4D4411yescharacteristic
253C2×C4⋊C4D4411yescharacteristic
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42C22×D1111yescharacteristic
261#107—442no—
262#106—442no—
263#103—442no—
264#102—442no—
265#97—21no—
266#97—21no—
267#97—21no—
268#97—21no—
269#97—112no—
270#97—221no—
271#95—21no—
272#95—21no—
273#95—221no—
274#95—221no—
275C2×C11#165611yescharacteristic
276C2×C11#166011yescharacteristic
277C2×C11#166111yescharacteristic
278C2×C11#166411yescharacteristic
279C2×C11#203711yescharacteristic
280C2×C11#203811yescharacteristic
281C2×C11#203911yescharacteristic
282D11—161no—
283C24—221no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—441no—
291C2×D4—441no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—441no—
298C22×C4C2×D4411yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—222no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—442no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—881no—
326C4⋊C4—881no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—881no—
332C22⋊C4—881no—
333C22⋊C4—881no—
334C22⋊C4—881no—
335C42#433911yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434311yescharacteristic
339C11#1042711yescharacteristic, complemented, Sylow
340C23—441no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23#6693511yescharacteristic
348Q8—442no—
349Q8—881no—
350D4—442no—
351D4—881no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4#6692811yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4#6694711yescharacteristic
380C2×C4#6694711yescharacteristic
381C2×C4#6694811yescharacteristic
382C8—42no—
383C8—42no—
384C8—224no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22#1062228511yescharacteristic
393C22#1062236011yescharacteristic
394C22#1062236511yescharacteristic
395C22#1062243511yescharacteristic
396C22#1062243811yescharacteristic
397C22#1062243911yescharacteristic
398C22#1062244011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—881no—
408C4—881no—
409C4—881no—
410C4—1761no—
411C2—1761no—
412C2#1306791011yescharacteristic
413C2#1306792911yescharacteristic
414C2#1306793411yescharacteristic
415C2#1306795211yescharacteristic
416C2#1306982911yescharacteristic
417C2#1306983611yescharacteristic
418C2#1306984111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1295D11
hypocenterC11#10427
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #13069585C2semidirect
4. #13068785C2semidirect
5. C2×#10622103C2semidirect
7. C11×#1295C2semidirect
137. #1295D11semidirect
339. C11#10427semidirect

Maximal subgroups

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

subgroupindex
#130766682
#130695852
#130694322
#130687852
C2×#106221032
C2×#106221022
C11×#12952
#1042711