Finite Group Databasebeta

← #14792707

Subgroups — #14792707

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078552C211yesmaximal, characteristic
2#13077270C211yesmaximal, characteristic, complemented
3C2×#10622838C211yesmaximal, characteristic, complemented
4#13069981C212yesmaximal, complemented
5#13069874C212yesmaximal, complemented
6#13069521C212yesmaximal, complemented
7#13069268C212yesmaximal, complemented
8#13069080C211yesmaximal, characteristic
9#13068823C211yesmaximal, characteristic, complemented
10#13068540C211yesmaximal, characteristic, complemented
11C2×C11×#448C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#448—21no—
18C11×#448—21no—
19C11×#448—22no—
20C2×C11×#103C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×#66900C2212yes—
23C2×#66900C2212yes—
24#10622838—21no—
25#10622838—21no—
26#10622838C2212yes—
27#10622838C2212yes—
28C2×#66899—21no—
29C2×#66899—21no—
30C2×#66897C2212yes—
31#10622828C2211yescharacteristic
32#10622828C2211yescharacteristic
33#10622820C2211yescharacteristic
34#10622820C2211yescharacteristic
35C2×#66883C2212yes—
36#10622715C2212yes—
37#10622714C2212yes—
38#10622648—21no—
39#10622648—21no—
40#10622647—21no—
41#10622646—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×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—42no—
65C22×C8×C11C2312yes—
66C11×#121—21no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121—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#66899—22no—
97#66899—22no—
98#66899—22no—
99#66899—22no—
100#66897—42no—
101#66896—21no—
102#66896—21no—
103#66896—21no—
104#66896—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#24523—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11#4111yescharacteristic
121C2×Q8×C11—22no—
122C2×Q8×C11—24no—
123C2×Q8×C11—24no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—41no—
134C2×Q8×C11—41no—
135C2×Q8×C11#4114yes—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—82no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—44no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C11×SD16—44no—
159C11×SD16—44no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C2×D412yes—
163C2×C8×C11C2×D412yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C22⋊Dic11—21no—
169C22⋊Dic11—21no—
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×D411yescharacteristic
175C4⋊Dic11C2×D411yescharacteristic
176C4⋊Dic11C2×D411yescharacteristic
177C4⋊Dic11C2×D411yescharacteristic
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194#3094—111no—
195C2×#448D1111yescharacteristic
196#2924—111no—
197C2×#419—111no—
198#2064—112no—
199#2046—112no—
200#1977—112no—
201#1930—112no—
202#1900—111no—
203#1855—111no—
204#1784—111no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11#12111yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11C2×#4111yescharacteristic
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—44no—
218Q8×C11—44no—
219Q8×C11—42no—
220Q8×C11—42no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—82no—
225D4×C11—82no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—81no—
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—42no—
251C2×Dic11—81no—
252C8×C11—22no—
253C8×C11—22no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256C11⋊C8—41no—
257C11⋊C8—42no—
258C23×Q8C2×D1111yescharacteristic
259C22×SD16C2×D1112yes—
260C22×M16—111no—
261C2×#121C2×D1111yescharacteristic
262C2×#117—111no—
263#482—221no—
264#482—221no—
265#481—221no—
266#480—221no—
267#448—21no—
268#448—21no—
269#448—22no—
270#433—222no—
271#432—221no—
272#431—221no—
273C2×#108—112no—
274#428—111no—
275#428—111no—
276#424—112no—
277#419—112no—
278#419—112no—
279#419—221no—
280#419—221no—
281#418—111no—
282#418—111no—
283C2×#103—221no—
284C2×#103—221no—
285C2×#103C2×D1112yes—
286C2×#101—112no—
287C2×#101—112no—
288C2×#100—112no—
289#407—111no—
290#407—111no—
291C2×C22⋊C8C2×D1111yescharacteristic
292#405—112no—
293#343—112no—
294#341—112no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—44no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—162no—
307C22×C11#47112yes—
308C22×C11C2×#12111yescharacteristic
309C22×C11#55112yes—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—44no—
