Finite Group Databasebeta

← C113×#19010 #43287030

Subgroups — C113×#19010 #43287030

Order 28928.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3529C211yesmaximal, characteristic, complemented
2C113×#3219C211yesmaximal, characteristic, complemented
3C113×#3214C211yesmaximal, characteristic, complemented
4C113×#3180C211yesmaximal, characteristic, complemented
5C113×#1664C211yesmaximal, characteristic, complemented
6C113×#1662C211yesmaximal, characteristic, complemented
7C113×#1661C211yesmaximal, characteristic, complemented
8C113×#1659C211yesmaximal, characteristic, complemented
9C113×#1657C211yesmaximal, characteristic, complemented
10C113×#1656C211yesmaximal, characteristic, complemented
11C113×#1656C211yesmaximal, characteristic, complemented
12C113×#1655C211yesmaximal, characteristic, complemented
13C113×#1535C211yesmaximal, characteristic, complemented
14C113×#1532C211yesmaximal, characteristic, complemented
15C113×#1530C211yesmaximal, characteristic, complemented
16#563×C113—21no—
17#563×C113C2211yescharacteristic
18#562×C113—21no—
19#562×C113—21no—
20#562×C113C2211yescharacteristic
21#562×C113C2211yescharacteristic
22H(3,𝔽4)×C113C2211yescharacteristic
23#560×C113—21no—
24#560×C113—21no—
25#560×C113—21no—
26#532×C113—21no—
27#532×C113C2211yescharacteristic
28#532×C113C2211yescharacteristic, complemented
29#529×C113—21no—
30#529×C113—21no—
31#529×C113C2211yescharacteristic
32#529×C113C2211yescharacteristic
33#525×C113—21no—
34#525×C113—21no—
35#525×C113—21no—
36#501×C113C2211yescharacteristic, complemented
37#497×C113C2211yescharacteristic
38#496×C113C2211yescharacteristic
39#496×C113C2211yescharacteristic
40#496×C113C2211yescharacteristic
41#496×C113C2211yescharacteristic, complemented
42#491×C113C2211yescharacteristic, complemented
43#490×C113C2211yescharacteristic, complemented
44#490×C113C2211yescharacteristic, complemented
45#489×C113C2211yescharacteristic
46#489×C113C2211yescharacteristic
47#489×C113C2211yescharacteristic, complemented
48#466×C113—21no—
49#465×C113—21no—
50#464×C113—21no—
51#463×C113—21no—
52#461×C113—21no—
53#459×C113—21no—
54#452×C113—21no—
55#449×C113—21no—
56#449×C113—21no—
57#449×C113—21no—
58#442×C113—21no—
59#440×C113—21no—
60#432×C113C2211yescharacteristic, complemented
61#432×C113C2211yescharacteristic, complemented
62C2×#97×C113C2211yescharacteristic, complemented
63#330×C113C2211yescharacteristic, complemented
64#330×C113C2211yescharacteristic, complemented
65#330×C113C2211yescharacteristic, complemented
66#330×C113C2211yescharacteristic, complemented
67#329×C113C2211yescharacteristic
68#329×C113C2211yescharacteristic
69#329×C113C2211yescharacteristic
70#329×C113C2211yescharacteristic
71#329×C113C2211yescharacteristic
72#329×C113C2211yescharacteristic
73#329×C113C2211yescharacteristic, complemented
74#329×C113C2211yescharacteristic, complemented
75C2×#41×C113—21no—
76C2×#41×C113—21no—
77C2×#41×C113D411yescharacteristic
78C2×#41×C113D411yescharacteristic
79C23×C4×C113—21no—
80C2×Q16×C113—21no—
81C2×SD16×C113—21no—
82C2×SD16×C113—21no—
83C2×SD16×C113—21no—
84C2×SD16×C113—21no—
85C2×SD16×C113—21no—
86C2×D8×C113—21no—
87C2×D8×C113—21no—
88C2×D8×C113—21no—
89C2×D8×C113—21no—
90C22×C8×C113—21no—
91C4⋊Q8×C113—21no—
92C4⋊Q8×C113D411yescharacteristic
93C4⋊Q8×C113C2311yescharacteristic
94#127×C113—21no—
95#127×C113D411yescharacteristic
96#127×C113C2311yescharacteristic
97#126×C113—21no—
98#126×C113—21no—
99#126×C113—21no—
