Finite Group Databasebeta

← #14853506

Subgroups — #14853506

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076977C211yesmaximal, characteristic, complemented
2C4×#66993C211yesmaximal, characteristic
3#13070182C212yesmaximal, complemented
4#13069849C212yesmaximal
5#13069311C212yesmaximal, complemented
6#13069310C212yesmaximal, complemented
7#13068617C211yesmaximal, characteristic, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic, complemented
10#13068471C211yesmaximal, characteristic, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66993C2211yescharacteristic
14C2×C4×C22⋊D11—21no—
15C2×C4×C22⋊D11—21no—
16C2×#66943—21no—
17C2×C4×D44C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20C11×#384C2211yescharacteristic
21#10622834C2211yescharacteristic
22C2×#66896C2212yes—
23C2×#66885C2212yes—
24C2×#66879C2212yes—
25#10622601C2211yescharacteristic
26#10622598—21no—
27#10622598C2212yes—
28#10622590—21no—
29#10622589C2211yescharacteristic
30#10622586—21no—
31#10622586C2212yes—
32C2×#66873C2212yes—
33#10622570—21no—
34#10622570—21no—
35#10622548C2211yescharacteristic
36C42×Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60#66993—22no—
61#66993—22no—
62C4×C22⋊D11—44no—
63C4×C22⋊D11—44no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82#66943—44no—
83C4×D44—22no—
84C4×D44—22no—
85C11×C4⋊C8—22no—
86C11×#102—42no—
87#66896—24no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90#66885—24no—
91#66879—42no—
92#66873—42no—
93C4⋊(C11⋊C8)—22no—
94#29130—111nomaximal, Sylow
95C24×C11—21no—
96C23×D11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11#4112yes—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—42no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C22×Dic11—22no—
118C22×Dic11—21no—
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44#4112yes—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C22⋊C4—42no—
142C42×C11#4112yes—
143C42×C11#4112yes—
144C22⋊Dic11—42no—
145C22⋊Dic11—42no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C4⋊Dic11—44no—
155C4⋊Dic11—42no—
156Dic11⋊C4—44no—
157Dic11⋊C4—42no—
158Dic11⋊C4—42no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170#2859—111no—
171C4×#127—111no—
172#2100—112no—
173#2041—112no—
174#1936—112no—
175#1936—112no—
176#1802—111no—
177#1802—111no—
178#1802—111no—
179#1802D1111yescharacteristic, complemented
180#1767—111no—
181C23×C11—22no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—41no—
199D4×C11—41no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—84no—
209C2×C4×C11#12412yes—
210C2×C4×C11#12412yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C22⋊D11—48no—
220C22⋊D11—48no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11AGL(1,ℤ/8)12yes—
238C2×Dic11#13712yes—
239D44—22no—
240D44—22no—
241D44—41no—
242D44—41no—
243C4×D11—84no—
244C8×C11—42no—
245C11⋊C8—42no—
246C2×#127—111no—
247C2×#125—221no—
248C2×C4×D4—111no—
249C2×C4×D4—221no—
250C2×C4×D4—221no—
251C2×C4×D4C2×D1111yescharacteristic
252C2×C4⋊C8—111no—
253C2×C4⋊C8C2×D1111yescharacteristic
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—112no—
257C2×#102C2×D1112yes—
258C2×#97—112no—
259#390—111no—
260#390—111no—
261#390—221no—
262#390—221no—
263#389—112no—
264#389—112no—
265#389—221no—
266#389—221no—
267#384—111no—
268#384—111no—
269#384C2×D1111yescharacteristic
270#382—221no—
271C43—111no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340C2×D1112yes—
276#336—112no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11#52511yescharacteristic
285C22×C11C2×#12411yescharacteristic
286C22×C11#53711yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C4×C11—22no—
299C4×C11—81no—
300C4×C11—82no—
301C4×C11#49014yes—
302C4×C11#55211yescharacteristic
303C4×C11#55211yescharacteristic
304C4×C11#55311yescharacteristic
305C4×C11#55311yescharacteristic
306Dic11—22no—
307Dic11—22no—
308Dic11—41no—
309Dic11—41no—
310Dic11—82no—
311Dic11—81no—
312C22×D4—111no—
313C22×D4—221no—
