Finite Group Databasebeta

← #14737640

Subgroups — #14737640

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic, complemented
3C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068034C212yesmaximal, complemented
5#13068030C212yesmaximal, complemented
6#13068018C212yesmaximal, complemented
7#13067974C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067312C211yesmaximal, characteristic, complemented
10#13067311C211yesmaximal, characteristic, complemented
11C11×#3112C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#480—21no—
16C11×#477C2212yes—
17C11×#460C2212yes—
18C11×#448—21no—
19C11×#440—22no—
20C11×#432C2211yescharacteristic
21#10622840—21no—
22#10622701C2211yescharacteristic
23#10622691C2211yescharacteristic
24#10622686C2211yescharacteristic
25#10622683C2211yescharacteristic
26#10622651—21no—
27#10622651—21no—
28#10622640C2212yes—
29#10622639—22no—
30Q8×C11⋊C8—21no—
31Q8×C11⋊C8—21no—
32Q8×C11⋊C8C2212yes—
33Q8×C11⋊C8C2212yes—
34#10622634C2212yes—
35C4×#4323—21no—
36C4×#4323—21no—
37#10622580—21no—
38#10622539C2211yescharacteristic
39C2×C4⋊(C11⋊C8)—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8—21no—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622184C2212yes—
44#10622182C2212yes—
45#10622123C2212yes—
46#10622119C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C2×#4339—21no—
52C2×C11×SD16—22no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127C2311yescharacteristic
55C11×#124—21no—
56C11×#121—21no—
57C11×#121—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11D412yes—
61C4×Q8×C11C2312yes—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4325—22no—
69C2×#4323—21no—
70C2×#4323—21no—
71#66983—21no—
72#66983—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8D411yescharacteristic
75C22×C11⋊C8D411yescharacteristic
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922C2311yescharacteristic
81C11×#107—22no—
82C11×C4⋊C8C2312yes—
83C11×#103—22no—
84C11×#102—22no—
85C11×C22⋊C8—21no—
86C11×#97—21no—
87#66899—22no—
88#66896—21no—
89#66896—21no—
90C22⋊(C11⋊C8)—21no—
91#66873—22no—
92#66873—21no—
93#66873—21no—
94#66871—22no—
95#66871—21no—
96#66871—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#66867—21no—
103C4×C11⋊C8—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19264—111nomaximal, Sylow
110C11×#41—82no—
111C2×Q8×C11—24no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—41no—
126#4339—82no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C11×SD16—44no—
133C2×C8×C11—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—44no—
149#4323—42no—
150#4323—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8—42no—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164#3169—111no—
165#3112—111no—
166#3112D1111yescharacteristic, complemented
167C2×C8×Q8—111no—
168#1678—112no—
169#1678—112no—
170#1676—112no—
171#1668—112no—
172#1568—111no—
173#1551—111no—
174#1551—111no—
175C23×C11—41no—
176C23×C11#12111yescharacteristic
177C22×D11—41no—
178Q8×C11—24no—
179Q8×C11—22no—
180Q8×C11—81no—
181Q8×C11#13514yes—
182D4×C11—42no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—81no—
186D4×C11—82no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—82no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C22⋊D11—82no—
204C2×Dic11—41no—
205D44—42no—
206D44—41no—
207D44—41no—
208D44—81no—
209C4×D11—82no—
210Dic22—81no—
211C8×C11—42no—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C11⋊C8—21no—
215C11⋊C8—42no—
216C11⋊C8—42no—
217C11⋊C8#13712yes—
218#532—111no—
219#532C2×D1111yescharacteristic
220C2×C4×Q8C2×D1111yescharacteristic
221#500—111no—
222#493—111no—
223#486—111no—
224#486—111no—
225#480—21no—
226#480—221no—
227#477—112no—
228#477C2×D1112yes—
229#466—221no—
230#466—221no—
231#460—112no—
232#460C2×D1112yes—
233#448—21no—
234#448—221no—
235C8×Q8—112no—
236C8×Q8—112no—
237C8×Q8—221no—
238C8×Q8—221no—
239#440—22no—
240#440—222no—
241C4×D8—221no—
242C4×D8—221no—
243#432—111no—
244#432C2×D1111yescharacteristic
245C2×C4⋊C8—111no—
246C2×C4⋊C8—221no—
