Finite Group Databasebeta

← #14651646

Subgroups — #14651646

Order 2816.

522 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 105 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#13077699C211yesmaximal, characteristic, complemented
2#13073526C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic
5#13067040C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×C4×D44C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#382C2211yescharacteristic
14C2×#66888—21no—
15#10622600—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622444—22no—
19#10622332—22no—
20#10622292—22no—
21#10622285C412yes—
22#10622283—22no—
23#10622274C412yes—
24#10622192—21no—
25#10622121—22no—
26#10622097—22no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4C2×C412yes—
40C2×C4×Dic11D412yes—
41C2×#4318—21no—
42#66950—42no—
43#66950—42no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C4×C8×C11D412yes—
57C11×#95—21no—
58C11×#95C2×C412yes—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—21no—
61#66888—42no—
62#66879—24no—
63Dic11⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8D412yes—
68#9490—111nomaximal, Sylow
69C23×D11—21no—
70C22×C4×C11—22no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11C22⋊C412yes—
76C22×Dic11C22⋊C412yes—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—42no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—44no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—44no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113C4×Dic11—22no—
114C4×Dic11—22no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#2983—111no—
120#2536—111no—
121#1801—111no—
122#1486—111no—
123#1486—111no—
124#1286—111no—
125#1286D1111yescharacteristic, complemented
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—22no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157D44—22no—
158D44—22no—
159D44—41no—
160D44—41no—
161C4×D11—81no—
162C4×D11—81no—
163C4×D11—81no—
164C4×D11—81no—
165Dic22—41no—
166Dic22—41no—
167Dic22—41no—
168Dic22—41no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C2×C22⋊Q8—221no—
174C2×C4×Q8—111no—
175C2×C4×D4—111no—
176#446—222no—
177#446—222no—
178#432—222no—
179#431—111no—
180#431C2×D1111yescharacteristic
181#423—111no—
182#423C2×D1111yescharacteristic
183C2×#101—221no—
184#398—112no—
185#394—112no—
186#388—222no—
187#382C2×D1111yescharacteristic
188#380—221no—
189#343—221no—
190D4⋊C8—222no—
191D4⋊C8—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#38611yescharacteristic
195C22×C11#41711yescharacteristic
196C22×C11#41811yescharacteristic
197C2×D11—42no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—82no—
209C4×C11#46811yescharacteristic
210C4×C11#46811yescharacteristic
211C4×C11#46911yescharacteristic
212C4×C11#46911yescharacteristic
213Dic11—42no—
214Dic11—42no—
215Dic11—81no—
216C22×Q8—111no—
217C22×D4—111no—
218C23×C4—221no—
219C2×M16—21no—
220C2×M16—221no—
221C22⋊Q8—442no—
222C22⋊Q8—442no—
223C4×Q8—221no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—221no—
239C2×C42—112no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—224no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#101—442no—
249C22⋊C8—21no—
250C22⋊C8—221no—
251#97—224no—
252C4×C8—112no—
253C4×C8D4412yes—
254#95—21no—
255#95—222no—
256#95C4×D1112yes—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#189111yescharacteristic
260C2×C11#189511yescharacteristic
261C2×C11#191211yescharacteristic
262D11—82no—
263C24—221no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—442no—
273C22×C4—22no—
274C22×C4—112no—
275C22×C4—112no—
276C22×C4—221no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286M16—41no—
287M16—41no—
288M16—441no—
289M16—441no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—222no—
293C2×C8—441no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—444no—
303C22⋊C4—444no—
304C22⋊C4—444no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—222no—
308C42—222no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42#434311yescharacteristic
313C11#949011yescharacteristic, complemented, Sylow
314C23—222no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23C22⋊C4×D1111yescharacteristic
322Q8—441no—
323Q8—441no—
324Q8—441no—
325Q8—441no—
326D4—222no—
327D4—222no—
328D4—441no—
329D4—441no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4C4×D4411yescharacteristic
348C2×C4#6693511yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6694611yescharacteristic
351C2×C4#6694711yescharacteristic
352C2×C4#6694811yescharacteristic
353C2×C4#6696411yescharacteristic
354C2×C4#6696711yescharacteristic
355C2×C4#6696711yescharacteristic
356C2×C4#6697111yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—442no—
364C22—442no—
365C22—442no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22#1062227811yescharacteristic
371C22#1062238311yescharacteristic
372C22#1062241611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—442no—
379C4—442no—
380C4—881no—
381C4#1062239511yescharacteristic
382C4#1062242511yescharacteristic
383C4#1062247811yescharacteristic
384C4#1062249911yescharacteristic
385C2—21no—
386C2—21no—
387C2—882no—
388C2#1306903311yescharacteristic
389C2#1306905311yescharacteristic
390C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9490
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
1. #13077699C2semidirect
3. #13068609C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
125. #1286D11semidirect
313. C11#9490semidirect

Maximal subgroups

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

subgroupindex
#130776992
#130735262
#130686092
#130670422
#130670402
#130664742
C11×#12862
#949011