100#126×C113—21no—
101#126×C113—21no—
102#126×C113—21no—
103#125×C113—21no—
104#125×C113—21no—
105#125×C113C2311yescharacteristic
106#125×C113C2311yescharacteristic
107#124×C113—21no—
108#124×C113—21no—
109#124×C113—21no—
110#124×C113—21no—
111#124×C113—21no—
112#124×C113C2311yescharacteristic
113#124×C113C2311yescharacteristic
114#124×C113C2311yescharacteristic
115#124×C113C2311yescharacteristic
116#123×C113—21no—
117#123×C113—21no—
118#123×C113—21no—
119#123×C113—21no—
120#123×C113—21no—
121#123×C113—21no—
122#123×C113—21no—
123#123×C113—21no—
124#123×C113—21no—
125#123×C113—21no—
126#123×C113—21no—
127#123×C113—21no—
128C22⋊Q8×C113—21no—
129C22⋊Q8×C113—21no—
130C22⋊Q8×C113—21no—
131C22⋊Q8×C113—21no—
132C22⋊Q8×C113—21no—
133C22⋊Q8×C113—21no—
134C22⋊Q8×C113—21no—
135C22⋊Q8×C113—21no—
136C22⋊Q8×C113D411yescharacteristic
137C22⋊Q8×C113D411yescharacteristic
138#121×C113—21no—
139#121×C113—21no—
140#121×C113—21no—
141#121×C113—21no—
142#121×C113—21no—
143#121×C113—21no—
144#121×C113—21no—
145#121×C113—21no—
146#121×C113—21no—
147#121×C113—21no—
148#121×C113—21no—
149#121×C113—21no—
150#121×C113—21no—
151#121×C113—21no—
152#121×C113—21no—
153#121×C113—21no—
154#121×C113D411yescharacteristic
155#121×C113D411yescharacteristic
156#120×C113—21no—
157#120×C113—21no—
158#120×C113—21no—
159#120×C113—21no—
160#120×C113—21no—
161#120×C113—21no—
162C4×Q8×C113D411yescharacteristic
163C4×Q8×C113D411yescharacteristic
164C4×D4×C113—21no—
165C4×D4×C113—21no—
166C4×D4×C113—21no—
167C4×D4×C113—21no—
168C4×D4×C113—21no—
169C4×D4×C113—21no—
170C4×D4×C113—21no—
171C4×D4×C113—21no—
172C4×D4×C113—21no—
173C4×D4×C113—21no—
174C4×D4×C113D411yescharacteristic
175C4×D4×C113D411yescharacteristic
176#117×C113—21no—
177#117×C113—21no—
178#117×C113—21no—
179C2×C42×C113—21no—
180C2×C42×C113C2311yescharacteristic
181#107×C113—21no—
182#106×C113—21no—
183C4⋊C8×C113—21no—
184C4⋊C8×C113—21no—
185#103×C113—21no—
186#103×C113—21no—
187#103×C113—21no—
188#103×C113—21no—
189#103×C113—21no—
190#102×C113—21no—
191#102×C113—21no—
192#102×C113—21no—
193#102×C113—21no—
194#102×C113—21no—
195#102×C113—21no—
196#102×C113—21no—
197C22⋊C8×C113—21no—
198C22⋊C8×C113—21no—
199#97×C113—21no—
200#97×C113C2311yescharacteristic
201#97×C113C2311yescharacteristic
202#97×C113C2311yescharacteristic
203#97×C113C2311yescharacteristic
204#97×C113C2311yescharacteristic
205#97×C113C2311yescharacteristic
206C24×C113—21no—
207#41×C113—81no—
208#41×C113—81no—
209#41×C113—82no—
210#41×C113—81no—
211#41×C113—81no—
212C2×Q8×C113—21no—
213C2×Q8×C113—21no—
214C2×Q8×C113C2×D411yescharacteristic
215C2×Q8×C113C2×D411yescharacteristic
216C2×Q8×C113C2×D411yescharacteristic
217C2×Q8×C113C2×D411yescharacteristic
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—41no—
235C2×D4×C113C2×D411yescharacteristic
236C2×D4×C113C2×D411yescharacteristic
237C2×D4×C113C2×D411yescharacteristic
238C2×D4×C113C2×D411yescharacteristic
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—21no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—41no—
249C22×C4×C113—82no—
250C22×C4×C113C2×D411yescharacteristic
251C22×C4×C113C2×D411yescharacteristic
252C22×C4×C113C2×D411yescharacteristic
253Q16×C113—81no—
254SD16×C113—42no—
255SD16×C113—81no—
256SD16×C113—81no—
257SD16×C113—81no—
258SD16×C113—81no—
259D8×C113—42no—
260D8×C113—81no—
261D8×C113—81no—
262D8×C113—81no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—42no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—21no—
