Finite Group Databasebeta

← #14792711

Subgroups — #14792711

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#13078556C211yesmaximal, characteristic
2C2×#10622840C211yesmaximal, characteristic
3#13077274C211yesmaximal, characteristic, complemented
4#13069983C212yesmaximal, complemented
5#13069876C212yesmaximal, complemented
6#13069518C212yesmaximal, complemented
7#13069274C212yesmaximal, complemented
8#13069079C211yesmaximal, characteristic
9#13068821C211yesmaximal, characteristic, complemented
10#13068540C211yesmaximal, characteristic, complemented
11C2×C11×#419C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4325C2212yes—
16C2×#66983C2211yescharacteristic
17C11×#419—21no—
18C11×#419—21no—
19C11×#419C2212yes—
20C11×#419C2212yes—
21C2×C11×#103—21no—
22C2×C11×#103—21no—
23#10622840—21no—
24#10622840—21no—
25#10622840—22no—
26C2×#66900C2212yes—
27C2×#66900C2212yes—
28C2×#66899C2212yes—
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66887C2212yes—
33C2×#66886C2212yes—
34#10622616—21no—
35#10622616—21no—
36#10622614C2211yescharacteristic
37#10622614C2211yescharacteristic
38#10622613—22no—
39#10622612C2212yes—
40#10622610C2212yes—
41#10622608C2211yescharacteristic
42#10622608C2211yescharacteristic
43#10622581—21no—
44#10622580—21no—
45#10622539—21no—
46#10622538—21no—
47#10622196C2212yes—
48#10622192C2212yes—
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—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C22×D44C2311yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—42no—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C11×#117D411yescharacteristic
69C11×#117C2311yescharacteristic
70C11×#117C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×#4325—24no—
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325—42no—
79#66983—21no—
80#66983—21no—
81#66983—21no—
82#66983—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C2×#4318C2312yes—
87C2×#4318C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C11×#103—22no—
90C11×#103—22no—
91C11×#103—22no—
92C11×#103—22no—
93#66900—24no—
94#66900—42no—
95#66899—22no—
96#66899—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102C22⋊(C11⋊C8)D411yescharacteristic
103C22⋊(C11⋊C8)D412yes—
104#66887—42no—
105#66886—42no—
106#66873—21no—
107#66873—21no—
108#66873—21no—
109#66873—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117C4×C11⋊C8—22no—
118#24523—111nomaximal, Sylow
119C24×C11#4111yescharacteristic
120C23×D11—21no—
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—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—44no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11—82no—
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—42no—
161C2×C8×C11—22no—
162C2×C8×C11—42no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C4⋊C4C2×D411yescharacteristic
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177#4325—44no—
178#4325—44no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8C2×D412yes—
193C2×C11⋊C8C2×D412yes—
194#3094—111no—
195C2×#448—111no—
196#2924—111no—
197C2×#419D1111yescharacteristic, complemented
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#12111yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C22×D11—41no—
212C22×D11—42no—
213C22×D11—81no—
214C22×D11—81no—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—44no—
218Q8×C11—44no—
219Q8×C11—42no—
220Q8×C11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—81no—
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C22⋊D11—82no—
246C22⋊D11—82no—
247C2×Dic11—41no—
248C2×Dic11—81no—
249D44—41no—
250D44—41no—
251D44—42no—
252C8×C11—42no—
253C11⋊C8—22no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—41no—
257C11⋊C8—42no—
258C23×Q8C2×D1111yescharacteristic
259C22×SD16—112no—
260C22×M16C2×D1111yescharacteristic
261C2×#121—111no—
262C2×#117C2×D1111yescharacteristic
263#482—221no—
264#482—221no—
265#481—221no—
266#480—221no—
267#448—221no—
268#448—221no—
269#448—222no—
270#433—222no—
271#432—221no—
272#431—221no—
273C2×#108—112no—
274#428—111no—
275#428—111no—
276#424—112no—
277#419—21no—
278#419—21no—
279#419C2×D1112yes—
280#419C2×D1112yes—
281#418—111no—
282#418—111no—
283C2×#103—21no—
284C2×#103—21no—
285C2×#103—112no—
286C2×#101—112no—
287C2×#101—112no—
288C2×#100—112no—
289#407—111no—
290#407—111no—
291C2×C22⋊C8—111no—
