Finite Group Databasebeta

← #14726757

Subgroups — #14726757

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C212yesmaximal, complemented
2#13072933C211yesmaximal, characteristic, complemented
3#13067653C214yesmaximal, complemented
4#13067636C214yesmaximal, complemented
5#13067184C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537C2212yes—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic, complemented
20#10622833—21no—
21C2×#66896—22no—
22#10622825—21no—
23#10622825C2211yescharacteristic, complemented
24C2×C22⋊(C11⋊C8)C2212yescomplemented
25#10622647—24no—
26#10622647C2218yescomplemented
27#10622599C2212yescomplemented
28C2×#66872—22no—
29#10622562C2212yescomplemented
30#10622559—21no—
31#10622541—21no—
32#10622175C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yescomplemented
35C11×H(5,𝔽2)—44no—
36C11×H(5,𝔽2)—44no—
37C2×C11×#41—24no—
38C2×C11×#41—22no—
39C22×D4×C11—24no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11D412yes—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C11×C4⋊Q8—21no—
49C11×#127—21no—
50C11×#124—22no—
51C11×#123—24no—
52C11×#123—24no—
53C11×C22⋊Q8—24no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—24no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121D414yes—
62C11×#121C2314yes—
63C11×#120—24no—
64C11×#120—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4C2311yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C22×C11⋊C8—22no—
86#66896—28no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95C2312yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66872—28no—
93#18203—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C24×C11C2×D411yescharacteristic
98C11×#41—44no—
99C11×#41—416no—
100C11×#41—44no—
101C2×Q8×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—44no—
112C2×D4×C11—416no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—82no—
118C2×D4×C11SD1614yes—
119C2×D4×C11C2×D414yes—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—82no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D414yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C42×C11—21no—
150C42×C11—21no—
151C22⋊Dic11—42no—
152C22⋊Dic11—82no—
153C4⋊Dic11—24no—
154C4⋊Dic11—42no—
155C4⋊Dic11—41no—
156C4⋊Dic11—41no—
157Dic11⋊C4—82no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—44no—
160#3496D1111yescharacteristic
161C2×#481—112no—
162#2487—111no—
163#1616—114no—
164#1613—114no—
165#1519—112no—
166#1459—111no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—24no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11—82no—
180C23×C11#12012yes—
181C23×C11C2×SD1612yes—
182C23×C11C2×SD1612yes—
183C23×C11AGL(1,ℤ/8)12yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—44no—
186D4×C11—28no—
187D4×C11—44no—
188D4×C11—44no—
189D4×C11—48no—
190D4×C11—44no—
191D4×C11—44no—
192D4×C11—48no—
193D4×C11—44no—
194D4×C11—82no—
195D4×C11—82no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—48no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—81no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11C2×SD1612yes—
215C2×C4×C11C22×D412yes—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—84no—
223C11⋊C8—44no—
224C2×H(5,𝔽2)—21no—
225#547—22no—
226#546—24no—
227D42—22no—
228#537C2×D1112yes—
229#534—21no—
230#534C2×D1112yes—
231#532—21no—
232C2×#121—21no—
233C2×#121C2×D1112yes—
234C2×C4×D4C2×D1111yescharacteristic
235C22×C4⋊C4—111no—
236#481—118no—
237#481—224no—
238C2×#106—222no—
239C2×#102—222no—
240C2×C22⋊C8—112no—
241#400—112no—
242#399—112no—
243#389—221no—
244#386—221no—
245#385—221no—
246#380—111no—
247#380—221no—
248#327—118no—
249#324—112no—
250#323—112no—
251C22×C11—21no—
252C22×C11—22no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—81no—
265C22×C11—164no—
266C22×C11—164no—
267C22×C11#45014yes—
268C22×C11C2×#12011yescharacteristic
269C22×C11C22×SD1611yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11—22no—
272C4×C11—21no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11#45812yes—
