Finite Group Databasebeta

← #14737099

Subgroups — #14737099

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13078941C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068172C212yesmaximal, complemented
5#13068158C212yesmaximal, complemented
6#13068076C212yesmaximal, complemented
7#13068062C212yesmaximal, complemented
8C2×#10622117C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic
11C11×#3249C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#477—21no—
16C11×#477C2212yes—
17C11×#467—22no—
18C11×#462—21no—
19C11×#462C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21#10622706C2211yescharacteristic
22#10622706C2211yescharacteristic
23#10622701C2211yescharacteristic
24#10622701C2211yescharacteristic
25#10622697—21no—
26#10622696—21no—
27#10622681—21no—
28#10622681—21no—
29#10622661—22no—
30#10622640C2212yes—
31#10622637—21no—
32#10622637C2212yes—
33Q8×C11⋊C8—21no—
34Q8×C11⋊C8C2212yes—
35#10622633C2212yes—
36#10622615—21no—
37#10622615—21no—
38#10622612—21no—
39#10622610—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622184C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622117C2212yes—
48#10622117C2212yes—
49C2×#4339—21no—
50C2×C11×Q16—22no—
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125—21no—
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8D412yes—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11C2312yes—
66C11×#117—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—22no—
70#66983—21no—
71#66983—21no—
72C2×#4318—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⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#103—22no—
86#66899—22no—
87#66874—21no—
88#66874—21no—
89#66874—21no—
90#66874—21no—
91#66873—22no—
92#66873—21no—
93#66873—21no—
94#66873—21no—
95#66873—21no—
96#66872—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2312yes—
103#66867—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19217—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118#4339—42no—
119#4339—42no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×C4×D11—41no—
124C2×Dic22—21no—
125C11×Q16—82no—
126C2×C8×C11—22no—
127C2×C8×C11—81no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C42×C11—22no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—82no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153#4318—42no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—81no—
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163#3249D1111yescharacteristic, complemented
164#3246—111no—
165#3131—111no—
166#2960—111no—
167#1700—112no—
168#1698—112no—
169#1684—112no—
170#1682—112no—
171C2×#335—111no—
172#1550—111no—
173#1547—111no—
174C23×C11#12111yescharacteristic
175C22×D11—41no—
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—81no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#13512yes—
193C2×C4×C11#13712yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—82no—
198C2×Dic11—41no—
199D44—41no—
200D44—41no—
201D44—41no—
202D44—41no—
203D44—81no—
204C4×D11—82no—
205Dic22—41no—
206Dic22—41no—
207C8×C11—42no—
208C11⋊C8—21no—
209C11⋊C8—21no—
210C11⋊C8—21no—
211C11⋊C8—21no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214#533C2×D1111yescharacteristic
215#533C2×D1111yescharacteristic
216#532—111no—
217#488—221no—
218#488—221no—
219#487—111no—
220#487—111no—
221#486—111no—
222#486—111no—
223#477—21no—
224#477C2×D1112yes—
225#476—221no—
226#475—112no—
227#467—22no—
228#465—222no—
229#462—21no—
230#462C2×D1112yes—
231#461—221no—
232#460—112no—
233#446—112no—
234#446—221no—
235C8×Q8—112no—
236C8×Q8—221no—
237#424—221no—
238#423—111no—
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241#416—221no—
242#416—221no—
243#405—221no—
244C2×C4×C8—111no—
245#335—112no—
246#335—112no—
247#333—112no—
248#332—112no—
249#332—112no—
250#331—112no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11#46412yes—
254C22×C11C2×#12111yescharacteristic
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11#46412yes—
266C4×C11C2×#13511yescharacteristic
267C4×C11C2×#13711yescharacteristic
268C4×C11#57611yescharacteristic
269C4×C11#57811yescharacteristic
270Dic11—81no—
271C2×#41—221no—
272C2×Q16—22no—
273C2×SD16—222no—
274C2×M16—221no—
275C22×C8—21no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8—221no—
279C4⋊Q8—111no—
280C4⋊Q8C22⋊D1111yescharacteristic
281C4⋊Q8C22⋊D1111yescharacteristic
282C4⋊Q8C22×D1111yescharacteristic
283C4⋊Q8C22×D1111yescharacteristic
284#127—111no—
285#125—21no—
286#125—21no—
287#124—221no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8C22⋊D1112yes—
292#121—221no—
293#121—221no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8C22×D1112yes—
298C4×D4—221no—
299C4×D4—221no—
300#117—21no—
301#117—21no—
302C2×C42C22×D1111yescharacteristic
303#107—22no—
304#106—222no—
305C4⋊C8—21no—
306C4⋊C8—112no—
307C4⋊C8—112no—
308C4⋊C8—222no—
309C4⋊C8—222no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8C22×D1112yes—
313#103—22no—
314#103—22no—
315#103—221no—
316#103—221no—
317#103—221no—
318#103—221no—
319#103—222no—
320#102—221no—
321#102—221no—
322#102—221no—
323#102—221no—
324#102—222no—
325#97—222no—
326C4×C8—111no—
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—111no—
330C4×C8—222no—
331C2×C11—22no—
332C2×C11C2×#46411yescharacteristic
333C2×C11#306111yescharacteristic
334C2×C11#306711yescharacteristic
335D11—161no—
336#41—442no—
337#41—442no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—221no—
342C2×Q8C2×C22⋊D1112yes—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349C22×C4#434111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—82no—
352SD16—882no—
353M16—442no—
354C2×C8—22no—
355C2×C8—81no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—881no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4C2×C22⋊D1112yes—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C42—22no—
384C42—41no—
385C42D4×D1111yescharacteristic
386C42#434111yescharacteristic
387C42C2×C22⋊D1111yescharacteristic
388C42C23×D1111yescharacteristic
389C11#1921711yescharacteristic, complemented, Sylow
390C23—441no—
391C23#6699211yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—81no—
398Q8—441no—
399Q8—441no—
400D4—441no—
401D4—441no—
402D4—441no—
403D4—441no—
404D4—881no—
405D4—882no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4#6697112yes—
416C2×C4#6697212yes—
417C2×C4#6699211yescharacteristic
418C2×C4#6699211yescharacteristic
419C2×C4#6699211yescharacteristic
420C2×C4C2×D4×D1111yescharacteristic
421C2×C4C2×#434111yescharacteristic
422C2×C4C22×C22⋊D1111yescharacteristic
423C8—42no—
424C8—221no—
425C8—221no—
426C8—221no—
427C8—221no—
428C8—442no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22—881no—
433C22—881no—
434C22—881no—
435C22#1062279812yes—
436C22C2×#6699211yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—881no—
445C4#1062279812yes—
446C4C2×#6697111yescharacteristic
447C4C2×#6697211yescharacteristic
448C4#1062336611yescharacteristic
449C4#1062336911yescharacteristic
450C2—22no—
451C2—1761no—
452C2C2×#1062279811yescharacteristic
453C2#1307828311yescharacteristic
454C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3249C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3249D11
hypocenterC11#19217
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #13077551C2semidirect
4. #13068172C2semidirect
5. #13068158C2semidirect
6. #13068076C2semidirect
7. #13068062C2semidirect
8. C2×#10622117C2semidirect
9. #13067306C2semidirect
11. C11×#3249C2semidirect
163. #3249D11semidirect
389. C11#19217semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130789412
#130775512
#130681722
#130681582
#130680762
#130680622
C2×#106221172
#130673062
#130672912
C11×#32492
#1921711