Finite Group Databasebeta

← C113×#18224 #43286244

Subgroups — C113×#18224 #43286244

Order 28928.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3534C211yesmaximal, characteristic, complemented
2C113×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C113C211yesmaximal, characteristic, complemented
4C113×#2613C211yesmaximal, characteristic, complemented
5C113×#1600C212yesmaximal, complemented
6C113×#1598C212yesmaximal, complemented
7C113×#1597C212yesmaximal, complemented
8C113×#1595C212yesmaximal, complemented
9C113×#1516C211yesmaximal, characteristic, complemented
10C113×#1510C211yesmaximal, characteristic, complemented
11C113×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C113C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C113—21no—
14C22×D8×C113—21no—
15#562×C113—21no—
16#560×C113—21no—
17#553×C113—21no—
18#551×C113—21no—
19#546×C113—21no—
20#546×C113—21no—
21#546×C113—21no—
22D42×C113—21no—
23#540×C113—21no—
24#539×C113—21no—
25#539×C113C2211yescharacteristic, complemented
26#538×C113—21no—
27#538×C113C2211yescharacteristic, complemented
28#537×C113C2211yescharacteristic, complemented
29#534×C113—21no—
30#534×C113C2211yescharacteristic, complemented
31#525×C113C2211yescharacteristic
32C2×#123×C113C2211yescharacteristic
33C2×#121×C113C2211yescharacteristic
34C2×#120×C113—21no—
35#450×C113—21no—
36#450×C113C2212yescomplemented
37#447×C113—21no—
38#447×C113—21no—
39#447×C113—21no—
40#447×C113C2212yes—
41#447×C113C2212yescomplemented
42#447×C113C2212yescomplemented
43#418×C113—21no—
44C2×#102×C113—21no—
45#407×C113C2211yescharacteristic, complemented
46C2×C22⋊C8×C113C2211yescharacteristic, complemented
47#394×C113—21no—
48#394×C113C2212yescomplemented
49#392×C113—21no—
50#392×C113C2212yescomplemented
51#381×C113C2211yescharacteristic, complemented
52#379×C113—21no—
53#328×C113C2212yescomplemented
54#327×C113C2212yescomplemented
55#327×C113C2212yescomplemented
56#327×C113C2212yescomplemented
57#324×C113C2212yescomplemented
58#323×C113C2212yescomplemented
59C25×C113—21no—
60C2×#41×C113—21no—
61C2×#41×C113D411yescharacteristic, complemented
62C22×D4×C113—21no—
63C22×D4×C113—21no—
64C22×D4×C113—21no—
65C22×D4×C113—22no—
66C22×D4×C113—21no—
67C22×D4×C113—21no—
68C22×D4×C113—21no—
69C22×D4×C113—21no—
70C22×D4×C113—21no—
71C22×D4×C113—44no—
72C22×D4×C113D411yescharacteristic
73C22×D4×C113D411yescharacteristic, complemented
74C22×D4×C113C2312yes—
75C23×C4×C113C2311yescharacteristic
76AGL(1,ℤ/8)×C113—44no—
77C2×SD16×C113—22no—
78C2×D8×C113—22no—
79C2×D8×C113—22no—
80C2×D8×C113—22no—
81C2×D8×C113—44no—
82C2×M16×C113—21no—
83C22×C8×C113—21no—
84#127×C113—21no—
85#126×C113—21no—
86#126×C113—21no—
87#126×C113—21no—
88#126×C113—21no—
89#125×C113—21no—
90#125×C113—21no—
91#124×C113—21no—
92#124×C113—21no—
93#124×C113—21no—
94#123×C113—21no—
95#123×C113—21no—
96#123×C113—21no—
97#123×C113—21no—
98#123×C113—21no—
99#123×C113—21no—
100#123×C113—21no—
101#123×C113—21no—
102#123×C113—21no—
103#123×C113—21no—
104#123×C113—21no—
105#123×C113—21no—
106#123×C113—21no—
107#123×C113—21no—
108C22⋊Q8×C113—21no—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113—21no—
112C22⋊Q8×C113—21no—
113C22⋊Q8×C113D411yescharacteristic, complemented
114C22⋊Q8×C113C2311yescharacteristic
115#121×C113—21no—
116#121×C113—21no—
117#121×C113—21no—
118#121×C113—21no—
