Finite Group Databasebeta

← #14737288

Subgroups — #14737288

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079933C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic
3#13079158C211yesmaximal, characteristic, complemented
4#13077359C211yesmaximal, characteristic
5#13068138C212yesmaximal, complemented
6#13068118C212yesmaximal, complemented
7#13068014C212yesmaximal, complemented
8#13067994C212yesmaximal, complemented
9#13067366C211yesmaximal, characteristic, complemented
10#13067274C211yesmaximal, characteristic, complemented
11C2×C11×#333C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66954—21no—
14#10623008C2211yescharacteristic
15#10623001C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622727—22no—
19#10622723—21no—
20#10622701—21no—
21#10622697C2212yes—
22#10622697C2212yes—
23#10622693—22no—
24#10622692—21no—
25#10622692C2212yes—
26#10622691C2212yes—
27#10622581—22no—
28#10622577—21no—
29#10622577—21no—
30#10622538C2211yescharacteristic
31C4×#4318C2211yescharacteristic
32#10622464—21no—
33#10622461—21no—
34#10622455C2212yes—
35#10622454C2212yes—
36#10622451C2212yes—
37#10622449—22no—
38#10622447C2212yes—
39C11×#333C2212yes—
40C11×#333C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622119C2211yescharacteristic
44#10622119C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58#66983—21no—
59#66983D412yes—
60#66979—21no—
61#66977—21no—
62#66977—21no—
63C2×#4318D411yescharacteristic
64C2×#4318D411yescharacteristic
65C2×#4314—22no—
66#66954—44no—
67C2×#4313—22no—
68C2×C8×D11—22no—
69#66928—21no—
70#66927D411yescharacteristic
71C4×D44—21no—
72C4×D44C2312yes—
73#66923—21no—
74#66922D411yescharacteristic
75#66922C2311yescharacteristic
76#66922C2311yescharacteristic
77C4×Dic22—21no—
78C4×Dic22—21no—
79C11×C4⋊C8—21no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2312yes—
82C11×C4⋊C8C2311yescharacteristic
83C11×C4⋊C8C2311yescharacteristic
84C22⋊(C11⋊C8)—21no—
85#66885—22no—
86(C2×D11)⋊C8—22no—
87(C2×D11)⋊C8—22no—
88#66881—22no—
89#66880—22no—
90#66873—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66872—22no—
95#66872—22no—
96#66871—22no—
97#66871—22no—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867D412yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103#19233—111nomaximal, Sylow
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—82no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×C22⋊D11—22no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44C2×D412yes—
117C2×C4×D11—22no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—42no—
125C2×C8×C11—81no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C22⋊Dic11—41no—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11C2×D412yes—
143Dic11⋊C4—41no—
144Dic11⋊C4—41no—
145C4×Dic11—41no—
146#4318—22no—
147#4318SD1614yescomplemented
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×D412yes—
151C2×C11⋊C8C2×D412yes—
152#4314—82no—
153#4313—44no—
154C8×D11—44no—
155#3246—111no—
156#3227—111no—
157#3165—111no—
158#2935—111no—
159#1695—112no—
160#1691—112no—
161#1675—112no—
162#1671—112no—
163#1565—111no—
164#1542—111no—
165C2×#333D1111yescharacteristic, complemented
166C23×C11#12111yescharacteristic
167C22×D11—22no—
168Q8×C11—82no—
169Q8×C11—82no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—82no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C2×SD1612yes—
179C2×C4×C11#13712yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—44no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187D44—22no—
188D44—22no—
189D44—42no—
190D44—81no—
191C4×D11—42no—
192C4×D11—42no—
193Dic22—42no—
194Dic22—41no—
195Dic22—41no—
196Dic22—81no—
197C8×C11—41no—
198C8×C11—41no—
199C8×C11—42no—
200C11⋊C8—22no—
201C11⋊C8—41no—
202C11⋊C8—41no—
203C11⋊C8C2×SD1614yes—
204C2×#131—221no—
205#533—111no—
206#532—111no—
207C2×C4⋊Q8C2×D1111yescharacteristic
208#501—222no—
209#500—112no—
210#498—112no—
211#498—221no—
212#486—221no—
213#481—222no—
214#476—112no—
215#476—112no—
216#476—112no—
217#475—221no—
218#465—222no—
219#461—112no—
220#460—221no—
221#436—112no—
222#435—222no—
223C8×D4—112no—
224#431—111no—
225#428—221no—
226#428—221no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×C4⋊C8C2×D1111yescharacteristic
229#408—221no—
230C4×M16—111no—
