Finite Group Databasebeta

← #14808276

Subgroups — #14808276

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079163C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic, complemented
4#13069823C214yesmaximal, complemented
5#13069561C211yesmaximal, characteristic, complemented
6#13069536C211yesmaximal, characteristic, complemented
7#13068842C214yesmaximal, complemented
8C4×#66897C211yesmaximal, characteristic, complemented
9C11×#3506C211yesmaximal, characteristic
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538—22no—
17C11×#535C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C11×#520C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66977—22no—
24C2×#66922C2211yescharacteristic
25C2×#66901C2214yes—
26#10622845C2214yes—
27#10622834C2212yes—
28C2×#66897C2212yes—
29#10622694—21no—
30#10622692—21no—
31#10622691—21no—
32#10622683—21no—
33#10622678—22no—
34#10622668—22no—
35#10622608C2214yes—
36#10622589C2212yes—
37#10622562—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622170C2214yes—
42#10622168C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41C2312yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11D412yes—
47C22×Dic22—21no—
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8D411yescharacteristic
51C11×#127—22no—
52C11×#127D411yescharacteristic
53C11×#126—24no—
54C11×#125D412yes—
55C11×#124—24no—
56C11×#124—22no—
57C11×#124D412yes—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×#121—22no—
64C11×#121—24no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#120—24no—
70C4×Q8×C11—22no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×D4×C11—24no—
74C4×D4×C11—22no—
75C4×D4×C11—24no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C11×#117—22no—
83C11×#117—22no—
84C11×#117C2312yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—24no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93#66977—48no—
94C2×Dic11⋊C4—24no—
95C2×C4×Dic11C2312yes—
96C2×#4318C2312yes—
97C2×#4318C2312yes—
98#66922—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102#66901—28no—
103#66899—24no—
104#66897—24no—
105#66896—24no—
106C11⋊#95—21no—
107#66872—24no—
108#66871—24no—
109#66867—21no—
110#66867—21no—
111C4×C11⋊C8—21no—
112C4×C11⋊C8—21no—
113#25694—111nomaximal, Sylow
114C24×C11C2×D412yes—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—84no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—44no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—22no—
141C22×Dic11—22no—
142C2×Dic22—44no—
143C2×Dic22—41no—
144C2×Dic22—41no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—24no—
165C42×C11—22no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C22⋊Dic11—48no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—41no—
175C4⋊Dic11—41no—
176Dic11⋊C4—48no—
177C4×Dic11—24no—
178#4318—22no—
179#4318—22no—
180#4318—22no—
181#4318#4114yescomplemented
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184#3506D1111yescharacteristic
185#3165—111no—
186#3141—111no—
187#2542—111no—
188#2037—114no—
189#1986—111no—
190#1980—111no—
191#1859—114no—
192C4×#100—111no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200Q8×C11—24no—
201Q8×C11—42no—
202Q8×C11—81no—
203D4×C11—24no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—81no—
210D4×C11—84no—
211D4×C11—84no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11—84no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4112yes—
230C2×C4×C112−1+412yes—
231C2×Dic11—24no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236Dic22—82no—
237Dic22—82no—
238C11⋊C8—24no—
239C11⋊C8—42no—
240#559—22no—
241#556—21no—
242#555—21no—
243#553—22no—
244#550—21no—
245#547—21no—
246#538—22no—
247#535C2×D1112yes—
248#533C2×D1111yescharacteristic
249#532C2×D1111yescharacteristic
250C2×C4⋊Q8—111no—
251#525—22no—
252C2×C22⋊Q8—222no—
253#520C2×D1112yes—
254C2×C4×D4C2×D1111yescharacteristic
255#501—222no—
256#500—221no—
257#498—221no—
258#489—222no—
259#487—221no—
260#486—221no—
261#428—114no—
262C2×#104—114no—
263#417—114no—
264C2×#100—112no—
265C4×M16—111no—
266C4×M16—111no—
267#399—222no—
268#390—112no—
269#384—112no—
270C4×C4⋊C4—111no—
271#343—112no—
