Finite Group Databasebeta

← C113×#25147 #43293167

Subgroups — C113×#25147 #43293167

Order 28928.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C113C211yesmaximal, characteristic, complemented
2C113×#3055C211yesmaximal, characteristic, complemented
3C113×#3005C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C113×#2933C211yesmaximal, characteristic, complemented
6C2×#413×C113C211yesmaximal, characteristic, complemented
7C113×#2063C211yesmaximal, characteristic, complemented
8C113×#2052C211yesmaximal, characteristic, complemented
9C113×#2046C211yesmaximal, characteristic, complemented
10C113×#2018C211yesmaximal, characteristic, complemented
11C113×#1978C211yesmaximal, characteristic, complemented
12C113×#1930C211yesmaximal, characteristic, complemented
13C113×#1907C211yesmaximal, characteristic, complemented
14C113×#1900C211yesmaximal, characteristic, complemented
15C113×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C2×#137×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
20C22×SD16×C113C2211yescharacteristic
21C22×D8×C113C2211yescharacteristic
22C2×#131×C113C2211yescharacteristic
23C22×M16×C113C2211yescharacteristic
24C22×M16×C113C2211yescharacteristic
25#525×C113C2211yescharacteristic
26C2×#121×C113C2211yescharacteristic
27#471×C113—24no—
28#469×C113—21no—
29#468×C113—21no—
30#466×C113—21no—
31#465×C113—21no—
32#452×C113—21no—
33#452×C113—21no—
34#449×C113—21no—
35#449×C113—21no—
36#449×C113—21no—
37#449×C113—21no—
38#449×C113—21no—
39#449×C113—21no—
40#436×C113—21no—
41#435×C113—21no—
42#435×C113—21no—
43C8×D4×C113—21no—
44C2×#108×C113C2211yescharacteristic
45C2×#108×C113C2211yescharacteristic
46#428×C113C2211yescharacteristic
47#424×C113C2211yescharacteristic
48#419×C113C2211yescharacteristic
49#418×C113C2211yescharacteristic
50#418×C113C2211yescharacteristic
51#417×C113C2211yescharacteristic
52C2×#103×C113C2211yescharacteristic
53C2×#102×C113C2211yescharacteristic
54#413×C113—24no—
55C2×#101×C113C2211yescharacteristic
56C2×#101×C113C2211yescharacteristic
57C2×#100×C113C2211yescharacteristic
58C2×#100×C113C2211yescharacteristic
59C2×#100×C113C2211yescharacteristic
60C2×#100×C113C2211yescharacteristic
61#408×C113C2211yescharacteristic
62#407×C113C2211yescharacteristic
63C2×C22⋊C8×C113C2211yescharacteristic
64#405×C113C2211yescharacteristic
65#343×C113C2211yescharacteristic
66#343×C113C2211yescharacteristic
67#341×C113C2211yescharacteristic
68#341×C113C2211yescharacteristic
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C2×#41×C113—21no—
74C2×#41×C113—21no—
75C2×#41×C113—41no—
76C2×#41×C113—41no—
77C2×#41×C113C2311yescharacteristic
78C22×Q8×C113C2311yescharacteristic
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113C2311yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113C2311yescharacteristic
85#137×C113—22no—
86#137×C113—41no—
87AGL(1,ℤ/8)×C113—22no—
88AGL(1,ℤ/8)×C113—22no—
89AGL(1,ℤ/8)×C113—41no—
90AGL(1,ℤ/8)×C113—41no—
91C2×Q16×C113—21no—
92C2×SD16×C113—22no—
93C2×SD16×C113—21no—
94C2×SD16×C113—21no—
95C2×SD16×C113—21no—
96C2×SD16×C113—21no—
97C2×SD16×C113—21no—
98C2×SD16×C113—41no—
99C2×D8×C113—21no—
100C2×D8×C113—21no—
101C2×D8×C113—22no—
102C2×D8×C113—21no—
103C2×D8×C113—21no—
104C2×D8×C113—41no—
105#131×C113—22no—
106#131×C113—41no—
107C2×M16×C113—21no—
108C2×M16×C113—21no—
109C2×M16×C113—21no—
110C2×M16×C113—22no—
111C2×M16×C113—22no—
112C2×M16×C113—41no—
113C2×M16×C113—41no—
114C2×M16×C113C2311yescharacteristic
115C2×M16×C113C2311yescharacteristic
116C2×M16×C113C2311yescharacteristic
117C2×M16×C113C2311yescharacteristic
118C2×M16×C113C2311yescharacteristic
119C2×M16×C113C2311yescharacteristic
120C22×C8×C113—21no—
121C22×C8×C113—21no—
122C22×C8×C113—21no—
123C22×C8×C113C2311yescharacteristic
124C22×C8×C113C2311yescharacteristic
125#123×C113—21no—
126C22⋊Q8×C113D411yescharacteristic
127C22⋊Q8×C113D411yescharacteristic
128#121×C113—21no—
129#121×C113—21no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113D411yescharacteristic
133#121×C113D411yescharacteristic
