Finite Group Databasebeta

← C113×#10960 #43278980

Subgroups — C113×#10960 #43278980

Order 28928.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C113C212yesmaximal
2C2×#386×C113C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
4C2×#342×C113C212yesmaximal, complemented
5C113×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C113C2211yescharacteristic
7C24×C4×C113C2211yescharacteristic
8C22×C22⋊C4×C113C412yescomplemented
9C22×C22⋊C4×C113C2211yescharacteristic
10C22×C22⋊C4×C113C2212yes—
11C22×C22⋊C4×C113C2212yes—
12C22×C42×C113—21no—
13C2×#99×C113—24no—
14C2×#99×C113—24no—
15C2×#99×C113C418yescomplemented
16#386×C113—21no—
17#386×C113—22no—
18#386×C113—21no—
19C4×C22⋊C4×C113—24no—
20C2×#95×C113—21no—
21C2×#95×C113—22no—
22C2×#95×C113C412yescomplemented
23#342×C113—24no—
24C25×C113C2×C411yescharacteristic
25C25×C113C2311yescharacteristic
26C22×D4×C113—21no—
27C22×D4×C113—21no—
28C22×D4×C113—22no—
29C22×D4×C113—22no—
30C22×D4×C113—22no—
31C22×D4×C113—22no—
32C22×D4×C113—22no—
33C22×D4×C113C2×C414yes—
34C23×C4×C113—22no—
35C23×C4×C113—22no—
36C23×C4×C113—22no—
37C23×C4×C113—22no—
38C23×C4×C113—44no—
39C23×C4×C113C2×C411yescharacteristic
40C23×C4×C113C2×C412yes—
41C23×C4×C113C2×C412yes—
42C23×C4×C113D411yescharacteristic
43C23×C4×C113D412yes—
44C23×C4×C113D411yescharacteristic
45C2×C22⋊C4×C113—22no—
46C2×C22⋊C4×C113—22no—
47C2×C22⋊C4×C113—22no—
48C2×C22⋊C4×C113—22no—
49C2×C22⋊C4×C113—22no—
50C2×C22⋊C4×C113—22no—
51C2×C22⋊C4×C113—22no—
52C2×C22⋊C4×C113—22no—
53C2×C22⋊C4×C113—21no—
54C2×C22⋊C4×C113—21no—
55C2×C22⋊C4×C113—22no—
56C2×C22⋊C4×C113—22no—
57C2×C22⋊C4×C113—22no—
58C2×C22⋊C4×C113—22no—
59C2×C22⋊C4×C113—44no—
60C2×C22⋊C4×C113C2×C414yes—
61C2×C22⋊C4×C113C2×C414yes—
62C2×C22⋊C4×C113D414yes—
63C2×C22⋊C4×C113D414yes—
64C2×C42×C113—24no—
65C2×C42×C113—44no—
66#99×C113—216no—
67#95×C113—24no—
68#95×C113—22no—
69#95×C113—22no—
70#95×C113—44no—
71C24×C113—21no—
72C24×C113—21no—
73C24×C113—22no—
74C24×C113—22no—
75C24×C113—42no—
76C24×C113—42no—
77C24×C113—42no—
78C24×C113—42no—
79C24×C113C4212yescomplemented
80C24×C113C22×C411yescharacteristic
81C24×C113C22×C412yes—
82C24×C113C2×D411yescharacteristic
83C24×C113C2×D411yescharacteristic
84C24×C113C2×D412yes—
85C24×C113C2×D412yes—
86C24×C113#4112yes—
87C24×C113#4112yes—
88C24×C113#4112yes—
89C2×D4×C113—24no—
90C2×D4×C113—24no—
91C2×D4×C113—24no—
92C2×D4×C113—24no—
93C2×D4×C113—24no—
94C2×D4×C113—24no—
95C2×D4×C113—41no—
96C2×D4×C113—42no—
97C2×D4×C113—42no—
98C2×D4×C113—42no—
99C2×D4×C113—41no—
100C2×D4×C113—42no—
101C2×D4×C113—42no—
102C2×D4×C113—41no—
103C2×D4×C113—42no—
104C2×D4×C113—41no—
105C22×C4×C113—21no—
106C22×C4×C113—21no—
107C22×C4×C113—24no—
108C22×C4×C113—21no—
109C22×C4×C113—21no—
110C22×C4×C113—24no—
111C22×C4×C113—24no—
112C22×C4×C113—22no—
113C22×C4×C113—22no—
114C22×C4×C113—21no—
115C22×C4×C113—24no—
116C22×C4×C113—24no—
117C22×C4×C113—24no—
118C22×C4×C113—21no—
119C22×C4×C113—24no—
120C22×C4×C113—24no—
121C22×C4×C113—22no—
122C22×C4×C113—24no—
123C22×C4×C113—24no—
124C22×C4×C113—42no—
125C22×C4×C113—42no—
126C22×C4×C113—42no—
127C22×C4×C113—48no—
128C22×C4×C113—48no—
129C22×C4×C113—44no—
130C22×C4×C113—44no—
131C22×C4×C113—44no—
132C22×C4×C113—44no—
133C22×C4×C113—42no—
134C22×C4×C113—42no—
135C22×C4×C113—42no—
136C22×C4×C113—42no—
137C22×C4×C113C4212yescomplemented
138C22×C4×C113C22⋊C412yes—
139C22×C4×C113C22⋊C412yes—
140C22⋊C4×C113—24no—
141C22⋊C4×C113—24no—
142C22⋊C4×C113—24no—
143C22⋊C4×C113—24no—
144C22⋊C4×C113—24no—
145C22⋊C4×C113—44no—
146C22⋊C4×C113—42no—
147C22⋊C4×C113—42no—
