Finite Group Databasebeta

← #14781670

Subgroups — #14781670

Order 2816.

1326 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
1C2×#10622737C211yesmaximal, characteristic, complemented
2#13077135C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C22×#66900C211yesmaximal, characteristic, complemented
5#13077061C211yesmaximal, characteristic
6#13069912C218yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C22×C11×#137C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C2×C11×#137—22no—
12C2×C11×#137—24no—
13C2×C11×#137—24no—
14C2×C11×#137C2214yes—
15C22×C11×Q16—21no—
16C22×C11×SD16—21no—
17C22×C11×M16C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22#10622847—22no—
23#10622847C2214yes—
24#10622846—22no—
25#10622845C2214yes—
26C2×#66900—24no—
27C2×#66900C2214yescomplemented
28#10622838—21no—
29#10622838—22no—
30#10622838—22no—
31C2×#66899C2214yescomplemented
32#10622828—21no—
33#10622820—22no—
34#10622737—24no—
35C2×#66886C2214yescomplemented
36#10622192C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D412yes—
44C2×C11×#41C2312yes—
45C22×Q8×C11—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11D411yescharacteristic
54C22×Q8×C11D414yes—
55C22×Q8×C11C2312yes—
56C22×D4×C11—21no—
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C11×#137—216no—
62C11×#137—28no—
63C11×#137—28no—
64C2×C11×Q16—28no—
65C2×C11×Q16—24no—
66C2×C11×SD16—28no—
67C2×C11×SD16—24no—
68C2×C11×M16—22no—
69C2×C11×M16—21no—
70C2×C11×M16D414yes—
71C2×C11×M16C2312yes—
72C22×C8×C11—21no—
73C2×C22⋊Dic11—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—21no—
80C2×#4318—22no—
81C2×#4318—22no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318D412yes—
89C2×#4318D412yes—
90C2×#4318C2312yes—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8C2312yes—
95#66900—28no—
96#66899—24no—
97#66899—28no—
98#66896—24no—
99C22⋊(C11⋊C8)—28no—
100#66886—28no—
101#23532—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11#4111yescharacteristic
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—42no—
111C11×#41—42no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—24no—
118C2×Q8×C11—22no—
119C2×Q8×C11—24no—
120C2×Q8×C11—24no—
121C2×Q8×C11—24no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—41no—
128C2×Q8×C11—41no—
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D414yes—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4112yes—
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—22no—
165C11×Q16—216no—
166C11×SD16—216no—
167C11×M16—24no—
168C11×M16—22no—
169C11×M16C2×D414yes—
170C2×C8×C11—24no—
171C2×C8×C11—22no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4×Dic11—41no—
177C4×Dic11—41no—
178#4318—24no—
179#4318—24no—
180#4318—22no—
181#4318—22no—
182#4318—22no—
183#4318—22no—
184#4318—42no—
185#4318—42no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—42no—
191C2×C11⋊C8—42no—
192C2×C11⋊C8C2×D414yes—
193C22×#137D1111yescharacteristic
194C2×#430—111no—
195#2896—111no—
196C2×#419—111no—
197C22×#101—111no—
198#2879—111no—
199#2052—118no—
200#1742—111no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—82no—
205C23×C11#12111yescharacteristic
206C23×C11#12111yescharacteristic
207C23×C11#12312yes—
208C23×C11#12412yes—
209C23×C11C2×#4111yescharacteristic
210Q8×C11—24no—
211Q8×C11—22no—
212Q8×C11—24no—
213Q8×C11—22no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—44no—
217Q8×C11—44no—
218Q8×C11—42no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—42no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12312yes—
244C2×C4×C11#12312yes—
245C2×C4×C11#12312yes—
246C2×C4×C11#12412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—42no—
254C2×Dic11—82no—
255C8×C11—24no—
256C11⋊C8—24no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259C22×#41C2×D1111yescharacteristic
260C23×Q8C2×D1111yescharacteristic
261C2×#137—22no—
262C2×#137—24no—
263C2×#137—24no—
264C2×#137C2×D1114yes—
265C22×Q16—21no—
266C22×SD16—21no—
267C22×M16—111no—
268C22×M16—111no—
269C22×M16—111no—
270C22×M16C2×D1111yescharacteristic
271C2×#117—111no—
272#430—224no—
273C2×#108—114no—
274#419—222no—
275#419—222no—
276#419—221no—
277#418—221no—
278#417—114no—
279#416—222no—
280C2×#103—114no—
281C2×#101—114no—
282C2×#101—224no—
283#408—114no—
284#408—222no—
285#407—222no—
286#343—114no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—44no—
294C22×C11—84no—
295C22×C11#39412yes—
296C22×C11#39412yes—
297C22×C11C2×#12111yescharacteristic
298C22×C11C2×#12311yescharacteristic
299C22×C11C2×#12411yescharacteristic
300C4×C11—42no—