284C4⋊C4×C113—21no—
285C4⋊C4×C113—21no—
286C4⋊C4×C113—21no—
287C4⋊C4×C113—21no—
288C4⋊C4×C113C2×D411yescharacteristic
289C4⋊C4×C113C2×D411yescharacteristic
290C4⋊C4×C113C2×D411yescharacteristic
291C4⋊C4×C113C2×D411yescharacteristic
292C22⋊C4×C113—21no—
293C22⋊C4×C113—21no—
294C22⋊C4×C113—21no—
295C22⋊C4×C113—21no—
296C22⋊C4×C113—21no—
297C22⋊C4×C113—21no—
298C22⋊C4×C113—21no—
299C22⋊C4×C113—21no—
300C22⋊C4×C113—21no—
301C22⋊C4×C113—21no—
302C22⋊C4×C113—21no—
303C22⋊C4×C113—21no—
304C22⋊C4×C113—21no—
305C22⋊C4×C113—21no—
306C22⋊C4×C113—21no—
307C22⋊C4×C113—21no—
308C22⋊C4×C113—21no—
309C22⋊C4×C113—21no—
310C22⋊C4×C113—21no—
311C22⋊C4×C113—21no—
312C22⋊C4×C113—21no—
313C22⋊C4×C113—21no—
314C22⋊C4×C113—21no—
315C22⋊C4×C113—21no—
316C22⋊C4×C113—41no—
317C22⋊C4×C113—41no—
318C42×C113—21no—
319C42×C113—21no—
320C42×C113—21no—
321C42×C113—21no—
322C42×C113C2×D411yescharacteristic
323C42×C113C2×D411yescharacteristic
324C42×C113C2×D411yescharacteristic
325C42×C113C2411yescharacteristic
326C23×C113—21no—
327C23×C113—21no—
328C23×C113—21no—
329C23×C113—21no—
330C23×C113—41no—
331C23×C113—81no—
332C23×C113—81no—
333C23×C113—81no—
334C23×C113#12011yescharacteristic
335Q8×C113—41no—
336Q8×C113—41no—
337Q8×C113—41no—
338Q8×C113—41no—
339Q8×C113—41no—
340Q8×C113—41no—
341Q8×C113—81no—
342D4×C113—41no—
343D4×C113—41no—
344D4×C113—41no—
345D4×C113—41no—
346D4×C113—41no—
347D4×C113—41no—
348D4×C113—41no—
349D4×C113—41no—
350D4×C113—41no—
351D4×C113—41no—
352D4×C113—81no—
353D4×C113—81no—
354D4×C113—81no—
355D4×C113—81no—
356D4×C113—81no—
357D4×C113—81no—
358D4×C113—81no—
359D4×C113—81no—
360D4×C113—81no—
361D4×C113—81no—
362D4×C113—81no—
363D4×C113—81no—
364D4×C113—81no—
365D4×C113—82no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—21no—
369C2×C4×C113—21no—
370C2×C4×C113—21no—
371C2×C4×C113—21no—
372C2×C4×C113—21no—
373C2×C4×C113—21no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—42no—
378C2×C4×C113—42no—
379C2×C4×C113—42no—
380C2×C4×C113—42no—
381C2×C4×C113—41no—
382C2×C4×C113—82no—
383C2×C4×C113—81no—
384C2×C4×C113—81no—
385C2×C4×C113—81no—
386C2×C4×C113—81no—
387C2×C4×C113—81no—
388C2×C4×C113#12011yescharacteristic
389C2×C4×C113#12011yescharacteristic
390C2×C4×C113#12011yescharacteristic
391C2×C4×C113C22×D411yescharacteristic
392C2×C4×C113C22×D411yescharacteristic
393C2×C4×C113C22×D411yescharacteristic
394C8×C113—22no—
395C8×C113—41no—
396C8×C113—41no—
397C8×C113—41no—
398C8×C113—41no—
399C8×C113—41no—
400C22×C113—21no—
401C22×C113—21no—
402C22×C113—21no—
403C22×C113—41no—
404C22×C113—41no—
405C22×C113—41no—
406C22×C113—41no—
407C22×C113—41no—
408C22×C113—41no—
409C22×C113—41no—
410C22×C113—41no—
411C22×C113—41no—
412C22×C113—41no—
413C22×C113—41no—
414C22×C113—41no—
415C22×C113—84no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113C2×#12011yescharacteristic
420C4×C113—21no—
421C4×C113—21no—
422C4×C113—21no—
423C4×C113—21no—
424C4×C113—21no—
425C4×C113—21no—
426C4×C113—41no—
427C4×C113—41no—
428C4×C113—41no—
429C4×C113—41no—
430C4×C113—41no—
431C4×C113—41no—
432C4×C113—41no—
433C4×C113—41no—
434C4×C113—81no—
435#19010C11311yesmaximal, characteristic, direct product factor, Sylow
436C2×C113—41no—
437C2×C113—81no—
438C2×C113—81no—
439C2×C113—81no—
440C2×C113—81no—
441C2×C113—161no—
442C2×C113#301811yescharacteristic
443C2×C113#301911yescharacteristic
444C2×C113#302111yescharacteristic
445#3529C2×C11311yescharacteristic, complemented
