Finite Group Databasebeta

← C113×#10972 #43278992

Subgroups — C113×#10972 #43278992

Order 28928.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C113C211yesmaximal, characteristic
2C22×#99×C113C212yesmaximal, complemented
3C22×#99×C113C211yesmaximal, characteristic, complemented
4C113×#2308C211yesmaximal, characteristic, complemented
5C2×#342×C113C212yesmaximal, complemented
6C23×D4×C113C2211yescharacteristic
7C23×D4×C113C2211yescharacteristic
8#534×C113—24no—
9#534×C113—24no—
10C2×#123×C113—21no—
11C2×#123×C113C412yescomplemented
12C2×#121×C113—22no—
13C2×#120×C113—21no—
14C2×#120×C113C412yescomplemented
15C22×C22⋊C4×C113C2212yes—
16C22×C22⋊C4×C113C2212yes—
17C22×C22⋊C4×C113C2211yescharacteristic
18C2×#99×C113—22no—
19C2×#99×C113—24no—
20C2×#99×C113—24no—
21C2×#99×C113—24no—
22C2×#99×C113—24no—
23#386×C113—24no—
24#381×C113—21no—
25#379×C113—21no—
26#342×C113—24no—
27C25×C113C2×C411yescharacteristic
28C25×C113D411yescharacteristic
29C25×C113C2311yescharacteristic
30C22×D4×C113—21no—
31C22×D4×C113—21no—
32C22×D4×C113—22no—
33C22×D4×C113—22no—
34C22×D4×C113—22no—
35C22×D4×C113—22no—
36C22×D4×C113—22no—
37C22×D4×C113—22no—
38C22×D4×C113—22no—
39C22×D4×C113—22no—
40C22×D4×C113—22no—
41C22×D4×C113—22no—
42C22×D4×C113—22no—
43C22×D4×C113—22no—
44C22×D4×C113C2×C412yes—
45C22×D4×C113D412yes—
46C22×D4×C113D414yes—
47C23×C4×C113—21no—
48C23×C4×C113—22no—
49C23×C4×C113—22no—
50C23×C4×C113C2×C411yescharacteristic
51C23×C4×C113D411yescharacteristic
52#123×C113—28no—
53#123×C113—24no—
54#123×C113—24no—
55#121×C113—216no—
56#120×C113—28no—
57#120×C113—24no—
58#120×C113—24no—
59C2×C4⋊C4×C113—22no—
60C2×C22⋊C4×C113—22no—
61C2×C22⋊C4×C113—21no—
62C2×C22⋊C4×C113—22no—
63C2×C22⋊C4×C113—22no—
64C2×C22⋊C4×C113—22no—
65C2×C22⋊C4×C113—22no—
66C2×C22⋊C4×C113—22no—
67C2×C22⋊C4×C113—22no—
68C2×C22⋊C4×C113—22no—
69C2×C22⋊C4×C113—22no—
70C2×C22⋊C4×C113—22no—
71C2×C22⋊C4×C113—22no—
72C2×C22⋊C4×C113—22no—
73C2×C22⋊C4×C113—22no—
74C2×C22⋊C4×C113—24no—
75C2×C22⋊C4×C113C2×C412yes—
76C2×C22⋊C4×C113D414yes—
77C2×C22⋊C4×C113D414yescomplemented
78C2×C22⋊C4×C113D414yescomplemented
79#99×C113—216no—
80#99×C113—28no—
81#95×C113—24no—
82C24×C113—21no—
83C24×C113—21no—
84C24×C113—21no—
85C24×C113—22no—
86C24×C113—22no—
87C24×C113—22no—
88C24×C113—22no—
89C24×C113—21no—
90C24×C113—82no—
91C24×C113—82no—
92C24×C113—82no—
93C24×C113C22⋊C412yes—
94C24×C113C22⋊C412yescomplemented
95C24×C113C22×C411yescharacteristic
96C24×C113C2×D411yescharacteristic
97C24×C113C2×D411yescharacteristic
98C24×C113C2×D412yes—
99C24×C113C2×D412yes—
100C24×C113C2×D412yes—
101C24×C113C2×D412yes—
102C24×C113#4112yes—
103C24×C113#4112yes—
104C2×D4×C113—22no—
