Finite Group Databasebeta

← #14739163

Subgroups — #14739163

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#13079538C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068048C212yesmaximal, complemented
5#13068041C212yesmaximal, complemented
6#13067962C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067386C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622124C211yesmaximal, characteristic, complemented
11C11×#3035C211yesmaximal, characteristic
12C2×C11×#135—21no—
13C11×#532C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#464—21no—
17C11×#463—21no—
18C11×#462C2211yescharacteristic
19C11×#461C2211yescharacteristic
20C11×#460C2211yescharacteristic
21C11×#459C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#416—21no—
24#10622845—21no—
25#10622706C2212yes—
26#10622689C2212yes—
27#10622653—22no—
28Q8×C11⋊C8C2212yes—
29#10622634—21no—
30#10622633C2212yes—
31#10622632—21no—
32#10622632—21no—
33D4×C11⋊C8—22no—
34D4×C11⋊C8C2212yes—
35#10622621—21no—
36#10622620C2212yes—
37#10622608—21no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)—21no—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622185C2212yes—
44#10622182C2212yes—
45#10622124C2212yes—
46#10622124C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×Dic22—21no—
52C11×#135—44no—
53C2×C11×Q16—21no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×D8—21no—
57C22×C8×C11—21no—
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#124—21no—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11C2311yescharacteristic
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11D411yescharacteristic
70C4×D4×C11C2311yescharacteristic
71C11×#117—21no—
72C11×#117D411yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×#4324—22no—
76C2×#4324—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×#4318—21no—
80C22×C11⋊C8—21no—
81C22×C11⋊C8—22no—
82#66922—21no—
83#66922—21no—
84#66922—21no—
85#66922C2312yes—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89C11×#103—21no—
90C11×#103—21no—
91C11×#102—21no—
92C11×#102—21no—
93#66899—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)D412yes—
97#66874—22no—
98#66874—22no—
99#66872—22no—
100#66871—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19408—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41SD1614yescomplemented
115C2×Q8×C11—21no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11C2×D411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×Dic11—41no—
131C2×Dic22—22no—
132C2×Dic22—41no—
133C2×Dic22—81no—
134C2×Dic22—81no—
135C11×Q16—42no—
136C11×SD16—42no—
137C11×SD16—42no—
138C11×D8—42no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—42no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11#4111yescharacteristic
159C42×C11C2411yescharacteristic
160#4324—82no—
161#4324—82no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—81no—
170C2×C11⋊C8—82no—
171C2×C11⋊C8C2×D412yes—
172C2×C11⋊C8C2×D412yes—
173#3206—111no—
174#3079—111no—
175#3035D1111yescharacteristic
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—21no—
185C23×C11—41no—
186C23×C11#12111yescharacteristic
187Q8×C11—21no—
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11C2×SD1612yes—
191D4×C11—24no—
192D4×C11—21no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—81no—
198D4×C11—82no—
199D4×C11C2×SD1612yes—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—81no—
211C2×C4×C11—82no—
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11C2×SD1612yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×Dic11—42no—
221C2×Dic11—82no—
222Dic22—42no—
223Dic22—42no—
224Dic22—82no—
225C8×C11—41no—
226C8×C11—41no—
227C11⋊C8—22no—
228C11⋊C8—22no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×#135—21no—
232#532C2×D1111yescharacteristic
233C2×C4⋊Q8—111no—
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#487—112no—
237#477—221no—
238#476—221no—
239#475—112no—
240#474—112no—
241#464—21no—
242#463—21no—
243#462C2×D1111yescharacteristic
244#461—221no—
245#461—221no—
246#461C2×D1111yescharacteristic
247#460C2×D1111yescharacteristic
248#459C2×D1111yescharacteristic
249#448—222no—
250C8×Q8—112no—
251C8×D4—112no—
252C8×D4—222no—
