Finite Group Databasebeta

← C113×#18957 #43286977

Subgroups — C113×#18957 #43286977

Order 28928.

874 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3547C211yesmaximal, characteristic
2C113×#3238C211yesmaximal, characteristic, complemented
3C113×#3227C211yesmaximal, characteristic, complemented
4C113×#3209C211yesmaximal, characteristic, complemented
5C113×#1637C212yesmaximal, complemented
6C113×#1635C212yesmaximal, complemented
7C113×#1634C212yesmaximal, complemented
8C113×#1632C212yesmaximal, complemented
9C113×#1554C211yesmaximal, characteristic, complemented
10C113×#1496C211yesmaximal, characteristic, complemented
11C113×#1482C211yesmaximal, characteristic, complemented
12#562×C113—22no—
13#555×C113—21no—
14#555×C113C2211yescharacteristic
15#554×C113C2211yescharacteristic
16#553×C113—21no—
17#552×C113—21no—
18D4×Q8×C113C2211yescharacteristic
19#548×C113—21no—
20#547×C113C2211yescharacteristic
21#544×C113—21no—
22#542×C113—22no—
23#540×C113—21no—
24#537×C113—21no—
25#536×C113—21no—
26#533×C113C2211yescharacteristic
27#532×C113C2211yescharacteristic
28C2×C4⋊Q8×C113C2211yescharacteristic
29#529×C113C2211yescharacteristic
30#501×C113—21no—
31#498×C113—21no—
32#494×C113C2212yes—
33#489×C113—21no—
34#487×C113C2212yes—
35#486×C113—21no—
36#483×C113—21no—
37#481×C113—21no—
38#481×C113—21no—
39#480×C113—21no—
40#477×C113C2212yes—
41#476×C113C2212yes—
42#476×C113C2212yes—
43#476×C113C2212yes—
44#462×C113—22no—
45#451×C113—22no—
46#432×C113C2211yescharacteristic
47#431×C113C2211yescharacteristic
48#431×C113C2211yescharacteristic
49#333×C113C2212yes—
50#332×C113C2212yes—
51Q8⋊C8×C113C2212yes—
52D4⋊C8×C113C2212yes—
53D4⋊C8×C113C2212yes—
54D4⋊C8×C113C2212yes—
55C2×#41×C113—21no—
56C2×#41×C113—21no—
57C22×Q8×C113—21no—
58C22×Q8×C113—21no—
59C2×Q16×C113—24no—
60C4⋊Q8×C113—22no—
61C4⋊Q8×C113—21no—
62C4⋊Q8×C113—21no—
63C4⋊Q8×C113—21no—
64C4⋊Q8×C113—21no—
65C4⋊Q8×C113D411yescharacteristic
66C4⋊Q8×C113C2312yes—
67C4⋊Q8×C113C2311yescharacteristic
68C4⋊Q8×C113C2311yescharacteristic
69#127×C113D411yescharacteristic
70#126×C113—22no—
71#126×C113—21no—
72#125×C113—22no—
73#125×C113—21no—
74#125×C113—21no—
75#125×C113D411yescharacteristic
76#124×C113—22no—
77#124×C113—22no—
78#124×C113—22no—
79#124×C113—21no—
80#124×C113D411yescharacteristic
81#123×C113—22no—
82#123×C113—22no—
83#123×C113—22no—
84#123×C113—21no—
85#123×C113—22no—
86C22⋊Q8×C113—22no—
87C22⋊Q8×C113—22no—
88C22⋊Q8×C113—21no—
89C22⋊Q8×C113—22no—
90C22⋊Q8×C113—21no—
91C22⋊Q8×C113—21no—
92C22⋊Q8×C113—21no—
93C22⋊Q8×C113—22no—
94C22⋊Q8×C113D411yescharacteristic
95C22⋊Q8×C113D412yes—
96#121×C113—22no—
97#121×C113—22no—
98#121×C113—22no—
99#121×C113—22no—
100#121×C113—21no—
101#121×C113—21no—
102#121×C113—21no—
103#121×C113—21no—
104#121×C113D411yescharacteristic
105#121×C113D411yescharacteristic
106#121×C113D411yescharacteristic
107C4×Q8×C113—21no—
108C4×Q8×C113D412yes—
109C4×Q8×C113C2311yescharacteristic
110C4×D4×C113—22no—
111C4×D4×C113—21no—
112C4×D4×C113—21no—
113C4×D4×C113—21no—
114C4×D4×C113—21no—
115C4×D4×C113C2311yescharacteristic
116C4×D4×C113C2311yescharacteristic
117C4×D4×C113C2311yescharacteristic
118#117×C113—22no—
119#117×C113—21no—
120#117×C113—21no—
