Finite Group Databasebeta

← C113×#10322 #43278342

Subgroups — C113×#10322 #43278342

Order 28928.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3187C211yesmaximal, characteristic, complemented
2C113×#2848C211yesmaximal, characteristic, complemented
3C113×#2847C211yesmaximal, characteristic
4C113×#1779C211yesmaximal, characteristic, complemented
5C113×#1520C211yesmaximal, characteristic, complemented
6C113×#1519C211yesmaximal, characteristic, complemented
7C113×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C113C2211yescharacteristic
9C2×C22⋊Q8×C113—21no—
10C2×C22⋊Q8×C113C2211yescharacteristic
11C2×#121×C113—21no—
12C2×#121×C113C2211yescharacteristic
13C2×#120×C113—21no—
14#483×C113—21no—
15#481×C113—21no—
16#465×C113—22no—
17#450×C113—21no—
18#448×C113—21no—
19C2×C22⋊C8×C113—22no—
20C2×C22⋊C8×C113C2211yescharacteristic
21C2×C22⋊C8×C113C2211yescharacteristic
22#386×C113—21no—
23#386×C113—22no—
24#385×C113—21no—
25#385×C113—22no—
26#380×C113—21no—
27#380×C113—21no—
28#380×C113C2211yescharacteristic
29#380×C113C2211yescharacteristic
30#379×C113—21no—
31#328×C113—22no—
32#327×C113—22no—
33C25×C113D411yescharacteristic
34C22×Q8×C113D411yescharacteristic, complemented
35C22×D4×C113—22no—
36C22×D4×C113—21no—
37C22×D4×C113D411yescharacteristic
38C23×C4×C113—21no—
39C23×C4×C113—21no—
40C23×C4×C113—21no—
41C23×C4×C113—21no—
42C23×C4×C113—21no—
43C23×C4×C113—21no—
44C23×C4×C113—44no—
45C23×C4×C113D411yescharacteristic
46C23×C4×C113C2311yescharacteristic
47C2×SD16×C113—22no—
48C22×C8×C113—21no—
49C22×C8×C113D412yescomplemented
50C22⋊Q8×C113—21no—
51C22⋊Q8×C113—21no—
52C22⋊Q8×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113—44no—
55#121×C113—21no—
56#121×C113—21no—
57#121×C113—21no—
58#121×C113—21no—
59#121×C113—44no—
60#120×C113—42no—
61#120×C113—42no—
62C2×C4⋊C4×C113—22no—
63C2×C4⋊C4×C113—21no—
64C2×C4⋊C4×C113—21no—
65C2×C4⋊C4×C113—21no—
66C2×C4⋊C4×C113D411yescharacteristic
67C2×C4⋊C4×C113D411yescharacteristic, complemented
68C2×C22⋊C4×C113—22no—
69C2×C22⋊C4×C113—22no—
70C2×C22⋊C4×C113—22no—
71C2×C22⋊C4×C113—22no—
72C2×C22⋊C4×C113—21no—
73C2×C22⋊C4×C113—21no—
74C2×C22⋊C4×C113—21no—
75C2×C22⋊C4×C113—21no—
76#106×C113—22no—
77#103×C113—22no—
78#102×C113—22no—
79C22⋊C8×C113—21no—
80C22⋊C8×C113—21no—
81C22⋊C8×C113—21no—
82C22⋊C8×C113—21no—
83C22⋊C8×C113—44no—
84#95×C113—22no—
85#95×C113—22no—
86#95×C113D412yes—
87#95×C113D412yescomplemented
88C24×C113—21no—
89C24×C113—21no—
90C24×C113—21no—
91C24×C113—21no—
92C24×C113—21no—
93C24×C113—21no—
94C24×C113—21no—
95C24×C113—42no—
96C24×C113—42no—
97C24×C113SD1612yescomplemented
98C24×C113C2×D411yescharacteristic
99C2×Q8×C113—21no—
100C2×Q8×C113—21no—
101C2×Q8×C113—42no—
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113—42no—
105C2×D4×C113—44no—
106C2×D4×C113—44no—
107C2×D4×C113—44no—
108C2×D4×C113—41no—
109C2×D4×C113—41no—
110C2×D4×C113—41no—
111C2×D4×C113—41no—
112C2×D4×C113—41no—
113C2×D4×C113—41no—
114C22×C4×C113—24no—
115C22×C4×C113—24no—
116C22×C4×C113—24no—
117C22×C4×C113—21no—
118C22×C4×C113—21no—
119C22×C4×C113—21no—
120C22×C4×C113—21no—
121C22×C4×C113—21no—
122C22×C4×C113—22no—
123C22×C4×C113—22no—
124C22×C4×C113—21no—
125C22×C4×C113—42no—
126C22×C4×C113—42no—
127C22×C4×C113—42no—
128C22×C4×C113—42no—
129C22×C4×C113—42no—
130C22×C4×C113—42no—
131C22×C4×C113—42no—
132C22×C4×C113—42no—
133C22×C4×C113—42no—
134C22×C4×C113—42no—
135C22×C4×C113—42no—
136C22×C4×C113—41no—
137C22×C4×C113—41no—
138C22×C4×C113—41no—
139C22×C4×C113—41no—
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142C22×C4×C113C2×D411yescharacteristic
143C22×C4×C113C2×D411yescharacteristic
