Finite Group Databasebeta

← C113×#13347 #43281367

Subgroups — C113×#13347 #43281367

Order 28928.

830 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 98 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×#458×C113C211yesmaximal, characteristic, complemented
2C2×#453×C113C211yesmaximal, characteristic
3C113×#2709C211yesmaximal, characteristic, complemented
4C2×#353×C113C211yesmaximal, characteristic, complemented
5C2×#352×C113C211yesmaximal, characteristic, complemented
6C113×#1790C211yesmaximal, characteristic, complemented
7C113×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C113C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C113—21no—
10C2×#127×C113C2211yescharacteristic
11C2×#123×C113—21no—
12C2×#123×C113C2211yescharacteristic
13#458×C113—22no—
14#458×C113—22no—
15#453×C113—22no—
16#453×C113—22no—
17C2×#104×C113—21no—
18C2×#100×C113C2211yescharacteristic
19C2×#99×C113—21no—
20C2×#99×C113—21no—
21C2×#99×C113C2211yescharacteristic
22C2×#99×C113C2211yescharacteristic
23#394×C113—21no—
24#394×C113—21no—
25#394×C113—21no—
26#387×C113—21no—
27#386×C113—21no—
28#386×C113—21no—
29#386×C113—21no—
30#386×C113C2211yescharacteristic
31#353×C113—22no—
32#352×C113—22no—
33H(5,𝔽2)×C113—21no—
34H(5,𝔽2)×C113—21no—
35H(5,𝔽2)×C113—21no—
36H(5,𝔽2)×C113—42no—
37H(5,𝔽2)×C113D412yes—
38C2×#41×C113—21no—
39C2×#41×C113—41no—
40C22×D4×C113—21no—
41C22×D4×C113—21no—
42C22×D4×C113—21no—
43C22×D4×C113—21no—
44C22×D4×C113—41no—
45C22×D4×C113D411yescharacteristic
46C22×D4×C113C2311yescharacteristic
47C23×C4×C113D411yescharacteristic
48C23×C4×C113D411yescharacteristic
49AGL(1,ℤ/8)×C113—24no—
50AGL(1,ℤ/8)×C113—42no—
51C2×SD16×C113—41no—
52C2×D8×C113—41no—
53C2×M16×C113—21no—
54#127×C113—21no—
55#127×C113—21no—
56#127×C113—21no—
57#127×C113—21no—
58#123×C113—24no—
59#123×C113—21no—
60#123×C113—21no—
61#123×C113—21no—
62#123×C113—21no—
63#123×C113—42no—
64C2×C4⋊C4×C113—21no—
65C2×C4⋊C4×C113—21no—
66C2×C4⋊C4×C113—41no—
67C2×C22⋊C4×C113—21no—
68C2×C22⋊C4×C113—21no—
69C2×C22⋊C4×C113—21no—
70C2×C22⋊C4×C113—21no—
71C2×C22⋊C4×C113—21no—
72C2×C22⋊C4×C113—21no—
73C2×C22⋊C4×C113—21no—
74C2×C22⋊C4×C113—21no—
75C2×C22⋊C4×C113—41no—
76C2×C22⋊C4×C113—41no—
77C2×C22⋊C4×C113D411yescharacteristic
78C2×C22⋊C4×C113D411yescharacteristic
79C2×C42×C113D411yescharacteristic
80#104×C113—24no—
81#100×C113—21no—
82#100×C113D412yes—
83#99×C113—24no—
84#99×C113—21no—
85#99×C113—21no—
86#99×C113—21no—
87#99×C113—42no—
88#99×C113D412yes—
89#95×C113—21no—
90#95×C113—21no—
91#95×C113—21no—
92#95×C113—21no—
93#95×C113—41no—
94C24×C113—21no—
95C24×C113—21no—
96C24×C113—21no—
97C24×C113C2×D411yescharacteristic
98C24×C113C2×D411yescharacteristic
99#41×C113—22no—
100#41×C113—22no—
101#41×C113—42no—
102#41×C113—41no—
103#41×C113—42no—
104#41×C113—42no—
105#41×C113—42no—
106#41×C113—41no—
107C2×Q8×C113—21no—
108C2×D4×C113—21no—
109C2×D4×C113—22no—
110C2×D4×C113—22no—
111C2×D4×C113—22no—
112C2×D4×C113—22no—
113C2×D4×C113—21no—