121#117×C113—21no—
122#117×C113—21no—
123C2×C4⋊C4×C113—21no—
124C2×C4⋊C4×C113—21no—
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113—21no—
127C2×C42×C113C2311yescharacteristic
128#107×C113—22no—
129#106×C113—22no—
130#106×C113—22no—
131#106×C113—22no—
132C4⋊C8×C113—21no—
133C4⋊C8×C113C2312yes—
134C4⋊C8×C113C2312yes—
135#103×C113—22no—
136#103×C113—24no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140C22⋊C8×C113—21no—
141C22⋊C8×C113—21no—
142C22⋊C8×C113—21no—
143#97×C113—21no—
144C4×C8×C113—21no—
145C4×C8×C113C2312yes—
146#41×C113—82no—
147#41×C113—82no—
148C2×Q8×C113—22no—
149C2×Q8×C113—21no—
150C2×Q8×C113—21no—
151C2×Q8×C113—22no—
152C2×Q8×C113—41no—
153C2×Q8×C113—82no—
154C2×Q8×C113—82no—
155C2×Q8×C113C2×D411yescharacteristic
156C2×Q8×C113C2×D412yes—
157C2×D4×C113—22no—
158C2×D4×C113—22no—
159C2×D4×C113—21no—
160C2×D4×C113—21no—
161C2×D4×C113—21no—
162C2×D4×C113—21no—
163C2×D4×C113—21no—
164C2×D4×C113C2×D411yescharacteristic
165C2×D4×C113C2×D411yescharacteristic
166C2×D4×C113C2×D411yescharacteristic
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—21no—
171C22×C4×C113—21no—
172C22×C4×C113—21no—
173C22×C4×C113—41no—
174C22×C4×C113C2×D411yescharacteristic
175C22×C4×C113C2×D411yescharacteristic
176C22×C4×C113C2×D411yescharacteristic
177Q16×C113—84no—
178C2×C8×C113—22no—
179C2×C8×C113—22no—
180C2×C8×C113—22no—
181C4⋊C4×C113—22no—
182C4⋊C4×C113—22no—
183C4⋊C4×C113—22no—
184C4⋊C4×C113—22no—
185C4⋊C4×C113—21no—
186C4⋊C4×C113—21no—
187C4⋊C4×C113—21no—
188C4⋊C4×C113—21no—
189C4⋊C4×C113—22no—
190C4⋊C4×C113—22no—
191C4⋊C4×C113—21no—
192C4⋊C4×C113—21no—
193C4⋊C4×C113—21no—
194C4⋊C4×C113—21no—
195C4⋊C4×C113—22no—
196C4⋊C4×C113—22no—
197C4⋊C4×C113—41no—
198C4⋊C4×C113—41no—
199C4⋊C4×C113C2×D412yes—
200C4⋊C4×C113C2×D411yescharacteristic
201C4⋊C4×C113C2×D411yescharacteristic
202C4⋊C4×C113C2×D411yescharacteristic
203C4⋊C4×C113C2×D411yescharacteristic
204C22⋊C4×C113—22no—
205C22⋊C4×C113—22no—
206C22⋊C4×C113—22no—
207C22⋊C4×C113—22no—
208C22⋊C4×C113—22no—
209C22⋊C4×C113—22no—
210C22⋊C4×C113—21no—
211C22⋊C4×C113—21no—
212C22⋊C4×C113—21no—
213C22⋊C4×C113—21no—
214C22⋊C4×C113—21no—
215C22⋊C4×C113—21no—
216C22⋊C4×C113—21no—
217C22⋊C4×C113—21no—
218C22⋊C4×C113—21no—
219C42×C113—22no—
220C42×C113—22no—
221C42×C113—21no—
222C42×C113C2×D411yescharacteristic
223C42×C113C2×D411yescharacteristic
224C42×C113C2×D411yescharacteristic
225C42×C113C2411yescharacteristic
226C23×C113—21no—
227C23×C113—21no—
228C23×C113—21no—
229C23×C113#12011yescharacteristic
230Q8×C113—22no—
231Q8×C113—42no—
232Q8×C113—44no—
233Q8×C113—42no—
234Q8×C113—81no—
235Q8×C113—82no—
236Q8×C113—82no—
237D4×C113—22no—
238D4×C113—22no—
239D4×C113—22no—
240D4×C113—81no—
241D4×C113—81no—
242D4×C113—81no—
243D4×C113—81no—
244D4×C113—81no—
245D4×C113—82no—
246D4×C113—82no—
247C2×C4×C113—22no—
248C2×C4×C113—22no—
249C2×C4×C113—21no—
250C2×C4×C113—22no—
251C2×C4×C113—21no—
252C2×C4×C113—21no—
253C2×C4×C113—21no—
254C2×C4×C113—22no—
255C2×C4×C113—21no—
256C2×C4×C113—41no—
257C2×C4×C113—42no—
258C2×C4×C113—42no—
259C2×C4×C113—42no—
260C2×C4×C113—42no—
261C2×C4×C113—82no—
262C2×C4×C113—82no—
263C2×C4×C113—82no—
264C2×C4×C113—82no—
265C2×C4×C113#12011yescharacteristic
