Finite Group Databasebeta

← C113×#19068 #43287088

Subgroups — C113×#19068 #43287088

Order 28928.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3545C211yesmaximal, characteristic, complemented
2C113×#3219C211yesmaximal, characteristic, complemented
3C113×#3213C211yesmaximal, characteristic, complemented
4C113×#3171C211yesmaximal, 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×#1529C211yesmaximal, characteristic, complemented
15C113×#1527C211yesmaximal, characteristic, complemented
16#563×C113C2211yescharacteristic
17#562×C113C2211yescharacteristic
18#562×C113C2211yescharacteristic
19H(3,𝔽4)×C113C2211yescharacteristic
20#555×C113—21no—
21#551×C113—21no—
22#551×C113—21no—
23#551×C113—21no—
24#546×C113—21no—
25#546×C113—21no—
26#542×C113—21no—
27#542×C113—21no—
28#538×C113—21no—
29#538×C113—21no—
30#536×C113—21no—
31#534×C113—21no—
32#532×C113C2211yescharacteristic, complemented
33#529×C113C2211yescharacteristic
34#529×C113C2211yescharacteristic
35C2×#124×C113C2211yescharacteristic
36#501×C113C2211yescharacteristic, complemented
37#497×C113C2211yescharacteristic, complemented
38#496×C113C2211yescharacteristic
39#496×C113C2211yescharacteristic, complemented
40#496×C113C2211yescharacteristic, complemented
41#496×C113C2211yescharacteristic, complemented
42#491×C113C2211yescharacteristic, complemented
43#490×C113C2211yescharacteristic, complemented
44#490×C113C2211yescharacteristic, complemented
45#489×C113C2211yescharacteristic
46#489×C113C2211yescharacteristic, complemented
47#489×C113C2211yescharacteristic, complemented
48#469×C113—21no—
49#468×C113—21no—
50#464×C113—21no—
51#463×C113—21no—
52#463×C113—21no—
53#463×C113—21no—
54#452×C113—21no—
55#449×C113—21no—
56#448×C113—21no—
57#447×C113—21no—
58C4×SD16×C113—21no—
59C4×D8×C113—21no—
60#432×C113C2211yescharacteristic, complemented
61#432×C113C2211yescharacteristic, complemented
62C4×M16×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, complemented
70#329×C113C2211yescharacteristic, complemented
71#329×C113C2211yescharacteristic, complemented
72#329×C113C2211yescharacteristic, complemented
73#329×C113C2211yescharacteristic, complemented
74#329×C113C2211yescharacteristic, complemented
75C2×#41×C113—21no—
76C2×#41×C113—21no—
77C22×Q8×C113D411yescharacteristic
78C22×D4×C113—21no—
79C22×D4×C113D411yescharacteristic
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—
90C2×M16×C113—21no—
91C4⋊Q8×C113—21no—
92C4⋊Q8×C113—21no—
93C4⋊Q8×C113C2311yescharacteristic
94#127×C113C2311yescharacteristic
95#126×C113—21no—
96#126×C113—21no—
97#126×C113—21no—
98#126×C113—21no—
99#126×C113—21no—
100#126×C113—21no—
101#125×C113C2311yescharacteristic
102#125×C113C2311yescharacteristic
103#124×C113—21no—
104#124×C113—21no—
105#124×C113—21no—
106#124×C113—21no—
107#124×C113—21no—
108#124×C113—21no—
109#124×C113—21no—
110#124×C113—21no—
111#124×C113—21no—
112#124×C113D411yescharacteristic
113#124×C113D411yescharacteristic
114#124×C113C2311yescharacteristic
115#124×C113C2311yescharacteristic
116#124×C113C2311yescharacteristic
117#124×C113C2311yescharacteristic
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—
128#123×C113—21no—
129#123×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×C113—21no—
137C22⋊Q8×C113—21no—
138C22⋊Q8×C113D411yescharacteristic
139C22⋊Q8×C113D411yescharacteristic
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×C113D411yescharacteristic
151#121×C113D411yescharacteristic
152#120×C113—21no—
153#120×C113—21no—
154#120×C113—21no—
155#120×C113—21no—
156#120×C113—21no—
157#120×C113—21no—
158C4×Q8×C113D411yescharacteristic
159C4×Q8×C113D411yescharacteristic
160C4×D4×C113—21no—