231#335—112no—
232#334—112no—
233#333—111no—
234#333—111no—
235#333C2×D1112yes—
236#333C2×D1112yes—
237#332—111no—
238#332—111no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11#46112yes—
242C22×C11C2×#12111yescharacteristic
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—82no—
250C4×C11#46112yes—
251C4×C11C22×SD1611yescharacteristic
252C4×C11C2×#13711yescharacteristic
253C4×C11#57711yescharacteristic
254C4×C11#57811yescharacteristic
255Dic11—42no—
256Dic11—81no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—21no—
260C2×SD16—222no—
261#131—444no—
262C2×M16—111no—
263C2×M16—111no—
264C2×M16—222no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—222no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—111no—
272C4⋊Q8—111no—
273C4⋊Q8—111no—
274C4⋊Q8C22×D1112yes—
275#127—111no—
276#125—221no—
277#124—221no—
278C22⋊Q8—221no—
279C22⋊Q8—221no—
280#121—112no—
281#121—221no—
282C4×Q8—221no—
283C4×Q8—221no—
284C4×D4—112no—
285C4×D4—221no—
286#117—221no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C42C22×D1111yescharacteristic
290#107—222no—
291#107—222no—
292#106—222no—
293#106—222no—
294#106—222no—
295#106—222no—
296#106—222no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—111no—
300C4⋊C8—111no—
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303C4⋊C8C22×D1112yes—
304#103—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—222no—
309C22⋊C8—222no—
310C22⋊C8—221no—
311#97—112no—
312C4×C8—112no—
313C4×C8—221no—
314C2×C11—22no—
315C2×C11C2×#46111yescharacteristic
316C2×C11#306311yescharacteristic
317C2×C11#306811yescharacteristic
318D11—82no—
319#41—442no—
320#41—442no—
321C2×Q8—22no—
322C2×Q8—41no—
323C2×Q8—82no—
324C2×Q8—221no—
325C2×Q8—221no—
326C2×Q8—221no—
327C2×D4—112no—
328C2×D4—222no—
329C2×D4—221no—
330C2×D4—221no—
331C22×C4—41no—
332C22×C4—222no—
333C22×C4#433911yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336SD16—882no—
337M16—114no—
338M16—222no—
339M16—444no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—81no—
345C2×C8—112no—
346C2×C8—112no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—444no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—112no—
355C4⋊C4—221no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C22⋊C4—222no—
363C22⋊C4—222no—
364C22⋊C4—441no—
365C42—441no—
366C42#433911yescharacteristic
367C42D4×D1111yescharacteristic
368C42D4×D1111yescharacteristic
369C42C23×D1111yescharacteristic
370C11#1923311yescharacteristic, complemented, Sylow
371C23—222no—
372C23#6693711yescharacteristic
373Q8—82no—
374Q8—82no—
375Q8—442no—
376Q8—441no—
377Q8—441no—
378Q8—881no—
379D4—222no—
380D4—222no—
381D4—444no—
382D4—442no—
383D4—881no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—222no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4#6693711yescharacteristic
395C2×C4#6693711yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4SD16×D1112yes—
398C2×C4#6697112yes—
399C2×C4C2×#433911yescharacteristic
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×D4×D1111yescharacteristic
402C8—41no—
403C8—41no—
404C8—42no—
405C8—114no—
406C8—222no—
407C8—441no—
408C8—441no—
409C22—21no—
410C22—21no—
411C22—442no—
412C22—442no—
413C22—442no—
414C22#1062243112yes—
415C22C2×#6693711yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—82no—
420C4—442no—
421C4—881no—
422C4—881no—
423C4#1062243112yes—
424C4C2×SD16×D1111yescharacteristic
425C4#1062329311yescharacteristic
426C4C2×#6697111yescharacteristic
427C4#1062329711yescharacteristic
428C2—22no—
429C2—882no—
430C2C2×#1062243111yescharacteristic
431C2#1307830511yescharacteristic
432C2#1307834311yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#333C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#333D11
hypocenterC11#19233
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #13079158C2semidirect
5. #13068138C2semidirect
6. #13068118C2semidirect
7. #13068014C2semidirect
8. #13067994C2semidirect
9. #13067366C2semidirect
10. #13067274C2semidirect
11. C2×C11×#333C2semidirect
147. #4318SD16semidirect
165. C2×#333D11semidirect
370. C11#19233semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130797442
#130791582
#130773592
#130681382
#130681182
#130680142
#130679942
#130673662
#130672742
C2×C11×#3332
#1923311