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#47112yes—
304C22×C11C2×#12111yescharacteristic
305C22×C11#55112yes—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—162no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—44no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11#52511yescharacteristic
318C4×C11#53511yescharacteristic
319C4×C11#54612yes—
320Dic11—81no—
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—111no—
330C22×D4—221no—
331C23×C4—21no—
332C23×C4C22×D1111yescharacteristic
333C2×SD16—222no—
334C2×SD16—222no—
335C2×SD16—224no—
336C2×SD16—442no—
337C2×M16—21no—
338C2×M16—42no—
339C2×M16—111no—
340C2×M16—112no—
341C2×M16—111no—
342C2×M16C22×D1112yes—
343C22×C8—21no—
344C22×C8—112no—
345#121—221no—
346#121—221no—
347#121—221no—
348#121—221no—
349#117—21no—
350#117—21no—
351#117C22⋊D1111yescharacteristic
352#117C22⋊D1111yescharacteristic
353#117C22×D1111yescharacteristic
354#117C22×D1111yescharacteristic
355C2×C4⋊C4—111no—
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—221no—
360C2×C42—21no—
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—22no—
371#103—22no—
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—111no—
382C22⋊C8—111no—
383C22⋊C8—112no—
384C22⋊C8—221no—
385C22⋊C8—221no—
386C22⋊C8—221no—
387C22⋊C8—221no—
388#97—222no—
389C4×C8—222no—
390C2×C11—22no—
391C2×C11—22no—
392C2×C11—41no—
393C2×C11#241111yescharacteristic
394C2×C11C2×#47111yescharacteristic
395C2×C11#306911yescharacteristic
396D11—161no—
397C24—221no—
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#433914yes—
414C2×D4—222no—
415C2×D4—221no—
416C2×D4—222no—
417C2×D4—221no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—882no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—44no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—221no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436SD16—444no—
437SD16—444no—
438M16—22no—
439M16—22no—
440M16—42no—
441M16—222no—
442M16—222no—
443M16—222no—
444M16—222no—
445C2×C8—22no—
446C2×C8—42no—
447C2×C8—112no—
448C2×C8—112no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—221no—
453C2×C8—221no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4C2×C22⋊D1111yescharacteristic
459C4⋊C4C2×C22⋊D1111yescharacteristic
460C4⋊C4C2×C22⋊D1111yescharacteristic
461C4⋊C4C2×C22⋊D1111yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C11#2452311yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—41no—
476C23—441no—
477C23—442no—
478C23—881no—
479C23—881no—
480C23#6699211yescharacteristic
481C23#6699211yescharacteristic
482C23C2×#434111yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—44no—
486Q8—44no—
487Q8—42no—
488Q8—42no—
489D4—442no—
490D4—441no—
491D4—441no—
492D4—882no—
493D4—882no—
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—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—81no—
512C2×C4—441no—
513C2×C4—881no—
514C2×C4#6699211yescharacteristic
515C2×C4#6699211yescharacteristic
516C2×C4C2×#433912yes—
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4#6703712yes—
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—42no—
521C8—222no—
522C8—222no—
523C8—442no—
524C8—441no—
525C8—441no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—44no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—1762no—
538C22#1062281612yes—
539C22#1062302612yes—
540C22C2×#6699211yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—44no—
548C4—881no—
549C4#1062302112yes—
550C4#1062332211yescharacteristic
551C4#1062333611yescharacteristic
552C2—22no—
553C2—22no—
554C2—41no—
555C2—1761no—
556C2#1307200111yescharacteristic
557C2C2×#1062281611yescharacteristic
558C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC22×C11C2×#121
prime radicalC2×#66983C22
hypercenterC2×#419D11
hypocenterC11#24523
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #13077274C2semidirect
4. #13069983C2semidirect
5. #13069876C2semidirect
6. #13069518C2semidirect
7. #13069274C2semidirect
9. #13068821C2semidirect
10. #13068540C2semidirect
11. C2×C11×#419C2semidirect
197. C2×#419D11semidirect
472. C11#24523semidirect

Maximal subgroups

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

subgroupindex
#130785562
C2×#106228402
#130772742
#130699832
#130698762
#130695182
#130692742
#130690792
#130688212
#130685402
C2×C11×#4192
#2452311