161C4×D4×C113—21no—
162C4×D4×C113—21no—
163C4×D4×C113—21no—
164C4×D4×C113—21no—
165C4×D4×C113—21no—
166C4×D4×C113—21no—
167C4×D4×C113—21no—
168C4×D4×C113D411yescharacteristic
169C4×D4×C113D411yescharacteristic
170#117×C113—21no—
171#117×C113—21no—
172#117×C113—21no—
173#117×C113—21no—
174#117×C113—21no—
175C2×C22⋊C4×C113—21no—
176C2×C22⋊C4×C113—21no—
177C2×C22⋊C4×C113—21no—
178C2×C22⋊C4×C113—21no—
179C2×C22⋊C4×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×C113C2311yescharacteristic
200#97×C113C2311yescharacteristic
201#97×C113C2311yescharacteristic
202#97×C113C2311yescharacteristic
203#97×C113C2311yescharacteristic
204#97×C113C2311yescharacteristic
205C4×C8×C113—21no—
206C24×C113—21no—
207C24×C113—21no—
208#41×C113—82no—
209#41×C113—81no—
210#41×C113—81no—
211C2×Q8×C113—21no—
212C2×Q8×C113—21no—
213C2×Q8×C113—21no—
214C2×Q8×C113—81no—
215C2×Q8×C113C2×D411yescharacteristic
216C2×Q8×C113C2×D411yescharacteristic
217C2×Q8×C113C2×D411yescharacteristic
218C2×Q8×C113C2×D411yescharacteristic
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—41no—
233C2×D4×C113—81no—
234C2×D4×C113—82no—
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—41no—
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2×D411yescharacteristic
251Q16×C113—81no—
252SD16×C113—42no—
253SD16×C113—81no—
254SD16×C113—81no—
255SD16×C113—81no—
256SD16×C113—81no—
257D8×C113—42no—
258D8×C113—81no—
259D8×C113—81no—
260D8×C113—81no—
261M16×C113—42no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
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×C113C2×D411yescharacteristic
285C4⋊C4×C113C2×D411yescharacteristic
286C4⋊C4×C113C2×D411yescharacteristic
287C4⋊C4×C113C2×D411yescharacteristic
288C22⋊C4×C113—21no—
289C22⋊C4×C113—21no—
290C22⋊C4×C113—21no—
291C22⋊C4×C113—21no—
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—42no—
331C23×C113—41no—
332C23×C113—81no—
333C23×C113—81no—
334C23×C113—81no—
335C23×C113—81no—
336C23×C113—81no—
337C23×C113#12011yescharacteristic
338Q8×C113—41no—
339Q8×C113—41no—
340Q8×C113—41no—
341Q8×C113—41no—
342Q8×C113—41no—
343Q8×C113—41no—
344Q8×C113—81no—
345Q8×C113—81no—
346D4×C113—41no—
347D4×C113—41no—
348D4×C113—41no—
349D4×C113—41no—
350D4×C113—41no—
351D4×C113—41no—
352D4×C113—41no—
353D4×C113—41no—
354D4×C113—41no—
355D4×C113—41no—
356D4×C113—42no—
357D4×C113—42no—
358D4×C113—81no—
359D4×C113—81no—
360D4×C113—81no—
361D4×C113—81no—
362D4×C113—81no—
363D4×C113—81no—
364D4×C113—81no—
365D4×C113—81no—
366D4×C113—82no—
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—21no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—42no—
379C2×C4×C113—41no—
380C2×C4×C113—81no—
381C2×C4×C113—81no—
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—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—162no—
419C22×C113—162no—
420C22×C113C2×#12011yescharacteristic
421C4×C113—21no—
422C4×C113—21no—
423C4×C113—21no—
424C4×C113—21no—
425C4×C113—21no—
426C4×C113—21no—
427C4×C113—41no—
428C4×C113—41no—
429C4×C113—41no—
430C4×C113—41no—
431C4×C113—41no—
432C4×C113—41no—
433C4×C113—41no—
434C4×C113—41no—
435C4×C113—81no—
436#19068C11311yesmaximal, characteristic, direct product factor, Sylow
437C2×C113—41no—
438C2×C113—81no—
439C2×C113—81no—
440C2×C113—81no—
441C2×C113—81no—
442C2×C113—161no—
443C2×C113#301811yescharacteristic
444C2×C113#301911yescharacteristic
445C2×C113#302111yescharacteristic
446#3545C2×C11311yescharacteristic, complemented
447#3219C2×C11311yescharacteristic, complemented
448#3213C2×C11311yescharacteristic, complemented
449#3171C2×C11311yescharacteristic, complemented
450#1664C2×C11311yescharacteristic, complemented
451#1662C2×C11311yescharacteristic, complemented
