Finite Group Databasebeta

← #14807385

Subgroups — #14807385

Order 2816.

1280 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3C2×#10622684C211yesmaximal, characteristic, complemented
4#13069612C214yesmaximal, complemented
5#13069580C211yesmaximal, characteristic, complemented
6#13069439C211yesmaximal, characteristic, complemented
7#13068967C214yesmaximal, complemented
8#13068382C211yesmaximal, characteristic, complemented
9C11×#2619C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C2×C11×#121C2212yes—
12C2×C11×#117C2211yescharacteristic
13C22×#4323C2214yes—
14C2×#66983C2212yes—
15#10623066—24no—
16#10623066—24no—
17C2×#66947—22no—
18C2×#66937—22no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2212yes—
21C2×#66923C2211yescharacteristic
22C11×#394—22no—
23C11×#392—22no—
24C11×#390C2212yes—
25C11×#382C2211yescharacteristic
26C2×#66896C2214yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622686—24no—
29#10622684—24no—
30C2×#66873C2214yes—
31C2×#66867C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622167C2214yes—
34#10622162C2212yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C22×D44—22no—
41C22×D44C2312yes—
42C22×C4×D11—22no—
43C11×#127—22no—
44C11×#127—22no—
45C11×#121—44no—
46C11×#117—22no—
47C11×#117—22no—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×#4323—28no—
56C2×#4323—28no—
57C2×#4323—44no—
58#66983—24no—
59#66983—24no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2312yes—
66#66947—216no—
67#66937—216no—
68#66927—22no—
69#66927D414yescomplemented
70C4×D44—24no—
71C4×D44—24no—
72#66923—22no—
73#66923D414yescomplemented
74C11×#95—22no—
75#66896—28no—
76C22⋊(C11⋊C8)—24no—
77#66873—44no—
78#66867—22no—
79C4×C11⋊C8—22no—
80#25608—111nomaximal, Sylow
81C24×C11—22no—
82C24×C11C2×D411yescharacteristic
83C23×D11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—44no—
89C2×D4×C11—44no—
90C2×D4×C11—84no—
91C2×D4×C11—84no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C2×C22⋊D11—28no—
102C2×C22⋊D11—84no—
103C22×Dic11—22no—
104C2×D44—28no—
105C2×D44—22no—
106C2×D44—24no—
107C2×D44—24no—
108C2×D44—84no—
109C2×D44C2×D414yes—
110C2×C4×D11—28no—
111C2×C4×D11—84no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—44no—
116C11×C22⋊C4—84no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11C2×D412yes—
120C42×C11C2×D412yes—
121#4323—416no—
122(C2×D11)⋊C4—28no—
123(C2×D11)⋊C4—28no—
124C4⋊Dic11—22no—
125C4⋊Dic11C2×D414yes—
126Dic11⋊C4—28no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8#4114yes—
133C2×#540—111no—
134C2×#493—111no—
135C2×#490—111no—
136#2619D1111yescharacteristic, complemented
137#1999—114no—
138#1991—111no—
139#1961—111no—
140#1879—114no—
141#1750—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—24no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11C22×D411yescharacteristic
152C22×D11—24no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—44no—
156C22×D11—44no—
157D4×C11—44no—
158D4×C11—44no—
159D4×C11—88no—
160D4×C11—88no—
161C2×C4×C11—24no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—24no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11#12014yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4112yes—
175C2×C4×C11H(5,𝔽2)12yes—
176C22⋊D11—88no—
177C2×Dic11—24no—
178C2×Dic11—44no—
179D44—28no—
180D44—44no—
181D44—88no—
182C4×D11—88no—
183C11⋊C8—24no—
184C11⋊C8—42no—
185C22×D8—114no—
186#540—224no—
187#540—224no—
188C2×#127—111no—
189C2×#127C2×D1111yescharacteristic
190C2×#125—111no—
191C2×#123—222no—
192C2×#121—112no—
193C2×#121—222no—
194C2×#121C2×D1112yes—
195C2×C4×D4—112no—
196C2×#117C2×D1111yescharacteristic
197#493—224no—
198#490—224no—
199C2×#102—114no—
200C2×#102—114no—
201C2×C22⋊C8—112no—
202C2×#97—111no—
203C2×C4×C8—111no—
204#394—22no—
205#392—22no—
206#390C2×D1112yes—
207#382C2×D1111yescharacteristic
208#340—114no—
209#336—112no—
210C22×C11—42no—
211C22×C11—41no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—84no—
215C22×C11—82no—
216C22×C11—82no—
217C22×C11—82no—
218C22×C11—84no—
219C22×C11C2×#12011yescharacteristic