247C2×C4×C8—111no—
248C2×C4×C8—221no—
249#335—112no—
250#334—112no—
251#333—112no—
252#333—112no—
253#331—112no—
254#331—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11#47212yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—21no—
266C4×C11—24no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11C2×#13512yes—
273C4×C11C2×#13711yescharacteristic
274C4×C11#57511yescharacteristic
275Dic11—81no—
276C2×#41—21no—
277C2×#41—221no—
278C22×Q8C22⋊D1111yescharacteristic
279C2×SD16—22no—
280C2×SD16—222no—
281C2×D8—221no—
282C2×D8—221no—
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—221no—
286C4⋊Q8—111no—
287C4⋊Q8C22×D1111yescharacteristic
288#127—111no—
289#127C22×D1111yescharacteristic
290#124—21no—
291#124—221no—
292#121—21no—
293#121—21no—
294#121—221no—
295#121—221no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C22⋊D1112yes—
299C4×Q8C22×D1112yes—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—221no—
303C4×D4—221no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C22⋊D1111yescharacteristic
306C2×C42—21no—
307C2×C42C22×D1111yescharacteristic
308#107—22no—
309#107—221no—
310#107—221no—
311#107—222no—
312C4⋊C8—112no—
313C4⋊C8—112no—
314C4⋊C8—222no—
315C4⋊C8—222no—
316C4⋊C8—221no—
317C4⋊C8C22×D1112yes—
318#103—22no—
319#103—222no—
320#102—22no—
321#102—221no—
322#102—221no—
323#102—221no—
324#102—221no—
325#102—222no—
326C22⋊C8—21no—
327C22⋊C8—221no—
328#97—21no—
329#97—221no—
330C4×C8—111no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—222no—
335C4×C8—222no—
336C2×C11—22no—
337C2×C11—161no—
338C2×C11#303711yescharacteristic
339C2×C11#305011yescharacteristic
340C2×C11C2×#47211yescharacteristic
341D11—161no—
342#41—82no—
343#41—882no—
344C2×Q8—24no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—221no—
348C2×Q8C2×C22⋊D1112yes—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—441no—
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364SD16—44no—
365SD16—444no—
366D8—442no—
367D8—442no—
368C2×C8—22no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—441no—
377C2×C8—442no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—22no—
391C42—22no—
392C42D4×D1111yescharacteristic
393C42#434111yescharacteristic
394C42C2×C22⋊D1111yescharacteristic
395C42C23×D1111yescharacteristic
396C11#1926411yescharacteristic, complemented, Sylow
397C23—41no—
398C23—441no—
399C23#6699211yescharacteristic
400Q8—24no—
401Q8—22no—
402Q8—81no—
403Q8—881no—
404Q8#6700314yes—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—81no—
409D4—82no—
410D4—441no—
411D4—441no—
412D4—442no—
413D4—881no—
414D4—882no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4#6699211yescharacteristic
428C2×C4#6699211yescharacteristic
429C2×C4#6699211yescharacteristic
430C2×C4C2×D4×D1111yescharacteristic
431C2×C4C2×#434111yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C8—42no—
434C8—112no—
435C8—221no—
436C8—221no—
437C8—221no—
438C8—442no—
439C8—442no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22#1062281212yes—
449C22C2×#6699211yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—24no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—881no—
458C4D11×#13711yescharacteristic
459C4#1062330811yescharacteristic
460C4C2×#6700312yes—
461C2—22no—
462C2—161no—
463C2—1761no—
464C2#1307808511yescharacteristic
465C2#1307819411yescharacteristic
466C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3112C2
socleC22×C11C2×#121
prime radical#13079191C2
hypercenter#3112D11
hypocenterC11#19264
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
2. #13078738C2semidirect
3. C2×Q8×C11⋊C8C2semidirect
4. #13068034C2semidirect
5. #13068030C2semidirect
6. #13068018C2semidirect
7. #13067974C2semidirect
8. #13067377C2semidirect
9. #13067312C2semidirect
10. #13067311C2semidirect
11. C11×#3112C2semidirect
166. #3112D11semidirect
396. C11#19264semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130787382
C2×Q8×C11⋊C82
#130680342
#130680302
#130680182
#130679742
#130673772
#130673122
#130673112
C11×#31122
#1926411