119#121×C113—21no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113—21no—
123#121×C113—21no—
124#121×C113—21no—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113—21no—
129#121×C113—21no—
130#121×C113D411yescharacteristic, complemented
131#121×C113D411yescharacteristic, complemented
132#121×C113D411yescharacteristic, complemented
133#121×C113C2311yescharacteristic
134#121×C113C2311yescharacteristic
135#121×C113C2311yescharacteristic
136#120×C113—21no—
137#120×C113—21no—
138#120×C113—21no—
139#120×C113—21no—
140#120×C113—21no—
141#120×C113—21no—
142#120×C113—21no—
143#120×C113—21no—
144#120×C113—44no—
145C4×D4×C113—21no—
146C4×D4×C113—21no—
147C4×D4×C113—21no—
148C4×D4×C113—21no—
149C4×D4×C113—21no—
150C4×D4×C113—21no—
151C4×D4×C113—21no—
152C4×D4×C113—21no—
153#117×C113—21no—
154#117×C113D411yescharacteristic, complemented
155C2×C4⋊C4×C113D411yescharacteristic
156C2×C4⋊C4×C113D411yescharacteristic, complemented
157C2×C4⋊C4×C113C2311yescharacteristic
158C2×C22⋊C4×C113—21no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—21no—
161C2×C22⋊C4×C113—21no—
162C2×C22⋊C4×C113—22no—
163C2×C22⋊C4×C113—22no—
164C2×C22⋊C4×C113—22no—
165C2×C22⋊C4×C113D411yescharacteristic
166C2×C22⋊C4×C113D411yescharacteristic
167C2×C22⋊C4×C113C2311yescharacteristic
168#102×C113—22no—
169#102×C113—22no—
170#102×C113—22no—
171#102×C113—22no—
172C22⋊C8×C113—21no—
173C22⋊C8×C113—21no—
174C22⋊C8×C113C2312yes—
175C22⋊C8×C113C2312yes—
176#95×C113—21no—
177#95×C113C2312yes—
178C24×C113—24no—
179C24×C113—21no—
180C24×C113—22no—
181C24×C113—21no—
182C24×C113—42no—
183C24×C113—41no—
184C24×C113—41no—
185C24×C113—82no—
186C24×C113—82no—
187C24×C113C2×D411yescharacteristic
188C24×C113C2×D411yescharacteristic
189#41×C113—42no—
190#41×C113—82no—
191C2×Q8×C113—21no—
192C2×Q8×C113C2×D411yescharacteristic
193C2×D4×C113—24no—
194C2×D4×C113—24no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—21no—
210C2×D4×C113—21no—
211C2×D4×C113—21no—
212C2×D4×C113—22no—
213C2×D4×C113—22no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—44no—
218C2×D4×C113—44no—
219C2×D4×C113—44no—
220C2×D4×C113—44no—
221C2×D4×C113—42no—
222C2×D4×C113—44no—
223C2×D4×C113—41no—
224C2×D4×C113—41no—
225C2×D4×C113—82no—
226C2×D4×C113—82no—
227C2×D4×C113—82no—
228C2×D4×C113—82no—
229C2×D4×C113—82no—
230C2×D4×C113C2×D411yescharacteristic
231C2×D4×C113C2×D411yescharacteristic
232C2×D4×C113C2×D411yescharacteristic
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—22no—
241C22×C4×C113—42no—
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2411yescharacteristic
251SD16×C113—44no—
252D8×C113—44no—
253D8×C113—44no—
254D8×C113—44no—
255M16×C113—42no—
256C2×C8×C113—22no—
257C2×C8×C113—22no—
258C2×C8×C113—42no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—21no—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—21no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113C2×D411yescharacteristic
273C4⋊C4×C113C2×D411yescharacteristic
274C4⋊C4×C113C2×D411yescharacteristic
275C4⋊C4×C113C2×D411yescharacteristic
276C22⋊C4×C113—21no—
277C22⋊C4×C113—21no—
278C22⋊C4×C113—21no—
279C22⋊C4×C113—21no—
280C22⋊C4×C113—21no—
281C22⋊C4×C113—21no—
282C22⋊C4×C113—21no—
283C22⋊C4×C113—21no—
284C22⋊C4×C113—21no—
285C22⋊C4×C113—21no—
286C22⋊C4×C113—21no—
287C22⋊C4×C113—21no—
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—44no—
