Finite Group Databasebeta

← C113×#13344 #43281364

Subgroups — C113×#13344 #43281364

Order 28928.

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

normal subgroups only

This group has 892 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×B(4,𝔽2)×C113C211yesmaximal, characteristic
3C113×#2697C211yesmaximal, characteristic, complemented
4C2×#352×C113C211yesmaximal, characteristic, complemented
5C2×AΣL(1,𝔽16)×C113C211yesmaximal, characteristic, complemented
6C113×#1792C211yesmaximal, characteristic, complemented
7C113×#1393C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C113C2211yescharacteristic
9C2×#123×C113—21no—
10C2×#123×C113C2211yescharacteristic
11C2×#120×C113—21no—
12C2×#120×C113C2211yescharacteristic
13#458×C113—22no—
14#458×C113—22no—
15B(4,𝔽2)×C113—22no—
16B(4,𝔽2)×C113—22no—
17C2×#104×C113—21no—
18#417×C113—21no—
19C2×#100×C113C2211yescharacteristic
20C2×#99×C113—21no—
21C2×#99×C113—21no—
22C2×#99×C113C2211yescharacteristic
23C2×#99×C113C2211yescharacteristic
24#397×C113—21no—
25#396×C113—21no—
26#394×C113—21no—
27#390×C113C2211yescharacteristic
28#388×C113—21no—
29#386×C113—21no—
30#379×C113—21no—
31#352×C113—22no—
32AΣL(1,𝔽16)×C113—22no—
33C25×C113D411yescharacteristic
34H(5,𝔽2)×C113—21no—
35H(5,𝔽2)×C113—21no—
36H(5,𝔽2)×C113—21no—
37H(5,𝔽2)×C113—42no—
38H(5,𝔽2)×C113D412yes—
39C2×#41×C113—21no—
40C2×#41×C113—41no—
41C22×D4×C113—21no—
42C22×D4×C113—21no—
43C22×D4×C113—21no—
44C22×D4×C113—41no—
45C22×D4×C113—41no—
46C22×D4×C113C2311yescharacteristic
47C23×C4×C113D411yescharacteristic, complemented
48C2×M16×C113—21no—
49#123×C113—24no—
50#123×C113—21no—
51#123×C113—21no—
52#123×C113—21no—
53#123×C113—21no—
54#123×C113—42no—
55#120×C113—24no—
56#120×C113—21no—
57#120×C113—21no—
58#120×C113—21no—
59#120×C113—21no—
60#120×C113—42no—
61C2×C4⋊C4×C113—21no—
62C2×C4⋊C4×C113—21no—
63C2×C4⋊C4×C113—41no—
64C2×C4⋊C4×C113D411yescharacteristic, complemented
65C2×C22⋊C4×C113—21no—
66C2×C22⋊C4×C113—21no—
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, complemented
79C2×C42×C113D411yescharacteristic, complemented
80#104×C113—42no—
81#103×C113—41no—
82#102×C113—41no—
83#100×C113—21no—
84#100×C113—21no—
85#99×C113—24no—
86#99×C113—24no—
87#99×C113—21no—
88#99×C113—21no—
89#99×C113D412yes—
90#99×C113D412yescomplemented
91#95×C113—21no—
92#95×C113—21no—
93#95×C113—21no—
94C24×C113—21no—
95C24×C113—21no—
96C24×C113—21no—
97C24×C113—21no—
98C24×C113—21no—
99C24×C113—41no—
100C24×C113—41no—
101C24×C113—42no—
102C24×C113—81no—
103C24×C113C2×D411yescharacteristic
104C24×C113C2×D411yescharacteristic
105#41×C113—22no—
106#41×C113—22no—
107#41×C113—42no—
108#41×C113—41no—
109#41×C113—42no—
110#41×C113—42no—
111#41×C113—42no—
112#41×C113—41no—
113C2×Q8×C113—21no—
114C2×D4×C113—21no—
115C2×D4×C113—22no—
116C2×D4×C113—22no—
117C2×D4×C113—22no—
118C2×D4×C113—22no—
119C2×D4×C113—41no—
120C2×D4×C113—41no—
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—44no—
133C2×D4×C113—42no—
134C2×D4×C113—41no—
135C2×D4×C113—41no—
