Finite Group Databasebeta

← #14804157

Subgroups — #14804157

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079009C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3#13078076C211yesmaximal, characteristic
4#13070061C212yesmaximal, complemented
5#13069907C212yesmaximal, complemented
6#13069605C211yesmaximal, characteristic, complemented
7#13069392C211yesmaximal, characteristic, complemented
8#13069124C212yesmaximal, complemented
9#13068675C212yesmaximal, complemented
10C4×#66887C211yesmaximal, characteristic, complemented
11C11×#2935C211yesmaximal, characteristic, complemented
12C2×C11×#131C2212yes—
13C11×#532C2211yescharacteristic
14C2×#67002C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C11×#436—21no—
18C11×#435—22no—
19C8×D4×C11—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#408C2212yes—
22C4×C11×M16C2211yescharacteristic
23#10622845C2212yes—
24#10622845C2212yes—
25#10622845C2212yes—
26C2×#66887C2211yescharacteristic
27C2×#66887C2211yescharacteristic
28C2×#66885C2212yes—
29C2×#66883C2212yes—
30C2×#66881C2212yes—
31#10622696—21no—
32#10622694—21no—
33#10622685—21no—
34#10622683—21no—
35#10622670—22no—
36#10622668—22no—
37#10622537C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622455—21no—
40#10622455—22no—
41#10622455—21no—
42#10622192C2212yes—
43#10622192C2212yes—
44#10622192C2211yescharacteristic
45#10622192C2211yescharacteristic
46#10622190C2212yes—
47C2×C11×#41C2312yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22—21no—
51C11×#131—24no—
52C11×#131—42no—
53C2×C11×M16—22no—
54C2×C11×M16C2311yescharacteristic
55C2×C11×M16C2311yescharacteristic
56C22×C8×C11—22no—
57C22×C8×C11C2312yes—
58C11×C4⋊Q8D411yescharacteristic
59C11×#127D411yescharacteristic
60C11×#124D412yes—
61C11×#121—21no—
62C11×#121—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C2×C42×C11C2311yescharacteristic
66#67002—24no—
67#67002—42no—
68C2×#4325—22no—
69C2×#4323—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2312yes—
76C2×#4318C2311yescharacteristic
77C4×D44—21no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44—21no—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84#66922—21no—
85C11×C4⋊C8D411yescharacteristic
86C11×C4⋊C8D412yes—
87C11×C4⋊C8D411yescharacteristic
88C11×C22⋊C8—22no—
89C11×C22⋊C8—22no—
90C11×#97—21no—
91C4×C8×C11—21no—
92#66899—22no—
93#66899—22no—
94#66899—22no—
95#66896—22no—
96#66896—22no—
97#66896—22no—
98#66887—22no—
99#66887—22no—
100#66885—22no—
101#66885—22no—
102#66883—42no—
103#66881—22no—
104#66881—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107#66867—21no—
108C4×C11⋊C8—21no—
109#25359—111nomaximal, Sylow
110C23×D11—21no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—22no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—22no—
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44#4112yes—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—82no—
135C2×Dic22—41no—
136C2×Dic22—41no—
137C2×Dic22—82no—
138C11×M16—21no—
139C11×M16—21no—
140C11×M16—21no—
141C11×M16—44no—
142C11×M16#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—44no—
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158#4325—44no—
159#4323—44no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168#4318—21no—
169#4318—21no—
170#4318—22no—
171#4318—21no—
172#4318—22no—
173#4318—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177#3141—111no—
178C2×#476—111no—
179#3036—111no—
180#2935D1111yescharacteristic, complemented
181#2079—112no—
182#2051—112no—
183#1997—111no—
184#1950—111no—
185#1907—112no—
186#1815—112no—
187C4×#100—111no—
188C23×C11—22no—
189C23×C11C2×#4111yescharacteristic
190C22×D11—22no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—81no—
194C22×D11—81no—
195Q8×C11—22no—
196Q8×C11—22no—
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—81no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—82no—
221C2×Dic11—81no—
222D44—22no—
223D44—22no—
224D44—41no—
225D44—41no—
226C4×D11—82no—
227C4×D11—82no—
228Dic22—82no—
229Dic22—82no—
230C8×C11—22no—
231C8×C11—22no—
232C8×C11—22no—
233C8×C11—41no—
234C11⋊C8—41no—
235C11⋊C8—42no—
236C11⋊C8—41no—
237C2×AGL(1,ℤ/8)—112no—
238C2×#131C2×D1112yes—
239#532C2×D1111yescharacteristic
240C2×C4⋊Q8—111no—
241C2×C4×D4—111no—
242#489—222no—
243#487—221no—
244#486—221no—
245#476—221no—
246#476—222no—
247#476—221no—
248#463—222no—
249#461—221no—
250#459—221no—
251#436—21no—
252#435—22no—
253C8×D4—21no—
254C2×#108—112no—
255C2×#106—112no—
256#423—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258#417—112no—
259#417—112no—
260#417—112no—
261C2×#102—112no—
262C2×#100—111no—
263C2×#100—111no—
264#408C2×D1112yes—
265C4×M16—111no—
266C4×M16C2×D1111yescharacteristic
267#343—112no—
268#343—111no—
269#343—112no—
270#343—111no—
