Finite Group Databasebeta

← #14792696

Subgroups — #14792696

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078560C211yesmaximal, characteristic
2#13077270C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic
4#13069981C212yesmaximal, complemented
5#13069881C212yesmaximal, complemented
6#13069532C212yesmaximal, complemented
7#13069268C212yesmaximal, complemented
8#13069085C211yesmaximal, characteristic
9#13068823C211yesmaximal, characteristic
10#13068540C211yesmaximal, characteristic
11C2×C11×#451C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#451—21no—
18C11×#451—21no—
19C11×#451—22no—
20C2×C11×#103C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×#66900C2212yes—
23C2×#66900C2212yes—
24C2×#66900C2212yes—
25#10622838—21no—
26#10622838—21no—
27#10622838C2211yescharacteristic
28#10622838C2211yescharacteristic
29#10622838C2212yes—
30#10622838C2212yes—
31C2×#66899—21no—
32C2×#66899—21no—
33#10622820C2211yescharacteristic
34#10622820C2211yescharacteristic
35C2×#66883C2212yes—
36#10622715C2212yes—
37#10622714C2212yes—
38#10622658—21no—
39#10622658—21no—
40#10622657—21no—
41#10622656—21no—
42#10622577C2211yescharacteristic
43#10622577C2211yescharacteristic
44#10622333—22no—
45#10622332—21no—
46#10622331—21no—
47#10622190C2212yes—
48#10622168C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11—24no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—42no—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C2×C11×Q16—24no—
61C2×C11×Q16—22no—
62C2×C11×Q16—22no—
63C2×C11×Q16—42no—
64C22×C8×C11C2312yes—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73#66979—21no—
74#66979—21no—
75#66979D411yescharacteristic
76#66979D411yescharacteristic
77#66979C2311yescharacteristic
78#66979C2311yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C2×#4318—42no—
84C2×#4318C2311yescharacteristic
85C2×#4318C2312yes—
86C2×#4318C2311yescharacteristic
87C2×#4318C2312yes—
88C22×C11⋊C8—21no—
89C11×#103—22no—
90C11×#103—22no—
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C11×C22⋊C8D412yes—
94#66900—24no—
95#66900—42no—
96#66900—42no—
97#66899—22no—
98#66899—22no—
99#66899—22no—
100#66899—22no—
101#66899—21no—
102#66899—21no—
103#66899—21no—
104#66899—21no—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109#66883—42no—
110#66879—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114#66872—21no—
115#66872—21no—
116#66871—21no—
117#66871—21no—
118#24522—111nomaximal, Sylow
119C24×C11#4111yescharacteristic
120C2×Q8×C11—22no—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11—44no—
133C2×Q8×C11—44no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—41no—
137C2×Q8×C11—41no—
138C2×Q8×C11#4114yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—44no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C11×Q16—44no—
156C11×Q16—44no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D412yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C22⋊Dic11—21no—
168C22⋊Dic11—21no—
169C22⋊Dic11—21no—
170C22⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C2×D411yescharacteristic
174C4⋊Dic11C2×D411yescharacteristic
175C4⋊Dic11C2×D411yescharacteristic
176C4⋊Dic11C2×D411yescharacteristic
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181#4318—22no—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—42no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193#3095—111no—
194C2×#451D1111yescharacteristic
195#2924—111no—
196C2×#419—111no—
197#2064—112no—
198#2047—112no—
199#1979—112no—
200#1930—112no—
201#1901—111no—
202#1855—111no—
203#1784—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11#12111yescharacteristic
208C23×C11#12111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—44no—
213Q8×C11—44no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—42no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—81no—
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—42no—
246C2×Dic11—81no—
247C8×C11—22no—
248C8×C11—22no—
249C11⋊C8—41no—
250C11⋊C8—42no—
251C11⋊C8—41no—
252C11⋊C8—42no—
253C23×Q8C2×D1111yescharacteristic
254C22×Q16C2×D1112yes—
255C22×M16—111no—
256C2×C22⋊Q8C2×D1111yescharacteristic
257C2×#117—111no—
258#485—221no—
259#485—221no—
260#484—221no—
261#483—221no—
262#451—21no—
263#451—21no—
264#451—22no—
265#433—222no—
266#432—221no—
267#431—221no—
268C2×#108—112no—
269#428—111no—
270#428—111no—
271#424—112no—
272#419—112no—
273#419—111no—
274#419—111no—
275#419—112no—
276#419—221no—
277#419—221no—
