Finite Group Databasebeta

← #14762346

Subgroups — #14762346

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622780C211yesmaximal, characteristic
2C2×#10622329C211yesmaximal, characteristic, complemented
3C2×#10622643C211yesmaximal, characteristic, complemented
4C2×#10622631C211yesmaximal, characteristic
5C4×#66997C211yesmaximal, characteristic, complemented
6C4×#66989C211yesmaximal, characteristic
7#13069475C211yesmaximal, characteristic, complemented
8#13069474C211yesmaximal, characteristic, complemented
9#13069472C211yesmaximal, characteristic
10#13069471C211yesmaximal, characteristic
11#13069434C211yesmaximal, characteristic, complemented
12#13069431C211yesmaximal, characteristic
13#13068783C211yesmaximal, characteristic, complemented
14#97×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#97C2211yescharacteristic
31#10622843C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622834C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C4×C22⋊Dic11—22no—
36#10622780C418yescomplemented
37C2×#66881C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622643—24no—
45#10622631—24no—
46#10622590C2211yescharacteristic
47#10622589C2211yescharacteristic
48#10622587C2211yescharacteristic
49#10622587C2211yescharacteristic
50#10622585—22no—
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622558—22no—
56C4×Dic11⋊C4—22no—
57C42×Dic11C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622329—24no—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82#66997—22no—
83#66997C2×C414yescomplemented
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326C2×C414yescomplemented
87#66989—22no—
88#66989C2×C414yes—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324C2×C414yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11D412yes—
101C2×C4×Dic11D412yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×Dic44—22no—
107C2×Dic44—22no—
108C2×Dic44C2×C414yescomplemented
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C4×Dic22—22no—
113C11×#107—22no—
114C11×#103—22no—
115C11×#102—22no—
116C11×#97D414yes—
117#66899—22no—
118#66896—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123#66881—22no—
124#66880—22no—
125#66880—22no—
126#66879—22no—
127#66879C2×C414yescomplemented
128C8×Dic11—22no—
129C8×Dic11—22no—
130#66874—22no—
131#66874—22no—
132#66872—22no—
133#66871—22no—
134#66867D414yes—
135#21702—111nomaximal, Sylow
136C24×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C22×C412yes—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—44no—
153C22×C4×C11—42no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22C22×C412yes—
174C2×Dic22C22×C412yes—
175C11×SD16—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D412yes—
181C2×C8×C11#4112yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C22⋊C4—42no—
188C42×C11—42no—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C22⋊Dic11—28no—
192C22⋊Dic11—44no—
193#4326—28no—
194#4324—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199Dic11⋊C4—28no—
200Dic11⋊C4—44no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—24no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11C22×C412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C22×C412yes—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217Dic44—28no—
218C2×#497—111no—
219C2×#441—111no—
220C2×#441—111no—
221C2×#440—111no—
222C2×#440D1111yescharacteristic
223C4×C4⋊Q8—111no—
224C4×#124—111no—
225#1969—111no—
226#1969—111no—
227#1968—111no—
228#1968—111no—
229#1960—111no—
230#1959—111no—
231#1847—111no—
232C4×#97—111no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11C22×D411yescharacteristic
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—41no—
242Q8×C11—41no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—41no—
246D4×C11—41no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—84no—
257C2×C4×C11#12712yes—
258C2×C4×C11#12712yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11C4×D414yes—
280C2×Dic11#13714yes—
281Dic22—22no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289C8×C11—22no—
290C8×C11C4×D414yes—
291C11⋊C8—22no—
292C11⋊C8C4×D414yes—
293C22×Q16—111no—
294C22×Q16—111no—
295C22×SD16—111no—
296C22×SD16C2×D1111yescharacteristic
297C2×C4⋊Q8—111no—
298C2×#124—111no—
299C2×C4×Q8—111no—
300C2×C4×Q8—111no—
301C2×C4×Q8C2×D1111yescharacteristic
302C2×C4×D4C2×D1111yescharacteristic
303#497—118no—
304#441—224no—
305#441—224no—
306#440—24no—
307#440—224no—
308C2×#107—111no—
309C2×#107C2×D1111yescharacteristic
310C2×#106—111no—
311C2×#106—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103C2×D1111yescharacteristic
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97—111no—
322C2×#97—111no—
323C2×#97C2×D1111yescharacteristic
324C2×C4×C8—111no—
325C2×C4×C8—111no—
326#391—111no—
327#391—111no—
328#391—111no—