313C4×C11—81no—
314C4×C11#52511yescharacteristic
315C4×C11#53511yescharacteristic
316C4×C11#54612yes—
317Dic11—41no—
318Dic11—41no—
319Dic11—41no—
320Dic11—41no—
321C22×Q8—21no—
322C22×Q8—24no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—42no—
328C22×Q8C22×D1112yes—
329C22×D4—21no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4C22×D1111yescharacteristic
333C2×SD16—24no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—42no—
337C2×M16—112no—
338C2×M16—111no—
339C2×M16—112no—
340C2×M16—111no—
341C2×M16—221no—
342C2×M16—442no—
343C22×C8—221no—
344C22×C8C22×D1112yes—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#117—111no—
350#117—111no—
351#117—111no—
352#117—111no—
353#117—221no—
354#117—221no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—221no—
360C2×C42—221no—
361#108—442no—
362#107—221no—
363#107—221no—
364#106—221no—
365#106—221no—
366C4⋊C8—222no—
367C4⋊C8—222no—
368#103—22no—
369#103—22no—
370#103—222no—
371#103—222no—
372#103—222no—
373#103—222no—
374#102—221no—
375#102—221no—
376#102—221no—
377#102—221no—
378#101—224no—
379#101—442no—
380#100—442no—
381C22⋊C8—221no—
382C22⋊C8—221no—
383C22⋊C8—221no—
384C22⋊C8—221no—
385C22⋊C8C22⋊D1111yescharacteristic
386C22⋊C8C22⋊D1111yescharacteristic
387C22⋊C8C22⋊D1112yes—
388#97—222no—
389C4×C8—222no—
390C2×C11—22no—
391C2×C11—22no—
392C2×C11—41no—
393C2×C11—161no—
394C2×C11#241111yescharacteristic
395C2×C11C2×#47111yescharacteristic
396C2×C11#306911yescharacteristic
397C24—21no—
398C24#434111yescharacteristic
399C2×Q8—22no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—44no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8#434114yes—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—44no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436SD16—44no—
437SD16—44no—
438M16—222no—
439M16—222no—
440M16—222no—
441M16—222no—
442M16—222no—
443M16—222no—
444M16—442no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—442no—
452C2×C8C2×C22⋊D1112yes—
453C2×C8C2×C22⋊D1112yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—111no—
457C4⋊C4—111no—
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—221no—
465C22⋊C4—221no—
466C22⋊C4—221no—
467C22⋊C4—221no—
468C42—221no—
469C42—221no—
470C42—221no—
471C42—221no—
472C11#2452311yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—81no—
479C23—81no—
480C23#6699111yescharacteristic
481C23#6699111yescharacteristic
482C23C2×#434111yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—44no—
486Q8—44no—
487Q8—42no—
488Q8—42no—
489D4—42no—
490D4—41no—
491D4—41no—
492D4—82no—
493D4—82no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—81no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—442no—
513C2×C4—881no—
514C2×C4#6699111yescharacteristic
515C2×C4#6699111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434112yes—
518C2×C4#6703712yes—
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—22no—
521C8—22no—
522C8—442no—
523C8—441no—
524C8—442no—
525C8—441no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—44no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—162no—
538C22#1062279012yes—
539C22#1062311812yes—
540C22C2×#6699111yescharacteristic
541C4—21no—
542C4—21no—
543C4—44no—
544C4—81no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4#1062311711yescharacteristic
550C4#1062312311yescharacteristic
551C4#1062333712yes—
552C2—22no—
553C2—22no—
554C2—41no—
555C2—161no—
556C2#1307199711yescharacteristic
557C2C2×#1062279011yescharacteristic
558C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#448C2
socleC22×C11C2×#121
prime radicalC2×C11×#121C22
hypercenterC2×#448D11
hypocenterC11#24523
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. #13077270C2semidirect
3. C2×#10622838C2semidirect
4. #13069981C2semidirect
5. #13069874C2semidirect
6. #13069521C2semidirect
7. #13069268C2semidirect
9. #13068823C2semidirect
10. #13068540C2semidirect
472. C11#24523semidirect

Maximal subgroups

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

subgroupindex
#130785522
#130772702
C2×#106228382
#130699812
#130698742
#130695212
#130692682
#130690802
#130688232
#130685402
C2×C11×#4482
#2452311