105C2×D4×C113—22no—
106C2×D4×C113—24no—
107C2×D4×C113—24no—
108C2×D4×C113—22no—
109C2×D4×C113—24no—
110C2×D4×C113—24no—
111C2×D4×C113—24no—
112C2×D4×C113—24no—
113C2×D4×C113—24no—
114C2×D4×C113—24no—
115C2×D4×C113—24no—
116C2×D4×C113—22no—
117C2×D4×C113—24no—
118C2×D4×C113—28no—
119C2×D4×C113—41no—
120C2×D4×C113—41no—
121C2×D4×C113—42no—
122C2×D4×C113—42no—
123C2×D4×C113—42no—
124C2×D4×C113—42no—
125C2×D4×C113—42no—
126C2×D4×C113—42no—
127C2×D4×C113—42no—
128C2×D4×C113—42no—
129C2×D4×C113—42no—
130C2×D4×C113—41no—
131C2×D4×C113—41no—
132C2×D4×C113—42no—
133C2×D4×C113—42no—
134C2×D4×C113—42no—
135C2×D4×C113—42no—
136C2×D4×C113—42no—
137C2×D4×C113—84no—
138C22×C4×C113—22no—
139C22×C4×C113—21no—
140C22×C4×C113—21no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—21no—
144C22×C4×C113—22no—
145C22×C4×C113—22no—
146C22×C4×C113—21no—
147C22×C4×C113—24no—
148C22×C4×C113—24no—
149C22×C4×C113—24no—
150C22×C4×C113—42no—
151C22×C4×C113—42no—
152C22×C4×C113—42no—
153C22×C4×C113—42no—
154C22×C4×C113—82no—
155C22×C4×C113—84no—
156C22×C4×C113—84no—
157C22×C4×C113C22⋊C412yes—
158C22×C4×C113C22⋊C412yescomplemented
159C4⋊C4×C113—28no—
160C22⋊C4×C113—28no—
161C22⋊C4×C113—28no—
162C22⋊C4×C113—22no—
163C22⋊C4×C113—24no—
164C22⋊C4×C113—24no—
165C22⋊C4×C113—24no—
166C22⋊C4×C113—24no—
167C22⋊C4×C113—24no—
168C22⋊C4×C113—42no—
169C22⋊C4×C113—42no—
170C22⋊C4×C113—42no—
171C22⋊C4×C113—42no—
172C22⋊C4×C113—84no—
173C22⋊C4×C113C22⋊C414yescomplemented
174C23×C113—22no—
175C23×C113—22no—
176C23×C113—22no—
177C23×C113—22no—
178C23×C113—24no—
179C23×C113—44no—
180C23×C113—42no—
181C23×C113—44no—
182C23×C113—42no—
183C23×C113—42no—
184C23×C113—44no—
185C23×C113—44no—
186C23×C113—44no—
187C23×C113—41no—
188C23×C113—41no—
189C23×C113—42no—
190C23×C113—42no—
191C23×C113—42no—
192C23×C113—82no—
193C23×C113—84no—
194C23×C113—82no—
195C23×C113—82no—
196C23×C113—82no—
197C23×C113—82no—
198C23×C113—82no—
199C23×C113—82no—
200C23×C113—84no—
201C23×C113—84no—
202C23×C113—84no—
203C23×C113C2×C22⋊C411yescharacteristic
204C23×C113C2×C22⋊C411yescharacteristic
205C23×C113C2×C22⋊C411yescharacteristic
206C23×C113C4×D412yes—
207C23×C113C4×D412yes—
208C23×C113#12011yescharacteristic
209C23×C113#12012yes—
210C23×C113#12012yes—
211C23×C113#12011yescharacteristic
212C23×C113#12012yes—
213C23×C113#12112yes—
214C23×C113#12112yes—
215C23×C113#12112yes—
216C23×C113#12112yes—
217C23×C113#12112yes—
218C23×C113#12112yes—
219C23×C113#12311yescharacteristic
220C23×C113#12311yescharacteristic
221C23×C113#12312yes—
222C23×C113#12412yes—
223C23×C113#12712yes—
224D4×C113—44no—
225D4×C113—44no—
226D4×C113—44no—
227D4×C113—44no—
228D4×C113—44no—
229D4×C113—44no—