302C22⋊C4×C113—42no—
303C22⋊C4×C113—82no—
304C22⋊C4×C113—82no—
305C42×C113—21no—
306C42×C113—21no—
307C42×C113—21no—
308C23×C113—22no—
309C23×C113—22no—
310C23×C113—24no—
311C23×C113—21no—
312C23×C113—21no—
313C23×C113—21no—
314C23×C113—21no—
315C23×C113—22no—
316C23×C113—41no—
317C23×C113—42no—
318C23×C113—42no—
319C23×C113—44no—
320C23×C113—42no—
321C23×C113—41no—
322C23×C113—41no—
323C23×C113—42no—
324C23×C113—42no—
325C23×C113—42no—
326C23×C113—44no—
327C23×C113—42no—
328C23×C113—81no—
329C23×C113—81no—
330C23×C113—82no—
331C23×C113—82no—
332C23×C113—82no—
333C23×C113—82no—
334C23×C113—88no—
335C23×C113—81no—
336C23×C113—81no—
337C23×C113—81no—
338C23×C113—88no—
339C23×C113#12011yescharacteristic
340C23×C113#12011yescharacteristic
341C23×C113C22×D411yescharacteristic
342Q8×C113—41no—
343Q8×C113—81no—
344D4×C113—24no—
345D4×C113—24no—
346D4×C113—41no—
347D4×C113—41no—
348D4×C113—41no—
349D4×C113—42no—
350D4×C113—42no—
351D4×C113—44no—
352D4×C113—44no—
353D4×C113—42no—
354D4×C113—42no—
355D4×C113—42no—
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—81no—
367D4×C113—81no—
368D4×C113—81no—
369D4×C113—81no—
370D4×C113—88no—
371C2×C4×C113—22no—
372C2×C4×C113—22no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—21no—
377C2×C4×C113—21no—
378C2×C4×C113—21no—
379C2×C4×C113—21no—
380C2×C4×C113—21no—
381C2×C4×C113—22no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—42no—
389C2×C4×C113—42no—
390C2×C4×C113—42no—
391C2×C4×C113—81no—
392C2×C4×C113—81no—
393C2×C4×C113—81no—
394C2×C4×C113—81no—
395C2×C4×C113—81no—
396C2×C4×C113—81no—
397C2×C4×C113—81no—
398C2×C4×C113#12011yescharacteristic
399C2×C4×C113#12011yescharacteristic
400C2×C4×C113C22×D411yescharacteristic
401C2×C4×C113C22×D411yescharacteristic
402C8×C113—42no—
403C8×C113—42no—
404C22×C113—21no—
405C22×C113—21no—
406C22×C113—21no—
407C22×C113—21no—
408C22×C113—21no—
409C22×C113—21no—
410C22×C113—21no—
411C22×C113—44no—
412C22×C113—44no—
413C22×C113—44no—
414C22×C113—41no—
415C22×C113—41no—
416C22×C113—41no—
417C22×C113—41no—
418C22×C113—41no—
419C22×C113—41no—
420C22×C113—41no—
421C22×C113—41no—
422C22×C113—41no—
423C22×C113—41no—
424C22×C113—44no—
425C22×C113—41no—
426C22×C113—41no—
427C22×C113—82no—
428C22×C113—82no—
429C22×C113—82no—
430C22×C113—88no—
431C22×C113—88no—
432C22×C113—82no—
433C22×C113—82no—
434C22×C113—162no—
435C22×C113—162no—
436C22×C113B(4,𝔽2)12yes—
437C22×C113C2×#12011yescharacteristic
438C22×C113#57612yes—
439C4×C113—21no—
440C4×C113—21no—
441C4×C113—21no—
442C4×C113—21no—
443C4×C113—41no—
444C4×C113—41no—
445C4×C113—41no—
446C4×C113—41no—
447C4×C113—41no—
448C4×C113—41no—
449C4×C113—41no—
450C4×C113—41no—
451C4×C113—82no—
452#18224C11311yesmaximal, characteristic, direct product factor, Sylow
453C2×C113—22no—
454C2×C113—22no—
455C2×C113—41no—
456C2×C113—84no—
457C2×C113—81no—
458C2×C113—81no—
459C2×C113—81no—
460C2×C113—81no—
461C2×C113#300811yescharacteristic
462C2×C113#302111yescharacteristic
463C2×C113C2×B(4,𝔽2)11yescharacteristic
464#3534C2×C11311yescharacteristic, complemented
465#3003C2×C11311yescharacteristic, complemented
466C2×#447C2×C11311yescharacteristic, complemented
467#2613C2×C11311yescharacteristic, complemented
468#1600C2×C11312yescomplemented
469#1598C2×C11312yescomplemented
470#1597C2×C11312yescomplemented
471#1595C2×C11312yescomplemented