253#431—111no—
254#431—221no—
255#428—221no—
256#423—111no—
257C2×C4⋊C8—111no—
258C2×C4⋊C8—221no—
259C2×C4⋊C8C2×D1111yescharacteristic
260#417—221no—
261#416—21no—
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—22no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11#46512yes—
277C22×C11C2×#12111yescharacteristic
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11—81no—
285C4×C11#46512yes—
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—82no—
291C2×#41—21no—
292C2×#41C22⋊D1111yescharacteristic
293C22×Q8—221no—
294#135—44no—
295C2×Q16—21no—
296C2×SD16—21no—
297C2×SD16—21no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—21no—
301C2×M16—221no—
302C22×C8—21no—
303C22×C8—222no—
304C22×C8—221no—
305C4⋊Q8—112no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
309C4⋊Q8C22×D1111yescharacteristic
310#127C22×D1111yescharacteristic
311#124—21no—
312#121—21no—
313#121—21no—
314C4×Q8C22⋊D1111yescharacteristic
315C4×Q8C22×D1111yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4C22⋊D1111yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117C22⋊D1111yescharacteristic
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328#107—222no—
329#106—222no—
330C4⋊C8—21no—
331C4⋊C8—111no—
332C4⋊C8—111no—
333C4⋊C8—112no—
334C4⋊C8—112no—
335C4⋊C8—222no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22×D1111yescharacteristic
339C4⋊C8C22×D1111yescharacteristic
340#103—21no—
341#103—21no—
342#103—222no—
343#103—222no—
344#103—222no—
345#102—21no—
346#102—21no—
347#102—222no—
348C22⋊C8—112no—
349C22⋊C8—222no—
350C4×C8—112no—
351C4×C8—222no—
352C2×C11—22no—
353C2×C11—42no—
354C2×C11—161no—
355C2×C11#304511yescharacteristic
356C2×C11C2×#46511yescharacteristic
357C2×C11#306911yescharacteristic
358#41—22no—
359#41—42no—
360#41—42no—
361#41#432414yescomplemented
362C2×Q8—21no—
363C2×Q8—222no—
364C2×Q8—441no—
365C2×Q8—881no—
366C2×Q8—881no—
367C2×Q8C2×C22⋊D1111yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4C2×C22⋊D1111yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—441no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382Q16—42no—
383SD16—42no—
384SD16—42no—
385SD16—882no—
386SD16—882no—
387D8—42no—
388M16—442no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—42no—
392C2×C8—112no—
393C2×C8—112no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—882no—
397C2×C8—881no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×C22⋊D1111yescharacteristic
407C4⋊C4C2×C22⋊D1111yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940811yescharacteristic, complemented, Sylow
421C23—21no—
422C23—41no—
423C23#6699211yescharacteristic
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—442no—
428Q8—442no—
429Q8—882no—
430Q8C2×#432412yes—
431D4—24no—
432D4—21no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4C2×#432412yes—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—442no—
453C2×C4—882no—
454C2×C4C2×#432412yes—
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4#6700312yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—41no—
463C8—41no—
464C8—222no—
465C8—222no—
466C8—442no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22#1062265412yes—
477C22C2×#6699211yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—81no—
485C4—882no—
486C4#1062265412yes—
487C4#1062330011yescharacteristic
488C4#1062330111yescharacteristic
489C4C22×#432411yescharacteristic
490C4C2×#6700311yescharacteristic
491C2—22no—
492C2—42no—
493C2—161no—
494C2#1307815311yescharacteristic
495C2C2×#1062265411yescharacteristic
496C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3035C2
socleC22×C11C2×#121
hypercenter#3035D11
hypocenterC11#19408
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. #13078431C2semidirect
3. #13077727C2semidirect
4. #13068048C2semidirect
5. #13068041C2semidirect
6. #13067962C2semidirect
7. #13067955C2semidirect
8. #13067386C2semidirect
9. #13067293C2semidirect
10. C2×#10622124C2semidirect
114. C11×#41SD16semidirect
361. #41#4324semidirect
420. C11#19408semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130784312
#130777272
#130680482
#130680412
#130679622
#130679552
#130673862
#130672932
C2×#106221242
C11×#30352
#1940811