Finite Group Databasebeta

← #14738394

Subgroups — #14738394

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic, complemented
2#13079994C211yesmaximal, characteristic
3#13077329C211yesmaximal, characteristic, complemented
4#13068112C212yesmaximal, complemented
5#13068078C212yesmaximal, complemented
6#13068064C212yesmaximal, complemented
7#13068050C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067354C211yesmaximal, characteristic, complemented
10#13067351C211yesmaximal, characteristic, complemented
11C11×#3167C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#66954—21no—
15#10623008C2211yescharacteristic
16C11×#498C2211yescharacteristic
17C11×#492C2211yescharacteristic
18C11×#487C2211yescharacteristic
19C11×#486C2211yescharacteristic
20C11×#465—21no—
21C11×#465—21no—
22C4×C11×SD16—21no—
23C4×C11×SD16—21no—
24C2×C4×C8×C11C2211yescharacteristic
25#10622723—21no—
26#10622700C2212yes—
27#10622697C2212yes—
28#10622696C2212yes—
29#10622685C2212yes—
30#10622662—22no—
31#10622652—22no—
32#10622640—21no—
33#10622634—21no—
34#10622628—21no—
35#10622621—21no—
36#10622537C2211yescharacteristic
37#10622537C2211yescharacteristic
38#10622537C2211yescharacteristic
39#10622301—21no—
40#10622301C2212yes—
41C8×D44—21no—
42C8×D44C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622184C2212yes—
46#10622182C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C2×C11×#41—21no—
50C2×#4339—21no—
51C2×C11×SD16—21no—
52C2×C11×SD16—21no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127C2311yescharacteristic
59C11×#125—21no—
60C11×#124—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64C11×#121—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C11×#117—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4325—22no—
72C2×#4323—22no—
73#66983—21no—
74#66983D412yes—
75C2×#4318—21no—
76C2×#4318—21no—
77C2×#4318—21no—
78#66954—44no—
79C2×#4313—22no—
80C2×C8×D11—22no—
81#66928—21no—
82#66927D411yescharacteristic
83C4×D44—21no—
84C4×D44C2312yes—
85#66922D411yescharacteristic
86C11×#106—21no—
87C11×#106—21no—
88C11×#103—21no—
89C11×#103—21no—
90C11×#102—21no—
91C11×#102—21no—
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D411yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96#66899—22no—
97#66896—22no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100#66873—22no—
101#66873—22no—
102#66872—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#19339—111nomaximal, Sylow
111C11×#41—82no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C2×C22⋊D11—22no—
124#4339—42no—
125#4339—42no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44C2×D412yes—
129C2×C4×D11—22no—
130C2×Dic22—21no—
131C11×SD16—42no—
132C11×SD16—42no—
133C2×C8×C11—22no—
134C2×C8×C11—41no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11—41no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4325—82no—
156#4323—82no—
157(C2×D11)⋊C4—22no—
158(C2×D11)⋊C4—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11C2×D412yes—
161#4318—42no—
162#4318—81no—
163#4318—81no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167#4313—44no—
168C8×D11—44no—
169#3254—111no—
170#3253—111no—
171#3167D1111yescharacteristic, complemented
172#2931—111no—
173#1691—112no—
174#1685—112no—
175#1683—112no—
176#1681—112no—
177#1567—111no—
178#1561—111no—
179#1560—111no—
180C23×C11—41no—
181C23×C11#12111yescharacteristic
182C22×D11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—81no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—81no—
193D4×C11—82no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—82no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C22⋊D11—44no—
210C2×Dic11—22no—
211D44—22no—
212D44—22no—
213D44—42no—
214D44—42no—
215C4×D11—42no—
216C4×D11—42no—
217Dic22—42no—
218C8×C11—21no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11AGL(1,ℤ/8)12yes—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C11⋊C8—42no—
225C2×#131—221no—
226#533C2×D1111yescharacteristic
227#532—111no—
228#532C2×D1111yescharacteristic
229#498C2×D1111yescharacteristic
230#492C2×D1111yescharacteristic
231#487C2×D1111yescharacteristic
232#486C2×D1111yescharacteristic
233#477—221no—
234#476—112no—
235#476—221no—
236#474—112no—
237#469—222no—
238#468—222no—
239#465—21no—
240#465—21no—
241#461—112no—
242#460—221no—
243#459—112no—
244#459—221no—
245C4×SD16—21no—
246C4×SD16—21no—
247#436—112no—
248#436—221no—
249C8×D4—112no—
250C8×D4—221no—
251#423—111no—
252#423—111no—
253#423—111no—
254#408—221no—
255C2×C4×C8C2×D1111yescharacteristic
256#335—112no—