266C2×C4×C113#12011yescharacteristic
267C2×C4×C113#12011yescharacteristic
268C2×C4×C113C22×D411yescharacteristic
269C2×C4×C113C22×D411yescharacteristic
270C2×C4×C113C22×D411yescharacteristic
271C8×C113—42no—
272C8×C113—42no—
273C8×C113—42no—
274C22×C113—21no—
275C22×C113—21no—
276C22×C113—21no—
277C22×C113—41no—
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×C113C2×#12011yescharacteristic
287C4×C113—21no—
288C4×C113—21no—
289C4×C113—21no—
290C4×C113—21no—
291C4×C113—41no—
292C4×C113—41no—
293C4×C113—42no—
294C4×C113—41no—
295C4×C113—41no—
296C4×C113—41no—
297C4×C113—42no—
298C4×C113—82no—
299C4×C113#57712yes—
300C4×C113#57812yes—
301#18957C11311yesmaximal, characteristic, direct product factor, Sylow
302C2×C113—41no—
303C2×C113—81no—
304C2×C113—81no—
305C2×C113—81no—
306C2×C113#300911yescharacteristic
307C2×C113#301111yescharacteristic
308C2×C113#302111yescharacteristic
309#3547C2×C11311yescharacteristic
310#3238C2×C11311yescharacteristic, complemented
311#3227C2×C11311yescharacteristic, complemented
312#3209C2×C11311yescharacteristic, complemented
313#1637C2×C11312yescomplemented
314#1635C2×C11312yescomplemented
315#1634C2×C11312yescomplemented
316#1632C2×C11312yescomplemented
317#1554C2×C11311yescharacteristic, complemented
318#1496C2×C11311yescharacteristic, complemented
319#1482C2×C11311yescharacteristic, complemented
320C113#1895711yescharacteristic, direct product factor, Sylow
321#562—22no—
322#555—21no—
323#555C22×C11311yescharacteristic
324#554C22×C11311yescharacteristic
325#553—21no—
326#552—21no—
327D4×Q8C22×C11311yescharacteristic
328#548—21no—
329#547C22×C11311yescharacteristic
330#544—21no—
331#542—22no—
332#540—21no—
333#537—21no—
334#536—21no—
335#533C22×C11311yescharacteristic
336#532C22×C11311yescharacteristic
337C2×C4⋊Q8C22×C11311yescharacteristic
338#529C22×C11311yescharacteristic
339#501—21no—
340#498—21no—
341#494C22×C11312yes—
342#489—21no—
343#487C22×C11312yes—
344#486—21no—
345#483—21no—
346#481—21no—
347#481—21no—
348#480—21no—
349#477C22×C11312yes—
350#476C22×C11312yes—
351#476C22×C11312yes—
352#476C22×C11312yes—
353#462—22no—
354#451—22no—
355#432C22×C11311yescharacteristic
356#431C22×C11311yescharacteristic
357#431C22×C11311yescharacteristic
358#333C22×C11312yes—
359#332C22×C11312yes—
360Q8⋊C8C22×C11312yes—
361D4⋊C8C22×C11312yes—
362D4⋊C8C22×C11312yes—
363D4⋊C8C22×C11312yes—
364C2×#41—21no—
365C2×#41—21no—
366C22×Q8—21no—
367C22×Q8—21no—
368C2×Q16—24no—
369C4⋊Q8—22no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8D4×C11311yescharacteristic
375C4⋊Q8C23×C11312yes—
376C4⋊Q8C23×C11311yescharacteristic
377C4⋊Q8C23×C11311yescharacteristic
378#127D4×C11311yescharacteristic
379#126—22no—
380#126—21no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125D4×C11311yescharacteristic
385#124—22no—
386#124—22no—
387#124—22no—
388#124—21no—
389#124D4×C11311yescharacteristic
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8D4×C11311yescharacteristic
404C22⋊Q8D4×C11312yes—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121D4×C11311yescharacteristic
414#121D4×C11311yescharacteristic
415#121D4×C11311yescharacteristic
416C4×Q8—21no—
417C4×Q8D4×C11312yes—