136C2×D4×C113—81no—
137C2×D4×C113—82no—
138C2×D4×C113—82no—
139C2×D4×C113C2×D411yescharacteristic
140C2×D4×C113C2×D411yescharacteristic
141C2×D4×C113C2×D411yescharacteristic
142C2×D4×C113#4111yescharacteristic
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—21no—
152C22×C4×C113—41no—
153C22×C4×C113—41no—
154C22×C4×C113—41no—
155C22×C4×C113—41no—
156C22×C4×C113—41no—
157C22×C4×C113C2×D411yescharacteristic
158M16×C113—41no—
159M16×C113—41no—
160C2×C8×C113—41no—
161C4⋊C4×C113—41no—
162C4⋊C4×C113—44no—
163C4⋊C4×C113—41no—
164C4⋊C4×C113—41no—
165C4⋊C4×C113—81no—
166C22⋊C4×C113—21no—
167C22⋊C4×C113—21no—
168C22⋊C4×C113—22no—
169C22⋊C4×C113—22no—
170C22⋊C4×C113—21no—
171C22⋊C4×C113—21no—
172C22⋊C4×C113—44no—
173C22⋊C4×C113—42no—
174C22⋊C4×C113—41no—
175C22⋊C4×C113—41no—
176C22⋊C4×C113—44no—
177C22⋊C4×C113—41no—
178C22⋊C4×C113—41no—
179C22⋊C4×C113—41no—
180C22⋊C4×C113—41no—
181C22⋊C4×C113—81no—
182C22⋊C4×C113—81no—
183C22⋊C4×C113—81no—
184C22⋊C4×C113—81no—
185C22⋊C4×C113—81no—
186C42×C113—41no—
187C23×C113—21no—
188C23×C113—21no—
189C23×C113—21no—
190C23×C113—21no—
191C23×C113—22no—
192C23×C113—22no—
193C23×C113—22no—
194C23×C113—41no—
195C23×C113—41no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—42no—
199C23×C113—41no—
200C23×C113—41no—
201C23×C113—41no—
202C23×C113—41no—
203C23×C113—41no—
204C23×C113—42no—
205C23×C113—42no—
206C23×C113—41no—
207C23×C113—41no—
208C23×C113—41no—
209C23×C113—41no—
210C23×C113—81no—
211C23×C113—82no—
212C23×C113—81no—
213C23×C113—82no—
214C23×C113—84no—
215C23×C113—81no—
216C23×C113—81no—
217C23×C113—81no—
218C23×C113—81no—
219C23×C113—81no—
220C23×C113#12011yescharacteristic
221C23×C113#12011yescharacteristic
222C23×C113#12011yescharacteristic
223C23×C113#12111yescharacteristic
224C23×C113#12111yescharacteristic
225Q8×C113—22no—
226Q8×C113—41no—
227D4×C113—22no—
228D4×C113—41no—
229D4×C113—41no—
230D4×C113—41no—
231D4×C113—41no—
232D4×C113—41no—
233D4×C113—42no—
234D4×C113—42no—
235D4×C113—42no—
236D4×C113—42no—
237D4×C113—42no—
238D4×C113—42no—
239D4×C113—82no—
240D4×C113—82no—
241D4×C113—88no—
242C2×C4×C113—21no—
243C2×C4×C113—21no—
244C2×C4×C113—22no—
245C2×C4×C113—22no—
246C2×C4×C113—42no—
247C2×C4×C113—42no—
248C2×C4×C113—41no—
249C2×C4×C113—41no—
250C2×C4×C113—41no—
251C2×C4×C113—42no—
252C2×C4×C113—42no—
253C2×C4×C113—42no—
254C2×C4×C113—41no—
255C2×C4×C113—41no—
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—41no—
263C2×C4×C113—41no—
264C2×C4×C113—41no—
265C2×C4×C113—41no—
266C2×C4×C113—41no—
267C2×C4×C113—41no—
268C2×C4×C113—41no—
269C2×C4×C113—81no—
270C2×C4×C113—81no—
271C2×C4×C113—81no—
272C2×C4×C113—81no—
273C2×C4×C113—81no—
274C2×C4×C113#12111yescharacteristic
275C2×C4×C113#12711yescharacteristic
276C8×C113—81no—
277C22×C113—21no—
278C22×C113—21no—
279C22×C113—21no—
280C22×C113—21no—
281C22×C113—21no—
282C22×C113—21no—
283C22×C113—41no—
284C22×C113—41no—
285C22×C113—41no—
286C22×C113—41no—
287C22×C113—42no—
288C22×C113—42no—
289C22×C113—41no—
290C22×C113—41no—