278C2×#103—221no—
279C2×#103—221no—
280C2×#103C2×D1112yes—
281C2×#101—112no—
282C2×#101—112no—
283C2×#101—112no—
284#407—111no—
285#407—111no—
286C2×C22⋊C8C2×D1111yescharacteristic
287#405—112no—
288#343—112no—
289#341—112no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—44no—
298C22×C11#47312yes—
299C22×C11C2×#12111yescharacteristic
300C22×C11#55112yes—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—44no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#52511yescharacteristic
307C4×C11#53511yescharacteristic
308C4×C11#54612yes—
309Dic11—41no—
310Dic11—41no—
311Dic11—41no—
312Dic11—41no—
313C22×Q8—21no—
314C22×Q8—24no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8—21no—
319C22×Q8—42no—
320C22×Q8C22×D1111yescharacteristic
321C22×Q8C22×D1112yes—
322C23×C4—21no—
323C23×C4C22×D1111yescharacteristic
324C2×Q16—24no—
325C2×Q16—22no—
326C2×Q16—22no—
327C2×Q16—42no—
328C2×M16—112no—
329C2×M16—111no—
330C2×M16—112no—
331C2×M16—111no—
332C2×M16—221no—
333C2×M16—442no—
334C22×C8—221no—
335C22×C8C22×D1112yes—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340#117—111no—
341#117—111no—
342#117—111no—
343#117—111no—
344#117—221no—
345#117—221no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—221no—
352C2×C42—221no—
353#108—442no—
354#107—221no—
355#107—221no—
356#106—221no—
357#106—221no—
358C4⋊C8—222no—
359C4⋊C8—222no—
360#103—22no—
361#103—22no—
362#103—222no—
363#103—222no—
364#103—222no—
365#103—222no—
366#103—221no—
367#103—221no—
368#103—221no—
369#103—221no—
370#101—224no—
371#101—442no—
372#101—442no—
373C22⋊C8—221no—
374C22⋊C8—221no—
375C22⋊C8—221no—
376C22⋊C8—221no—
377C22⋊C8C22⋊D1111yescharacteristic
378C22⋊C8C22⋊D1111yescharacteristic
379C22⋊C8C22⋊D1112yes—
380#97—222no—
381C4×C8—222no—
382C2×C11—22no—
383C2×C11—22no—
384C2×C11—41no—
385C2×C11#241111yescharacteristic
386C2×C11C2×#47311yescharacteristic
387C2×C11#306911yescharacteristic
388C24#434111yescharacteristic
389C2×Q8—22no—
390C2×Q8—24no—
391C2×Q8—24no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—44no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8#434114yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—44no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4#434111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424Q16—44no—
425Q16—44no—
426M16—222no—
427M16—222no—
428M16—222no—
429M16—222no—
430M16—222no—
431M16—222no—
432M16—442no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—442no—
440C2×C8C2×C22⋊D1112yes—
441C2×C8C2×C22⋊D1112yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—111no—
447C4⋊C4—111no—
448C4⋊C4—111no—
449C4⋊C4—111no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—221no—
455C22⋊C4—221no—
456C22⋊C4—221no—
457C22⋊C4—221no—
458C42—221no—
459C42—221no—
460C42—221no—
461C42—221no—
462C11#2452211yescharacteristic, complemented, Sylow
463C23—22no—
464C23—22no—
465C23—41no—
466C23#6699111yescharacteristic
467C23#6699111yescharacteristic
468C23C2×#434111yescharacteristic
469Q8—24no—
470Q8—24no—
471Q8—44no—
472Q8—44no—
473Q8—42no—
474Q8—42no—
475Q8—42no—
476Q8—41no—
477Q8—41no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—81no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—442no—
499C2×C4—881no—
500C2×C4#6699111yescharacteristic
501C2×C4#6699111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4C2×#434112yes—
504C2×C4#6703712yes—
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—22no—
507C8—22no—
508C8—442no—
509C8—441no—
510C8—442no—
511C8—441no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—44no—
520C22#1062280512yes—
521C22#1062311812yes—
522C22C2×#6699111yescharacteristic
523C4—21no—
524C4—21no—
525C4—44no—
526C4—81no—
527C4—81no—
528C4—441no—
529C4—441no—
530C4—441no—
531C4—441no—
532C4#1062311711yescharacteristic
533C4#1062312311yescharacteristic
534C4#1062333712yes—
535C2—22no—
536C2—22no—
537C2—41no—
538C2#1307199711yescharacteristic
539C2C2×#1062280511yescharacteristic
540C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#451C2
socleC22×C11C2×#121
prime radicalC24×C11#41
hypercenterC2×#451D11
hypocenterC11#24522
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
4. #13069981C2semidirect
5. #13069881C2semidirect
6. #13069532C2semidirect
7. #13069268C2semidirect
462. C11#24522semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130772702
C2×#106228382
#130699812
#130698812
#130695322
#130692682
#130690852
#130688232
#130685402
C2×C11×#4512
#2452211