314C22×D4—221no—
315C22×D4C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—221no—
318C22×C8—112no—
319C22×C8C22×D1112yes—
320#127—222no—
321#127—222no—
322#125—444no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—222no—
326C4×D4—222no—
327C4×D4—444no—
328C4×D4—444no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22×D1111yescharacteristic
340C2×C4⋊C4C22×D1112yes—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42C22×D1111yescharacteristic
354C4⋊C8—22no—
355C4⋊C8—222no—
356#102—42no—
357#102—224no—
358#102—224no—
359#102—442no—
360#97—442no—
361#95—222no—
362#95—222no—
363C2×C11—82no—
364C2×C11#256211yescharacteristic
365C2×C11#310911yescharacteristic
366C2×C11#311011yescharacteristic
367C2×C11C2×#49011yescharacteristic
368C2×C11#314111yescharacteristic
369C2×C11#325311yescharacteristic
370C2×C11#325411yescharacteristic
371D11—82no—
372C24—21no—
373C24—221no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—112no—
380C2×D4—224no—
381C2×D4—224no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—442no—
388C2×D4—442no—
389C2×D4—442no—
390C2×D4—442no—
391C2×D4#434312yes—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4—442no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—442no—
426C4⋊C4—444no—
427C4⋊C4—442no—
428C4⋊C4—442no—
429C4⋊C4—444no—
430C4⋊C4—442no—
431C22⋊C4—42no—
432C22⋊C4—442no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C22⋊C4—442no—
436C22⋊C4—442no—
437C42—222no—
438C42—222no—
439C42—222no—
440C42—222no—
441C42—221no—
442C42—221no—
443C42—221no—
444C42—221no—
445C42#433912yes—
446C42#434112yes—
447C11#2913011yescharacteristic, complemented, Sylow
448C23—22no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—222no—
456C23—441no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23—441no—
462C23C2×D4×D1111yescharacteristic
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467D4—222no—
468D4—222no—
469D4—448no—
470D4—448no—
471D4—441no—
472D4—441no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—84no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—884no—
501C2×C4#6693812yes—
502C2×C4#6693812yes—
503C2×C4#6696412yes—
504C2×C4#6696712yes—
505C2×C4C2×#433911yescharacteristic
506C2×C4C2×#434111yescharacteristic
507C2×C4#6703711yescharacteristic
508C2×C4C2×#434311yescharacteristic
509C2×C4#41×D1111yescharacteristic
510C2×C4#6704311yescharacteristic
511C8—42no—
512C8—442no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—442no—
521C22—442no—
522C22—442no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—881no—
527C22C2×#6693811yescharacteristic
528C22#1062313911yescharacteristic
529C22#1062315811yescharacteristic
530C22C2×#6696411yescharacteristic
531C22C2×#6696711yescharacteristic
532C22D11×AGL(1,ℤ/8)11yescharacteristic
533C22D11×#13711yescharacteristic
534C4—22no—
535C4—81no—
536C4—82no—
537C4—222no—
538C4—222no—
539C4—441no—
540C4—441no—
541C4—881no—
542C4—882no—
543C4#1062237714yes—
544C4#1062304511yescharacteristic
545C4#1062306011yescharacteristic
546C4#1062314511yescharacteristic
547C4#1062317311yescharacteristic
548C2—82no—
549C2—882no—
550C2#1307378111yescharacteristic
551C2#1307870911yescharacteristic
552C2#1307871711yescharacteristic
553C2C2×#1062237711yescharacteristic
554C2#1307900711yescharacteristic
555C2#1307999511yescharacteristic
556C2#1308000011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1802D11
hypocenterC11#29130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. #13076977C2semidirect
3. #13070182C2semidirect
5. #13069311C2semidirect
6. #13069310C2semidirect
7. #13068617C2semidirect
8. #13068616C2semidirect
9. #13068613C2semidirect
10. #13068471C2semidirect
11. C11×#1802C2semidirect
179. #1802D11semidirect
447. C11#29130semidirect

Maximal subgroups

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

subgroupindex
#130769772
C4×#669932
#130701822
#130698492
#130693112
#130693102
#130686172
#130686162
#130686132
#130684712
C11×#18022
#2913011