291C22×C113—41no—
292C22×C113—41no—
293C22×C113—44no—
294C22×C113—42no—
295C22×C113—42no—
296C22×C113—81no—
297C22×C113—81no—
298C22×C113—81no—
299C22×C113—81no—
300C22×C113—82no—
301C22×C113—82no—
302C22×C113—82no—
303C22×C113—82no—
304C22×C113—82no—
305C22×C113—81no—
306C22×C113—81no—
307C22×C113—81no—
308C22×C113—81no—
309C22×C113—161no—
310C22×C113—161no—
311C22×C113#39211yescharacteristic
312C22×C113B(4,𝔽2)11yescharacteristic
313C22×C113B(4,𝔽2)11yescharacteristic
314C4×C113—21no—
315C4×C113—21no—
316C4×C113—42no—
317C4×C113—81no—
318C4×C113—81no—
319C4×C113—81no—
320C4×C113—82no—
321C4×C113—82no—
322C4×C113—81no—
323C4×C113—81no—
324#13344C11311yesmaximal, characteristic, direct product factor, Sylow
325C2×C113—21no—
326C2×C113—21no—
327C2×C113—41no—
328C2×C113—41no—
329C2×C113—41no—
330C2×C113—41no—
331C2×C113—82no—
332C2×C113—82no—
333C2×C113#202111yescharacteristic
334C2×C113#219711yescharacteristic
335C2×C113#220011yescharacteristic
336C2×#458C2×C11311yescharacteristic, complemented
337C2×B(4,𝔽2)C2×C11311yescharacteristic
338#2697C2×C11311yescharacteristic, complemented
339C2×#352C2×C11311yescharacteristic, complemented
340C2×AΣL(1,𝔽16)C2×C11311yescharacteristic, complemented
341#1792C2×C11311yescharacteristic, complemented
342#1393C2×C11311yescharacteristic, complemented
343C113#1334411yescharacteristic, direct product factor, Sylow
344C2×H(5,𝔽2)C22×C11311yescharacteristic
345C2×#123—21no—
346C2×#123C22×C11311yescharacteristic
347C2×#120—21no—
348C2×#120C22×C11311yescharacteristic
349#458—22no—
350#458—22no—
351B(4,𝔽2)—22no—
352B(4,𝔽2)—22no—
353C2×#104—21no—
354#417—21no—
355C2×#100C22×C11311yescharacteristic
356C2×#99—21no—
357C2×#99—21no—
358C2×#99C22×C11311yescharacteristic
359C2×#99C22×C11311yescharacteristic
360#397—21no—
361#396—21no—
362#394—21no—
363#390C22×C11311yescharacteristic
364#388—21no—
365#386—21no—
366#379—21no—
367#352—22no—
368AΣL(1,𝔽16)—22no—
369C25D4×C11311yescharacteristic
370H(5,𝔽2)—21no—
371H(5,𝔽2)—21no—
372H(5,𝔽2)—21no—
373H(5,𝔽2)—42no—
374H(5,𝔽2)D4×C11312yes—
375C2×#41—21no—
376C2×#41—41no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—41no—
381C22×D4—41no—
382C22×D4C23×C11311yescharacteristic
383C23×C4D4×C11311yescharacteristic, complemented
384C2×M16—21no—
385#123—24no—
386#123—21no—
387#123—21no—
388#123—21no—
389#123—21no—
390#123—42no—
391#120—24no—
392#120—21no—
393#120—21no—
394#120—21no—
395#120—21no—
396#120—42no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4D4×C11311yescharacteristic, complemented
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4D4×C11311yescharacteristic
414C2×C22⋊C4D4×C11311yescharacteristic, complemented
415C2×C42D4×C11311yescharacteristic, complemented
416#104—42no—
417#103—41no—
418#102—41no—
419#100—21no—
420#100—21no—
421#99—24no—
422#99—24no—
423#99—21no—
424#99—21no—
425#99D4×C11312yes—
426#99D4×C11312yescomplemented
427#95—21no—
428#95—21no—
429#95—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—41no—
436C24—41no—
437C24—42no—
438C24—81no—
