Finite Group Databasebeta

← #14808218

Subgroups — #14808218

Order 2816.

964 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#13079163C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic
3#13076993C211yesmaximal, characteristic, complemented
4#13069830C214yesmaximal
5#13069594C211yesmaximal, characteristic, complemented
6#13069461C211yesmaximal, characteristic, complemented
7#13068831C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic
9C11×#3509C211yesmaximal, characteristic
10C11×#557—21no—
11C11×#557—21no—
12C11×#556—21no—
13C11×#556—21no—
14C11×#552—22no—
15C11×#552—22no—
16C11×#541—22no—
17C11×#536C2212yes—
18C11×#533—21no—
19C11×#533—21no—
20C11×#533C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#519C2212yes—
23C4×C11×#41C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×#66901C2212yes—
26#10622845C2212yes—
27#10622843C2214yes—
28C2×#66900C2214yes—
29#10622692—21no—
30#10622691—21no—
31#10622678—22no—
32#10622634—21no—
33#10622633—21no—
34#10622621—21no—
35#10622620—21no—
36#10622608C2214yes—
37#10622608C2212yes—
38#10622590—22no—
39#10622587—22no—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2214yes—
44#10622170C2212yes—
45C2×C11×#41C2311yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Dic22—21no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#126—24no—
56C11×#126—24no—
57C11×#125—22no—
58C11×#125—22no—
59C11×#125—24no—
60C11×#125—24no—
61C11×#125D412yes—
62C11×#124—22no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11D411yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11D411yescharacteristic
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—24no—
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C11×#117C2312yes—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4D412yes—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2312yes—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2312yes—
99C2×#4318C2312yes—
100C2×#4318C2312yes—
101#66922—21no—
102#66922—21no—
103#66922—21no—
104#66922—21no—
105#66901—24no—
106#66900—28no—
107#66899—22no—
108#66896—22no—
109C11⋊#95—28no—
110#66872—22no—
111#66872—24no—
112#66871—22no—
113#66871—24no—
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)—21no—
116#66867—21no—
117C4×C11⋊C8—21no—
118#25688—111nomaximal, Sylow
119C11×#41—22no—
120C11×#41—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—24no—
126C2×Q8×C11—24no—
127C2×Q8×C11C2×D411yescharacteristic
128C2×D4×C11—21no—
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—22no—
138C22×Dic11—22no—
139C2×Dic22—44no—
140C2×Dic22—41no—
141C2×Dic22—41no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C2×D411yescharacteristic
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D411yescharacteristic
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C42×C11—24no—
167C42×C11—24no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—22no—
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—41no—
179C4⋊Dic11—41no—
180C4×Dic11—24no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—42no—
184#4318—24no—
185#4318—22no—
186#4318#4114yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189#3509D1111yescharacteristic
190#3165—111no—
191#3079—111no—
192#2862—111no—
193#2038—114no—
194#1994—111no—
195#1966—111no—
196#1857—114no—
197C4×#104—111no—
198C23×C11—21no—
199C23×C11C22×D411yescharacteristic
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—42no—
203Q8×C11—42no—
204Q8×C11—44no—
205Q8×C11—42no—
206Q8×C11—42no—
207D4×C11—21no—
208D4×C11—21no—
209D4×C11—42no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—21no—
218C2×C4×C11—28no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4112yes—
229C2×C4×C112−1+412yes—
230C2×Dic11—24no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235Dic22—82no—
236Dic22—82no—
237C11⋊C8—24no—
238C11⋊C8—42no—
239#557—21no—
240#557—21no—
241#556—21no—
242#556—21no—
243#552—22no—
244#552—22no—
245#541—22no—
246#536C2×D1112yes—
247#533—21no—
248#533—21no—
249#533C2×D1111yescharacteristic
250C2×C4⋊Q8—111no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252#519C2×D1112yes—
253C4×#41C2×D1111yescharacteristic
254#501—222no—
255#500—221no—
256#498—221no—
257#477—221no—
258#476—221no—
259#475—221no—
260#474—221no—
261#428—112no—
262#428—114no—
263#423—111no—
264C2×#104—112no—
265#417—112no—
266C2×#101—114no—
267C4×M16—111no—