148C22⋊C4×C113—42no—
149C22⋊C4×C113—41no—
150C22⋊C4×C113—41no—
151C22⋊C4×C113—44no—
152C22⋊C4×C113C22⋊C418yescomplemented
153C42×C113—48no—
154C23×C113—22no—
155C23×C113—22no—
156C23×C113—22no—
157C23×C113—22no—
158C23×C113—22no—
159C23×C113—22no—
160C23×C113—22no—
161C23×C113—24no—
162C23×C113—42no—
163C23×C113—42no—
164C23×C113—44no—
165C23×C113—42no—
166C23×C113—44no—
167C23×C113—42no—
168C23×C113—44no—
169C23×C113—44no—
170C23×C113—44no—
171C23×C113—44no—
172C23×C113—41no—
173C23×C113—42no—
174C23×C113—41no—
175C23×C113—42no—
176C23×C113—42no—
177C23×C113—82no—
178C23×C113—82no—
179C23×C113—84no—
180C23×C113C2×C4211yescharacteristic
181C23×C113C2×C22⋊C412yes—
182C23×C113C2×C22⋊C411yescharacteristic
183C23×C113#11711yescharacteristic
184C23×C113#11712yes—
185C23×C113C4×D412yes—
186C23×C113C4×D412yes—
187C23×C113C4×D412yes—
188C23×C113C4×D412yes—
189C23×C113C4×D412yes—
190C23×C113C4×D412yes—
191C23×C113#12011yescharacteristic
192C23×C113#12112yes—
193C23×C113#12112yes—
194C23×C113#12112yes—
195C23×C113#12311yescharacteristic
196C23×C113#12312yes—
197C23×C113#12411yescharacteristic
198C23×C113#12412yes—
199C23×C113#12612yes—
200C23×C113#12711yescharacteristic
201D4×C113—44no—
202D4×C113—44no—
203D4×C113—44no—
204D4×C113—44no—
205C2×C4×C113—24no—
206C2×C4×C113—24no—
207C2×C4×C113—22no—
208C2×C4×C113—22no—
209C2×C4×C113—24no—
210C2×C4×C113—22no—
211C2×C4×C113—28no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—48no—
216C2×C4×C113—48no—
217C2×C4×C113—44no—
218C2×C4×C113—44no—
219C2×C4×C113—48no—
220C2×C4×C113—48no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—41no—
224C2×C4×C113—42no—
225C2×C4×C113—41no—
226C2×C4×C113—48no—
227C2×C4×C113—44no—
228C2×C4×C113—42no—
229C2×C4×C113—42no—
230C2×C4×C113—42no—
231C2×C4×C113—82no—
232C2×C4×C113—82no—
233C2×C4×C113—84no—
234C2×C4×C113—84no—
235C2×C4×C113#9914yescomplemented
236C22×C113—21no—
237C22×C113—21no—
238C22×C113—22no—
239C22×C113—22no—
240C22×C113—21no—
241C22×C113—22no—
242C22×C113—22no—
243C22×C113—21no—
244C22×C113—24no—
245C22×C113—22no—
246C22×C113—24no—
247C22×C113—22no—
248C22×C113—24no—
249C22×C113—24no—
250C22×C113—22no—
251C22×C113—22no—
252C22×C113—42no—
253C22×C113—42no—
254C22×C113—42no—
255C22×C113—42no—
256C22×C113—42no—
257C22×C113—42no—
258C22×C113—42no—
259C22×C113—42no—
260C22×C113—42no—
261C22×C113—44no—
262C22×C113—84no—
263C22×C113—84no—
264C22×C113—81no—
265C22×C113—81no—
266C22×C113—82no—
267C22×C113C4×C22⋊C412yes—
268C22×C113C4×C22⋊C411yescharacteristic
269C22×C113#38612yes—
270C22×C113#38611yescharacteristic
271C22×C113#38812yes—
272C22×C113#38812yes—
273C22×C113#38812yes—
274C22×C113#39012yes—
275C22×C113#39011yescharacteristic
276C22×C113C2×#9912yes—
277C22×C113#41012yes—
278C4×C113—24no—
279C4×C113—48no—
280C4×C113—42no—
281C4×C113—42no—
282C4×C113—84no—
283C4×C113—82no—
284#10960C11311yesmaximal, characteristic, direct product factor, Sylow
285C2×C113—22no—
286C2×C113—22no—
287C2×C113—22no—
288C2×C113—22no—
289C2×C113—22no—
290C2×C113—22no—
291C2×C113—82no—
292C2×C113#143711yescharacteristic
293C2×C113C4×#9912yes—
294C2×C113#189811yescharacteristic
295C2×C113#189911yescharacteristic
296C2×C113#196412yes—
297C22×#99C2×C11312yes—
298C2×#386C2×C11311yescharacteristic
299C2×C4×C22⋊C4C2×C11311yescharacteristic, complemented
300C2×#342C2×C11312yescomplemented
301C22⋊#95C2×C11311yescharacteristic, complemented
302C113#1096011yescharacteristic, direct product factor, Sylow
303C23×D4C22×C11311yescharacteristic
304C24×C4C22×C11311yescharacteristic
305C22×C22⋊C4C4×C11312yescomplemented