452#1661C2×C11311yescharacteristic, complemented
453#1659C2×C11311yescharacteristic, complemented
454#1657C2×C11311yescharacteristic, complemented
455#1656C2×C11311yescharacteristic, complemented
456#1656C2×C11311yescharacteristic, complemented
457#1655C2×C11311yescharacteristic, complemented
458#1535C2×C11311yescharacteristic, complemented
459#1529C2×C11311yescharacteristic, complemented
460#1527C2×C11311yescharacteristic, complemented
461C113#1906811yescharacteristic, direct product factor, Sylow
462#563C22×C11311yescharacteristic
463#562C22×C11311yescharacteristic
464#562C22×C11311yescharacteristic
465H(3,𝔽4)C22×C11311yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C11311yescharacteristic, complemented
479#529C22×C11311yescharacteristic
480#529C22×C11311yescharacteristic
481C2×#124C22×C11311yescharacteristic
482#501C22×C11311yescharacteristic, complemented
483#497C22×C11311yescharacteristic, complemented
484#496C22×C11311yescharacteristic
485#496C22×C11311yescharacteristic, complemented
486#496C22×C11311yescharacteristic, complemented
487#496C22×C11311yescharacteristic, complemented
488#491C22×C11311yescharacteristic, complemented
489#490C22×C11311yescharacteristic, complemented
490#490C22×C11311yescharacteristic, complemented
491#489C22×C11311yescharacteristic
492#489C22×C11311yescharacteristic, complemented
493#489C22×C11311yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C11311yescharacteristic, complemented
507#432C22×C11311yescharacteristic, complemented
508C4×M16C22×C11311yescharacteristic, complemented
509#330C22×C11311yescharacteristic, complemented
510#330C22×C11311yescharacteristic, complemented
511#330C22×C11311yescharacteristic, complemented
512#330C22×C11311yescharacteristic, complemented
513#329C22×C11311yescharacteristic
514#329C22×C11311yescharacteristic
515#329C22×C11311yescharacteristic, complemented
516#329C22×C11311yescharacteristic, complemented
517#329C22×C11311yescharacteristic, complemented
518#329C22×C11311yescharacteristic, complemented
519#329C22×C11311yescharacteristic, complemented
520#329C22×C11311yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C11311yescharacteristic
524C22×D4—21no—
525C22×D4D4×C11311yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C11311yescharacteristic
540#127C23×C11311yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C11311yescharacteristic
548#125C23×C11311yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C11311yescharacteristic
559#124D4×C11311yescharacteristic
560#124C23×C11311yescharacteristic
561#124C23×C11311yescharacteristic
562#124C23×C11311yescharacteristic
563#124C23×C11311yescharacteristic
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—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C11311yescharacteristic
585C22⋊Q8D4×C11311yescharacteristic
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#121D4×C11311yescharacteristic
597#121D4×C11311yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C11311yescharacteristic
605C4×Q8D4×C11311yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C11311yescharacteristic
615C4×D4D4×C11311yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C11311yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C11311yescharacteristic
646#97C23×C11311yescharacteristic
647#97C23×C11311yescharacteristic
648#97C23×C11311yescharacteristic
649#97C23×C11311yescharacteristic
650#97C23×C11311yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C11311yescharacteristic
662C2×Q8C2×D4×C11311yescharacteristic
663C2×Q8C2×D4×C11311yescharacteristic
664C2×Q8C2×D4×C11311yescharacteristic