418C4×Q8C23×C11311yescharacteristic
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C11311yescharacteristic
425C4×D4C23×C11311yescharacteristic
426C4×D4C23×C11311yescharacteristic
427#117—22no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C42C23×C11311yescharacteristic
437#107—22no—
438#106—22no—
439#106—22no—
440#106—22no—
441C4⋊C8—21no—
442C4⋊C8C23×C11312yes—
443C4⋊C8C23×C11312yes—
444#103—22no—
445#103—24no—
446#102—22no—
447#102—22no—
448#102—22no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453C4×C8—21no—
454C4×C8C23×C11312yes—
455#41—82no—
456#41—82no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—41no—
462C2×Q8—82no—
463C2×Q8—82no—
464C2×Q8C2×D4×C11311yescharacteristic
465C2×Q8C2×D4×C11312yes—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×D4×C11311yescharacteristic
474C2×D4C2×D4×C11311yescharacteristic
475C2×D4C2×D4×C11311yescharacteristic
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4C2×D4×C11311yescharacteristic
484C22×C4C2×D4×C11311yescharacteristic
485C22×C4C2×D4×C11311yescharacteristic
486Q16—84no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C11312yes—
509C4⋊C4C2×D4×C11311yescharacteristic
510C4⋊C4C2×D4×C11311yescharacteristic
511C4⋊C4C2×D4×C11311yescharacteristic
512C4⋊C4C2×D4×C11311yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—22no—
529C42—22no—
530C42—21no—
531C42C2×D4×C11311yescharacteristic
532C42C2×D4×C11311yescharacteristic
533C42C2×D4×C11311yescharacteristic
534C42C24×C11311yescharacteristic
535C23—21no—
536C23—21no—
537C23—21no—
538C23#120×C11311yescharacteristic
539Q8—22no—
540Q8—42no—
541Q8—44no—
542Q8—42no—
543Q8—81no—
544Q8—82no—
545Q8—82no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4—81no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#120×C11311yescharacteristic
575C2×C4#120×C11311yescharacteristic
576C2×C4#120×C11311yescharacteristic
577C2×C4C22×D4×C11311yescharacteristic
578C2×C4C22×D4×C11311yescharacteristic
579C2×C4C22×D4×C11311yescharacteristic
580C8—42no—
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×#120×C11311yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—82no—
608C4#577×C11312yes—
609C4#578×C11312yes—
610C2—41no—
611C2—81no—
612C2—81no—
613C2—81no—
614C2C113×#300911yescharacteristic
615C2C113×#301111yescharacteristic
616C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3547C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3238C2semidirect
3. C113×#3227C2semidirect
4. C113×#3209C2semidirect
5. C113×#1637C2semidirect
6. C113×#1635C2semidirect
7. C113×#1634C2semidirect
8. C113×#1632C2semidirect
9. C113×#1554C2semidirect
10. C113×#1496C2semidirect
11. C113×#1482C2semidirect
301. #18957C113direct (N × H)
310. #3238C2×C113semidirect
311. #3227C2×C113semidirect
312. #3209C2×C113semidirect
313. #1637C2×C113semidirect
314. #1635C2×C113semidirect
315. #1634C2×C113semidirect
316. #1632C2×C113semidirect
317. #1554C2×C113semidirect
318. #1496C2×C113semidirect
319. #1482C2×C113semidirect
320. C113#18957direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35472
C113×#32382
C113×#32272
C113×#32092
C113×#16372
C113×#16352
C113×#16342
C113×#16322
C113×#15542
C113×#14962
C113×#14822
#18957113