Finite Group Databasebeta

← #14807457

Subgroups — #14807457

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079076C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic, complemented
3#13076993C211yesmaximal, characteristic, complemented
4#13069663C214yesmaximal, complemented
5#13069606C211yesmaximal, characteristic, complemented
6#13069445C211yesmaximal, characteristic, complemented
7#13068985C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556—21no—
11C11×#555—21no—
12C11×#554—21no—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537C2212yes—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24C2×#67004C2214yes—
25C2×#67004C2212yes—
26C2×#66922C2211yescharacteristic
27C2×#66901C2212yes—
28C2×#66901C2214yes—
29#10622843—22no—
30#10622705—21no—
31#10622689—21no—
32#10622673—22no—
33#10622644—21no—
34#10622644—21no—
35#10622632—21no—
36#10622632—21no—
37#10622617C2212yes—
38#10622590—22no—
39#10622587C2214yes—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2212yes—
44#10622168C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41C2311yescharacteristic
47C2×C11×#41C2312yes—
48C22×Q8×C11D412yes—
49C22×Dic22C2312yes—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#125—22no—
58C11×#124—22no—
59C11×#124—24no—
60C11×#124D412yes—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121—24no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11D411yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—28no—
95#67004—44no—
96#67004—44no—
97C2×#4326—22no—
98C2×#4326—24no—
99C2×#4324—22no—
100C2×#4324—24no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2312yes—
106C2×#4318C2312yes—
107C2×#4318C2312yes—
108#66922—21no—
109#66922—21no—
110#66922—21no—
111#66922—21no—
112#66901—24no—
113#66901—44no—
114C11⋊#95—28no—
115#66874—22no—
116#66874—22no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)—21no—
119#66867—21no—
120C4×C11⋊C8—21no—
121#25615—111nomaximal, Sylow
122C11×#41—22no—
123C11×#41—24no—
124C11×#41—24no—
125C11×#41—22no—
126C11×#41—84no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C2×Q8×C11C2×D412yes—
131C2×Q8×C11C2×D411yescharacteristic
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×D412yes—
138C2×D4×C11C2×D411yescharacteristic
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—22no—
149C22×Dic11—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—24no—
153C2×Dic22—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D411yescharacteristic
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11—24no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182#4326—48no—
183#4326—44no—
184#4324—48no—
185#4324—44no—
186C4⋊Dic11—41no—
187C4⋊Dic11—41no—
188C4⋊Dic11—41no—
189C4⋊Dic11—41no—
190C4×Dic11—24no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—42no—
194#4318—22no—
195#4318—24no—
196#4318#4114yescomplemented
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199#3511D1111yescharacteristic
200#3152—111no—
201#3039—111no—
202#2862—111no—
203#2007—114no—
204#1997—111no—
205#1962—111no—
206#1882—114no—
207C4×#104—111no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11C22×D411yescharacteristic
211Q8×C11—21no—
212Q8×C11—21no—
213Q8×C11—24no—
214Q8×C11—44no—
215Q8×C11—82no—
216D4×C11—21no—
217D4×C11—21no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—84no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—84no—
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C2×Dic11—24no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251Dic22—42no—
252Dic22—42no—
253Dic22—44no—
254C11⋊C8—24no—
255C11⋊C8—42no—
256C2×#137—114no—
257C2×#137—112no—
258#556—21no—
259#555—21no—
260#554—21no—
261#553—22no—
262#548—22no—
263#547—21no—
264#542—22no—
265#537C2×D1112yes—
266#533—21no—
267#532—21no—
268#532C2×D1111yescharacteristic
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271#520C2×D1112yes—
272C4×#41C2×D1111yescharacteristic
273#497—222no—
274#494—221no—
275#492—221no—
276#462—221no—
277#462—221no—
278#461—221no—
279#461—221no—
280#423—111no—
281C2×#104—112no—
282C2×#104—114no—
283#419—112no—
284C4×M16—111no—
285#391—114no—
286#391—222no—
287#382—222no—
288C43—111no—
289#343—114no—
290#339—112no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—42no—
299C22×C11C2×#12011yescharacteristic
300C22×C11#55012yes—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11—44no—
307C4×C11—41no—
308C4×C11#45512yes—
309C4×C11#45612yes—
310C4×C11#53211yescharacteristic
311C4×C11#53511yescharacteristic