257#335—112no—
258#333—112no—
259#332—112no—
260#332—112no—
261#331—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11C2×#12111yescharacteristic
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#47112yes—
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11#57511yescharacteristic
281C4×C11#57611yescharacteristic
282C4×C11#57811yescharacteristic
283Dic11—42no—
284C2×#41—21no—
285C2×#41—221no—
286C2×SD16—21no—
287C2×SD16—21no—
288C2×SD16—222no—
289C2×D8—222no—
290#131—444no—
291C2×M16—221no—
292C2×M16—221no—
293C2×M16—221no—
294C2×M16—222no—
295C22×C8—222no—
296C22×C8C22⋊D1111yescharacteristic
297C22×C8C22⋊D1111yescharacteristic
298C4⋊Q8—111no—
299C4⋊Q8C22×D1111yescharacteristic
300C4⋊Q8C22×D1111yescharacteristic
301C4⋊Q8C22×D1111yescharacteristic
302#127—111no—
303#127C22×D1111yescharacteristic
304#125—21no—
305#124—21no—
306#124—221no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309#121—21no—
310#121—21no—
311#121—112no—
312#121—221no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—112no—
318C4×D4—221no—
319#117—21no—
320C2×C42C22×D1111yescharacteristic
321#107—222no—
322#106—21no—
323#106—21no—
324#106—222no—
325C4⋊C8—112no—
326C4⋊C8—112no—
327C4⋊C8—112no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330C4⋊C8—221no—
331#103—21no—
332#103—21no—
333#103—222no—
334#102—21no—
335#102—21no—
336#102—222no—
337#102—222no—
338#102—222no—
339C22⋊C8—222no—
340C22⋊C8—222no—
341C4×C8C22⋊D1111yescharacteristic
342C4×C8C22⋊D1111yescharacteristic
343C4×C8C22×D1111yescharacteristic
344C4×C8C22×D1111yescharacteristic
345C2×C11—41no—
346C2×C11—161no—
347C2×C11#303611yescharacteristic
348C2×C11#306111yescharacteristic
349C2×C11C2×#47111yescharacteristic
350D11—82no—
351#41—82no—
352#41—442no—
353#41—442no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—221no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—112no—
363C2×D4—222no—
364C2×D4—221no—
365C2×D4—221no—
366C22×C4—41no—
367C22×C4—222no—
368C22×C4D4×D1111yescharacteristic
369C22×C4#434111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371SD16—42no—
372SD16—42no—
373SD16—882no—
374D8—882no—
375M16—442no—
376M16—444no—
377M16—881no—
378M16—881no—
379C2×C8—22no—
380C2×C8—41no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—444no—
385C2×C8C2×C22⋊D1111yescharacteristic
386C2×C8C2×C22⋊D1111yescharacteristic
387C2×C8C2×C22⋊D1111yescharacteristic
388C2×C8C2×C22⋊D1111yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—112no—
398C4⋊C4—221no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—222no—
403C22⋊C4—222no—
404C42—41no—
405C42D4×D1111yescharacteristic
406C42#434111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C23×D1111yescharacteristic
409C11#1933911yescharacteristic, complemented, Sylow
410C23—41no—
411C23—222no—
412C23#6699111yescharacteristic
413Q8—41no—
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—81no—
418Q8—442no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—81no—
424D4—82no—
425D4—222no—
426D4—222no—
427D4—442no—
428D4—444no—
429D4—442no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—222no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4#6699111yescharacteristic
443C2×C4#6699111yescharacteristic
444C2×C4#6699111yescharacteristic
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4C2×#434111yescharacteristic
447C2×C4C22×C22⋊D1111yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8—442no—
452C8—442no—
453C8—442no—
454C8#6700212yes—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—442no—
462C22—442no—
463C22—442no—
464C22C2×#6699111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—442no—
472C4#1062279012yes—
473C4#1062330011yescharacteristic
474C4#1062330211yescharacteristic
475C4C2×#6700211yescharacteristic
476C4#1062335311yescharacteristic
477C2—41no—
478C2—161no—
479C2—882no—
480C2#1307807611yescharacteristic
481C2#1307828211yescharacteristic
482C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#121
prime radical#13079994C2
hypercenter#3167D11
hypocenterC11#19339
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13079999C2semidirect
3. #13077329C2semidirect
4. #13068112C2semidirect
5. #13068078C2semidirect
6. #13068064C2semidirect
7. #13068050C2semidirect
8. #13067375C2semidirect
9. #13067354C2semidirect
10. #13067351C2semidirect
11. C11×#3167C2semidirect
171. #3167D11semidirect
409. C11#19339semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130799942
#130773292
#130681122
#130680782
#130680642
#130680502
#130673752
#130673542
#130673512
C11×#31672
#1933911