Finite Group Databasebeta

← #14788696

Subgroups — #14788696

Order 2816.

1380 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
1C2×#10622688C211yesmaximal, characteristic, complemented
2C2×#10622631C211yesmaximal, characteristic, complemented
3#13073982C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069704C212yesmaximal, complemented
6#13069557C211yesmaximal, characteristic, complemented
7#13069441C211yesmaximal, characteristic, complemented
8#13068950C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41—21no—
13C11×#550—24no—
14C11×#550—24no—
15C2×C11×#127C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4324C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622842—21no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622688—24no—
32#10622631—24no—
33#10622595—21no—
34#10622591—22no—
35C2×#66874C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622549C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—48no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11C2312yes—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11—21no—
56C22×Dic22C2311yescharacteristic
57C11×#127—24no—
58C11×#127—24no—
59C11×#127—22no—
60C11×#127D414yes—
61C11×#121—28no—
62C11×#121—216no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11D414yes—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4324—22no—
77C2×#4324—22no—
78C2×#4324—24no—
79C2×#4324—24no—
80C2×#4324—22no—
81C2×#4324—42no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C4×Dic22—22no—
91C4×Dic22—22no—
92#66896—22no—
93#66896—24no—
94#66896—24no—
95#66896—42no—
96#66896—42no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102#66874—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—22no—
105#66867—22no—
106#24200—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—21no—
109C11×#41—432no—
110C2×Q8×C11—22no—
111C2×Q8×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—82no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D414yes—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—28no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22#4112yescomplemented
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4324—28no—
165#4324—48no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170Dic11⋊C4—42no—
171Dic11⋊C4—44no—
172C4×Dic11—42no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8#4112yescomplemented
182C2×#550D1111yescharacteristic
183C2×#460—111no—
184C2×#440—111no—
185#2581—111no—
186#2041—112no—
187#2014—112no—
188#1985—111no—
189#1961—111no—
190#1877—112no—
191#1862—112no—
192#1804—111no—
193C23×C11—24no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206Q8×C11—28no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—24no—
210D4×C11—24no—
211D4×C11—48no—
212D4×C11—416no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—84no—
218D4×C11—88no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—48no—
228C2×C4×C11—416no—
229C2×C4×C11—42no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11AGL(1,ℤ/8)14yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247Dic22—22no—
248Dic22—22no—
249Dic22—41no—
250Dic22—41no—
251C11⋊C8—22no—
252C11⋊C8—41no—
253C11⋊C8—42no—
254C22×#41—21no—
255C22×SD16—111no—
256C22×SD16—112no—
257#550—24no—
258#550—24no—
259C2×#127C2×D1112yes—
260C2×#127C2×D1111yescharacteristic
261C2×#121—22no—
262C2×#121—21no—
263C2×C4×Q8—111no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4C2×D1112yes—
266C2×C4×D4C2×D1111yescharacteristic
267#460—224no—
268#440—224no—
269C2×#107—111no—
270C2×C4⋊C8—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102—112no—
276C2×#102—112no—
277C2×#97—111no—
278#400—221no—
279#395—221no—
280#391—112no—
281#389—112no—
282#387—222no—
283#382—111no—
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11—42no—
288C22×C11—44no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11C2×#12011yescharacteristic
300C22×C11#54811yescharacteristic
301C22×C11#55011yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57712yes—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#52511yescharacteristic
310C4×C11#53711yescharacteristic
311C4×C11#54611yescharacteristic
