Finite Group Databasebeta

← #14737264

Subgroups — #14737264

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068103C212yesmaximal, complemented
5#13068083C212yesmaximal, complemented
6#13067979C212yesmaximal, complemented
7#13067959C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3226C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67001—21no—
15C2×#66995—21no—
16C2×#66995—21no—
17#10623008C2211yescharacteristic
18C11×#500—21no—
19C11×#486—21no—
20C11×#480—22no—
21C11×#474C2212yes—
22C11×#474C2212yes—
23C11×#431C2211yescharacteristic
24#10622847—21no—
25#10622705C2212yes—
26#10622700—21no—
27#10622699—22no—
28#10622698C2212yes—
29#10622685—21no—
30#10622651—22no—
31#10622628C2212yes—
32#10622625C2212yes—
33#10622624—22no—
34D4×C11⋊C8C2212yes—
35#10622620C2212yes—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2212yes—
40#10622185C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622123C2211yescharacteristic
44#10622123C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×#127D411yescharacteristic
56C11×#124—21no—
57C11×#121—21no—
58C11×#121D412yes—
59C4×D4×C11—21no—
60C4×D4×C11C2312yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64#67001—44no—
65C2×#4326—22no—
66C2×#4326—22no—
67#66995—44no—
68#66995—44no—
69C2×#4325—22no—
70C2×#4325—22no—
71C2×#4323—22no—
72#66983—21no—
73#66983—21no—
74C2×#4318—22no—
75C2×#4318D411yescharacteristic
76C2×#4318D411yescharacteristic
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79C22×C11⋊C8—22no—
80#66928—21no—
81#66927C2311yescharacteristic
82C4×D44—21no—
83C4×D44—21no—
84#66922C2311yescharacteristic
85C11×#107—22no—
86C11×#107—22no—
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89C11×#102—22no—
90C11×#102—22no—
91C11×C22⋊C8—21no—
92C4×C8×C11—21no—
93#66896—22no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66873—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103#66867D412yes—
104C4×C11⋊C8C2312yes—
105#19231—111nomaximal, Sylow
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—41no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4326—44no—
145#4326—44no—
146#4325—44no—
147#4325—44no—
148#4323—82no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153#4318—22no—
154#4318—44no—
155#4318D814yescomplemented
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—44no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—81no—
162C2×C11⋊C8C2×D412yes—
163C2×C11⋊C8C2×D412yes—
164#3245—111no—
165#3226D1111yescharacteristic, complemented
166#3152—111no—
167#2935—111no—
168#1689—112no—
169#1685—112no—
170#1669—112no—
171#1665—112no—
172#1565—111no—
173#1540—111no—
174C2×#332—111no—
175C23×C11—22no—
176C23×C11#12111yescharacteristic
177C22×D11—41no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—82no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—44no—
185D4×C11—42no—
186D4×C11—81no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—82no—
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11C2×D812yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C22⋊D11—82no—
204C2×Dic11—41no—
205D44—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—81no—
210C4×D11—82no—
211Dic22—41no—
212Dic22—41no—
213C8×C11—41no—
214C8×C11—41no—
215C11⋊C8—22no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C11⋊C8—42no—
219C11⋊C8C2×D814yes—
220C2×#137—221no—
221C2×#137—221no—
222C2×#131—221no—
223#532—111no—
224#532C2×D1111yescharacteristic
225C2×C4⋊Q8C2×D1111yescharacteristic
226#500—21no—
227#497—222no—
228#494—112no—
229#492—112no—
230#486—21no—
231#480—22no—
232#474—112no—
233#474—221no—
234#474C2×D1112yes—
235#474C2×D1112yes—
236#466—222no—
237#459—112no—
238#459—221no—
239#436—112no—
240#435—222no—
241C8×D4—112no—
242#431C2×D1111yescharacteristic
243C2×C4⋊C8—111no—
244C2×C4⋊C8—111no—
245#408—221no—
246C4×M16—111no—
247#335—112no—
248#334—112no—
249#332—112no—
250#332—112no—
251#332—111no—
252#332—111no—
253#331—111no—
254#331—111no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11#45912yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11#45912yes—