134#120×C113—21no—
135C4×D4×C113—21no—
136C4×D4×C113—21no—
137#117×C113C2311yescharacteristic
138C2×C4⋊C4×C113C2311yescharacteristic
139C2×C22⋊C4×C113—21no—
140#108×C113—22no—
141#108×C113—41no—
142#107×C113—21no—
143#106×C113—21no—
144C4⋊C8×C113—21no—
145C4⋊C8×C113—21no—
146#103×C113—21no—
147#103×C113—21no—
148#103×C113—21no—
149#103×C113—21no—
150#103×C113—21no—
151#102×C113—21no—
152#102×C113—21no—
153#102×C113—21no—
154#102×C113—21no—
155#102×C113—21no—
156#102×C113—21no—
157#102×C113—21no—
158#101×C113—22no—
159#101×C113D414yescomplemented
160#100×C113—22no—
161#100×C113—22no—
162#100×C113—22no—
163#100×C113—41no—
164C22⋊C8×C113—21no—
165C22⋊C8×C113—21no—
166C22⋊C8×C113—21no—
167C22⋊C8×C113—21no—
168C22⋊C8×C113D411yescharacteristic
169C22⋊C8×C113D411yescharacteristic
170C22⋊C8×C113D411yescharacteristic
171C22⋊C8×C113D411yescharacteristic
172#97×C113—21no—
173C4×C8×C113—21no—
174C24×C113—21no—
175C24×C113—21no—
176C24×C113#4111yescharacteristic
177#41×C113—21no—
178#41×C113—21no—
179#41×C113—21no—
180#41×C113—21no—
181#41×C113—42no—
182#41×C113—42no—
183#41×C113—42no—
184#41×C113—42no—
185#41×C113—42no—
186#41×C113—42no—
187#41×C113—42no—
188#41×C113—42no—
189C2×Q8×C113—21no—
190C2×Q8×C113—21no—
191C2×Q8×C113—21no—
192C2×Q8×C113—21no—
193C2×Q8×C113—21no—
194C2×Q8×C113C2×D412yes—
195C2×Q8×C113C2×D411yescharacteristic
196C2×D4×C113—24no—
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—42no—
212C2×D4×C113—41no—
213C2×D4×C113—41no—
214C2×D4×C113—41no—
215C2×D4×C113—41no—
216C2×D4×C113—82no—
217C2×D4×C113C2×D411yescharacteristic
218C2×D4×C113#4112yes—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—24no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—42no—
228C22×C4×C113—41no—
229C22×C4×C113—41no—
230C22×C4×C113C2×D411yescharacteristic
231C22×C4×C113C2×D411yescharacteristic
232C22×C4×C113C2×D411yescharacteristic
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113#4111yescharacteristic
235C22×C4×C113C2411yescharacteristic
236Q16×C113—42no—
237SD16×C113—42no—
238SD16×C113—42no—
239SD16×C113—42no—
240SD16×C113—42no—
241SD16×C113—42no—
242D8×C113—42no—
243D8×C113—42no—
244D8×C113—42no—
245D8×C113—42no—
246M16×C113—21no—
247M16×C113—21no—
248M16×C113—21no—
249M16×C113—21no—
250M16×C113—21no—
251M16×C113—21no—
252M16×C113—21no—
253M16×C113—21no—
254M16×C113—21no—
255M16×C113—21no—
256M16×C113—42no—
257M16×C113—42no—
258M16×C113—42no—
259M16×C113C2×D412yes—
260M16×C113C2×D412yes—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
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—21no—
270C2×C8×C113—21no—
271C2×C8×C113—42no—
272C2×C8×C113—42no—
273C2×C8×C113—42no—
274C2×C8×C113C2×D411yescharacteristic
275C2×C8×C113C2×D411yescharacteristic
276C2×C8×C113C2×D411yescharacteristic
277C2×C8×C113C2×D411yescharacteristic
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113C2×D411yescharacteristic
283C4⋊C4×C113C2×D411yescharacteristic
284C22⋊C4×C113—21no—
285C22⋊C4×C113—21no—
286C22⋊C4×C113—21no—
287C22⋊C4×C113—21no—
288C22⋊C4×C113—21no—
289C22⋊C4×C113—41no—
290C22⋊C4×C113—41no—
291C42×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—22no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—81no—
304C23×C113—81no—
305C23×C113—81no—
306C23×C113—81no—
307C23×C113#12111yescharacteristic
308C23×C113#12111yescharacteristic
309C23×C113C2×#4111yescharacteristic
310Q8×C113—21no—
311Q8×C113—22no—
312Q8×C113—22no—
313Q8×C113—21no—
314Q8×C113—41no—
315Q8×C113—41no—
316D4×C113—21no—
317D4×C113—22no—
318D4×C113—21no—
319D4×C113—22no—
320D4×C113—42no—
321D4×C113—44no—
322D4×C113—44no—
323D4×C113—41no—
324D4×C113—41no—
325D4×C113—41no—
326D4×C113—41no—
327D4×C113—41no—
328D4×C113—41no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—81no—
332D4×C113—82no—
333D4×C113—82no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—21no—
341C2×C4×C113—21no—
342C2×C4×C113—21no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—22no—
348C2×C4×C113—44no—
349C2×C4×C113—44no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—81no—