312C4×C11#54711yescharacteristic
313Dic11—42no—
314Dic11—82no—
315Dic11—81no—
316C2×#41—28no—
317C2×#41—48no—
318C22×Q8—111no—
319C22×Q8C22⋊D1111yescharacteristic
320C22×D4—22no—
321C22×D4—21no—
322C22×D4—22no—
323C22×D4—21no—
324C22×D4C22×D1112yes—
325C22×D4C22×D1111yescharacteristic
326C23×C4—22no—
327C23×C4—21no—
328C2×SD16—222no—
329C2×SD16—222no—
330C2×SD16—222no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—442no—
334C22×C8—111no—
335C22×C8—112no—
336C22×C8—111no—
337#127—24no—
338#127—24no—
339#127—22no—
340#127C22⋊D1114yes—
341#121—28no—
342#121—216no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—222no—
346C4×Q8—222no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—22no—
350C4×D4C22⋊D1114yes—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4C22⋊D1112yes—
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C42—221no—
361C2×C42C22×D1112yes—
362C2×C42C22×D1111yescharacteristic
363#107—222no—
364C4⋊C8—222no—
365#103—222no—
366#102—224no—
367#102—222no—
368#102—224no—
369#102—442no—
370#102—442no—
371#97—222no—
372#95—221no—
373#95—221no—
374#95—222no—
375#95—222no—
376#95—222no—
377C2×C11—82no—
378C2×C11—84no—
379C2×C11#240711yescharacteristic
380C2×C11#300311yescharacteristic
381C2×C11#300911yescharacteristic
382C2×C11#336812yes—
383C2×C11#339712yes—
384C24—22no—
385C24—21no—
386#41—432no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—112no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—82no—
413C2×D4—82no—
414C2×D4—82no—
415C2×D4C2×C22⋊D1114yes—
416C2×D4C2×C22⋊D1112yes—
417C22×C4—28no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1112yes—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432SD16—448no—
433C2×C8—112no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—444no—
450C4⋊C4—442no—
451C4⋊C4C2×C22⋊D1112yes—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C42—22no—
455C42—22no—
456C42—442no—
457C42C2×C22⋊D1112yes—
458C42C2×C22⋊D1112yes—
459C11#2420011yescharacteristic, complemented, Sylow
460C23—24no—
461C23—22no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—41no—
467C23—42no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23C22×C22⋊D1111yescharacteristic
473Q8—28no—
474Q8—222no—
475Q8—222no—
476Q8—441no—
477Q8—441no—
478D4—24no—
479D4—22no—
480D4—24no—
481D4—22no—
482D4—416no—
483D4—48no—
484D4—41no—
485D4—42no—
486D4—41no—
487D4—42no—
488D4—84no—
489D4—88no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—416no—
499C2×C4—48no—
500C2×C4—42no—
501C2×C4—222no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—441no—
509C2×C4#6698514yes—
510C2×C4#6700612yes—
511C2×C4#6700612yes—
512C2×C4#41×D1111yescharacteristic
513C2×C4#41×D1111yescharacteristic
514C2×C4#6704211yescharacteristic
515C2×C4#6704311yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—222no—
519C8—442no—
520C8—441no—
521C22—44no—
522C22—42no—
523C22—44no—
524C22—42no—
525C22—44no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×#6698512yes—
534C22#1062336211yescharacteristic
535C22#1062336511yescharacteristic
536C22#1062336712yes—
537C22C2×#6700611yescharacteristic
538C4—24no—
539C4—22no—
540C4—22no—
541C4—42no—
542C4—42no—
543C4—442no—
544C4—882no—
545C4—881no—
546C4#1062335511yescharacteristic
547C4#1062335911yescharacteristic
548C4#1062336011yescharacteristic
549C4#1062336411yescharacteristic
550C2—84no—
551C2—82no—
552C2#1307195511yescharacteristic
553C2#1307784311yescharacteristic
554C2#1307789311yescharacteristic
555C2#1308134112yes—
556C2#1308163212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#24200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622688C2semidirect
2. C2×#10622631C2semidirect
3. #13073982C2semidirect
4. #13069847C2semidirect
5. #13069704C2semidirect
6. #13069557C2semidirect
7. #13069441C2semidirect
8. #13068950C2semidirect
9. #13068863C2semidirect
10. #13068626C2semidirect
153. C2×Dic22#41semidirect
181. C2×C11⋊C8#41semidirect
459. C11#24200semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
C2×#106226312
#130739822
#130698472
#130697042
#130695572
#130694412
#130689502
#130688632
#130686262
C2×C11×#5502
#2420011