Finite Group Databasebeta

← #14807387

Subgroups — #14807387

Order 2816.

1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C2×#10623229C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3#13074367C211yesmaximal, characteristic, complemented
4#13069613C214yesmaximal, complemented
5#13069582C211yesmaximal, characteristic, complemented
6#13069440C211yesmaximal, characteristic, complemented
7#13068961C214yesmaximal, complemented
8#13068385C211yesmaximal, characteristic, complemented
9C2×C11×#490C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C2×#66991C2212yes—
13C22×#4323C2214yes—
14#10623229—24no—
15#10623229—24no—
16C2×#66948—22no—
17C2×#66948C2212yes—
18C2×#66947—22no—
19C2×#66946C2212yes—
20C2×#66927C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C11×#490—24no—
23C2×C11×#102C2214yes—
24C2×C11×#97C2211yescharacteristic
25#10622836—22no—
26#10622835—22no—
27#10622834C2212yes—
28C2×#66885C2214yes—
29C2×(C2×D11)⋊C8C2212yes—
30#10622686—24no—
31#10622549C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622188C2212yes—
34#10622167C2214yes—
35C22×D4×C11—22no—
36C22×D4×C11C2312yes—
37C22×C22⋊D11—22no—
38C22×D44—22no—
39C22×D44—22no—
40C22×D44C2312yes—
41C22×C4×D11—22no—
42C22×C4×D11C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×#127—22no—
45C11×#127—22no—
46C11×#125—22no—
47C11×#125D414yescomplemented
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—24no—
53#66991—44no—
54C2×#4323—28no—
55C2×#4323—28no—
56C2×#4323—44no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4D412yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4D412yes—
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64#66948—216no—
65#66948—24no—
66#66948—24no—
67#66947—216no—
68#66946—24no—
69#66946—24no—
70#66927—22no—
71#66927D414yescomplemented
72#66925—22no—
73#66925—22no—
74C11×#102—28no—
75C11×#97—22no—
76C11⋊#95—22no—
77#66885—44no—
78(C2×D11)⋊C8—24no—
79C4×C11⋊C8—22no—
80#25608—111nomaximal, Sylow
81C24×C11—22no—
82C23×D11—22no—
83C23×D11C2×D411yescharacteristic
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—44no—
89C2×D4×C11—84no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C2×C22⋊D11—44no—
94C2×C22⋊D11—84no—
95C22×Dic11—22no—
96C22×Dic11C2×D412yes—
97C22×Dic11C2×D411yescharacteristic
98C2×D44—28no—
99C2×D44—28no—
100C2×D44—22no—
101C2×D44—24no—
102C2×D44—24no—
103C2×D44—84no—
104C2×D44—84no—
105C2×D44C2×D414yes—
106C2×C4×D11—28no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—84no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4C2×D414yes—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120C22⋊Dic11—44no—
121C22⋊Dic11—84no—
122#4323—416no—
123(C2×D11)⋊C4—28no—
124(C2×D11)⋊C4—28no—
125(C2×D11)⋊C4—24no—
126C4⋊Dic11—24no—
127Dic11⋊C4—24no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8#4114yes—
133C2×#540—111no—
134C2×#493—111no—
135C2×#490D1111yescharacteristic, complemented
136#2619—111no—
137#1999—114no—
138#1991—111no—
139#1961—111no—
140#1879—114no—
141#1750—111no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11C22×D411yescharacteristic
148C22×D11—21no—
149C22×D11—24no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—24no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—44no—
156C22×D11—44no—
157D4×C11—44no—
158D4×C11—44no—
159D4×C11—88no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—44no—
163C2×C4×C11#12014yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4112yes—
167C2×C4×C11H(5,𝔽2)12yes—
168C22⋊D11—88no—
169C2×Dic11—22no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—24no—
174C2×Dic11—42no—
175C2×Dic11—44no—
176D44—28no—
177D44—44no—
178D44—88no—
179D44—88no—
180C4×D11—42no—
181C4×D11—42no—
182C4×D11—88no—
183C8×C11—42no—
184C11⋊C8—24no—
185C22×D8—114no—
186#540—224no—
187#540—224no—
188C2×#127—111no—
189C2×#127C2×D1111yescharacteristic
190C2×#125C2×D1111yescharacteristic
191C2×#123—222no—
192C2×#121—112no—
193C2×#121—112no—
194C2×#121—222no—
195C2×C4×D4—112no—
196C2×#117—111no—
197#493—224no—
198#490—24no—
199C2×#102—114no—
200C2×#102C2×D1114yes—
201C2×C22⋊C8—112no—
202C2×#97C2×D1111yescharacteristic
203C2×C4×C8—111no—
204#394—222no—
205#392—222no—
206#390—112no—
207#382—111no—
208#340—114no—
209#336—112no—
210C22×C11—84no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—84no—
