Finite Group Databasebeta

← #14736946

Subgroups — #14736946

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13078938C211yesmaximal, characteristic, complemented
3#13077328C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068175C212yesmaximal, complemented
6#13068037C212yesmaximal, complemented
7#13068023C212yesmaximal, complemented
8C2×#10622118C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3245C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67001—21no—
15#10623001C2211yescharacteristic
16C11×#474—21no—
17C11×#474C2212yes—
18C11×#466—22no—
19C11×#459—21no—
20C11×#459C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622847—21no—
23#10622846—21no—
24#10622846—21no—
25#10622707—21no—
26#10622694C2211yescharacteristic
27#10622694C2211yescharacteristic
28#10622688—21no—
29#10622683C2211yescharacteristic
30#10622683C2211yescharacteristic
31#10622669—21no—
32#10622669—21no—
33#10622654—22no—
34#10622632C2212yes—
35#10622625—21no—
36#10622625C2212yes—
37D4×C11⋊C8—21no—
38D4×C11⋊C8C2212yes—
39#10622621C2212yes—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622182C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×D8—22no—
52C22×C8×C11—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#127D411yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#124—21no—
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C11×#121—21no—
62C11×#121D412yes—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68#67001—44no—
69C2×#4324—22no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C2×#4318—21no—
74C2×#4318—22no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×#107—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×#102—22no—
88C11×#102—22no—
89#66899—21no—
90#66899—21no—
91#66899—21no—
92#66899—21no—
93#66896—22no—
94#66896—21no—
95#66896—21no—
96#66896—21no—
97#66896—21no—
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100#66874—22no—
101#66872—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19200—111nomaximal, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—22no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×D8—82no—
133C2×C8×C11—22no—
134C2×C8×C11—81no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—41no—
148#4324—82no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156#4318—44no—
157#4318—42no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—44no—
163C2×C11⋊C8—81no—
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168#3246—111no—
169#3245D1111yescharacteristic
170#3131—111no—
171#2931—111no—
172#1703—112no—
173#1701—112no—
174#1679—112no—
175#1677—112no—
176C2×#334—111no—
177#1550—111no—
178#1547—111no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11#12111yescharacteristic
182Q8×C11—42no—
183Q8×C11—41no—
184Q8×C11—41no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—42no—
188D4×C11—44no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—42no—
194D4×C11—81no—
195D4×C11—82no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#13512yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×Dic11—41no—
213C2×Dic11—41no—
214Dic22—41no—
215Dic22—41no—
216Dic22—81no—
217C8×C11—42no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—21no—
221C11⋊C8—21no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×#131—221no—
225#533—111no—
226#532C2×D1111yescharacteristic
227#532C2×D1111yescharacteristic
228#488—221no—
229#488—221no—
230#487—111no—
231#487—111no—
232#486—111no—
233#486—111no—
234#476—112no—
235#475—221no—
236#474—21no—
237#474C2×D1112yes—
238#466—22no—
239#465—222no—
240#461—112no—
241#460—221no—
242#459—21no—
243#459C2×D1112yes—
244#436—112no—
245#436—221no—
246C8×D4—112no—
247C8×D4—221no—
248#423—111no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8C2×D1111yescharacteristic
251#416—221no—
252#416—221no—
253#408—221no—
254C2×C4×C8—111no—
255#334—112no—
256#334—112no—
257#333—112no—
258#332—112no—
259#332—112no—
260#331—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#46312yes—
270C22×C11C2×#12111yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11#46312yes—
277C4×C11C2×#13511yescharacteristic
278C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C11#57711yescharacteristic
280C4×C11#57711yescharacteristic
281Dic11—81no—
282Dic11—81no—
283C2×#41—21no—
284C2×#41—21no—
285C2×SD16—222no—
286C2×D8—22no—
287#131—444no—
288C2×M16—222no—
289C2×M16—221no—
290C22×C8—21no—
291C22×C8—111no—
292C22×C8—111no—
293C22×C8—222no—
294C22×C8—221no—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297C4⋊Q8C22⋊D1111yescharacteristic
298C4⋊Q8C22×D1111yescharacteristic
299#127C22⋊D1111yescharacteristic
300#127C22×D1111yescharacteristic
301#125—221no—
302#124—21no—
303#124—21no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121C22⋊D1112yes—
310C4×Q8—221no—
311C4×Q8—221no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C22×D1112yes—
316#117—221no—
317C2×C42C22×D1111yescharacteristic
318#107—22no—
319#106—222no—
320C4⋊C8—21no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—221no—
324C4⋊C8—221no—
325C4⋊C8C22×D1112yes—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330#103—222no—
331#102—22no—
332#102—22no—
333#102—221no—
334#102—221no—
335#102—221no—
336#102—221no—
337#102—222no—
338C22⋊C8—222no—
339C22⋊C8—222no—
340C4×C8—111no—
341C4×C8—111no—
342C4×C8—111no—
343C4×C8—111no—
344C2×C11—22no—
345C2×C11—82no—
346C2×C11—161no—
347C2×C11C2×#46311yescharacteristic
348C2×C11#306011yescharacteristic
349C2×C11#306711yescharacteristic
350#41—42no—
351#41—42no—
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4C2×C22⋊D1112yes—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4D4×D1111yescharacteristic
369C22×C4#434111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371SD16—882no—
372D8—82no—
373M16—444no—
374M16—442no—
375C2×C8—22no—
376C2×C8—81no—
377C2×C8—111no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—444no—
386C2×C8—881no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×C22⋊D1112yes—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—441no—
402C42—441no—
403C42D4×D1111yescharacteristic
404C42#434111yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C23×D1111yescharacteristic
407C11#1920011yescharacteristic, complemented, Sylow
408C23—22no—
409C23—41no—
410C23#6699211yescharacteristic
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—441no—
415Q8—441no—
416Q8—881no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—44no—
421D4—42no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—81no—
427D4—82no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4#6696412yes—
439C2×C4#6696512yes—
440C2×C4#6699211yescharacteristic
441C2×C4#6699211yescharacteristic
442C2×C4#6699211yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4C22×C22⋊D1111yescharacteristic
446C8—42no—
447C8—221no—
448C8—221no—
449C8—221no—
450C8—221no—
451C8—442no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1062276612yes—
462C22C2×#6699211yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—881no—
469C4—881no—
470C4#1062276612yes—
471C4C2×#6696411yescharacteristic
472C4C2×#6696511yescharacteristic
473C4#1062336711yescharacteristic
474C4#1062336811yescharacteristic
475C2—22no—
476C2—82no—
477C2—161no—
478C2C2×#1062276611yescharacteristic
479C2#1307827511yescharacteristic
480C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11C2×#121
hypercenter#3245D11
hypocenterC11#19200
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13078938C2semidirect
3. #13077328C2semidirect
4. #13068189C2semidirect
5. #13068175C2semidirect
6. #13068037C2semidirect
7. #13068023C2semidirect
8. C2×#10622118C2semidirect
9. #13067304C2semidirect
10. #13067293C2semidirect
407. C11#19200semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130789382
#130773282
#130681892
#130681752
#130680372
#130680232
C2×#106221182
#130673042
#130672932
C11×#32452
#1920011