144C22×C4×C113C2×D411yescharacteristic
145C22×C4×C113#4111yescharacteristic
146SD16×C113—82no—
147C2×C8×C113—22no—
148C2×C8×C113—42no—
149C2×C8×C113—42no—
150C2×C8×C113—41no—
151C4⋊C4×C113—21no—
152C4⋊C4×C113—21no—
153C4⋊C4×C113—21no—
154C4⋊C4×C113—21no—
155C4⋊C4×C113—42no—
156C4⋊C4×C113—42no—
157C4⋊C4×C113—44no—
158C4⋊C4×C113—41no—
159C4⋊C4×C113—41no—
160C22⋊C4×C113—44no—
161C22⋊C4×C113—44no—
162C22⋊C4×C113—44no—
163C22⋊C4×C113—44no—
164C22⋊C4×C113—41no—
165C22⋊C4×C113—41no—
166C22⋊C4×C113—41no—
167C22⋊C4×C113—41no—
168C22⋊C4×C113—41no—
169C22⋊C4×C113—41no—
170C22⋊C4×C113—41no—
171C22⋊C4×C113—41no—
172C23×C113—22no—
173C23×C113—22no—
174C23×C113—22no—
175C23×C113—22no—
176C23×C113—22no—
177C23×C113—22no—
178C23×C113—22no—
179C23×C113—22no—
180C23×C113—22no—
181C23×C113—41no—
182C23×C113—44no—
183C23×C113—41no—
184C23×C113—41no—
185C23×C113—41no—
186C23×C113—41no—
187C23×C113—41no—
188C23×C113—41no—
189C23×C113—41no—
190C23×C113—44no—
191C23×C113—44no—
192C23×C113—44no—
193C23×C113—42no—
194C23×C113—42no—
195C23×C113—41no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—41no—
200C23×C113—41no—
201C23×C113—41no—
202C23×C113#12011yescharacteristic
203C23×C113#12011yescharacteristic
204C23×C113#12111yescharacteristic
205C23×C113C2×SD1611yescharacteristic
206C23×C113#13511yescharacteristic
207C23×C113AGL(1,ℤ/8)11yescharacteristic
208C23×C113#13711yescharacteristic
209Q8×C113—42no—
210Q8×C113—81no—
211D4×C113—42no—
212D4×C113—81no—
213D4×C113—88no—
214D4×C113—81no—
215D4×C113—81no—
216D4×C113—81no—
217D4×C113—81no—
218C2×C4×C113—22no—
219C2×C4×C113—22no—
220C2×C4×C113—22no—
221C2×C4×C113—22no—
222C2×C4×C113—22no—
223C2×C4×C113—22no—
224C2×C4×C113—41no—
225C2×C4×C113—41no—
226C2×C4×C113—41no—
227C2×C4×C113—44no—
228C2×C4×C113—44no—
229C2×C4×C113—44no—
230C2×C4×C113—41no—
231C2×C4×C113—41no—
232C2×C4×C113—41no—
233C2×C4×C113—41no—
234C2×C4×C113—44no—
235C2×C4×C113—42no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—42no—
239C2×C4×C113—42no—
240C2×C4×C113—42no—
241C2×C4×C113—41no—
242C2×C4×C113—41no—
243C2×C4×C113—41no—
244C2×C4×C113—42no—
245C2×C4×C113—42no—
246C2×C4×C113—41no—
247C2×C4×C113—41no—
248C2×C4×C113#12011yescharacteristic
249C2×C4×C113#12111yescharacteristic
250C2×C4×C113#12111yescharacteristic
251C2×C4×C113#12711yescharacteristic
252C8×C113—42no—
253C8×C113—81no—
254C22×C113—21no—
255C22×C113—21no—
256C22×C113—21no—
257C22×C113—21no—
258C22×C113—21no—
259C22×C113—21no—
260C22×C113—24no—
261C22×C113—24no—
262C22×C113—24no—
263C22×C113—41no—
264C22×C113—41no—
265C22×C113—41no—
266C22×C113—41no—
267C22×C113—42no—
268C22×C113—42no—
269C22×C113—42no—
270C22×C113—42no—
271C22×C113—42no—
272C22×C113—42no—
273C22×C113—42no—
274C22×C113—42no—
275C22×C113—42no—
276C22×C113—42no—
277C22×C113—42no—
278C22×C113—42no—
279C22×C113—82no—
280C22×C113—82no—
281C22×C113—81no—
282C22×C113—81no—
283C22×C113—81no—
284C22×C113#39211yescharacteristic
285C22×C113#44811yescharacteristic
286C22×C113#44911yescharacteristic
287C22×C113#45011yescharacteristic
288C22×C113#45211yescharacteristic
289C22×C113#46511yescharacteristic
290C22×C113#46811yescharacteristic
291C4×C113—21no—
292C4×C113—21no—
293C4×C113—21no—
294C4×C113—42no—
295C4×C113—82no—
296C4×C113—82no—
297C4×C113—81no—
298C4×C113—81no—
299C4×C113—81no—
300C4×C113B(4,𝔽2)12yes—
301#10322C11311yesmaximal, characteristic, direct product factor, Sylow
302C2×C113—21no—
303C2×C113—21no—
304C2×C113—21no—
305C2×C113—21no—
306C2×C113—21no—
307C2×C113—21no—
308C2×C113—44no—
309C2×C113—161no—
310C2×C113#200011yescharacteristic
311C2×C113#201011yescharacteristic
312C2×C113#202111yescharacteristic
