Finite Group Databasebeta

← #14657256

Subgroups — #14657256

Order 2816.

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

normal subgroups only

This group has 444 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#13068749C211yesmaximal, 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—
17#10622548C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622290—21no—
20#10622287—21no—
21#10622285—21no—
22#10622269—21no—
23#10622189—21no—
24#10622189—21no—
25#10622167—21no—
26#10622167—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#66867—21no—
71#66867D412yes—
72#10426—111nomaximal, Sylow
73C23×D11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
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—21no—
89C2×Dic22—41no—
90C2×Dic22—41no—
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×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—81no—
108(C2×D11)⋊C4—81no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—81no—
120C4⋊Dic11—81no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128#2820—111no—
129#1992—111no—
130#1959—111no—
131#1836—111no—
132C2×#330—111no—
133C2×#329—111no—
134#1295D1111yescharacteristic, complemented
135C23×C11#12011yescharacteristic
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11#12411yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173D44—42no—
174D44—81no—
175Dic22—42no—
176Dic22—81no—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—42no—
180C2×#125—111no—
181C2×#124—111no—
182C2×#103—221no—
183C2×#102—221no—
184C2×#97—111no—
185C2×#97C2×D1111yescharacteristic
186C2×#97C2×D1111yescharacteristic
187#399—221no—
188#397—221no—
189#396—221no—
190#396—221no—
191#395—221no—
192#394—221no—
193#384—111no—
194#382C2×D1111yescharacteristic
195#340—221no—
196#340—221no—
197#340—221no—
198#340—221no—
199#330—222no—
200#329—222no—
201C22×C11#39411yescharacteristic
202C22×C11#45311yescharacteristic
203C22×C11#45411yescharacteristic
204C22×C11#45411yescharacteristic
205C22×C11#45511yescharacteristic
206C22×C11#45511yescharacteristic
207C22×C11#45611yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—81no—
222C4×C11—81no—
223Dic11—81no—
224Dic11—81no—
225Dic11—81no—
226Dic11—161no—
227C22×Q8—111no—
228C22×D4—111no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—221no—
232#125—221no—
233#125—221no—
234#125—221no—
235#125—221no—
236#124—221no—
237#124—221no—
238#124—221no—
239#124—221no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4D4411yescharacteristic
250C2×C4⋊C4D4411yescharacteristic
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C42C22×D1111yescharacteristic
258#103—442no—
259#102—442no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97—21no—
264#97—112no—
265#97—221no—
266#95—21no—
267#95—21no—
268#95—221no—
269#95—221no—
270C2×C11#165711yescharacteristic
271C2×C11#166111yescharacteristic
272C2×C11#166211yescharacteristic
273C2×C11#166411yescharacteristic
274C2×C11#203711yescharacteristic
275C2×C11#203811yescharacteristic
276C2×C11#204011yescharacteristic
277D11—161no—
278C24—221no—
279C2×Q8—221no—
280C2×Q8—221no—
281C2×Q8—441no—
282C2×Q8—441no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—441no—
286C2×D4—441no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4C2×D4411yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—222no—
303C2×C8—441no—
304C2×C8—441no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—881no—
320C4⋊C4—881no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—881no—
326C22⋊C4—881no—
327C22⋊C4—881no—
328C22⋊C4—881no—
329C42#433911yescharacteristic
330C42#433911yescharacteristic
331C42D4×D1111yescharacteristic
332C42#434311yescharacteristic
333C11#1042611yescharacteristic, complemented, Sylow
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23#6693511yescharacteristic
342Q8—442no—
343Q8—881no—
344D4—442no—
345D4—881no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4#6692811yescharacteristic
371C2×C4#6693711yescharacteristic
372C2×C4#6693711yescharacteristic
373C2×C4#6694711yescharacteristic
374C2×C4#6694711yescharacteristic
375C2×C4#6694811yescharacteristic
376C8—42no—
377C8—42no—
378C8—442no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22#1062228511yescharacteristic
387C22#1062235911yescharacteristic
388C22#1062236611yescharacteristic
389C22#1062243511yescharacteristic
390C22#1062243811yescharacteristic
391C22#1062243911yescharacteristic
392C22#1062244011yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—881no—
402C4—881no—
403C4—881no—
404C4—1761no—
405C2—1761no—
406C2#1306791611yescharacteristic
407C2#1306793611yescharacteristic
408C2#1306794111yescharacteristic
409C2#1306795111yescharacteristic
410C2#1306982911yescharacteristic
411C2#1306983611yescharacteristic
412C2#1306984611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1295D11
hypocenterC11#10426
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. #13068749C2semidirect
5. C2×#10622103C2semidirect
7. C11×#1295C2semidirect
134. #1295D11semidirect
333. C11#10426semidirect

Maximal subgroups

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

subgroupindex
#130766682
#130695852
#130694322
#130687492
C2×#106221032
C2×#106221022
C11×#12952
#1042611