472#1516C2×C11311yescharacteristic, complemented
473#1510C2×C11311yescharacteristic, complemented
474#1468C2×C11311yescharacteristic, complemented
475C113#1822411yescharacteristic, direct product factor, Sylow
476C23×D4C22×C11311yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C11311yescharacteristic, complemented
490#538—21no—
491#538C22×C11311yescharacteristic, complemented
492#537C22×C11311yescharacteristic, complemented
493#534—21no—
494#534C22×C11311yescharacteristic, complemented
495#525C22×C11311yescharacteristic
496C2×#123C22×C11311yescharacteristic
497C2×#121C22×C11311yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C11312yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C11312yes—
505#447C22×C11312yescomplemented
506#447C22×C11312yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C11311yescharacteristic, complemented
510C2×C22⋊C8C22×C11311yescharacteristic, complemented
511#394—21no—
512#394C22×C11312yescomplemented
513#392—21no—
514#392C22×C11312yescomplemented
515#381C22×C11311yescharacteristic, complemented
516#379—21no—
517#328C22×C11312yescomplemented
518#327C22×C11312yescomplemented
519#327C22×C11312yescomplemented
520#327C22×C11312yescomplemented
521#324C22×C11312yescomplemented
522#323C22×C11312yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C11311yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C11311yescharacteristic
537C22×D4D4×C11311yescharacteristic, complemented
538C22×D4C23×C11312yes—
539C23×C4C23×C11311yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
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—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C11311yescharacteristic, complemented
578C22⋊Q8C23×C11311yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
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#121D4×C11311yescharacteristic, complemented
595#121D4×C11311yescharacteristic, complemented
596#121D4×C11311yescharacteristic, complemented
597#121C23×C11311yescharacteristic
598#121C23×C11311yescharacteristic
599#121C23×C11311yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C11311yescharacteristic, complemented
619C2×C4⋊C4D4×C11311yescharacteristic
620C2×C4⋊C4D4×C11311yescharacteristic, complemented
621C2×C4⋊C4C23×C11311yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C11311yescharacteristic
630C2×C22⋊C4D4×C11311yescharacteristic
631C2×C22⋊C4C23×C11311yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C11312yes—
639C22⋊C8C23×C11312yes—
640#95—21no—
641#95C23×C11312yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C11311yescharacteristic
652C24C2×D4×C11311yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C11311yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
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—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C11311yescharacteristic
695C2×D4C2×D4×C11311yescharacteristic
696C2×D4C2×D4×C11311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C11311yescharacteristic
707C22×C4C2×D4×C11311yescharacteristic
708C22×C4C2×D4×C11311yescharacteristic
709C22×C4C2×D4×C11311yescharacteristic
710C22×C4C2×D4×C11311yescharacteristic
711C22×C4C2×D4×C11311yescharacteristic
712C22×C4C2×D4×C11311yescharacteristic
713C22×C4C2×D4×C11311yescharacteristic
714C22×C4C24×C11311yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