446#3219C2×C11311yescharacteristic, complemented
447#3214C2×C11311yescharacteristic, complemented
448#3180C2×C11311yescharacteristic, complemented
449#1664C2×C11311yescharacteristic, complemented
450#1662C2×C11311yescharacteristic, complemented
451#1661C2×C11311yescharacteristic, complemented
452#1659C2×C11311yescharacteristic, complemented
453#1657C2×C11311yescharacteristic, complemented
454#1656C2×C11311yescharacteristic, complemented
455#1656C2×C11311yescharacteristic, complemented
456#1655C2×C11311yescharacteristic, complemented
457#1535C2×C11311yescharacteristic, complemented
458#1532C2×C11311yescharacteristic, complemented
459#1530C2×C11311yescharacteristic, complemented
460C113#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C11311yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C11311yescharacteristic
466#562C22×C11311yescharacteristic
467H(3,𝔽4)C22×C11311yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C11311yescharacteristic
473#532C22×C11311yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C11311yescharacteristic
477#529C22×C11311yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C11311yescharacteristic, complemented
482#497C22×C11311yescharacteristic
483#496C22×C11311yescharacteristic
484#496C22×C11311yescharacteristic
485#496C22×C11311yescharacteristic
486#496C22×C11311yescharacteristic, complemented
487#491C22×C11311yescharacteristic, complemented
488#490C22×C11311yescharacteristic, complemented
489#490C22×C11311yescharacteristic, complemented
490#489C22×C11311yescharacteristic
491#489C22×C11311yescharacteristic
492#489C22×C11311yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C11311yescharacteristic, complemented
506#432C22×C11311yescharacteristic, complemented
507C2×#97C22×C11311yescharacteristic, complemented
508#330C22×C11311yescharacteristic, complemented
509#330C22×C11311yescharacteristic, complemented
510#330C22×C11311yescharacteristic, complemented
511#330C22×C11311yescharacteristic, complemented
512#329C22×C11311yescharacteristic
513#329C22×C11311yescharacteristic
514#329C22×C11311yescharacteristic
515#329C22×C11311yescharacteristic
516#329C22×C11311yescharacteristic
517#329C22×C11311yescharacteristic
518#329C22×C11311yescharacteristic, complemented
519#329C22×C11311yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C11311yescharacteristic
523C2×#41D4×C11311yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C11311yescharacteristic
538C4⋊Q8C23×C11311yescharacteristic
539#127—21no—
540#127D4×C11311yescharacteristic
541#127C23×C11311yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C11311yescharacteristic
551#125C23×C11311yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C11311yescharacteristic
558#124C23×C11311yescharacteristic
559#124C23×C11311yescharacteristic
560#124C23×C11311yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C11311yescharacteristic
582C22⋊Q8D4×C11311yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C11311yescharacteristic
600#121D4×C11311yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C11311yescharacteristic
608C4×Q8D4×C11311yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C11311yescharacteristic
620C4×D4D4×C11311yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C11311yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C11311yescharacteristic
646#97C23×C11311yescharacteristic
647#97C23×C11311yescharacteristic
648#97C23×C11311yescharacteristic
649#97C23×C11311yescharacteristic