271#341—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52911yescharacteristic
279C22×C11#54211yescharacteristic
280C2×D11—42no—
281C2×D11—82no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—82no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11#47112yes—
290C4×C11#54611yescharacteristic
291C4×C11#54611yescharacteristic
292C4×C11#54711yescharacteristic
293C4×C11#54811yescharacteristic
294Dic11—81no—
295Dic11—82no—
296C2×#41C22×D1112yes—
297C22×Q8—221no—
298C22×D4—111no—
299C23×C4—221no—
300AGL(1,ℤ/8)—224no—
301AGL(1,ℤ/8)—442no—
302C2×SD16—222no—
303C2×D8—222no—
304#131—24no—
305#131—42no—
306C2×M16—22no—
307C2×M16—112no—
308C2×M16—111no—
309C2×M16—111no—
310C2×M16C22×D1111yescharacteristic
311C2×M16C22×D1111yescharacteristic
312C22×C8—22no—
313C22×C8C22×D1112yes—
314C4⋊Q8—221no—
315C4⋊Q8—221no—
316C4⋊Q8—221no—
317C4⋊Q8—221no—
318C4⋊Q8D4411yescharacteristic
319#127D4411yescharacteristic
320#124D4412yes—
321#121—21no—
322#121—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—221no—
332C2×C22⋊C4—221no—
333C2×C42C22×D1111yescharacteristic
334#108—442no—
335#106—222no—
336#106—222no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1112yes—
341C4⋊C8C22⋊D1111yescharacteristic
342#103—222no—
343#103—222no—
344#103—222no—
345#102—222no—
346#102—222no—
347#102—222no—
348#102—222no—
349#102—222no—
350#100—222no—
351#100—222no—
352C22⋊C8—22no—
353C22⋊C8—22no—
354#97—21no—
355#97—221no—
356C4×C8—21no—
357C4×C8—221no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—82no—
361C2×C11#242711yescharacteristic
362C2×C11C2×#47111yescharacteristic
363C2×C11#306811yescharacteristic
364D11—82no—
365C24—221no—
366#41—22no—
367#41—22no—
368#41—22no—
369#41—22no—
370C2×Q8—441no—
371C2×Q8—441no—
372C2×Q8—882no—
373C2×Q8C2×D4412yes—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—112no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4—221no—
382C2×D4—221no—
383C2×D4C2×D4412yes—
384C22×C4—22no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—882no—
390C22×C4#433911yescharacteristic
391C22×C4#433911yescharacteristic
392C22×C4C23×D1111yescharacteristic
393SD16—444no—
394D8—444no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—44no—
399M16—221no—
400M16—221no—
401M16—222no—
402M16—221no—
403M16—222no—
404M16—221no—
405M16#434112yes—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—44no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—222no—
414C2×C8C2×C22⋊D1112yes—
415C2×C8C2×C22⋊D1112yes—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—221no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—221no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C42C2×D4411yescharacteristic
429C42C2×D4411yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C11#2535911yescharacteristic, complemented, Sylow
433C23—22no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—881no—
438C23—881no—
439C23C2×#433911yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—882no—
443Q8—882no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450D4—222no—
451D4—222no—
452D4—441no—
453D4—441no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—882no—
462C2×C4—882no—
463C2×C4—881no—
464C2×C4—882no—
465C2×C4#6698311yescharacteristic
466C2×C4#6698311yescharacteristic
467C2×C4#6698311yescharacteristic
468C2×C4#6698311yescharacteristic
469C2×C4C22×D4411yescharacteristic
470C2×C4C2×#434111yescharacteristic
471C2×C4#6703711yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#6704311yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—41no—
479C8—442no—
480C8—441no—
481C8—441no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—442no—
488C22—882no—
489C22—882no—
490C22—881no—
491C22—881no—
492C22#1062308811yescharacteristic
493C22#1062309211yescharacteristic
494C22C2×#6698311yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—881no—
500C4—882no—
501C4#1062275412yes—
502C4#1062308511yescharacteristic
503C4#1062308611yescharacteristic
504C4#1062333711yescharacteristic
505C4#1062336211yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—882no—
510C2#1307218711yescharacteristic
511C2C2×#1062275411yescharacteristic
512C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#2935D11
hypocenterC11#25359
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. C2×#10622455C2semidirect
4. #13070061C2semidirect
5. #13069907C2semidirect
6. #13069605C2semidirect
7. #13069392C2semidirect
8. #13069124C2semidirect
9. #13068675C2semidirect
10. C4×#66887C2semidirect
11. C11×#2935C2semidirect
180. #2935D11semidirect
432. C11#25359semidirect

Maximal subgroups

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

subgroupindex
#130790092
C2×#106224552
#130780762
#130700612
#130699072
#130696052
#130693922
#130691242
#130686752
C4×#668872
C11×#29352
#2535911