278Dic11—82no—
279Dic11—82no—
280H(5,𝔽2)—44no—
281H(5,𝔽2)—44no—
282C2×#41—24no—
283C2×#41—22no—
284C22×D4—24no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4C22⋊D1111yescharacteristic
289C22×D4C22⋊D1112yes—
290C23×C4—221no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C22×C8—222no—
294C4⋊Q8—21no—
295#127—21no—
296#124—22no—
297#123—24no—
298#123—24no—
299C22⋊Q8—24no—
300#121—22no—
301#121—22no—
302#121—24no—
303#121—22no—
304#121—22no—
305#121—22no—
306#121—22no—
307#121C22⋊D1114yes—
308#121C22×D1114yes—
309#120—24no—
310#120—24no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4C22⋊D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4C22⋊D1111yescharacteristic
329C2×C22⋊C4C22×D1111yescharacteristic
330C2×C42C22⋊D1111yescharacteristic
331#106—228no—
332#102—228no—
333C22⋊C8—114no—
334C22⋊C8—222no—
335#95—112no—
336#95—222no—
337#95—222no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—24no—
341C2×C11—42no—
342C2×C11—84no—
343C2×C11C2×#45011yescharacteristic
344C2×C11#302111yescharacteristic
345C2×C11C2×#45811yescharacteristic
346C24—22no—
347C24—22no—
348C24C2×C22⋊D1111yescharacteristic
349C24C2×C22⋊D1111yescharacteristic
350#41—44no—
351#41—416no—
352#41—44no—
353C2×Q8—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—44no—
364C2×D4—416no—
365C2×D4—44no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—82no—
370C2×D4#432414yes—
371C2×D4C2×C22⋊D1114yes—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—442no—
382C22×C4—882no—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1112yes—
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1112yes—
389C22×C4C23×D1111yescharacteristic
390C2×C8—224no—
391C2×C8—444no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—224no—
397C4⋊C4—442no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—882no—
401C4⋊C4C2×C22⋊D1114yes—
402C22⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—22no—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—442no—
409C22⋊C4—882no—
410C42—21no—
411C42—21no—
412C11#1820311yescharacteristic, complemented, Sylow
413C23—21no—
414C23—21no—
415C23—24no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—44no—
421C23—44no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#6698512yes—
427C23C2×#432412yes—
428C23C2×#432412yes—
429C23#6700612yes—
430C23C22×C22⋊D1111yescharacteristic
431Q8—44no—
432D4—28no—
433D4—44no—
434D4—44no—
435D4—48no—
436D4—44no—
437D4—44no—
438D4—48no—
439D4—44no—
440D4—82no—
441D4—82no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—48no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—884no—
465C2×C4C2×#432412yes—
466C2×C4#6700611yescharacteristic
467C2×C4#6700611yescharacteristic
468C2×C4C22×C22⋊D1112yes—
469C8—444no—
470C22—21no—
471C22—22no—
472C22—21no—
473C22—22no—
474C22—22no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—44no—
481C22—44no—
482C22—44no—
483C22—81no—
484C22—164no—
485C22—164no—
486C22#1062283114yes—
487C22C2×#6698511yescharacteristic
488C22C22×#432411yescharacteristic
489C22C2×#6700611yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—44no—
494C4—41no—
495C4—41no—
496C4—882no—
497C4—882no—
498C4#1062285612yes—
499C2—21no—
500C2—21no—
501C2—24no—
502C2—42no—
503C2—84no—
504C2C2×#1062283111yescharacteristic
505C2#1307798811yescharacteristic
506C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18203
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#10622647C2semidirect
2. #13072933C2semidirect
3. #13067653C2semidirect
4. #13067636C2semidirect
5. #13067184C2semidirect
6. #13066934C2semidirect
19. C22×C4⋊Dic11C22semidirect
23. #10622825C22semidirect
24. C2×C22⋊(C11⋊C8)C22semidirect
26. #10622647C22semidirect
27. #10622599C22semidirect
29. #10622562C22semidirect
32. #10622175C22semidirect
33. #10622166C22semidirect
34. #10622163C22semidirect
412. C11#18203semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
#130729332
#130676532
#130676362
#130671842
#130669342
C11×#34962
#1820311