306C22×C22⋊C4C22×C11311yescharacteristic
307C22×C22⋊C4C22×C11312yes—
308C22×C22⋊C4C22×C11312yes—
309C22×C42—21no—
310C2×#99—24no—
311C2×#99—24no—
312C2×#99C4×C11318yescomplemented
313#386—21no—
314#386—22no—
315#386—21no—
316C4×C22⋊C4—24no—
317C2×#95—21no—
318C2×#95—22no—
319C2×#95C4×C11312yescomplemented
320#342—24no—
321C25C2×C4×C11311yescharacteristic
322C25C23×C11311yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C11314yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C11311yescharacteristic
337C23×C4C2×C4×C11312yes—
338C23×C4C2×C4×C11312yes—
339C23×C4D4×C11311yescharacteristic
340C23×C4D4×C11312yes—
341C23×C4D4×C11311yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C11314yes—
358C2×C22⋊C4C2×C4×C11314yes—
359C2×C22⋊C4D4×C11314yes—
360C2×C22⋊C4D4×C11314yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C11312yescomplemented
377C24C22×C4×C11311yescharacteristic
378C24C22×C4×C11312yes—
379C24C2×D4×C11311yescharacteristic
380C24C2×D4×C11311yescharacteristic
381C24C2×D4×C11312yes—
382C24C2×D4×C11312yes—
383C24#41×C11312yes—
384C24#41×C11312yes—
385C24#41×C11312yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C11312yescomplemented
435C22×C4C22⋊C4×C11312yes—
436C22×C4C22⋊C4×C11312yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C11318yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—41no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C11311yescharacteristic
478C23C2×C22⋊C4×C11312yes—
479C23C2×C22⋊C4×C11311yescharacteristic
480C23#117×C11311yescharacteristic
481C23#117×C11312yes—
482C23C4×D4×C11312yes—
483C23C4×D4×C11312yes—
484C23C4×D4×C11312yes—
485C23C4×D4×C11312yes—
486C23C4×D4×C11312yes—
487C23C4×D4×C11312yes—
488C23#120×C11311yescharacteristic
489C23#121×C11312yes—
490C23#121×C11312yes—
491C23#121×C11312yes—
492C23#123×C11311yescharacteristic
493C23#123×C11312yes—
494C23#124×C11311yescharacteristic
495C23#124×C11312yes—
496C23#126×C11312yes—
497C23#127×C11311yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C11314yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C11312yes—
565C22C4×C22⋊C4×C11311yescharacteristic
566C22#386×C11312yes—
567C22#386×C11311yescharacteristic
568C22#388×C11312yes—
569C22#388×C11312yes—
570C22#388×C11312yes—
571C22#390×C11312yes—
572C22#390×C11311yescharacteristic
573C22C2×#99×C11312yes—
574C22#410×C11312yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2C113×#143711yescharacteristic
589C2C4×#99×C11312yes—
590C2C113×#189811yescharacteristic
591C2C113×#189911yescharacteristic
592C2C113×#196412yes—
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC23C2×C42×C113
Frattini, cosocleC25C23×C113
prime radicalC23×D4×C113C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C24×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C113C2semidirect
4. C2×#342×C113C2semidirect
5. C113×C22⋊#95C2semidirect
8. C22×C22⋊C4×C113C4semidirect
15. C2×#99×C113C4semidirect
22. C2×#95×C113C4semidirect
79. C24×C113C42semidirect
137. C22×C4×C113C42semidirect
152. C22⋊C4×C113C22⋊C4semidirect
235. C2×C4×C113#99semidirect
284. #10960C113direct (N × H)
299. C2×C4×C22⋊C4C2×C113semidirect
300. C2×#342C2×C113semidirect
301. C22⋊#95C2×C113semidirect
302. C113#10960direct (N × H)
305. C22×C22⋊C4C4×C113semidirect
312. C2×#99C4×C113semidirect
319. C2×#95C4×C113semidirect
376. C24C42×C113semidirect
434. C22×C4C42×C113semidirect
449. C22⋊C4C22⋊C4×C113semidirect
532. C2×C4#99×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1132
C2×#386×C1132
C2×C4×C22⋊C4×C1132
C2×#342×C1132
C113×C22⋊#952
#10960113