313#3187C2×C11311yescharacteristic, complemented
314#2848C2×C11311yescharacteristic, complemented
315#2847C2×C11311yescharacteristic
316#1779C2×C11311yescharacteristic, complemented
317#1520C2×C11311yescharacteristic, complemented
318#1519C2×C11311yescharacteristic, complemented
319#1289C2×C11311yescharacteristic, complemented
320C113#1032211yescharacteristic, direct product factor, Sylow
321C24×C4C22×C11311yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8C22×C11311yescharacteristic
324C2×#121—21no—
325C2×#121C22×C11311yescharacteristic
326C2×#120—21no—
327#483—21no—
328#481—21no—
329#465—22no—
330#450—21no—
331#448—21no—
332C2×C22⋊C8—22no—
333C2×C22⋊C8C22×C11311yescharacteristic
334C2×C22⋊C8C22×C11311yescharacteristic
335#386—21no—
336#386—22no—
337#385—21no—
338#385—22no—
339#380—21no—
340#380—21no—
341#380C22×C11311yescharacteristic
342#380C22×C11311yescharacteristic
343#379—21no—
344#328—22no—
345#327—22no—
346C25D4×C11311yescharacteristic
347C22×Q8D4×C11311yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C11311yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C11311yescharacteristic
359C23×C4C23×C11311yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C11312yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C11311yescharacteristic
380C2×C4⋊C4D4×C11311yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C11312yes—
400#95D4×C11312yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C11312yescomplemented
411C24C2×D4×C11311yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C11311yescharacteristic
454C22×C4C2×D4×C11311yescharacteristic
455C22×C4C2×D4×C11311yescharacteristic
456C22×C4C2×D4×C11311yescharacteristic
457C22×C4C2×D4×C11311yescharacteristic
458C22×C4#41×C11311yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C11311yescharacteristic
516C23#120×C11311yescharacteristic
517C23#121×C11311yescharacteristic
518C23C2×SD16×C11311yescharacteristic
519C23#135×C11311yescharacteristic
520C23AGL(1,ℤ/8)×C11311yescharacteristic
521C23#137×C11311yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C11311yescharacteristic
562C2×C4#121×C11311yescharacteristic
563C2×C4#121×C11311yescharacteristic
564C2×C4#127×C11311yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#392×C11311yescharacteristic
598C22#448×C11311yescharacteristic
599C22#449×C11311yescharacteristic
600C22#450×C11311yescharacteristic
601C22#452×C11311yescharacteristic
602C22#465×C11311yescharacteristic
603C22#468×C11311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4B(4,𝔽2)×C11312yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C113×#200011yescharacteristic
623C2C113×#201011yescharacteristic
624C2C113×#202111yescharacteristic
subgroupG/H
center, socleC22×C113#392
commutator, Frattini, cosocleC23×C4C23×C113
prime radicalC113×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3187C2semidirect
2. C113×#2848C2semidirect
4. C113×#1779C2semidirect
5. C113×#1520C2semidirect
6. C113×#1519C2semidirect
7. C113×#1289C2semidirect
34. C22×Q8×C113D4semidirect
49. C22×C8×C113D4semidirect
67. C2×C4⋊C4×C113D4semidirect
87. #95×C113D4semidirect
97. C24×C113SD16semidirect
301. #10322C113direct (N × H)
313. #3187C2×C113semidirect
314. #2848C2×C113semidirect
316. #1779C2×C113semidirect
317. #1520C2×C113semidirect
318. #1519C2×C113semidirect
319. #1289C2×C113semidirect
320. C113#10322direct (N × H)
347. C22×Q8D4×C113semidirect
362. C22×C8D4×C113semidirect
380. C2×C4⋊C4D4×C113semidirect
400. #95D4×C113semidirect
410. C24SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#31872
C113×#28482
C113×#28472
C113×#17792
C113×#15202
C113×#15192
C113×#12892
#10322113