356C2×C4×C113#12111yescharacteristic
357C2×C4×C113#12111yescharacteristic
358C2×C4×C113C22×D411yescharacteristic
359C2×C4×C113C22×D411yescharacteristic
360C2×C4×C113C22×D411yescharacteristic
361C2×C4×C113C2×#4111yescharacteristic
362C2×C4×C113H(5,𝔽2)11yescharacteristic
363C2×C4×C113H(5,𝔽2)11yescharacteristic
364C8×C113—21no—
365C8×C113—21no—
366C8×C113—22no—
367C8×C113—22no—
368C8×C113—21no—
369C8×C113—21no—
370C8×C113—41no—
371C8×C113—41no—
372C8×C113—41no—
373C8×C113—41no—
374C22×C113—21no—
375C22×C113—21no—
376C22×C113—21no—
377C22×C113—21no—
378C22×C113—21no—
379C22×C113—21no—
380C22×C113—21no—
381C22×C113—21no—
382C22×C113—42no—
383C22×C113—41no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—81no—
387C22×C113—81no—
388C22×C113—82no—
389C22×C113—82no—
390C22×C113—81no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113—81no—
395C22×C113—161no—
396C22×C113—161no—
397C22×C113C2×#12111yescharacteristic
398C22×C113#52511yescharacteristic
399C22×C113#53811yescharacteristic
400C4×C113—21no—
401C4×C113—21no—
402C4×C113—42no—
403C4×C113—41no—
404C4×C113—41no—
405C4×C113—41no—
406C4×C113—81no—
407C4×C113D4211yescharacteristic
408C4×C113D4211yescharacteristic
409C4×C113#54611yescharacteristic
410C4×C113#54611yescharacteristic
411#25147C11311yesmaximal, characteristic, direct product factor, Sylow
412C2×C113—21no—
413C2×C113—21no—
414C2×C113—41no—
415C2×C113—41no—
416C2×C113—81no—
417C2×C113—82no—
418C2×C113—161no—
419C2×C113#242411yescharacteristic
420C2×C113#306711yescharacteristic
421C2×C113#306811yescharacteristic
422C2×#471C2×C11311yescharacteristic, complemented
423#3055C2×C11311yescharacteristic, complemented
424#3005C2×C11311yescharacteristic, complemented
425C2×#449C2×C11311yescharacteristic, complemented
426#2933C2×C11311yescharacteristic, complemented
427C2×#413C2×C11311yescharacteristic, complemented
428#2063C2×C11311yescharacteristic, complemented
429#2052C2×C11311yescharacteristic, complemented
430#2046C2×C11311yescharacteristic, complemented
431#2018C2×C11311yescharacteristic, complemented
432#1978C2×C11311yescharacteristic, complemented
433#1930C2×C11311yescharacteristic, complemented
434#1907C2×C11311yescharacteristic, complemented
435#1900C2×C11311yescharacteristic, complemented
436#1855C2×C11311yescharacteristic, complemented
437C113#2514711yescharacteristic, direct product factor, Sylow
438C22×#41C22×C11311yescharacteristic
439C2×#137C22×C11311yescharacteristic
440C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
441C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
442C22×SD16C22×C11311yescharacteristic
443C22×D8C22×C11311yescharacteristic
444C2×#131C22×C11311yescharacteristic
445C22×M16C22×C11311yescharacteristic
446C22×M16C22×C11311yescharacteristic
447#525C22×C11311yescharacteristic
448C2×#121C22×C11311yescharacteristic
449#471—24no—
450#469—21no—
451#468—21no—
452#466—21no—
453#465—21no—
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#449—21no—
462#436—21no—
463#435—21no—
464#435—21no—
465C8×D4—21no—
466C2×#108C22×C11311yescharacteristic
467C2×#108C22×C11311yescharacteristic
468#428C22×C11311yescharacteristic
469#424C22×C11311yescharacteristic
470#419C22×C11311yescharacteristic
471#418C22×C11311yescharacteristic
472#418C22×C11311yescharacteristic
473#417C22×C11311yescharacteristic
474C2×#103C22×C11311yescharacteristic
475C2×#102C22×C11311yescharacteristic
476#413—24no—
477C2×#101C22×C11311yescharacteristic
478C2×#101C22×C11311yescharacteristic
479C2×#100C22×C11311yescharacteristic
480C2×#100C22×C11311yescharacteristic
481C2×#100C22×C11311yescharacteristic
482C2×#100C22×C11311yescharacteristic
483#408C22×C11311yescharacteristic
484#407C22×C11311yescharacteristic
485C2×C22⋊C8C22×C11311yescharacteristic
486#405C22×C11311yescharacteristic
487#343C22×C11311yescharacteristic
488#343C22×C11311yescharacteristic
489#341C22×C11311yescharacteristic
490#341C22×C11311yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C11311yescharacteristic