114C2×D4×C113—21no—
115C2×D4×C113—41no—
116C2×D4×C113—41no—
117C2×D4×C113—41no—
118C2×D4×C113—41no—
119C2×D4×C113—42no—
120C2×D4×C113—42no—
121C2×D4×C113—42no—
122C2×D4×C113—42no—
123C2×D4×C113—41no—
124C2×D4×C113—41no—
125C2×D4×C113—41no—
126C2×D4×C113—41no—
127C2×D4×C113—42no—
128C2×D4×C113—42no—
129C2×D4×C113—41no—
130C2×D4×C113—41no—
131C2×D4×C113—41no—
132C2×D4×C113—41no—
133C2×D4×C113—41no—
134C2×D4×C113—41no—
135C2×D4×C113—41no—
136C2×D4×C113—81no—
137C2×D4×C113—81no—
138C2×D4×C113C2×D411yescharacteristic
139C2×D4×C113C2×D411yescharacteristic
140C2×D4×C113C2×D411yescharacteristic
141C2×D4×C113#4111yescharacteristic
142C22×C4×C113—21no—
143C22×C4×C113—21no—
144C22×C4×C113—21no—
145C22×C4×C113—21no—
146C22×C4×C113—21no—
147C22×C4×C113—21no—
148C22×C4×C113—21no—
149C22×C4×C113—21no—
150C22×C4×C113—21no—
151C22×C4×C113—41no—
152C22×C4×C113—41no—
153C22×C4×C113—41no—
154C22×C4×C113—41no—
155C22×C4×C113—41no—
156C22×C4×C113—41no—
157C22×C4×C113—81no—
158C22×C4×C113C2×D411yescharacteristic
159SD16×C113—44no—
160D8×C113—44no—
161M16×C113—22no—
162M16×C113—41no—
163C2×C8×C113—41no—
164C4⋊C4×C113—42no—
165C4⋊C4×C113—44no—
166C4⋊C4×C113—41no—
167C4⋊C4×C113—41no—
168C22⋊C4×C113—21no—
169C22⋊C4×C113—22no—
170C22⋊C4×C113—21no—
171C22⋊C4×C113—41no—
172C22⋊C4×C113—44no—
173C22⋊C4×C113—41no—
174C22⋊C4×C113—41no—
175C22⋊C4×C113—41no—
176C22⋊C4×C113—41no—
177C22⋊C4×C113—41no—
178C22⋊C4×C113—81no—
179C22⋊C4×C113—81no—
180C22⋊C4×C113—81no—
181C22⋊C4×C113—81no—
182C22⋊C4×C113—81no—
183C22⋊C4×C113—82no—
184C42×C113—21no—
185C42×C113—21no—
186C23×C113—21no—
187C23×C113—21no—
188C23×C113—21no—
189C23×C113—21no—
190C23×C113—22no—
191C23×C113—22no—
192C23×C113—41no—
193C23×C113—41no—
194C23×C113—41no—
195C23×C113—41no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—41no—
200C23×C113—41no—
201C23×C113—41no—
202C23×C113—41no—
203C23×C113—41no—
204C23×C113—41no—
205C23×C113—41no—
206C23×C113—81no—
207C23×C113—81no—
208C23×C113—81no—
209C23×C113—81no—
210C23×C113#12011yescharacteristic
211C23×C113#12011yescharacteristic
212C23×C113#12111yescharacteristic
213C23×C113#12111yescharacteristic
214C23×C113#12711yescharacteristic
215Q8×C113—22no—
216Q8×C113—41no—
217D4×C113—22no—
218D4×C113—41no—
219D4×C113—41no—
220D4×C113—41no—
221D4×C113—41no—
222D4×C113—41no—
223D4×C113—42no—
224D4×C113—42no—
225D4×C113—42no—
226D4×C113—42no—
227D4×C113—42no—
228D4×C113—42no—
229D4×C113—42no—
230D4×C113—81no—
231D4×C113—82no—
232D4×C113—82no—
233D4×C113—82no—
234D4×C113—82no—
235C2×C4×C113—21no—
236C2×C4×C113—21no—
237C2×C4×C113—22no—
238C2×C4×C113—22no—
239C2×C4×C113—22no—
240C2×C4×C113—42no—
241C2×C4×C113—42no—
242C2×C4×C113—41no—
243C2×C4×C113—41no—
244C2×C4×C113—41no—
245C2×C4×C113—41no—
246C2×C4×C113—41no—
247C2×C4×C113—42no—
248C2×C4×C113—42no—
249C2×C4×C113—41no—
250C2×C4×C113—41no—
251C2×C4×C113—41no—
252C2×C4×C113—41no—
253C2×C4×C113—41no—
254C2×C4×C113—41no—
255C2×C4×C113—42no—
256C2×C4×C113—41no—