271C4×C11C22×D811yescharacteristic
272C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11#57711yescharacteristic
274C4×C11#57811yescharacteristic
275Dic11—81no—
276C2×#41—21no—
277C2×#41—221no—
278C22×Q8—21no—
279#137—444no—
280#137—444no—
281C2×Q16—222no—
282C2×Q16—222no—
283C2×SD16—222no—
284C2×SD16—222no—
285C2×D8—222no—
286#131—444no—
287C2×M16—111no—
288C2×M16—111no—
289C2×M16—222no—
290C22×C8—222no—
291C22×C8—221no—
292C22×C8—221no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—111no—
297C4⋊Q8C22⋊D1111yescharacteristic
298C4⋊Q8C22×D1112yes—
299#127—111no—
300#127C22⋊D1111yescharacteristic
301#124—21no—
302#124—221no—
303#121—21no—
304#121—221no—
305#121—221no—
306#121C22⋊D1112yes—
307C4×D4—21no—
308C4×D4—221no—
309C4×D4—221no—
310C4×D4C22×D1112yes—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C42C22×D1111yescharacteristic
314#107—22no—
315#107—22no—
316#107—222no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—112no—
320C4⋊C8—221no—
321C4⋊C8—221no—
322C4⋊C8C22×D1111yescharacteristic
323C4⋊C8C22×D1111yescharacteristic
324#102—22no—
325#102—22no—
326#102—222no—
327#102—222no—
328C22⋊C8—21no—
329C22⋊C8—222no—
330C22⋊C8—222no—
331#97—112no—
332C4×C8—21no—
333C4×C8—112no—
334C2×C11—22no—
335C2×C11—82no—
336C2×C11C2×#45911yescharacteristic
337C2×C11#306311yescharacteristic
338C2×C11#306911yescharacteristic
339D11—161no—
340#41—42no—
341#41—42no—
342#41—442no—
343#41—442no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—41no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—221no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4C2×C22⋊D1112yes—
358C22×C4—22no—
359C22×C4—41no—
360C22×C4—441no—
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364Q16—444no—
365Q16—444no—
366SD16—444no—
367SD16—444no—
368D8—882no—
369M16—114no—
370M16—222no—
371M16—444no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—112no—
375C2×C8—112no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—444no—
380C2×C8—442no—
381C2×C8—881no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4C2×C22⋊D1112yes—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42D4×D1111yescharacteristic
395C42#434111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C23×D1111yescharacteristic
398C11#1923111yescharacteristic, complemented, Sylow
399C23—22no—
400C23—441no—
401C23#6699211yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—82no—
406Q8—441no—
407Q8—441no—
408D4—22no—
409D4—22no—
410D4—44no—
411D4—42no—
412D4—81no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—441no—
417D4—881no—
418D4—882no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—441no—
428C2×C4—882no—
429C2×C4D8×D1112yes—
430C2×C4#6696412yes—
431C2×C4#6699211yescharacteristic
432C2×C4#6699211yescharacteristic
433C2×C4#6699211yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—41no—
438C8—41no—
439C8—114no—
440C8—222no—
441C8—441no—
442C8—441no—
443C8—442no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062276312yes—
453C22C2×#6699211yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—82no—
459C4—881no—
460C4#1062276312yes—
461C4C2×D8×D1111yescharacteristic
462C4C2×#6696411yescharacteristic
463C4#1062336811yescharacteristic
464C4#1062336911yescharacteristic
465C2—22no—
466C2—82no—
467C2—1761no—
468C2C2×#1062276311yescharacteristic
469C2#1307830311yescharacteristic
470C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3226C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3226D11
hypocenterC11#19231
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. #13079073C2semidirect
3. #13077360C2semidirect
4. #13068103C2semidirect
5. #13068083C2semidirect
6. #13067979C2semidirect
7. #13067959C2semidirect
8. #13067369C2semidirect
9. #13067263C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3226C2semidirect
155. #4318D8semidirect
165. #3226D11semidirect
398. C11#19231semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790732
#130773602
#130681032
#130680832
#130679792
#130679592
#130673692
#130672632
C2×#106221852
C11×#32262
#1923111