Finite Group Databasebeta

← #14739237

Subgroups — #14739237

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068030C212yesmaximal, complemented
5#13068023C212yesmaximal, complemented
6#13067996C212yesmaximal, complemented
7#13067989C212yesmaximal, complemented
8#13067386C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622119C211yesmaximal, 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#10622692C2212yes—
26#10622683C2212yes—
27#10622647—22no—
28Q8×C11⋊C8C2212yes—
29#10622634C2212yes—
30#10622633—21no—
31D4×C11⋊C8—22no—
32D4×C11⋊C8C2212yes—
33#10622621—21no—
34#10622621—21no—
35#10622621C2212yes—
36#10622620—21no—
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#10622119C2212yes—
46#10622119C2212yes—
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×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×#4318—21no—
78C22×C11⋊C8—21no—
79C22×C11⋊C8—22no—
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922C2312yes—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2311yescharacteristic
86C11×C4⋊C8C2311yescharacteristic
87C11×#103—21no—
88C11×#103—21no—
89C11×#102—21no—
90C11×#102—21no—
91#66899—22no—
92#66896—22no—
93#66896—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)D412yes—
97#66872—22no—
98#66872—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#19414—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41SD1614yes—
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—82no—
134C11×Q16—42no—
135C11×SD16—42no—
136C11×SD16—42no—
137C11×D8—42no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—42no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C2×D411yescharacteristic
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C42×C11—21no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11#4111yescharacteristic
158C42×C11C2411yescharacteristic
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—81no—
167C2×C11⋊C8—82no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170#3227—111no—
171#3079—111no—
172#3035D1111yescharacteristic
173#2988—111no—
174#1678—112no—
175#1677—112no—
176#1672—112no—
177#1671—112no—
178#1570—111no—
179#1547—111no—
180C2×#333—111no—
181C23×C11—21no—
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184Q8×C11—21no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11C2×SD1612yes—
188D4×C11—24no—
189D4×C11—21no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—81no—
195D4×C11—82no—
196D4×C11C2×SD1612yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—81no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11#13512yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×Dic11—42no—
218C2×Dic11—82no—
219Dic22—82no—
220Dic22—82no—
221C8×C11—41no—
222C8×C11—41no—
223C11⋊C8—22no—
224C11⋊C8—22no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×#135—21no—
228#532C2×D1111yescharacteristic
229C2×C4⋊Q8—111no—
230C4×#41C2×D1111yescharacteristic
231#498—112no—
232#486—112no—
233#481—222no—
234#477—112no—
235#476—112no—
236#476—221no—
237#476—221no—
238#475—221no—
239#474—221no—
240#464—21no—
241#463—21no—
242#462C2×D1111yescharacteristic
243#461C2×D1111yescharacteristic
244#460C2×D1111yescharacteristic
245#459C2×D1111yescharacteristic
246C8×Q8—112no—
247C8×D4—112no—
248C8×D4—222no—
249#431—111no—
250#431—221no—
251#428—221no—
252#423—111no—
253C2×C4⋊C8—111no—
254C2×C4⋊C8—221no—
255C2×C4⋊C8C2×D1111yescharacteristic
256#417—221no—
257#416—21no—
258#334—112no—
259#334—112no—
260#333—112no—
261#333—112no—
262#332—112no—
263#331—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11#46512yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—81no—
281C4×C11#46512yes—
282C4×C11C22×SD1611yescharacteristic
283C4×C11C2×#13511yescharacteristic
284C4×C11#57711yescharacteristic
285C4×C11#57811yescharacteristic
286Dic11—82no—
287C2×#41—21no—
288C2×#41C22⋊D1111yescharacteristic
289C22×Q8—221no—
290#135—44no—
291C2×Q16—21no—
292C2×SD16—21no—
293C2×SD16—21no—
294C2×D8—21no—
295C2×M16—221no—
296C22×C8—21no—
297C22×C8—222no—
298C22×C8—221no—
299C4⋊Q8—112no—
300C4⋊Q8—221no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303C4⋊Q8C22×D1111yescharacteristic
304#127C22×D1111yescharacteristic
305#124—21no—
306#121—21no—
307#121—21no—
308C4×Q8C22⋊D1111yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4C22⋊D1111yescharacteristic
315C4×D4C22×D1111yescharacteristic
316#117—21no—
317#117C22⋊D1111yescharacteristic
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C42—21no—
321C2×C42C22×D1111yescharacteristic
322#107—222no—
323#106—222no—
324#106—222no—
325#106—222no—
326C4⋊C8—21no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—112no—
330C4⋊C8—112no—
331C4⋊C8—222no—
332C4⋊C8—221no—
333C4⋊C8—221no—
334C4⋊C8C22×D1111yescharacteristic
335C4⋊C8C22×D1111yescharacteristic
336#103—21no—
337#103—21no—
338#103—222no—
339#102—21no—
340#102—21no—
341#102—222no—
342#102—222no—
343#102—222no—
344C22⋊C8—112no—
345C22⋊C8—222no—
346C4×C8—112no—
347C4×C8—222no—
348C2×C11—22no—
349C2×C11—42no—
350C2×C11—161no—
351C2×C11#304611yescharacteristic
352C2×C11C2×#46511yescharacteristic
353C2×C11#306811yescharacteristic
354#41—22no—
355#41—42no—
356#41—42no—
357#41#432414yes—
358C2×Q8—21no—
359C2×Q8—222no—
360C2×Q8—441no—
361C2×Q8—882no—
362C2×Q8C2×C22⋊D1111yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×C22⋊D1111yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—42no—
378SD16—42no—
379SD16—42no—
380D8—42no—
381M16—442no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—42no—
385C2×C8—112no—
386C2×C8—112no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8—882no—
390C2×C8—881no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4C2×C22⋊D1111yescharacteristic
400C4⋊C4C2×C22⋊D1111yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1941411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—41no—
416C23#6699211yescharacteristic
417Q8—21no—
418Q8—41no—
419Q8—41no—
420Q8—882no—
421Q8—882no—
422Q8C2×#432412yes—
423D4—24no—
424D4—21no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—81no—
430D4—82no—
431D4C2×#432412yes—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—442no—
445C2×C4—882no—
446C2×C4C2×#432412yes—
447C2×C4#6699211yescharacteristic
448C2×C4#6699211yescharacteristic
449C2×C4#6699211yescharacteristic
450C2×C4#6700312yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—41no—
455C8—41no—
456C8—222no—
457C8—222no—
458C8—442no—
459C8—442no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22#1062265412yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—882no—
478C4#1062265412yes—
479C4#1062330111yescharacteristic
480C4#1062330211yescharacteristic
481C4C22×#432411yescharacteristic
482C4C2×#6700311yescharacteristic
483C2—22no—
484C2—42no—
485C2—161no—
486C2#1307816411yescharacteristic
487C2C2×#1062265411yescharacteristic
488C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3035C2
socleC22×C11C2×#121
hypercenter#3035D11
hypocenterC11#19414
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. #13079741C2semidirect
2. #13078431C2semidirect
3. #13077727C2semidirect
4. #13068030C2semidirect
5. #13068023C2semidirect
6. #13067996C2semidirect
7. #13067989C2semidirect
8. #13067386C2semidirect
9. #13067293C2semidirect
10. C2×#10622119C2semidirect
413. C11#19414semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130784312
#130777272
#130680302
#130680232
#130679962
#130679892
#130673862
#130672932
C2×#106221192
C11×#30352
#1941411