Finite Group Databasebeta

← #14795274

Subgroups — #14795274

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078438C211yesmaximal, characteristic, complemented
2C2×#10622622C211yesmaximal, characteristic, complemented
3#13077282C211yesmaximal, characteristic, complemented
4#13070064C211yesmaximal, characteristic, complemented
5#13070059C211yesmaximal, characteristic, complemented
6#13069905C211yesmaximal, characteristic
7#13069905C211yesmaximal, characteristic
8#13069609C211yesmaximal, characteristic, complemented
9#13069398C211yesmaximal, characteristic, complemented
10#13069393C211yesmaximal, characteristic, complemented
11#13069391C211yesmaximal, characteristic, complemented
12#13069281C211yesmaximal, characteristic, complemented
13#13069281C211yesmaximal, characteristic, complemented
14#13068608C211yesmaximal, characteristic, complemented
15C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C11×#442—21no—
21C11×#440—21no—
22C4×C11×SD16—21no—
23C4×C11×D8—21no—
24C11×#428C2211yescharacteristic
25C11×#418C2211yescharacteristic
26C11×#417C2211yescharacteristic
27C4×C11×M16C2211yescharacteristic
28#10622847C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622845C2211yescharacteristic
31#10622845C2211yescharacteristic
32C2×#66897C2211yescharacteristic
33C2×#66897C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66886C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38#10622635—21no—
39#10622635—21no—
40#10622622—21no—
41#10622622—21no—
42#10622622—21no—
43#10622622—21no—
44#10622622—21no—
45#10622622—21no—
46#10622613—21no—
47#10622613—21no—
48#10622610C2211yescharacteristic
49#10622610C2211yescharacteristic
50#10622608C2211yescharacteristic
51#10622608C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622539—21no—
55#10622538—21no—
56#10622537C2211yescharacteristic
57#10622537C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C11×AGL(1,ℤ/8)—22no—
71C11×AGL(1,ℤ/8)—22no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C11×#117—21no—
87C11×#117C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66923—21no—
103#66923—21no—
104#66923—21no—
105#66923—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#97—21no—
113C4×C8×C11—21no—
114#66899—21no—
115#66899—21no—
116#66897—22no—
117#66897—22no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128#66886—22no—
129#66886—22no—
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66872—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)D411yescharacteristic
143C4⋊(C11⋊C8)D411yescharacteristic
144C4⋊(C11⋊C8)D411yescharacteristic
145C4⋊(C11⋊C8)D411yescharacteristic
146#66867—21no—
147#66867—21no—
148C4×C11⋊C8—21no—
149C4×C11⋊C8—21no—
150#24724—111nomaximal, Sylow
151C24×C11—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C11×#41—21no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—82no—
172C22×C4×C11#4111yescharacteristic
173C22×C4×C11#4111yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11—21no—
176C22×Dic11—21no—
177C11×SD16—24no—
178C11×D8—24no—
179C11×M16—21no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16#4112yes—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207Dic11⋊C4—41no—
208Dic11⋊C4—41no—
209Dic11⋊C4—41no—
210Dic11⋊C4—41no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218#4318—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C2×D411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231#3080—111no—
232C2×#478—111no—
233C4×AGL(1,ℤ/8)D1111yescharacteristic
234#2925—111no—
235#2079—111no—
236#2078—111no—
237#2051—111no—
238#2051—111no—
239#1998—111no—
240#1952—111no—
241#1951—111no—
242#1950—111no—
243#1931—111no—
244#1931—111no—
245#1800—111no—
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—81no—
251C23×C11—81no—
252C23×C11C2×#4111yescharacteristic
253Q8×C11—21no—
254Q8×C11—21no—
255D4×C11—21no—
256D4×C11—22no—
257D4×C11—21no—
258D4×C11—22no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—81no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11—81no—
276C2×C4×C11#12111yescharacteristic
277C2×C4×C11#12111yescharacteristic
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×C4×C112−1+411yescharacteristic
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—81no—
289C2×Dic11—81no—
290C8×C11—22no—
291C8×C11—41no—
292C11⋊C8—21no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
301C2×#125—111no—
302C4×#41C2×D1111yescharacteristic
303C2×C4×D4C2×D1111yescharacteristic
304#479—221no—
305#479—221no—
306#478—221no—
307#478—221no—
308#478—221no—
309#478—221no—
310#478—221no—
311#478—221no—
312#442—21no—
313#440—21no—
314C4×SD16—21no—
315C4×D8—21no—
316#433—221no—
317#433—221no—
318#432—221no—
319#431—221no—
320C2×#108—111no—
321C2×#108—111no—
322#428—111no—
323#428—111no—
324#428C2×D1111yescharacteristic
325C2×#107—111no—
326C2×#106—111no—
327#423—111no—
328#423—111no—
329C2×C4⋊C8—111no—
330#418C2×D1111yescharacteristic
331#417—111no—
332#417—111no—
333#417C2×D1111yescharacteristic
334C2×#102—111no—
335C2×#102—111no—
336C2×#100—111no—
337C2×#100—111no—
338#408—111no—
339#408—111no—
340#405—111no—
341#405—111no—
342C4×M16C2×D1111yescharacteristic
343#343—111no—
