Finite Group Databasebeta

← #14669591

Subgroups — #14669591

Order 2816.

944 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622183C211yesmaximal, characteristic, complemented
2C2×#10622177C211yesmaximal, characteristic, complemented
3C2×#10622174C211yesmaximal, characteristic, complemented
4#13069030C211yesmaximal, characteristic, complemented
5#13069025C211yesmaximal, characteristic, complemented
6#13069015C211yesmaximal, characteristic, complemented
7C2×C11×#560C211yesmaximal, characteristic
8C11×#560—22no—
9C11×#560—22no—
10C11×#560—22no—
11C11×#560C414yescomplemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#126—21no—
14C2×C11×#123—21no—
15C2×C11×#123C2211yescharacteristic
16C2×C11×#121—21no—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#120—21no—
20C2×C11×#120C2211yescharacteristic
21#10623329C2211yescharacteristic
22#10622860—21no—
23C2×#66898C2211yescharacteristic
24C2×#66898C2211yescharacteristic
25C2×#66897C2211yescharacteristic
26#10622828—21no—
27#10622824—21no—
28#10622183—22no—
29#10622177—22no—
30#10622174—22no—
31#10622165—21no—
32#10622165—21no—
33#10622161—21no—
34C25×C11D411yescharacteristic
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C11×#127—21no—
45C11×#127—21no—
46C11×#127C2×C412yes—
47C11×#127D412yes—
48C11×#126—24no—
49C11×#126—24no—
50C11×#123—24no—
51C11×#123—21no—
52C11×#123—21no—
53C11×#123—24no—
54C11×#123C2×C412yes—
55C11×#123D412yes—
56C11×#121—24no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—24no—
60C11×#121—24no—
61C11×#121—24no—
62C11×#120—24no—
63C11×#120—24no—
64C11×#120—21no—
65C11×#120—21no—
66C11×#120C2×C412yes—
67C11×#120D412yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—42no—
84D4×Dic11—42no—
85#66979—21no—
86C2×#4318—21no—
87#66898—21no—
88#66898—21no—
89#66898—21no—
90#66898—21no—
91#66897—21no—
92#66897—21no—
93#66896—42no—
94C11⋊#95—42no—
95#12762—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—82no—
102C24×C11C22⋊C412yes—
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—82no—
119C2×D4×C11—82no—
120C2×D4×C11—82no—
121C2×D4×C11—82no—
122C2×D4×C11—81no—
123C2×D4×C11—81no—
124C2×D4×C11C22⋊C412yescomplemented
125C2×D4×C11C22×C411yescharacteristic
126C2×D4×C11C2×D411yescharacteristic
127C2×D4×C11C2×D411yescharacteristic
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—21no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11—82no—
138C22×C4×C11C22⋊C412yescomplemented
139C22×C4×C11C2×D411yescharacteristic
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4C22⋊C412yes—
158C11×C22⋊C4C22⋊C412yescomplemented
159C42×C11—21no—
160C42×C11C22⋊C412yescomplemented
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C22⋊Dic11—41no—
164C22⋊Dic11—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—84no—
169C4⋊Dic11—22no—
170C4×Dic11—41no—
171#4318—41no—
172#4318—41no—
173C2×C11⋊C8—41no—
174C2×#560D1111yescharacteristic
175C2×#353—111no—
176C2×#352—111no—
177C2×AΣL(1,𝔽16)—111no—
178#1890—111no—
179#1889—111no—
180#1887—111no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—44no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—81no—
200C23×C11—82no—
201C23×C11—82no—
202C23×C11—82no—
203C23×C11—84no—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11#12011yescharacteristic
207C23×C11#12011yescharacteristic
208C23×C11#12011yescharacteristic
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—42no—
214D4×C11—81no—
215D4×C11—82no—
216D4×C11—82no—
217D4×C11—84no—
218D4×C11—82no—
219D4×C11—82no—
220D4×C11—82no—
221D4×C11—82no—
222D4×C11—84no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—81no—
236C2×C4×C11—84no—
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×Dic11—42no—
240C2×Dic11—82no—
241C2×Dic11—82no—
242C2×Dic11—81no—
243C2×Dic11—81no—
244C2×Dic11—82no—
245C2×Dic11—82no—
246C11⋊C8—81no—
247#560—22no—
248#560—22no—
249#560—22no—
250#560Dic1114yescomplemented
251C2×#127C2×D1111yescharacteristic
252C2×#126—21no—
253C2×#123—21no—
254C2×#123C2×D1111yescharacteristic
255C2×#121—21no—
256C2×#121—21no—
257C2×#121—21no—
258C2×#120—21no—
259C2×#120C2×D1111yescharacteristic
260#518—111no—
261#418—221no—
262C2×#100—111no—
263C2×#99—111no—
264C2×#99—111no—
265#381—221no—
266#379—221no—
267#353—222no—
268#352—222no—
269AΣL(1,𝔽16)—222no—
270#342—221no—
271#342—221no—
272#339—221no—
273C22×C11—22no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—44no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—84no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11#37911yescharacteristic
