Finite Group Databasebeta

← #14782875

Subgroups — #14782875

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic
3#13071238C211yesmaximal, characteristic
4#13071231C211yesmaximal, characteristic
5#13070119C211yesmaximal, characteristic, complemented
6#13070118C211yesmaximal, characteristic, complemented
7#13070115C211yesmaximal, characteristic, complemented
8#13070113C211yesmaximal, characteristic, complemented
9#13070109C211yesmaximal, characteristic, complemented
10#13070107C211yesmaximal, characteristic, complemented
11#13070106C211yesmaximal, characteristic, complemented
12#13068334C211yesmaximal, characteristic
13#13068331C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#2088C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622602—21no—
31#10622600—21no—
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622589—21no—
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622474—24no—
44#10622452—24no—
45#10622281—21no—
46#10622280—21no—
47#10622263—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313D414yes—
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105#66945Q814yes—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11Q814yes—
110#66925—22no—
111#66925—22no—
112C11×#106—22no—
113C11×C4⋊C8—22no—
114C11×#95—21no—
115C11×#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66882—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8—22no—
125#66872—22no—
126#66871—22no—
127C4⋊(C11⋊C8)—22no—
128#23671—111nomaximal, Sylow
129C23×D11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×C4×D11—24no—
145C2×C4×D11—42no—
146C2×C4×D11—81no—
147C2×C4×D11—81no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×C4×D11C2×D412yes—
151C2×C4×D11C2×Q812yes—
152C2×C4×D11C2×Q812yes—
153C2×C4×D11#4112yes—
154C2×C4×D11#4112yes—
155C2×C4×D11#4112yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D412yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4—81no—
170C11×C4⋊C4C2×Q812yes—
171C11×C4⋊C4C2×Q812yes—
172C42×C11—21no—
173C42×C11—21no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—81no—
185C4⋊Dic11—81no—
186C4⋊Dic11C2×Q812yes—
187C4⋊Dic11C2×Q812yes—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—24no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—24no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—42no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×D412yes—
206#4313—28no—
207C8×D11—44no—
208C2×#428—111no—
209C2×#424—111no—
210#2317—111no—
211#2316—111no—
212#2088—111no—
213#2088—111no—
214#2088—111no—
215#2088D1111yescharacteristic, complemented
216#2087—111no—
217#2087—111no—
218#2086—111no—
219#2086—111no—
220#1736—111no—
221#1735—111no—
222C2×#340—111no—
223C23×C11C22×D411yescharacteristic
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11#12112yes—
229C22×D11C22⋊Q812yes—
230C22×D11C22⋊Q812yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11#12112yes—
274C2×Dic11C22⋊Q812yes—
275C2×Dic11C22⋊Q812yes—
276C4×D11—84no—
277C4×D11—84no—
278C4×D11#12314yes—
279C4×D11#12514yes—
280C4×D11#12514yes—
281C4×D11C4⋊Q814yes—
282C8×C11—22no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C22×M16—111no—
287C23×C8—111no—
288C2×#117—111no—
289C2×#117—111no—
290C2×#117—111no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—111no—
293#428—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#106—111no—
297C2×#106C2×D1111yescharacteristic
298#424—224no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303#389—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—221no—
310#389—221no—
311#389C2×D1111yescharacteristic
312#389C2×D1111yescharacteristic
313#385—221no—
314#385—221no—
315#384—221no—
316#382—221no—
317#380—221no—
318#380—221no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331C22×C11C2×#12111yescharacteristic
332C22×C11C2×C22⋊Q811yescharacteristic
333C22×C11C2×C22⋊Q811yescharacteristic
334C22×C11#57611yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57711yescharacteristic
337C22×C11#57811yescharacteristic
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11#39814yes—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C2×#12311yescharacteristic
352C4×C11C2×#12511yescharacteristic
353C4×C11C2×#12511yescharacteristic
354C4×C11C2×C4⋊Q811yescharacteristic
355Dic11—42no—
356Dic11—42no—
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11#39814yes—
362C23×C4—111no—
363C23×C4—221no—
364C23×C4—221no—
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—222no—
371C22×C8—222no—
372C22×C8—222no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375#117—114no—
376#117—222no—
377#117—222no—
378#117—222no—
379#117—222no—
380#117—222no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414#107—222no—
415#106—22no—
416#106—222no—
417C4⋊C8—22no—
418C4⋊C8—222no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421#95—21no—
422#95—21no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11C2×#39811yescharacteristic
430C2×C11#306211yescharacteristic
431C2×C11#306311yescharacteristic
432C2×C11#308111yescharacteristic
433C2×C11#308211yescharacteristic
434C2×C11#308311yescharacteristic
435C2×C11#308411yescharacteristic
436D11—24no—
437C24—111no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—111no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—442no—
457C22×C4—881no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4—881no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464M16—228no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—444no—
477C2×C8D4×D1112yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4—881no—
501C4⋊C4—881no—
502C4⋊C4—881no—
503C4⋊C4—881no—
504C4⋊C4Q8×D1112yes—
505C4⋊C4Q8×D1112yes—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—224no—
509C22⋊C4—442no—
510C42—21no—
511C42—21no—
512C42—224no—
513C42—221no—
514C42—221no—
515C42—442no—
516C11#2367111yescharacteristic, complemented, Sylow
517C23—112no—
518C23—112no—
519C23—112no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23C2×D4×D1111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—114no—
549C2×C4—114no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—884no—
569C2×C4—884no—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4C2×Q8×D1111yescharacteristic
572C2×C4C2×Q8×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C8—22no—
577C8—41no—
578C8—222no—
579C8—441no—
580C22—114no—
581C22—222no—
582C22—222no—
583C22—222no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22D11×#12111yescharacteristic
588C22D11×C22⋊Q811yescharacteristic
589C22D11×C22⋊Q811yescharacteristic
590C22#1062329311yescharacteristic
591C22#1062330211yescharacteristic
592C22#1062330511yescharacteristic
593C22#1062330911yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—114no—
601C4—441no—
602C4—441no—
603C4—442no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4D11×#12311yescharacteristic
608C4D11×#12511yescharacteristic
609C4D11×#12511yescharacteristic
610C4D11×C4⋊Q811yescharacteristic
611C2—224no—
612C2D11×#39811yescharacteristic
613C2#1307829111yescharacteristic
614C2#1307830011yescharacteristic
615C2#1307844211yescharacteristic
616C2#1307845711yescharacteristic
617C2#1307846811yescharacteristic
618C2#1307847511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2088C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2088D11
hypocenterC11#23671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #13070119C2semidirect
6. #13070118C2semidirect
7. #13070115C2semidirect
8. #13070113C2semidirect
9. #13070109C2semidirect
10. #13070107C2semidirect
11. #13070106C2semidirect
15. C11×#2088C2semidirect
215. #2088D11semidirect
516. C11#23671semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
C2×#106224522
#130712382
#130712312
#130701192
#130701182
#130701152
#130701132
#130701092
#130701072
#130701062
#130683342
#130683312
D11×#3402
C11×#20882
#2367111