268#391—114no—
269#391—222no—
270#382—222no—
271C43—111no—
272#339—112no—
273#339—114no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11C2×#12011yescharacteristic
280C22×C11#54712yes—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—44no—
284C4×C11—41no—
285C4×C11—41no—
286C4×C11—42no—
287C4×C11—41no—
288C4×C11—42no—
289C4×C11#45412yes—
290C4×C11#45612yes—
291C4×C11#53211yescharacteristic
292C4×C11#53611yescharacteristic
293C4×C11#54812yes—
294Dic11—44no—
295Dic11—82no—
296C2×#41C22×D1111yescharacteristic
297C22×Q8—221no—
298C22×Q8C22×D1112yes—
299C2×M16—112no—
300C2×M16—112no—
301C4⋊Q8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310C4⋊Q8C22⋊D1111yescharacteristic
311C4⋊Q8C22⋊D1111yescharacteristic
312#126—24no—
313#126—24no—
314#125—22no—
315#125—22no—
316#125—24no—
317#125—24no—
318#125C22⋊D1112yes—
319#124—22no—
320#123—24no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22⋊D1111yescharacteristic
337C4×D4—21no—
338C4×D4—21no—
339C4×D4C22⋊D1111yescharacteristic
340C4×D4C22⋊D1111yescharacteristic
341#117—22no—
342#117—22no—
343#117—24no—
344#117—21no—
345#117C22×D1111yescharacteristic
346#117C22×D1112yes—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4C22⋊D1112yes—
350C2×C4⋊C4C22⋊D1112yes—
351C2×C42—21no—
352C2×C42—112no—
353C2×C42—221no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356#107—222no—
357#107—224no—
358#106—222no—
359#106—224no—
360C4⋊C8—221no—
361C4⋊C8—221no—
362#104—224no—
363#103—222no—
364#102—222no—
365#101—228no—
366#97—221no—
367C4×C8—221no—
368#95—228no—
369C2×C11—22no—
370C2×C11—81no—
371C2×C11#243211yescharacteristic
372C2×C11C2×#45411yescharacteristic
373C2×C11C2×#45611yescharacteristic
374#41—22no—
375#41—22no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—444no—
383C2×Q8—441no—
384C2×Q8—441no—
385C2×Q8C2×C22⋊D1111yescharacteristic
386C2×D4—21no—
387C2×D4C2×C22⋊D1111yescharacteristic
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4C2×C22⋊D1114yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397M16—114no—
398M16—222no—
399M16—224no—
400C2×C8—222no—
401C2×C8—222no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4C2×C22⋊D1111yescharacteristic
421C4⋊C4C2×C22⋊D1112yes—
422C4⋊C4C2×C22⋊D1111yescharacteristic
423C4⋊C4C2×C22⋊D1112yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—21no—
427C22⋊C4—22no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C42—24no—
431C42—24no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—22no—
436C42—224no—
437C42—222no—
438C42—222no—
439C42—442no—
440C42C2×C22⋊D1111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C2×C22⋊D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C11#2568811yescharacteristic, complemented, Sylow
445C23—21no—
446C23C22×C22⋊D1111yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—42no—
450Q8—44no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—882no—
455Q8—882no—
456D4—21no—
457D4—21no—
458D4—42no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—28no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—224no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—444no—
475C2×C4—442no—
476C2×C4#6700611yescharacteristic
477C2×C4#6700611yescharacteristic
478C2×C4#6700611yescharacteristic
479C2×C4#6700611yescharacteristic
480C2×C4#41×D1112yes—
481C2×C4#6704312yes—
482C2×C4C22×C22⋊D1111yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—224no—
485C8—442no—
486C22—21no—
487C22—21no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22#1062335512yes—
492C22C2×#6700611yescharacteristic
493C4—21no—
494C4—21no—
495C4—44no—
496C4—41no—
497C4—41no—
498C4—42no—
499C4—41no—
500C4—42no—
501C4—444no—
502C4—882no—
503C4#1062285812yes—
504C4#1062285912yes—
505C4#1062335611yescharacteristic
506C4#1062336212yes—
507C4#1062336311yescharacteristic
508C2—22no—
509C2—81no—
510C2#1307224011yescharacteristic
511C2C2×#1062285811yescharacteristic
512C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3509C2
socleC22×C11C2×#120
prime radicalC2×C11×#41C23
hypercenter#3509D11
hypocenterC11#25688
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
3. #13076993C2semidirect
5. #13069594C2semidirect
6. #13069461C2semidirect
7. #13068831C2semidirect
444. C11#25688semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130784312
#130769932
#130698302
#130695942
#130694612
#130688312
C4×#669012
C11×#35092
#2568811