257C2×C4×C113—41no—
258C2×C4×C113—41no—
259C2×C4×C113—41no—
260C2×C4×C113—41no—
261C2×C4×C113—41no—
262C2×C4×C113—81no—
263C2×C4×C113—81no—
264C2×C4×C113—81no—
265C2×C4×C113—81no—
266C2×C4×C113—81no—
267C2×C4×C113—81no—
268C2×C4×C113—81no—
269C2×C4×C113#12011yescharacteristic
270C2×C4×C113#12111yescharacteristic
271C8×C113—42no—
272C22×C113—21no—
273C22×C113—21no—
274C22×C113—21no—
275C22×C113—21no—
276C22×C113—21no—
277C22×C113—21no—
278C22×C113—41no—
279C22×C113—41no—
280C22×C113—41no—
281C22×C113—41no—
282C22×C113—41no—
283C22×C113—41no—
284C22×C113—41no—
285C22×C113—41no—
286C22×C113—42no—
287C22×C113—81no—
288C22×C113—81no—
289C22×C113—81no—
290C22×C113—81no—
291C22×C113—81no—
292C22×C113—81no—
293C22×C113—82no—
294C22×C113—82no—
295C22×C113—81no—
296C22×C113—81no—
297C22×C113—81no—
298C22×C113—81no—
299C22×C113—81no—
300C22×C113—161no—
301C22×C113—161no—
302C22×C113#39211yescharacteristic
303C22×C113B(4,𝔽2)11yescharacteristic
304C22×C113B(4,𝔽2)11yescharacteristic
305C4×C113—21no—
306C4×C113—21no—
307C4×C113—42no—
308C4×C113—42no—
309C4×C113—81no—
310C4×C113—81no—
311C4×C113—82no—
312C4×C113—81no—
313C4×C113—81no—
314C4×C113—161no—
315#13347C11311yesmaximal, characteristic, direct product factor, Sylow
316C2×C113—21no—
317C2×C113—21no—
318C2×C113—41no—
319C2×C113—41no—
320C2×C113—41no—
321C2×C113—41no—
322C2×C113—82no—
323C2×C113—161no—
324C2×C113#202111yescharacteristic
325C2×C113#219811yescharacteristic
326C2×C113#220011yescharacteristic
327C2×#458C2×C11311yescharacteristic, complemented
328C2×#453C2×C11311yescharacteristic
329#2709C2×C11311yescharacteristic, complemented
330C2×#353C2×C11311yescharacteristic, complemented
331C2×#352C2×C11311yescharacteristic, complemented
332#1790C2×C11311yescharacteristic, complemented
333#1390C2×C11311yescharacteristic, complemented
334C113#1334711yescharacteristic, direct product factor, Sylow
335C2×H(5,𝔽2)C22×C11311yescharacteristic
336C2×AGL(1,ℤ/8)—21no—
337C2×#127C22×C11311yescharacteristic
338C2×#123—21no—
339C2×#123C22×C11311yescharacteristic
340#458—22no—
341#458—22no—
342#453—22no—
343#453—22no—
344C2×#104—21no—
345C2×#100C22×C11311yescharacteristic
346C2×#99—21no—
347C2×#99—21no—
348C2×#99C22×C11311yescharacteristic
349C2×#99C22×C11311yescharacteristic
350#394—21no—
351#394—21no—
352#394—21no—
353#387—21no—
354#386—21no—
355#386—21no—
356#386—21no—
357#386C22×C11311yescharacteristic
358#353—22no—
359#352—22no—
360H(5,𝔽2)—21no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—21no—
363H(5,𝔽2)—42no—
364H(5,𝔽2)D4×C11312yes—
365C2×#41—21no—
366C2×#41—41no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—41no—
372C22×D4D4×C11311yescharacteristic
373C22×D4C23×C11311yescharacteristic
374C23×C4D4×C11311yescharacteristic
375C23×C4D4×C11311yescharacteristic
376AGL(1,ℤ/8)—24no—
377AGL(1,ℤ/8)—42no—
378C2×SD16—41no—
379C2×D8—41no—
380C2×M16—21no—
381#127—21no—
382#127—21no—
383#127—21no—
384#127—21no—
385#123—24no—
386#123—21no—
