Finite Group Databasebeta

← #14739161

Subgroups — #14739161

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic, complemented
2#13078065C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic, complemented
4#13068043C212yesmaximal, complemented
5#13068036C212yesmaximal, complemented
6#13067961C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3206C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67003—21no—
15C4×#4339C2211yescharacteristic
16C11×#492C2212yes—
17C11×#487C2212yes—
18C11×#461—21no—
19C11×#461—21no—
20C11×#448—22no—
21C11×#431C2211yescharacteristic
22#10622846—21no—
23#10622707C2212yes—
24#10622704—21no—
25#10622703C2211yescharacteristic
26#10622700C2212yes—
27#10622697—21no—
28#10622696C2211yescharacteristic
29#10622688C2211yescharacteristic
30#10622685C2211yescharacteristic
31#10622670—21no—
32#10622667—21no—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622185C2212yes—
46#10622182C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C2×#4339D411yescharacteristic
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#124—21no—
61C11×#121—21no—
62C11×#121—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68#67003—44no—
69C2×#4326—21no—
70C2×#4325—21no—
71C2×#4324—21no—
72C2×#4323—21no—
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75#66979D411yescharacteristic
76C2×#4318—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79C2×C8×D11—22no—
80C4×D44D411yescharacteristic
81C4×D44C2311yescharacteristic
82#66925—21no—
83C42×D11—21no—
84C4×Dic22D411yescharacteristic
85C4×Dic22C2311yescharacteristic
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×#103—22no—
89C11×#103—22no—
90C11×C22⋊C8D412yes—
91C4×C8×C11C2312yes—
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96(C2×D11)⋊C8—22no—
97Dic11⋊C8—22no—
98C8×Dic11—22no—
99#66874—22no—
100#66873—22no—
101#66872—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19408—111nomaximal, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—81no—
117C2×Q8×C11—81no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—21no—
128#4339—22no—
129#4339SD1614yescomplemented
130C2×D44C2×D411yescharacteristic
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×Dic22C2×D411yescharacteristic
135C11×SD16—82no—
136C11×SD16—82no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151C22⋊Dic11—21no—
152#4326—42no—
153#4325—42no—
154#4324—42no—
155#4323—42no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158C4⋊Dic11C2×D411yescharacteristic
159C4⋊Dic11C2×D411yescharacteristic
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8—81no—
172C8×D11—82no—
173#3206D1111yescharacteristic, complemented
174#3079—111no—
175#3035—111no—
176#2988—111no—
177#1680—112no—
178#1679—112no—
179#1666—112no—
180#1665—112no—
181#1570—111no—
182#1547—111no—
183C2×#332—111no—
184C23×C11—41no—
185C23×C11#12111yescharacteristic
186C22×D11—21no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—82no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—81no—
197D4×C11—82no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C2×SD1612yes—
209C2×C4×C11#13512yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C22⋊D11—24no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217D44—21no—
218D44C2×SD1612yes—
219C4×D11—24no—
220C4×D11—41no—
221C4×D11—41no—
222C4×D11—81no—
223Dic22—21no—
224Dic22C2×SD1612yes—
225C8×C11—22no—
226C8×C11—22no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×#135—221no—
232#532C2×D1111yescharacteristic
233C2×C4⋊Q8C2×D1111yescharacteristic
234C4×#41—111no—
235#492C2×D1112yes—
236#487C2×D1112yes—
237#477—221no—
238#476—221no—
239#475—112no—
240#474—112no—
241#464—221no—
242#463—221no—
243#462—111no—
244#461—21no—
245#461—21no—
246#461—111no—
247#460—111no—
248#459—111no—
249#448—22no—
250C8×Q8—112no—
251C8×D4—112no—
252C8×D4—222no—
253#431—221no—
254#431C2×D1111yescharacteristic
255#428—221no—
256#423—111no—
257C2×C4⋊C8—111no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8—221no—
260#417—221no—
261#416—221no—
262#334—112no—
263#334—112no—
264#332—112no—
265#332—112no—
266#332—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11#46512yes—
274C22×C11C2×#12111yescharacteristic