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—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C11311yescharacteristic
682C2×D4C2×D4×C11311yescharacteristic
683C2×D4C2×D4×C11311yescharacteristic
684C2×D4C2×D4×C11311yescharacteristic
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×C4C2×D4×C11311yescharacteristic
695C22×C4C2×D4×C11311yescharacteristic
696C22×C4C2×D4×C11311yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
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⋊C4C2×D4×C11311yescharacteristic
731C4⋊C4C2×D4×C11311yescharacteristic
732C4⋊C4C2×D4×C11311yescharacteristic
733C4⋊C4C2×D4×C11311yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
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—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C11311yescharacteristic
769C42C2×D4×C11311yescharacteristic
770C42C2×D4×C11311yescharacteristic
771C42C24×C11311yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C11311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C11311yescharacteristic
835C2×C4#120×C11311yescharacteristic
836C2×C4#120×C11311yescharacteristic
837C2×C4C22×D4×C11311yescharacteristic
838C2×C4C22×D4×C11311yescharacteristic
839C2×C4C22×D4×C11311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C11311yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C113×#301811yescharacteristic
889C2C113×#301911yescharacteristic
890C2C113×#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×#3545C2semidirect
2. C113×#3219C2semidirect
3. C113×#3213C2semidirect
4. C113×#3171C2semidirect
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×#1529C2semidirect
15. C113×#1527C2semidirect
32. #532×C113C22semidirect
36. #501×C113C22semidirect
37. #497×C113C22semidirect
39. #496×C113C22semidirect
40. #496×C113C22semidirect
41. #496×C113C22semidirect
42. #491×C113C22semidirect
43. #490×C113C22semidirect
44. #490×C113C22semidirect
46. #489×C113C22semidirect
47. #489×C113C22semidirect
60. #432×C113C22semidirect
61. #432×C113C22semidirect
62. C4×M16×C113C22semidirect
63. #330×C113C22semidirect
64. #330×C113C22semidirect
65. #330×C113C22semidirect
66. #330×C113C22semidirect
69. #329×C113C22semidirect
70. #329×C113C22semidirect
71. #329×C113C22semidirect
72. #329×C113C22semidirect
73. #329×C113C22semidirect
74. #329×C113C22semidirect
436. #19068C113direct (N × H)
446. #3545C2×C113semidirect
447. #3219C2×C113semidirect
448. #3213C2×C113semidirect
449. #3171C2×C113semidirect
450. #1664C2×C113semidirect
451. #1662C2×C113semidirect
452. #1661C2×C113semidirect
453. #1659C2×C113semidirect
454. #1657C2×C113semidirect
455. #1656C2×C113semidirect
456. #1656C2×C113semidirect
457. #1655C2×C113semidirect
458. #1535C2×C113semidirect
459. #1529C2×C113semidirect
460. #1527C2×C113semidirect
461. C113#19068direct (N × H)
478. #532C22×C113semidirect
482. #501C22×C113semidirect
483. #497C22×C113semidirect
485. #496C22×C113semidirect
486. #496C22×C113semidirect
487. #496C22×C113semidirect
488. #491C22×C113semidirect
489. #490C22×C113semidirect
490. #490C22×C113semidirect
492. #489C22×C113semidirect
493. #489C22×C113semidirect
506. #432C22×C113semidirect
507. #432C22×C113semidirect
508. C4×M16C22×C113semidirect
509. #330C22×C113semidirect
510. #330C22×C113semidirect
511. #330C22×C113semidirect
512. #330C22×C113semidirect
515. #329C22×C113semidirect
516. #329C22×C113semidirect
517. #329C22×C113semidirect
518. #329C22×C113semidirect
519. #329C22×C113semidirect
520. #329C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35452
C113×#32192
C113×#32132
C113×#31712
C113×#16642
C113×#16622
C113×#16612
C113×#16592
C113×#16572
C113×#16562
C113×#16552
C113×#15352
C113×#15292
C113×#15272
#19068113