301C4×C11—44no—
302C4×C11#39412yes—
303C4×C11#39412yes—
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12111yescharacteristic
307C4×C11C2×#12311yescharacteristic
308Dic11—82no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41C22⋊D1112yes—
316C2×#41C22×D1112yes—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—21no—
323C22×Q8—22no—
324C22×Q8—21no—
325C22×Q8C22⋊D1111yescharacteristic
326C22×Q8C22⋊D1114yes—
327C22×Q8C22×D1112yes—
328C22×D4—21no—
329C22×D4C22⋊D1111yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4C22×D1111yescharacteristic
333#137—216no—
334#137—28no—
335#137—28no—
336C2×Q16—28no—
337C2×Q16—24no—
338C2×SD16—28no—
339C2×SD16—24no—
340C2×M16—22no—
341C2×M16—21no—
342C2×M16—112no—
343C2×M16—112no—
344C2×M16—112no—
345C2×M16—112no—
346C2×M16—222no—
347C2×M16—222no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16—222no—
353C2×M16—222no—
354C2×M16C22⋊D1114yes—
355C2×M16C22×D1112yes—
356C22×C8—21no—
357C22×C8—112no—
358C22×C8—221no—
359C22×C8—221no—
360#117—221no—
361#117—221no—
362#117—221no—
363#117—221no—
364C2×C4⋊C4—112no—
365C2×C22⋊C4—221no—
366C2×C42—221no—
367#108—228no—
368#103—228no—
369#103—224no—
370#102—224no—
371#101—228no—
372C22⋊C8—228no—
373C2×C11—22no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—22no—
377C2×C11—82no—
378C2×C11C2×#39411yescharacteristic
379C2×C11#306912yes—
380C24—21no—
381C24#434111yescharacteristic
382#41—24no—
383#41—24no—
384#41—22no—
385#41—22no—
386#41—22no—
387#41—22no—
388#41—42no—
389#41—42no—
390#41—42no—
391#41—42no—
392C2×Q8—24no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—22no—
400C2×Q8—24no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8C2×C22⋊D1114yes—
413C2×Q8C2×C22⋊D1112yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4C2×C22⋊D1112yes—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—222no—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4#434112yes—
436C22×C4#434111yescharacteristic
437C22×C4#434112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C23×D1111yescharacteristic
443Q16—216no—
444SD16—216no—
445M16—24no—
446M16—22no—
447M16—224no—
448M16—224no—
449M16—222no—
450M16—222no—
451M16—222no—
452M16—222no—
453M16—442no—
454M16—442no—
455M16C2×C22⋊D1114yes—
456C2×C8—24no—
457C2×C8—22no—
458C2×C8—114no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—442no—
464C2×C8—442no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C42—441no—
470C42—441no—
471C11#2353211yescharacteristic, complemented, Sylow
472C23—22no—
473C23—42no—
474C23—42no—
475C23—82no—
476C23#6698812yes—
477C23#6698912yes—
478C23#6699211yescharacteristic
479C23#6699211yescharacteristic
480C23C2×#434111yescharacteristic
481Q8—22no—
482Q8—24no—
483Q8—24no—
484Q8—22no—
485Q8—42no—
486Q8—42no—
487Q8—44no—
488Q8—44no—
489Q8—42no—
490D4—22no—
491D4—22no—
492D4—42no—
493D4—42no—
494D4—44no—
495D4—42no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—442no—
507C2×C4—882no—
508C2×C4#6698812yes—
509C2×C4#6698812yes—
510C2×C4#6698812yes—
511C2×C4#6698912yes—
512C2×C4#6699112yes—
513C2×C4#6699112yes—
514C2×C4#6699212yes—
515C2×C4#6699212yes—
516C2×C4#6699211yescharacteristic
517C2×C4#6699211yescharacteristic
518C2×C4#6700612yes—
519C2×C4#6700612yes—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—24no—
527C8—224no—
528C8—442no—
529C8—442no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—44no—
536C22—42no—
537C22—84no—
538C22#1062283512yes—
539C22#1062283512yes—
540C22C2×#6698811yescharacteristic
541C22C2×#6698911yescharacteristic
542C22C2×#6699211yescharacteristic
543C4—42no—
544C4—44no—
545C4—882no—
546C4#1062283512yes—
547C4#1062283512yes—
548C4C2×#6698811yescharacteristic
549C4C2×#6699111yescharacteristic
550C4C2×#6699211yescharacteristic
551C4C2×#6700611yescharacteristic
552C2—22no—
553C2—21no—
554C2—21no—
555C2—22no—
556C2—82no—
557C2C2×#1062283511yescharacteristic
558C2#1307835012yes—
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC22×C11C2×#121
prime radicalC22×C11×#41C22
hypercenterC22×#137D11
hypocenterC11#23532
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
3. C2×#10622838C2semidirect
4. C22×#66900C2semidirect
6. #13069912C2semidirect
7. #13068354C2semidirect
27. C2×#66900C22semidirect
31. C2×#66899C22semidirect
35. C2×#66886C22semidirect
36. #10622192C22semidirect
471. C11#23532semidirect

Maximal subgroups

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

subgroupindex
C2×#106227372
#130771352
C2×#106228382
C22×#669002
#130770612
#130699122
#130683542
C22×C11×#1372
#2353211