230D4×C113—44no—
231D4×C113—44no—
232D4×C113—88no—
233C2×C4×C113—24no—
234C2×C4×C113—22no—
235C2×C4×C113—22no—
236C2×C4×C113—22no—
237C2×C4×C113—24no—
238C2×C4×C113—22no—
239C2×C4×C113—44no—
240C2×C4×C113—41no—
241C2×C4×C113—41no—
242C2×C4×C113—42no—
243C2×C4×C113—42no—
244C2×C4×C113—42no—
245C2×C4×C113—48no—
246C2×C4×C113—44no—
247C2×C4×C113—44no—
248C2×C4×C113—84no—
249C2×C4×C113—84no—
250C2×C4×C113—84no—
251C2×C4×C113—84no—
252C2×C4×C113—84no—
253C2×C4×C113—84no—
254C22×C113—22no—
255C22×C113—22no—
256C22×C113—24no—
257C22×C113—24no—
258C22×C113—22no—
259C22×C113—42no—
260C22×C113—42no—
261C22×C113—42no—
262C22×C113—42no—
263C22×C113—42no—
264C22×C113—41no—
265C22×C113—41no—
266C22×C113—42no—
267C22×C113—42no—
268C22×C113—42no—
269C22×C113—42no—
270C22×C113—41no—
271C22×C113—42no—
272C22×C113—41no—
273C22×C113—42no—
274C22×C113—42no—
275C22×C113—44no—
276C22×C113—44no—
277C22×C113—44no—
278C22×C113—42no—
279C22×C113—42no—
280C22×C113—82no—
281C22×C113—84no—
282C22×C113—84no—
283C22×C113—82no—
284C22×C113—84no—
285C22×C113—84no—
286C22×C113—82no—
287C22×C113#37911yescharacteristic
288C22×C113#38611yescharacteristic
289C22×C113#38612yes—
290C22×C113#38611yescharacteristic
291C22×C113#39012yes—
292C22×C113#39212yes—
293C22×C113#39212yes—
294C22×C113#39412yes—
295C22×C113#39412yes—
296C4×C113—44no—
297C4×C113—42no—
298C4×C113—42no—
299C4×C113—84no—
300C4×C113—84no—
301#10972C11311yesmaximal, characteristic, direct product factor, Sylow
302C2×C113—21no—
303C2×C113—22no—
304C2×C113—22no—
305C2×C113—21no—
306C2×C113—22no—
307C2×C113—22no—
308C2×C113—22no—
309C2×C113—22no—
310C2×C113—82no—
311C2×C113—82no—
312C2×C113#143811yescharacteristic
313C2×C113#191312yes—
314C2×#534C2×C11311yescharacteristic
315C22×#99C2×C11312yescomplemented
316C22×#99C2×C11311yescharacteristic, complemented
317#2308C2×C11311yescharacteristic, complemented
318C2×#342C2×C11312yescomplemented
319C113#1097211yescharacteristic, direct product factor, Sylow
320C23×D4C22×C11311yescharacteristic
321C23×D4C22×C11311yescharacteristic
322#534—24no—
323#534—24no—
324C2×#123—21no—
325C2×#123C4×C11312yescomplemented
326C2×#121—22no—
327C2×#120—21no—
328C2×#120C4×C11312yescomplemented
329C22×C22⋊C4C22×C11312yes—
330C22×C22⋊C4C22×C11312yes—
331C22×C22⋊C4C22×C11311yescharacteristic
332C2×#99—22no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336C2×#99—24no—
337#386—24no—
338#381—21no—
339#379—21no—
340#342—24no—
341C25C2×C4×C11311yescharacteristic
342C25D4×C11311yescharacteristic
343C25C23×C11311yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C11312yes—
359C22×D4D4×C11312yes—
360C22×D4D4×C11314yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C11311yescharacteristic