500C22×Q8C23×C11311yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C11311yescharacteristic
504C22×D4C23×C11311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C11311yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C11311yescharacteristic
537C2×M16C23×C11311yescharacteristic
538C2×M16C23×C11311yescharacteristic
539C2×M16C23×C11311yescharacteristic
540C2×M16C23×C11311yescharacteristic
541C2×M16C23×C11311yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C11311yescharacteristic
546C22×C8C23×C11311yescharacteristic
547#123—21no—
548C22⋊Q8D4×C11311yescharacteristic
549C22⋊Q8D4×C11311yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C11311yescharacteristic
555#121D4×C11311yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C11311yescharacteristic
560C2×C4⋊C4C23×C11311yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C11314yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C11311yescharacteristic
591C22⋊C8D4×C11311yescharacteristic
592C22⋊C8D4×C11311yescharacteristic
593C22⋊C8D4×C11311yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C11311yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C11312yes—
617C2×Q8C2×D4×C11311yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C11311yescharacteristic
640C2×D4#41×C11312yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C11311yescharacteristic
653C22×C4C2×D4×C11311yescharacteristic
654C22×C4C2×D4×C11311yescharacteristic
655C22×C4C2×D4×C11311yescharacteristic
656C22×C4#41×C11311yescharacteristic
657C22×C4C24×C11311yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C11312yes—
682M16C2×D4×C11312yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C11311yescharacteristic
697C2×C8C2×D4×C11311yescharacteristic
698C2×C8C2×D4×C11311yescharacteristic
699C2×C8C2×D4×C11311yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C11311yescharacteristic
705C4⋊C4C2×D4×C11311yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C11311yescharacteristic
730C23#121×C11311yescharacteristic
731C23C2×#41×C11311yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C11311yescharacteristic
779C2×C4#121×C11311yescharacteristic
780C2×C4C22×D4×C11311yescharacteristic
781C2×C4C22×D4×C11311yescharacteristic
782C2×C4C22×D4×C11311yescharacteristic
783C2×C4C2×#41×C11311yescharacteristic
784C2×C4H(5,𝔽2)×C11311yescharacteristic
785C2×C4H(5,𝔽2)×C11311yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C11311yescharacteristic
820C22#525×C11311yescharacteristic
821C22#538×C11311yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C11311yescharacteristic
830C4D42×C11311yescharacteristic
831C4#546×C11311yescharacteristic
832C4#546×C11311yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C113×#242411yescharacteristic
841C2C113×#306711yescharacteristic
842C2C113×#306811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#121
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C113C2semidirect
2. C113×#3055C2semidirect
3. C113×#3005C2semidirect
4. C2×#449×C113C2semidirect
5. C113×#2933C2semidirect
6. C2×#413×C113C2semidirect
7. C113×#2063C2semidirect
8. C113×#2052C2semidirect
9. C113×#2046C2semidirect
10. C113×#2018C2semidirect
11. C113×#1978C2semidirect
12. C113×#1930C2semidirect
13. C113×#1907C2semidirect
14. C113×#1900C2semidirect
15. C113×#1855C2semidirect
159. #101×C113D4semidirect
411. #25147C113direct (N × H)
422. C2×#471C2×C113semidirect
423. #3055C2×C113semidirect
424. #3005C2×C113semidirect
425. C2×#449C2×C113semidirect
426. #2933C2×C113semidirect
427. C2×#413C2×C113semidirect
428. #2063C2×C113semidirect
429. #2052C2×C113semidirect
430. #2046C2×C113semidirect
431. #2018C2×C113semidirect
432. #1978C2×C113semidirect
433. #1930C2×C113semidirect
434. #1907C2×C113semidirect
435. #1900C2×C113semidirect
436. #1855C2×C113semidirect
437. C113#25147direct (N × H)
581. #101D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C1132
C113×#30552
C113×#30052
C2×#449×C1132
C113×#29332
C2×#413×C1132
C113×#20632
C113×#20522
C113×#20462
C113×#20182
C113×#19782
C113×#19302
C113×#19072
C113×#19002
C113×#18552
#25147113