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⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C11311yescharacteristic
737C4⋊C4C2×D4×C11311yescharacteristic
738C4⋊C4C2×D4×C11311yescharacteristic
739C4⋊C4C2×D4×C11311yescharacteristic
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—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C11311yescharacteristic
804C23#120×C11311yescharacteristic
805C23C22×D4×C11311yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C11311yescharacteristic
863C2×C4#120×C11311yescharacteristic
864C2×C4C22×D4×C11311yescharacteristic
865C2×C4C22×D4×C11311yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C11312yes—
901C22C2×#120×C11311yescharacteristic
902C22#576×C11312yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C113×#300811yescharacteristic
925C2C113×#302111yescharacteristic
926C2C2×B(4,𝔽2)×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×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×#3534C2semidirect
2. C113×#3003C2semidirect
3. C2×#447×C113C2semidirect
4. C113×#2613C2semidirect
5. C113×#1600C2semidirect
6. C113×#1598C2semidirect
7. C113×#1597C2semidirect
8. C113×#1595C2semidirect
9. C113×#1516C2semidirect
10. C113×#1510C2semidirect
11. C113×#1468C2semidirect
12. C23×D4×C113C22semidirect
25. #539×C113C22semidirect
27. #538×C113C22semidirect
28. #537×C113C22semidirect
30. #534×C113C22semidirect
36. #450×C113C22semidirect
41. #447×C113C22semidirect
42. #447×C113C22semidirect
45. #407×C113C22semidirect
46. C2×C22⋊C8×C113C22semidirect
48. #394×C113C22semidirect
50. #392×C113C22semidirect
51. #381×C113C22semidirect
53. #328×C113C22semidirect
54. #327×C113C22semidirect
55. #327×C113C22semidirect
56. #327×C113C22semidirect
57. #324×C113C22semidirect
58. #323×C113C22semidirect
61. C2×#41×C113D4semidirect
73. C22×D4×C113D4semidirect
113. C22⋊Q8×C113D4semidirect
130. #121×C113D4semidirect
131. #121×C113D4semidirect
132. #121×C113D4semidirect
154. #117×C113D4semidirect
156. C2×C4⋊C4×C113D4semidirect
452. #18224C113direct (N × H)
464. #3534C2×C113semidirect
465. #3003C2×C113semidirect
466. C2×#447C2×C113semidirect
467. #2613C2×C113semidirect
468. #1600C2×C113semidirect
469. #1598C2×C113semidirect
470. #1597C2×C113semidirect
471. #1595C2×C113semidirect
472. #1516C2×C113semidirect
473. #1510C2×C113semidirect
474. #1468C2×C113semidirect
475. C113#18224direct (N × H)
476. C23×D4C22×C113semidirect
489. #539C22×C113semidirect
491. #538C22×C113semidirect
492. #537C22×C113semidirect
494. #534C22×C113semidirect
500. #450C22×C113semidirect
505. #447C22×C113semidirect
506. #447C22×C113semidirect
509. #407C22×C113semidirect
510. C2×C22⋊C8C22×C113semidirect
512. #394C22×C113semidirect
514. #392C22×C113semidirect
515. #381C22×C113semidirect
517. #328C22×C113semidirect
518. #327C22×C113semidirect
519. #327C22×C113semidirect
520. #327C22×C113semidirect
521. #324C22×C113semidirect
522. #323C22×C113semidirect
525. C2×#41D4×C113semidirect
537. C22×D4D4×C113semidirect
577. C22⋊Q8D4×C113semidirect
594. #121D4×C113semidirect
595. #121D4×C113semidirect
596. #121D4×C113semidirect
618. #117D4×C113semidirect
620. C2×C4⋊C4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35342
C113×#30032
C2×#447×C1132
C113×#26132
C113×#16002
C113×#15982
C113×#15972
C113×#15952
C113×#15162
C113×#15102
C113×#14682
#18224113