275C2×D11—22no—
276C2×D11—41no—
277C2×D11—41no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11#46512yes—
284C4×C11C22×SD1611yescharacteristic
285C4×C11C2×#13511yescharacteristic
286C4×C11#57611yescharacteristic
287C4×C11#57711yescharacteristic
288Dic11—22no—
289Dic11—41no—
290Dic11—41no—
291C2×#41—21no—
292C2×#41—111no—
293C22×Q8—21no—
294#135—444no—
295C2×Q16—221no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—221no—
299C2×SD16—221no—
300C2×D8—221no—
301C2×M16—221no—
302C22×C8—221no—
303C22×C8—221no—
304C22×C8—222no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C22×D1112yes—
309C4⋊Q8C22×D1111yescharacteristic
310#127C22×D1111yescharacteristic
311#124—21no—
312#121—21no—
313#121—21no—
314C4×Q8—111no—
315C4×Q8—111no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—111no—
319C4×D4—111no—
320C4×D4—221no—
321C4×D4—221no—
322#117—111no—
323#117—221no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328#107—222no—
329#106—222no—
330C4⋊C8—112no—
331C4⋊C8—112no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—222no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22⋊D1111yescharacteristic
339C4⋊C8C22⋊D1111yescharacteristic
340#103—22no—
341#103—22no—
342#103—222no—
343#103—221no—
344#103—221no—
345#102—222no—
346#102—221no—
347#102—221no—
348C22⋊C8—222no—
349C22⋊C8C22⋊D1112yes—
350C4×C8—222no—
351C4×C8C22×D1112yes—
352C2×C11—22no—
353C2×C11—161no—
354C2×C11#304511yescharacteristic
355C2×C11C2×#46511yescharacteristic
356C2×C11#306911yescharacteristic
357D11—42no—
358#41—42no—
359#41—42no—
360#41—114no—
361#41—222no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—41no—
365C2×Q8—81no—
366C2×Q8—81no—
367C2×Q8—111no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4—111no—
373C2×D4—221no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382Q16—442no—
383SD16—82no—
384SD16—82no—
385SD16—442no—
386SD16—442no—
387D8—442no—
388M16—442no—
389C2×C8—222no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—222no—
393C2×C8—442no—
394C2×C8—882no—
395C2×C8—881no—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—111no—
405C4⋊C4—111no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C22⋊C4—221no—
413C42—221no—
414C42—221no—
415C42—221no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940811yescharacteristic, complemented, Sylow
421C23—41no—
422C23—221no—
423C23#6699111yescharacteristic
424Q8—41no—
425Q8—41no—
426Q8—42no—
427Q8—42no—
428Q8—82no—
429Q8—112no—
430Q8—221no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—81no—
436D4—82no—
437D4—112no—
438D4—224no—
439D4—221no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—221no—
448C2×C4—224no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—881no—
454C2×C4SD16×D1112yes—
455C2×C4#6696912yes—
456C2×C4#6699111yescharacteristic
457C2×C4#6699111yescharacteristic
458C2×C4#6699111yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—22no—
463C8—22no—
464C8—441no—
465C8—441no—
466C8—442no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—222no—
474C22—441no—
475C22—441no—
476C22#1062278412yes—
477C22C2×#6699111yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—82no—
482C4—81no—
483C4—222no—
484C4—441no—
485C4—441no—
486C4#1062278412yes—
487C4C2×SD16×D1111yescharacteristic
488C4C2×#6696911yescharacteristic
489C4#1062336611yescharacteristic
490C4#1062336711yescharacteristic
491C2—22no—
492C2—161no—
493C2—442no—
494C2#1307815111yescharacteristic
495C2C2×#1062278411yescharacteristic
496C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3206C2
socleC22×C11C2×#121
prime radical#13078065C2
hypercenter#3206D11
hypocenterC11#19408
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. #13078425C2semidirect
3. #13077724C2semidirect
4. #13068043C2semidirect
5. #13068036C2semidirect
6. #13067961C2semidirect
7. #13067954C2semidirect
8. #13067387C2semidirect
9. #13067293C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3206C2semidirect
129. #4339SD16semidirect
173. #3206D11semidirect
420. C11#19408semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130780652
#130777242
#130680432
#130680362
#130679612
#130679542
#130673872
#130672932
C2×#106221852
C11×#32062
#1940811