387#123—21no—
388#123—21no—
389#123—21no—
390#123—42no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—41no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4D4×C11311yescharacteristic
405C2×C22⋊C4D4×C11311yescharacteristic
406C2×C42D4×C11311yescharacteristic
407#104—24no—
408#100—21no—
409#100D4×C11312yes—
410#99—24no—
411#99—21no—
412#99—21no—
413#99—21no—
414#99—42no—
415#99D4×C11312yes—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—41no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24C2×D4×C11311yescharacteristic
425C24C2×D4×C11311yescharacteristic
426#41—22no—
427#41—22no—
428#41—42no—
429#41—41no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—41no—
434C2×Q8—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4C2×D4×C11311yescharacteristic
466C2×D4C2×D4×C11311yescharacteristic
467C2×D4C2×D4×C11311yescharacteristic
468C2×D4#41×C11311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—81no—
485C22×C4C2×D4×C11311yescharacteristic
486SD16—44no—
487D8—44no—
488M16—22no—
489M16—41no—
490C2×C8—41no—
491C4⋊C4—42no—
492C4⋊C4—44no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—44no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—82no—
511C42—21no—
512C42—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23#120×C11311yescharacteristic
538C23#120×C11311yescharacteristic
539C23#121×C11311yescharacteristic
540C23#121×C11311yescharacteristic
541C23#127×C11311yescharacteristic
542Q8—22no—
543Q8—41no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—81no—
558D4—82no—
559D4—82no—
560D4—82no—
561D4—82no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4#120×C11311yescharacteristic
597C2×C4#121×C11311yescharacteristic
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—82no—
621C22—82no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22#392×C11311yescharacteristic
630C22B(4,𝔽2)×C11311yescharacteristic
631C22B(4,𝔽2)×C11311yescharacteristic
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—81no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4—161no—
642C2—21no—
643C2—21no—
644C2—41no—
645C2—41no—
646C2—41no—
647C2—41no—
648C2—82no—
649C2—161no—
650C2C113×#202111yescharacteristic
651C2C113×#219811yescharacteristic
652C2C113×#220011yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C113
prime radicalC2×#453×C113C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C22×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#458×C113C2semidirect
3. C113×#2709C2semidirect
4. C2×#353×C113C2semidirect
5. C2×#352×C113C2semidirect
6. C113×#1790C2semidirect
7. C113×#1390C2semidirect
315. #13347C113direct (N × H)
327. C2×#458C2×C113semidirect
329. #2709C2×C113semidirect
330. C2×#353C2×C113semidirect
331. C2×#352C2×C113semidirect
332. #1790C2×C113semidirect
333. #1390C2×C113semidirect
334. C113#13347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#458×C1132
C2×#453×C1132
C113×#27092
C2×#353×C1132
C2×#352×C1132
C113×#17902
C113×#13902
#13347113