272#339—114no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—82no—
283C22×C11C2×#12011yescharacteristic
284C22×C11#53211yescharacteristic
285C22×C11#53611yescharacteristic
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11#45312yes—
294C4×C11#54712yes—
295C4×C11#54812yes—
296Dic11—44no—
297Dic11—82no—
298C2×#41—22no—
299C2×#41C22×D1112yes—
300C22×Q8—221no—
301C22×D4C22×D1111yescharacteristic
302C23×C4C22⋊D1112yes—
303C2×M16—112no—
304C2×M16—112no—
305C4⋊Q8—221no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
309C4⋊Q8C22⋊D1111yescharacteristic
310C4⋊Q8C22⋊D1111yescharacteristic
311C4⋊Q8C22⋊D1111yescharacteristic
312#127—22no—
313#127C22⋊D1111yescharacteristic
314#126—24no—
315#125C22⋊D1112yes—
316#124—24no—
317#124—22no—
318#124C22⋊D1112yes—
319#123—24no—
320#123—24no—
321C22⋊Q8—22no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—448no—
325#121—22no—
326#121—24no—
327#121—21no—
328#121—21no—
329#121—22no—
330#121—22no—
331#120—24no—
332C4×Q8—22no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×D4—24no—
336C4×D4—22no—
337C4×D4—24no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344#117—22no—
345#117—22no—
346#117C22×D1112yes—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—224no—
354C2×C22⋊C4C22⋊D1112yes—
355C2×C42—112no—
356C2×C42C22×D1111yescharacteristic
357#107—224no—
358#106—224no—
359#104—228no—
360#103—224no—
361#102—224no—
362#100—224no—
363#97—221no—
364#97—221no—
365C4×C8—221no—
366C4×C8—221no—
367#95—221no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—82no—
371C2×C11—82no—
372C2×C11#243211yescharacteristic
373C2×C11C2×#45311yescharacteristic
374C2×C11#302211yescharacteristic
375C24C2×C22⋊D1112yes—
376#41—24no—
377#41—24no—
378#41—84no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—444no—
382C2×Q8—441no—
383C2×Q8—441no—
384C2×Q8C2×C22⋊D1112yes—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×C22⋊D1112yes—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—44no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C23×D1111yescharacteristic
406M16—114no—
407M16—222no—
408M16—222no—
409M16—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—448no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4C2×C22⋊D1112yes—
428C4⋊C4C2×C22⋊D1112yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—448no—
438C42—24no—
439C42—22no—
440C42—224no—
441C42C2×C22⋊D1111yescharacteristic
442C42C2×C22⋊D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C42C2×C22⋊D1111yescharacteristic
445C11#2569411yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23C22×C22⋊D1111yescharacteristic
453Q8—24no—
454Q8—42no—
455Q8—81no—
456Q8—882no—
457Q8—882no—
458D4—24no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—81no—
465D4—84no—
466D4—84no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—82no—
477C2×C4—84no—
478C2×C4—224no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—444no—
482C2×C4—442no—
483C2×C4#6700611yescharacteristic
484C2×C4#6700611yescharacteristic
485C2×C4#6700611yescharacteristic
486C2×C4#6700611yescharacteristic
487C2×C4#41×D1112yes—
488C2×C4#6704312yes—
489C2×C4C22×C22⋊D1111yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C8—224no—
492C8—442no—
493C22—21no—
494C22—21no—
495C22—44no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—82no—
503C22#1062335611yescharacteristic
504C22#1062336311yescharacteristic
505C22C2×#6700611yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—444no—
514C4—882no—
515C4#1062285412yes—
516C4#1062335512yes—
517C4#1062336212yes—
518C2—21no—
519C2—21no—
520C2—82no—
521C2—82no—
522C2#1307224011yescharacteristic
523C2C2×#1062285411yescharacteristic
524C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#25694
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
2. #13079009C2semidirect
3. #13073569C2semidirect
4. #13069823C2semidirect
5. #13069561C2semidirect
6. #13069536C2semidirect
7. #13068842C2semidirect
8. C4×#66897C2semidirect
181. #4318#41semidirect
445. C11#25694semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130790092
#130735692
#130698232
#130695612
#130695362
#130688422
C4×#668972
C11×#35062
#2569411