650#97C23×C11311yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C11311yescharacteristic
660C2×Q8C2×D4×C11311yescharacteristic
661C2×Q8C2×D4×C11311yescharacteristic
662C2×Q8C2×D4×C11311yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C11311yescharacteristic
681C2×D4C2×D4×C11311yescharacteristic
682C2×D4C2×D4×C11311yescharacteristic
683C2×D4C2×D4×C11311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C11311yescharacteristic
696C22×C4C2×D4×C11311yescharacteristic
697C22×C4C2×D4×C11311yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C11311yescharacteristic
734C4⋊C4C2×D4×C11311yescharacteristic
735C4⋊C4C2×D4×C11311yescharacteristic
736C4⋊C4C2×D4×C11311yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C11311yescharacteristic
768C42C2×D4×C11311yescharacteristic
769C42C2×D4×C11311yescharacteristic
770C42C24×C11311yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C11311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C11311yescharacteristic
834C2×C4#120×C11311yescharacteristic
835C2×C4#120×C11311yescharacteristic
836C2×C4C22×D4×C11311yescharacteristic
837C2×C4C22×D4×C11311yescharacteristic
838C2×C4C22×D4×C11311yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C11311yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C113×#301811yescharacteristic
887C2C113×#301911yescharacteristic
888C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
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
1. C113×#3529C2semidirect
2. C113×#3219C2semidirect
3. C113×#3214C2semidirect
4. C113×#3180C2semidirect
5. C113×#1664C2semidirect
6. C113×#1662C2semidirect
7. C113×#1661C2semidirect
8. C113×#1659C2semidirect
9. C113×#1657C2semidirect
10. C113×#1656C2semidirect
11. C113×#1656C2semidirect
12. C113×#1655C2semidirect
13. C113×#1535C2semidirect
14. C113×#1532C2semidirect
15. C113×#1530C2semidirect
28. #532×C113C22semidirect
36. #501×C113C22semidirect
41. #496×C113C22semidirect
42. #491×C113C22semidirect
43. #490×C113C22semidirect
44. #490×C113C22semidirect
47. #489×C113C22semidirect
60. #432×C113C22semidirect
61. #432×C113C22semidirect
62. C2×#97×C113C22semidirect
63. #330×C113C22semidirect
64. #330×C113C22semidirect
65. #330×C113C22semidirect
66. #330×C113C22semidirect
73. #329×C113C22semidirect
74. #329×C113C22semidirect
435. #19010C113direct (N × H)
445. #3529C2×C113semidirect
446. #3219C2×C113semidirect
447. #3214C2×C113semidirect
448. #3180C2×C113semidirect
449. #1664C2×C113semidirect
450. #1662C2×C113semidirect
451. #1661C2×C113semidirect
452. #1659C2×C113semidirect
453. #1657C2×C113semidirect
454. #1656C2×C113semidirect
455. #1656C2×C113semidirect
456. #1655C2×C113semidirect
457. #1535C2×C113semidirect
458. #1532C2×C113semidirect
459. #1530C2×C113semidirect
460. C113#19010direct (N × H)
473. #532C22×C113semidirect
481. #501C22×C113semidirect
486. #496C22×C113semidirect
487. #491C22×C113semidirect
488. #490C22×C113semidirect
489. #490C22×C113semidirect
492. #489C22×C113semidirect
505. #432C22×C113semidirect
506. #432C22×C113semidirect
507. C2×#97C22×C113semidirect
508. #330C22×C113semidirect
509. #330C22×C113semidirect
510. #330C22×C113semidirect
511. #330C22×C113semidirect
518. #329C22×C113semidirect
519. #329C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35292
C113×#32192
C113×#32142
C113×#31802
C113×#16642
C113×#16622
C113×#16612
C113×#16592
C113×#16572
C113×#16562
C113×#16552
C113×#15352
C113×#15322
C113×#15302
#19010113