344#343—111no—
345#343—111no—
346#343—111no—
347#343—111no—
348#343—111no—
349#341—111no—
350#341—111no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—41no—
354C22×C11—42no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—82no—
358C22×C11—82no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11C2×#12111yescharacteristic
362C22×C11#55211yescharacteristic
363C22×C11#55611yescharacteristic
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11#52511yescharacteristic
373C4×C11#53611yescharacteristic
374C4×C11#54711yescharacteristic
375C4×C11#54811yescharacteristic
376Dic11—81no—
377Dic11—81no—
378C2×#41C22×D1111yescharacteristic
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381AGL(1,ℤ/8)—22no—
382AGL(1,ℤ/8)—22no—
383C2×SD16—21no—
384C2×D8—21no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—111no—
388C2×M16—111no—
389C2×M16C22×D1111yescharacteristic
390C2×M16C22×D1111yescharacteristic
391C22×C8—111no—
392C22×C8—111no—
393#125—221no—
394#125—221no—
395#125—221no—
396#125—221no—
397C4×Q8C22⋊D1111yescharacteristic
398C4×Q8C22⋊D1111yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C22⋊D1111yescharacteristic
406C4×D4C22⋊D1111yescharacteristic
407#117—21no—
408#117C22×D1111yescharacteristic
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C42—21no—
416C2×C42C22×D1111yescharacteristic
417#108—222no—
418#108—222no—
419#107—21no—
420#107—221no—
421#107—221no—
422#107—221no—
423#107—221no—
424#106—21no—
425#106—221no—
426#106—221no—
427#106—221no—
428#106—221no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437#103—21no—
438#103—221no—
439#103—221no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—221no—
448#102—221no—
449#100—222no—
450#100—222no—
451C22⋊C8—221no—
452C22⋊C8—221no—
453C22⋊C8—221no—
454C22⋊C8—221no—
455#97—21no—
456#97—221no—
457#97—221no—
458C4×C8—21no—
459C4×C8—221no—
460C4×C8—221no—
461C2×C11—21no—
462C2×C11—21no—
463C2×C11—81no—
464C2×C11—82no—
465C2×C11#241511yescharacteristic
466C2×C11#306711yescharacteristic
467C2×C11#306811yescharacteristic
468C24—21no—
469#41—21no—
470#41—21no—
471#41—21no—
472#41—21no—
473C2×Q8C2×C22⋊D1111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4#433912yes—
481C2×D4C2×C22⋊D1111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—82no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4#434111yescharacteristic
492C22×C4#434111yescharacteristic
493C22×C4C23×D1111yescharacteristic
494SD16—24no—
495D8—24no—
496M16—21no—
497M16—21no—
498M16—21no—
499M16—221no—
500M16—221no—
501M16—221no—
502M16—221no—
503M16—221no—
504M16—221no—
505M16—221no—
506M16—221no—
507M16#433912yes—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—111no—
513C2×C8—111no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—441no—
531C4⋊C4—441no—
532C4⋊C4—441no—
533C4⋊C4—441no—
534C4⋊C4C2×C22⋊D1111yescharacteristic
535C4⋊C4C2×C22⋊D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42D4×D1111yescharacteristic
545C42D4×D1111yescharacteristic
546C42C2×C22⋊D1111yescharacteristic
547C42C2×C22⋊D1111yescharacteristic
548C11#2472411yescharacteristic, complemented, Sylow
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—81no—
554C23—81no—
555C23C2×#434111yescharacteristic
556Q8—21no—
557Q8—21no—
558D4—21no—
559D4—22no—
560D4—22no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—81no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—81no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—881no—
582C2×C4—881no—
583C2×C4#6699211yescharacteristic
584C2×C4#6699211yescharacteristic
585C2×C4#6699211yescharacteristic
586C2×C4#6699211yescharacteristic
587C2×C4C2×#433911yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#6704311yescharacteristic
591C2×C4#6704311yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—22no—
594C8—41no—
595C8—221no—
596C8—221no—
597C8—221no—
598C8—221no—
599C8—441no—
600C8—441no—
601C8—441no—
602C8—441no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22#1062307211yescharacteristic
614C22#1062307311yescharacteristic
615C22C2×#6699211yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—881no—
625C4—881no—
626C4#1062308211yescharacteristic
627C4#1062308311yescharacteristic
628C4#1062332211yescharacteristic
629C4#1062335611yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—82no—
634C2#1307204511yescharacteristic
635C2#1307833311yescharacteristic
636C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C2×#121
prime radicalC2×C11×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11#24724
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13078438C2semidirect
2. C2×#10622622C2semidirect
3. #13077282C2semidirect
4. #13070064C2semidirect
5. #13070059C2semidirect
8. #13069609C2semidirect
9. #13069398C2semidirect
10. #13069393C2semidirect
11. #13069391C2semidirect
12. #13069281C2semidirect
13. #13069281C2semidirect
14. #13068608C2semidirect
548. C11#24724semidirect

Maximal subgroups

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

subgroupindex
#130784382
C2×#106226222
#130772822
#130700642
#130700592
#130699052
#130696092
#130693982
#130693932
#130693912
#130692812
#130686082
C4×C11×AGL(1,ℤ/8)2
#2472411