Finite Group Databasebeta

← #14657461

Subgroups — #14657461

Order 2816.

460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078082C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic, complemented
3#13067371C211yesmaximal, characteristic, complemented
4#13067291C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×#66961—21no—
9#10623008C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622746—21no—
15C2×#66887—21no—
16#10622537C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622457—22no—
19#10622456—21no—
20#10622454—21no—
21#10622192—21no—
22#10622124—21no—
23#10622123—21no—
24#10622121—21no—
25#10622121—21no—
26#10622121—21no—
27#10622121—21no—
28#10622118—22no—
29C2×#4339—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C2×C42×C11C2311yescharacteristic
36#66983—21no—
37#66983—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×#4318—21no—
41C22×C11⋊C8—21no—
42#66961—42no—
43#66961—42no—
44C2×D88—22no—
45C2×#4314—22no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61#66887—42no—
62#66885—22no—
63#66880—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D411yescharacteristic
68C4×C11⋊C8D411yescharacteristic
69#10457—111nomaximal, Sylow
70C23×D11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—41no—
75C22×Dic11—21no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44SD1612yes—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—81no—
93C2×C4×D11—81no—
94C2×Dic22—21no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—81no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—41no—
121D88—44no—
122#4314—44no—
123#3036—111no—
124#1800—111no—
125#1566—111no—
126#1547—111no—
127#1492—111no—
128C2×D4⋊C8—111no—
129#1292D1111yescharacteristic, complemented
130C23×C11#12311yescharacteristic
131C22×D11—22no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—81no—
136C22×D11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C22⋊D11—81no—
151C22⋊D11—81no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—81no—
155D44—22no—
156D44—22no—
157D44—41no—
158D44—41no—
159D44—41no—
160D44—41no—
161D44—41no—
162D44—41no—
163D44—81no—
164C4×D11—82no—
165C4×D11—81no—
166C4×D11—81no—
167C4×D11—81no—
168C4×D11—81no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—42no—
172C8×C11—81no—
173C8×C11—81no—
174C11⋊C8—22no—
175C11⋊C8—41no—
176C11⋊C8—81no—
177C2×AGL(1,ℤ/8)—221no—
178#532—111no—
179C2×C4×D4—111no—
180#463—222no—
181#461—221no—
182#459—221no—
183#423—111no—
184#423C2×D1111yescharacteristic
185#423C2×D1111yescharacteristic
186C2×C4⋊C8C2×D1111yescharacteristic
187#417—221no—
188C2×#100—221no—
189C2×C4×C8—111no—
190#343—221no—
191#334—222no—
192#332—221no—
193#331—221no—
194D4⋊C8—221no—
195D4⋊C8—221no—
196D4⋊C8—221no—
197D4⋊C8—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#39411yescharacteristic
201C22×C11#48111yescharacteristic
202C22×C11#48211yescharacteristic
203C2×D11—42no—
204C2×D11—82no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—82no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11#44911yescharacteristic
215C4×C11#45011yescharacteristic
216C4×C11#46511yescharacteristic
217C4×C11#46911yescharacteristic
218C4×C11#47111yescharacteristic
219C4×C11#47211yescharacteristic
220Dic11—81no—
221Dic11—81no—
222C2×#41—221no—
223C22×D4—111no—
224C23×C4—221no—
225AGL(1,ℤ/8)—442no—
226AGL(1,ℤ/8)—442no—
227C2×SD16—222no—
228C2×D8—222no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—221no—
232C22×C8—21no—
233C22×C8—221no—
234C4⋊Q8—111no—
235#127—111no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×D4—221no—
240C4×D4—221no—
241C4×D4—221no—
242C4×D4—221no—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8D4412yes—
256#103—222no—
257#102—222no—
258#100—442no—
259C4×C8—111no—
260C4×C8—111no—
261C4×C8—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11#203411yescharacteristic
265C2×C11#205011yescharacteristic
266C2×C11#205111yescharacteristic
267D11—82no—
268D11—161no—
269C24—221no—
270#41—441no—
271#41—441no—
272#41—441no—
273#41—441no—
274C2×Q8—221no—
275C2×D4—112no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—441no—
285C22×C4—221no—
286C22×C4—441no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4—881no—
290C22×C4—881no—
291C22×C4#433911yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4#434311yescharacteristic
294SD16—444no—
295D8—444no—
296M16—41no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—441no—
301M16—441no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—81no—
306C2×C8—221no—
307C2×C8—221no—
308C2×C8—442no—
309C2×C8—441no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42C2×D4411yescharacteristic
319C42#433911yescharacteristic
320C42D4×D1111yescharacteristic
321C42D4×D1111yescharacteristic
322C11#1045711yescharacteristic, complemented, Sylow
323C23—222no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—881no—
328C23—881no—
329C23#6694711yescharacteristic
330Q8—441no—
331Q8—441no—
332D4—222no—
333D4—222no—
334D4—441no—
335D4—441no—
336D4—441no—
337D4—441no—
338D4—441no—
339D4—441no—
340D4—881no—
341D4—881no—
342D4—881no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—882no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4#6692811yescharacteristic
355C2×C4#6693511yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6694711yescharacteristic
359C2×C4#6694811yescharacteristic
360C2×C4#6696411yescharacteristic
361C2×C4SD16×D1111yescharacteristic
362C2×C4#6696711yescharacteristic
363C2×C4#6697211yescharacteristic
364C8—42no—
365C8—81no—
366C8—81no—
367C8—222no—
368C8—441no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—442no—
373C22—882no—
374C22—882no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22#1062228511yescharacteristic
381C22#1062247611yescharacteristic
382C22#1062249811yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—881no—
387C4—881no—
388C4#1062236211yescharacteristic
389C4#1062236711yescharacteristic
390C4#1062238911yescharacteristic
391C4#1062239511yescharacteristic
392C4#1062242011yescharacteristic
393C4#1062242411yescharacteristic
394C2—21no—
395C2—21no—
396C2—882no—
397C2—1761no—
398C2#1306980811yescharacteristic
399C2#1306990411yescharacteristic
400C2#1306991111yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#394
prime radical#13078082C2
hypercenter#1292D11
hypocenterC11#10457
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
2. #13068605C2semidirect
3. #13067371C2semidirect
4. #13067291C2semidirect
5. #13067066C2semidirect
6. C2×#10622121C2semidirect
7. C11×#1292C2semidirect
129. #1292D11semidirect
322. C11#10457semidirect

Maximal subgroups

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

subgroupindex
#130780822
#130686052
#130673712
#130672912
#130670662
C2×#106221212
C11×#12922
#1045711