215C22×C11C2×#12011yescharacteristic
216C22×C11#53211yescharacteristic
217C22×C11#53511yescharacteristic
218C22×C11#57614yes—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—44no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—44no—
225C2×D11—44no—
226C2×D11—84no—
227C2×D11—84no—
228C4×C11—24no—
229C4×C11—44no—
230C4×C11#54612yes—
231C4×C11#55012yes—
232Dic11—41no—
233Dic11—42no—
234Dic11—82no—
235C22×D4—22no—
236C22×D4—112no—
237C22×D4—222no—
238C22×D4—222no—
239C22×D4—222no—
240C22×D4C22×D1112yes—
241C23×C4—111no—
242C23×C4—222no—
243C2×D8—228no—
244C2×D8—228no—
245C2×D8—444no—
246C22×C8—112no—
247C22×C8C22×D1112yes—
248#127—22no—
249#127—22no—
250#127—114no—
251#127—222no—
252#125—22no—
253#125C22⋊D1114yescomplemented
254#123—2216no—
255#121—224no—
256#121—2216no—
257#121—224no—
258#121—444no—
259C4×D4—224no—
260C4×D4—224no—
261#117—222no—
262#117—222no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4C22×D1112yes—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—222no—
269C2×C22⋊C4—222no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—224no—
272C2×C42—111no—
273C2×C42C22×D1111yescharacteristic
274#102—28no—
275#102—444no—
276C22⋊C8—224no—
277#97—22no—
278C4×C8—222no—
279#95—222no—
280C2×C11—162no—
281C2×C11#243111yescharacteristic
282C2×C11#300812yes—
283C2×C11#317612yes—
284C2×C11#322012yes—
285D11—81no—
286D11—84no—
287C24—22no—
288C24—111no—
289C24—222no—
290C2×D4—22no—
291C2×D4—24no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—44no—
295C2×D4—84no—
296C2×D4—114no—
297C2×D4—228no—
298C2×D4—228no—
299C2×D4—224no—
300C2×D4—224no—
301C2×D4—222no—
302C2×D4—444no—
303C2×D4—884no—
304C2×D4—884no—
305C2×D4—884no—
306C22×C4—22no—
307C22×C4—112no—
308C22×C4—111no—
309C22×C4—228no—
310C22×C4—221no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—221no—
314C22×C4—222no—
315C22×C4—884no—
316C22×C4D4×D1112yes—
317C22×C4C23×D1111yescharacteristic
318D8—4416no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—114no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—28no—
326C4⋊C4—22no—
327C4⋊C4—224no—
328C4⋊C4—224no—
329C4⋊C4C2×C22⋊D1114yes—
330C22⋊C4—228no—
331C22⋊C4—228no—
332C22⋊C4—224no—
333C22⋊C4—444no—
334C22⋊C4—884no—
335C42—221no—
336C42—221no—
337C42D4×D1112yes—
338C42C2×C22⋊D1112yes—
339C11#2560811yescharacteristic, complemented, Sylow
340C23—44no—
341C23—44no—
342C23—42no—
343C23—42no—
344C23—42no—
345C23—224no—
346C23—224no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—444no—
351C23—444no—
352C23—442no—
353C23—442no—
354C23C2×D4×D1111yescharacteristic
355D4—44no—
356D4—44no—
357D4—88no—
358D4—228no—
359D4—444no—
360D4—888no—
361D4—888no—
362D4—888no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—44no—
366C2×C4—224no—
367C2×C4—222no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—444no—
374C2×C4—442no—
375C2×C4—888no—
376C2×C4#6699014yes—
377C2×C4C2×D4×D1111yescharacteristic
378C2×C4#41×D1112yes—
379C2×C4#6704212yes—
380C2×C4C22×C22⋊D1111yescharacteristic
381C8—42no—
382C8—224no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—84no—
387C22—84no—
388C22—441no—
389C22—444no—
390C22—442no—
391C22—444no—
392C22—442no—
393C22—444no—
394C22—442no—
395C22—884no—
396C22—884no—
397C22#1062319911yescharacteristic
398C22#1062320511yescharacteristic
399C22#1062330514yes—
400C22C2×#6699011yescharacteristic
401C4—24no—
402C4—44no—
403C4—441no—
404C4—442no—
405C4—882no—
406C4#1062320712yes—
407C4#1062336512yes—
408C2—162no—
409C2—881no—
410C2—884no—
411C2#1307223811yescharacteristic
412C2#1307788312yes—
413C2#1307926512yes—
414C2#1307966712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
hypercenterC2×#490D11
hypocenterC11#25608
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623229C2semidirect
2. C2×#10622686C2semidirect
3. #13074367C2semidirect
4. #13069613C2semidirect
5. #13069582C2semidirect
6. #13069440C2semidirect
7. #13068961C2semidirect
8. #13068385C2semidirect
9. C2×C11×#490C2semidirect
47. C11×#125D4semidirect
71. #66927D4semidirect
135. C2×#490D11semidirect
253. #125C22⋊D11semidirect
339. C11#25608semidirect

Maximal subgroups

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

subgroupindex
C2×#106232292
C2×#106226862
#130743672
#130696132
#130695822
#130694402
#130689612
#130683852
C2×C11×#4902
#2560811