365C23×C4D4×C11311yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C11312yes—
390C2×C22⋊C4D4×C11314yes—
391C2×C22⋊C4D4×C11314yescomplemented
392C2×C22⋊C4D4×C11314yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C11312yes—
408C24C22⋊C4×C11312yescomplemented
409C24C22×C4×C11311yescharacteristic
410C24C2×D4×C11311yescharacteristic
411C24C2×D4×C11311yescharacteristic
412C24C2×D4×C11312yes—
413C24C2×D4×C11312yes—
414C24C2×D4×C11312yes—
415C24C2×D4×C11312yes—
416C24#41×C11312yes—
417C24#41×C11312yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C11312yes—
472C22×C4C22⋊C4×C11312yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C11314yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C11311yescharacteristic
518C23C2×C22⋊C4×C11311yescharacteristic
519C23C2×C22⋊C4×C11311yescharacteristic
520C23C4×D4×C11312yes—
521C23C4×D4×C11312yes—
522C23#120×C11311yescharacteristic
523C23#120×C11312yes—
524C23#120×C11312yes—
525C23#120×C11311yescharacteristic
526C23#120×C11312yes—
527C23#121×C11312yes—
528C23#121×C11312yes—
529C23#121×C11312yes—
530C23#121×C11312yes—
531C23#121×C11312yes—
532C23#121×C11312yes—
533C23#123×C11311yescharacteristic
534C23#123×C11311yescharacteristic
535C23#123×C11312yes—
536C23#124×C11312yes—
537C23#127×C11312yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22#379×C11311yescharacteristic
602C22#386×C11311yescharacteristic
603C22#386×C11312yes—
604C22#386×C11311yescharacteristic
605C22#390×C11312yes—
606C22#392×C11312yes—
607C22#392×C11312yes—
608C22#394×C11312yes—
609C22#394×C11312yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2C113×#143811yescharacteristic
626C2C113×#191312yes—
subgroupG/H
center, socleC22×C113#386
commutatorC24C22×C4×C113
Frattini, cosocleC25C23×C113
prime radicalC2×#534×C113C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C113C2semidirect
3. C22×#99×C113C2semidirect
4. C113×#2308C2semidirect
5. C2×#342×C113C2semidirect
11. C2×#123×C113C4semidirect
14. C2×#120×C113C4semidirect
77. C2×C22⋊C4×C113D4semidirect
78. C2×C22⋊C4×C113D4semidirect
94. C24×C113C22⋊C4semidirect
158. C22×C4×C113C22⋊C4semidirect
173. C22⋊C4×C113C22⋊C4semidirect
301. #10972C113direct (N × H)
315. C22×#99C2×C113semidirect
316. C22×#99C2×C113semidirect
317. #2308C2×C113semidirect
318. C2×#342C2×C113semidirect
319. C113#10972direct (N × H)
325. C2×#123C4×C113semidirect
328. C2×#120C4×C113semidirect
391. C2×C22⋊C4D4×C113semidirect
392. C2×C22⋊C4D4×C113semidirect
408. C24C22⋊C4×C113semidirect
472. C22×C4C22⋊C4×C113semidirect
487. C22⋊C4C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1132
C22×#99×C1132
C113×#23082
C2×#342×C1132
#10972113