220C22×C11#53211yescharacteristic
221C22×C11#53511yescharacteristic
222C22×C11#57614yes—
223C2×D11—44no—
224C2×D11—44no—
225C2×D11—44no—
226C2×D11—84no—
227C2×D11—84no—
228C4×C11—24no—
229C4×C11—41no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11#54612yes—
233C4×C11#55012yes—
234Dic11—44no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—112no—
238C22×D4—222no—
239C22×D4—222no—
240C22×D4C22×D1112yes—
241C23×C4—222no—
242C23×C4C22×D1111yescharacteristic
243C2×D8—228no—
244C2×D8—228no—
245C2×D8—444no—
246C22×C8—112no—
247C22×C8—112no—
248#127—22no—
249#127—22no—
250#127—114no—
251#127—222no—
252#125—114no—
253#125—222no—
254#123—2216no—
255#121—44no—
256#121—2216no—
257#121—224no—
258#121—224no—
259C4×D4—224no—
260C4×D4—224no—
261#117—22no—
262#117—22no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4C22⋊D1112yes—
266C2×C4⋊C4C22×D1112yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—222no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4C22⋊D1112yes—
272C2×C42C22×D1111yescharacteristic
273C2×C42C22×D1111yescharacteristic
274#102—228no—
275#102—444no—
276C22⋊C8—224no—
277#97—222no—
278C4×C8—222no—
279#95—22no—
280C2×C11—81no—
281C2×C11—162no—
282C2×C11#243111yescharacteristic
283C2×C11#300812yes—
284C2×C11#317612yes—
285C2×C11#322012yes—
286D11—84no—
287C24—22no—
288C24—222no—
289C24C2×C22⋊D1111yescharacteristic
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—24no—
293C2×D4—24no—
294C2×D4—44no—
295C2×D4—44no—
296C2×D4—84no—
297C2×D4—84no—
298C2×D4—114no—
299C2×D4—228no—
300C2×D4—228no—
301C2×D4—222no—
302C2×D4—224no—
303C2×D4—224no—
304C2×D4—884no—
305C2×D4—884no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—228no—
312C22×C4—222no—
313C22×C4—884no—
314C22×C4C2×C22⋊D1112yes—
315C22×C4C2×C22⋊D1111yescharacteristic
316C22×C4C2×C22⋊D1112yes—
317C22×C4C23×D1111yescharacteristic
318D8—4416no—
319C2×C8—114no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—114no—
328C4⋊C4—228no—
329C4⋊C4—222no—
330C22⋊C4—24no—
331C22⋊C4—44no—
332C22⋊C4—84no—
333C22⋊C4—228no—
334C22⋊C4—228no—
335C42—21no—
336C42—21no—
337C42D4×D1112yes—
338C42D4×D1112yes—
339C11#2560811yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—21no—
343C23—24no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—44no—
348C23—44no—
349C23—224no—
350C23—442no—
351C23—442no—
352C23—444no—
353C23—444no—
354C23C22×C22⋊D1111yescharacteristic
355D4—44no—
356D4—44no—
357D4—88no—
358D4—88no—
359D4—228no—
360D4—444no—
361D4—888no—
362D4—888no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—24no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—224no—
374C2×C4—444no—
375C2×C4—888no—
376C2×C4#6699014yes—
377C2×C4C2×D4×D1111yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C2×C4#6703712yes—
380C2×C4#41×D1112yes—
381C8—224no—
382C8—442no—
383C22—41no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—82no—
388C22—82no—
389C22—82no—
390C22—84no—
391C22—84no—
392C22—444no—
393C22—444no—
394C22—444no—
395C22—884no—
396C22—884no—
397C22C2×#6699011yescharacteristic
398C22#1062333611yescharacteristic
399C22#1062336311yescharacteristic
400C22#1062336614yes—
401C4—24no—
402C4—41no—
403C4—42no—
404C4—82no—
405C4—444no—
406C4#1062313012yes—
407C4#1062314312yes—
408C2—81no—
409C2—162no—
410C2—884no—
411C2#1307223611yescharacteristic
412C2#1307788212yes—
413C2#1307926012yes—
414C2#1307966612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2619C2
socleC23×C11C22×D4
hypercenter#2619D11
hypocenterC11#25608
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. C2×#10623066C2semidirect
2. C2×#10622686C2semidirect
3. C2×#10622684C2semidirect
4. #13069612C2semidirect
5. #13069580C2semidirect
6. #13069439C2semidirect
7. #13068967C2semidirect
8. #13068382C2semidirect
9. C11×#2619C2semidirect
69. #66927D4semidirect
73. #66923D4semidirect
136. #2619D11semidirect
339. C11#25608semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
C2×#106226862
C2×#106226842
#130696122
#130695802
#130694392
#130689672
#130683822
C11×#26192
#2560811