300C22×C11B(4,𝔽2)11yescharacteristic
301C22×C11#45811yescharacteristic
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308Dic11—82no—
309Dic11—161no—
310Dic11—161no—
311C25C22⋊D1111yescharacteristic
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C22⋊D1111yescharacteristic
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4C22⋊D1111yescharacteristic
321C2×M16—221no—
322#127—21no—
323#127—21no—
324#127C2×Dic1112yes—
325#127C22⋊D1112yes—
326#126—24no—
327#126—24no—
328#123—24no—
329#123—21no—
330#123—21no—
331#123—24no—
332#123C2×Dic1112yes—
333#123C22⋊D1112yes—
334#121—24no—
335#121—24no—
336#121—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#120—24no—
341#120—24no—
342#120—21no—
343#120—21no—
344#120C2×Dic1112yes—
345#120C22⋊D1112yes—
346C4×D4—442no—
347#117—221no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4C22⋊D1111yescharacteristic
362C2×C22⋊C4C22⋊D1111yescharacteristic
363C2×C42C22⋊D1111yescharacteristic
364#102—442no—
365#100—221no—
366#100—221no—
367#99—221no—
368#99—221no—
369#99—221no—
370#99—221no—
371#95—442no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11—41no—
375C2×C11—41no—
376C2×C11—41no—
377C2×C11—41no—
378C2×C11—82no—
379C2×C11—82no—
380C2×C11#179011yescharacteristic
381C2×C11#220012yes—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—41no—
386C24—41no—
387C24—82no—
388C24C22⋊Dic1112yes—
389C24C2×C22⋊D1111yescharacteristic
390C24C2×C22⋊D1111yescharacteristic
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4—82no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4C22⋊Dic1112yescomplemented
411C2×D4C22×Dic1111yescharacteristic
412C2×D4C2×C22⋊D1111yescharacteristic
413C2×D4C2×C22⋊D1111yescharacteristic
414C2×D4C2×C22⋊D1111yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—82no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—441no—
427C22×C4—441no—
428C22×C4C22⋊Dic1112yescomplemented
429C22×C4C2×C22⋊D1111yescharacteristic
430M16—441no—
431M16—441no—
432C2×C8—441no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—222no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C22⋊C4—441no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C22⋊C4—441no—
454C22⋊C4—884no—
455C22⋊C4C22⋊Dic1112yes—
456C22⋊C4C22⋊Dic1112yescomplemented
457C42—21no—
458C42—441no—
459C42C22⋊Dic1112yescomplemented
460C11#1276211yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—81no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23—84no—
484C23C2×C22⋊Dic1111yescharacteristic
485C23C2×C22⋊Dic1111yescharacteristic
486C23#6700611yescharacteristic
487C23#6700611yescharacteristic
488C23#6700611yescharacteristic
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497D4—84no—
498D4—82no—
499D4—82no—
500D4—82no—
501D4—82no—
502D4—84no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—81no—
516C2×C4—84no—
517C2×C4—442no—
518C2×C4—882no—
519C2×C4—882no—
520C2×C4—881no—
521C2×C4—881no—
522C2×C4—882no—
523C2×C4—882no—
524C2×C4C2×C22⋊Dic1111yescharacteristic
525C2×C4#6700611yescharacteristic
526C8—881no—
527C22—22no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—84no—
551C22—82no—
552C22—82no—
553C22#1062285611yescharacteristic
554C22#1062285711yescharacteristic
555C22#1062286011yescharacteristic
556C4—21no—
557C4—21no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—882no—
563C4—1761no—
564C4—1761no—
565C2—21no—
566C2—21no—
567C2—41no—
568C2—41no—
569C2—41no—
570C2—41no—
571C2—82no—
572C2—82no—
573C2#1306856411yescharacteristic
574C2#1307062312yes—
subgroupG/H
centerC22#10622857
commutatorC2×D4×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC2×C11×#560C2
socleC22×C11B(4,𝔽2)
cosocleC22×D4×C11C23
hypercenterC2×#560D11
hypocenterC11#12762
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#560

Complements

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

NH ≅ G/Ntype
1. C2×#10622183C2semidirect
2. C2×#10622177C2semidirect
3. C2×#10622174C2semidirect
4. #13069030C2semidirect
5. #13069025C2semidirect
6. #13069015C2semidirect
11. C11×#560C4semidirect
124. C2×D4×C11C22⋊C4semidirect
138. C22×C4×C11C22⋊C4semidirect
158. C11×C22⋊C4C22⋊C4semidirect
160. C42×C11C22⋊C4semidirect
250. #560Dic11semidirect
410. C2×D4C22⋊Dic11semidirect
428. C22×C4C22⋊Dic11semidirect
456. C22⋊C4C22⋊Dic11semidirect
459. C42C22⋊Dic11semidirect
460. C11#12762semidirect

Maximal subgroups

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

subgroupindex
C2×#106221832
C2×#106221772
C2×#106221742
#130690302
#130690252
#130690152
C2×C11×#5602
#1276211