439C24C2×D4×C11311yescharacteristic
440C24C2×D4×C11311yescharacteristic
441#41—22no—
442#41—22no—
443#41—42no—
444#41—41no—
445#41—42no—
446#41—42no—
447#41—42no—
448#41—41no—
449C2×Q8—21no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—81no—
473C2×D4—82no—
474C2×D4—82no—
475C2×D4C2×D4×C11311yescharacteristic
476C2×D4C2×D4×C11311yescharacteristic
477C2×D4C2×D4×C11311yescharacteristic
478C2×D4#41×C11311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4C2×D4×C11311yescharacteristic
494M16—41no—
495M16—41no—
496C2×C8—41no—
497C4⋊C4—41no—
498C4⋊C4—44no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—81no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—44no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—42no—
512C22⋊C4—44no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C42—41no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—81no—
547C23—82no—
548C23—81no—
549C23—82no—
550C23—84no—
551C23—81no—
552C23—81no—
553C23—81no—
554C23—81no—
555C23—81no—
556C23#120×C11311yescharacteristic
557C23#120×C11311yescharacteristic
558C23#120×C11311yescharacteristic
559C23#121×C11311yescharacteristic
560C23#121×C11311yescharacteristic
561Q8—22no—
562Q8—41no—
563D4—22no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—82no—
576D4—82no—
577D4—88no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4#121×C11311yescharacteristic
611C2×C4#127×C11311yescharacteristic
612C8—81no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—44no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22—82no—
640C22—82no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—161no—
646C22—161no—
647C22#392×C11311yescharacteristic
648C22B(4,𝔽2)×C11311yescharacteristic
649C22B(4,𝔽2)×C11311yescharacteristic
650C4—21no—
651C4—21no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—82no—
657C4—82no—
658C4—81no—
659C4—81no—
660C2—21no—
661C2—21no—
662C2—41no—
663C2—41no—
664C2—41no—
665C2—41no—
666C2—82no—
667C2—82no—
668C2C113×#202111yescharacteristic
669C2C113×#219711yescharacteristic
670C2C113×#220011yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C113
prime radicalC2×B(4,𝔽2)×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×#2697C2semidirect
4. C2×#352×C113C2semidirect
5. C2×AΣL(1,𝔽16)×C113C2semidirect
6. C113×#1792C2semidirect
7. C113×#1393C2semidirect
47. C23×C4×C113D4semidirect
64. C2×C4⋊C4×C113D4semidirect
78. C2×C22⋊C4×C113D4semidirect
79. C2×C42×C113D4semidirect
90. #99×C113D4semidirect
324. #13344C113direct (N × H)
336. C2×#458C2×C113semidirect
338. #2697C2×C113semidirect
339. C2×#352C2×C113semidirect
340. C2×AΣL(1,𝔽16)C2×C113semidirect
341. #1792C2×C113semidirect
342. #1393C2×C113semidirect
343. C113#13344direct (N × H)
383. C23×C4D4×C113semidirect
400. C2×C4⋊C4D4×C113semidirect
414. C2×C22⋊C4D4×C113semidirect
415. C2×C42D4×C113semidirect
426. #99D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#458×C1132
C2×B(4,𝔽2)×C1132
C113×#26972
C2×#352×C1132
C2×AΣL(1,𝔽16)×C1132
C113×#17922
C113×#13932
#13344113