329#390—111no—
330#389—222no—
331#388—222no—
332#384—111no—
333#382—111no—
334C4×C4⋊C4—222no—
335C4×C22⋊C4—222no—
336C43—111no—
337C22×C11—42no—
338C22×C11—44no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—82no—
342C22×C11C2×C4×D411yescharacteristic
343C22×C11C2×#12711yescharacteristic
344C22×C11#53211yescharacteristic
345C22×C11C2×#13712yes—
346C22×C11#57512yes—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×C4×D411yescharacteristic
353C4×C11C2×C4×D411yescharacteristic
354C4×C11#53211yescharacteristic
355C4×C11#53211yescharacteristic
356Dic11—24no—
357Dic11—24no—
358Dic11—42no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—111no—
363C22×Q8—111no—
364C22×Q8C22×D1111yescharacteristic
365C22×D4C22×D1111yescharacteristic
366C23×C4—21no—
367C2×Q16—114no—
368C2×Q16—114no—
369C2×Q16—222no—
370C2×Q16—222no—
371C2×Q16—222no—
372C2×Q16—222no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16—114no—
376C2×SD16—222no—
377C2×SD16—222no—
378C2×SD16C4×D1114yes—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383C4⋊Q8—114no—
384C4⋊Q8—222no—
385#124—114no—
386#124—222no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×D4—22no—
394C4×D4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C42—21no—
408C2×C42—111no—
409C2×C42—112no—
410C2×C42—111no—
411C2×C42—112no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—22no—
416#107—222no—
417#106—222no—
418#106—222no—
419#103—22no—
420#103—222no—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#102—22no—
426#102—222no—
427#97—114no—
428#97—114no—
429#97—222no—
430#97C22⋊D1114yes—
431C4×C8—222no—
432C4×C8—222no—
433#95—222no—
434#95—222no—
435#95—222no—
436#95—222no—
437C2×C11—82no—
438C2×C11C4×#12711yescharacteristic
439C2×C11C4×#13712yes—
440C2×C11#315211yescharacteristic
441C2×C11#315311yescharacteristic
442C2×C11#318112yes—
443C24—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—112no—
450C2×Q8—112no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8C2×C4×D1112yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×C4×D1112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4C23×D1111yescharacteristic
482Q16—228no—
483Q16—228no—
484SD16—28no—
485SD16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×C4×D1112yes—
495C2×C8#433912yes—
496C2×C8C2×C22⋊D1112yes—
497C2×C8C2×C22⋊D1112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—228no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—444no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C22⋊C4—42no—
512C22⋊C4—228no—
513C22⋊C4—444no—
514C42—42no—
515C42—112no—
516C42—112no—
517C42—224no—
518C42—221no—
519C42—221no—
520C42—442no—
521C42—442no—
522C42—442no—
523C42D4×D1112yes—
524C42C2×C22⋊D1112yes—
525C11#2170211yescharacteristic, complemented, Sylow
526C23—22no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23C2×D4×D1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536Q8—222no—
537Q8—222no—
538Q8—222no—
539Q8—222no—
540Q8—441no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544D4—22no—
545D4—22no—
546D4—41no—
547D4—41no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4—114no—
559C2×C4—114no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4#6699312yes—
575C2×C4#6699312yes—
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4C22×C22⋊D1111yescharacteristic
582C8—22no—
583C8—114no—
584C8—222no—
585C8C4×C22⋊D1114yes—
586C22—42no—
587C22—44no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22C4×D4×D1111yescharacteristic
592C22#1062307911yescharacteristic
593C22#1062330412yes—
594C22D11×#13712yes—
595C22C2×#6699311yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—224no—
602C4—224no—
603C4—442no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4C4×D4×D1111yescharacteristic
608C4#1062307911yescharacteristic
609C4C2×C4×C22⋊D1111yescharacteristic
610C4#1062336311yescharacteristic
611C2—82no—
612C2C4×#6699311yescharacteristic
613C2#1307743812yes—
614C2#1307907111yescharacteristic
615C2#1307907811yescharacteristic
616C2#1307932112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#440D11
hypocenterC11#21702
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#10622329C2semidirect
3. C2×#10622643C2semidirect
5. C4×#66997C2semidirect
7. #13069475C2semidirect
8. #13069474C2semidirect
11. #13069434C2semidirect
13. #13068783C2semidirect
14. #97×Dic11C2semidirect
36. #10622780C4semidirect
83. #66997C2×C4semidirect
86. C2×#4326C2×C4semidirect
108. C2×Dic44C2×C4semidirect
127. #66879C2×C4semidirect
525. C11#21702semidirect

Maximal subgroups

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

subgroupindex
C2×#106227802
C2×#106223292
C2×#106226432
C2×#106226312
C4×#669972
C4×#669892
#130694752
#130694742
#130694722
#130694712
#130694342
#130694312
#130687832
#97×Dic112
C2×C11×#4402
#2170211