312C4×C11#54612yes—
313Dic11—44no—
314Dic11—82no—
315C2×#41—22no—
316C2×#41C22×D1111yescharacteristic
317C2×#41C22×D1112yes—
318C22×Q8—112no—
319C22×Q8C22⋊D1112yes—
320#137—228no—
321#137—444no—
322#137—444no—
323C2×Q16—222no—
324C2×Q16—224no—
325C2×SD16—222no—
326C2×SD16—224no—
327C2×M16—112no—
328C2×M16—112no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—221no—
334C4⋊Q8—221no—
335C4⋊Q8—221no—
336C4⋊Q8—221no—
337C4⋊Q8C22⋊D1111yescharacteristic
338#127C22⋊D1111yescharacteristic
339#126—24no—
340#125—22no—
341#124—22no—
342#124—24no—
343#124C22⋊D1112yes—
344#123—24no—
345C22⋊Q8—22no—
346C22⋊Q8—24no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—21no—
353#121—21no—
354#121—24no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8C22⋊D1111yescharacteristic
358C4×Q8C22⋊D1111yescharacteristic
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—24no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C22⋊D1111yescharacteristic
367C4×D4C22⋊D1111yescharacteristic
368#117—22no—
369#117—22no—
370#117—21no—
371#117C22×D1111yescharacteristic
372C2×C4⋊C4—22no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22⋊D1112yes—
376C2×C4⋊C4C22×D1112yes—
377C2×C42—21no—
378C2×C42—112no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—221no—
383C4⋊C8—221no—
384#104—224no—
385#104—444no—
386#103—222no—
387#103—222no—
388#97—221no—
389C4×C8—221no—
390#95—228no—
391C2×C11—22no—
392C2×C11—81no—
393C2×C11—82no—
394C2×C11#243111yescharacteristic
395C2×C11C2×#45511yescharacteristic
396C2×C11C2×#45611yescharacteristic
397#41—22no—
398#41—24no—
399#41—24no—
400#41—22no—
401#41—84no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—44no—
405C2×Q8—224no—
406C2×Q8—224no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8C2×C22⋊D1112yes—
410C2×Q8C2×C22⋊D1111yescharacteristic
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×C22⋊D1112yes—
417C2×D4C2×C22⋊D1111yescharacteristic
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1114yes—
428C22×C4C23×D1111yescharacteristic
429Q16—448no—
430Q16—444no—
431SD16—448no—
432SD16—444no—
433M16—114no—
434M16—222no—
435M16—224no—
436C2×C8—222no—
437C2×C8—222no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4C2×C22⋊D1111yescharacteristic
453C4⋊C4C2×C22⋊D1111yescharacteristic
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C42—24no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—224no—
467C42—222no—
468C42—222no—
469C42—442no—
470C42C2×C22⋊D1111yescharacteristic
471C42C2×C22⋊D1111yescharacteristic
472C42C2×C22⋊D1111yescharacteristic
473C42C2×C22⋊D1111yescharacteristic
474C11#2561511yescharacteristic, complemented, Sylow
475C23—21no—
476C23—22no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—24no—
479Q8—21no—
480Q8—21no—
481Q8—44no—
482Q8—82no—
483Q8—444no—
484Q8—442no—
485Q8—442no—
486D4—24no—
487D4—21no—
488D4—21no—
489D4—42no—
490D4—44no—
491D4—42no—
492D4—42no—
493D4—84no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—24no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—84no—
508C2×C4—224no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—444no—
512C2×C4—442no—
513C2×C4#6700611yescharacteristic
514C2×C4#6700611yescharacteristic
515C2×C4#6700611yescharacteristic
516C2×C4#6700611yescharacteristic
517C2×C4#41×D1112yes—
518C2×C4#6704212yes—
519C2×C4C22×C22⋊D1111yescharacteristic
520C2×C4C22×C22⋊D1111yescharacteristic
521C8—224no—
522C8—442no—
523C22—21no—
524C22—21no—
525C22—41no—
526C22—42no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—42no—
531C22#1062336512yes—
532C22C2×#6700611yescharacteristic
533C4—21no—
534C4—21no—
535C4—41no—
536C4—42no—
537C4—41no—
538C4—44no—
539C4—41no—
540C4—444no—
541C4—882no—
542C4#1062285512yes—
543C4#1062285912yes—
544C4#1062336012yes—
545C4#1062336111yescharacteristic
546C4#1062336311yescharacteristic
547C2—22no—
548C2—81no—
549C2—82no—
550C2#1307223111yescharacteristic
551C2C2×#1062285511yescharacteristic
552C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#25615
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079076C2semidirect
2. #13078103C2semidirect
3. #13076993C2semidirect
4. #13069663C2semidirect
5. #13069606C2semidirect
6. #13069445C2semidirect
7. #13068985C2semidirect
8. C4×#66901C2semidirect
196. #4318#41semidirect
474. C11#25615semidirect

Maximal subgroups

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

subgroupindex
#130790762
#130781032
#130769932
#130696632
#130696062
#130694452
#130689852
C4×#669012
C11×#35112
#2561511