Finite Group Databasebeta

← C113×#23894 #43291914

Subgroups — C113×#23894 #43291914

Order 28928.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3586C211yesmaximal, characteristic, complemented
2C113×#3585C211yesmaximal, characteristic, complemented
3C113×#3020C211yesmaximal, characteristic, complemented
4C113×#3019C211yesmaximal, characteristic, complemented
5C113×#3010C211yesmaximal, characteristic, complemented
6C113×#3009C211yesmaximal, characteristic, complemented
7C113×#2019C211yesmaximal, characteristic, complemented
8C113×#2017C211yesmaximal, characteristic, complemented
9C113×#2009C211yesmaximal, characteristic, complemented
10C113×#2008C211yesmaximal, characteristic, complemented
11C113×#1903C211yesmaximal, characteristic, complemented
12C113×#1902C211yesmaximal, characteristic, complemented
13C113×#1881C211yesmaximal, characteristic, complemented
14C113×#1881C211yesmaximal, characteristic, complemented
15C113×#1794C211yesmaximal, characteristic, complemented
16#585×C113C2211yescharacteristic
17C2×2−1+4×C113C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C113C2211yescharacteristic
19#578×C113—22no—
20#578×C113—22no—
21#577×C113—22no—
22#577×C113—22no—
23#577×C113—22no—
24#577×C113—22no—
25#576×C113—22no—
26#576×C113—22no—
27#575×C113—22no—
28#575×C113—22no—
29#575×C113C2211yescharacteristic
30#575×C113C2211yescharacteristic
31#575×C113C2211yescharacteristic
32#575×C113C2211yescharacteristic, complemented
33#575×C113C2211yescharacteristic, complemented
34C2×#137×C113—22no—
35C2×#137×C113C2211yescharacteristic
36C2×#137×C113C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C113—22no—
38C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
40C22×SD16×C113C2211yescharacteristic, complemented
41#568×C113C2211yescharacteristic
42#568×C113C2211yescharacteristic, complemented
43#536×C113C2211yescharacteristic, complemented
44#535×C113C2211yescharacteristic, complemented
45#456×C113—22no—
46#455×C113—22no—
47#454×C113—22no—
48#453×C113—22no—
49#452×C113—22no—
50#450×C113—22no—
51#449×C113—22no—
52#448×C113—22no—
53#421×C113C2211yescharacteristic
54#421×C113C2211yescharacteristic, complemented
55#421×C113C2211yescharacteristic, complemented
56#421×C113C2211yescharacteristic, complemented
57#419×C113C2211yescharacteristic, complemented
58#418×C113C2211yescharacteristic, complemented
59#416×C113C2211yescharacteristic
60#416×C113C2211yescharacteristic, complemented
61C2×#101×C113C2211yescharacteristic, complemented
62C2×#100×C113C2211yescharacteristic, complemented
63#410×C113C2211yescharacteristic, complemented
64#408×C113C2211yescharacteristic, complemented
65#408×C113C2211yescharacteristic, complemented
66#408×C113C2211yescharacteristic, complemented
67#344×C113C2211yescharacteristic, complemented
68#344×C113C2211yescharacteristic, complemented
69#341×C113C2211yescharacteristic, complemented
70#338×C113C2211yescharacteristic, complemented
712−1+4×C113—22no—
722−1+4×C113—21no—
732−1+4×C113—22no—
742−1+4×C113—21no—
752−1+4×C113—22no—
762−1+4×C113—41no—
772−1+4×C113D412yescomplemented
78H(5,𝔽2)×C113—22no—
79H(5,𝔽2)×C113—21no—
80H(5,𝔽2)×C113—22no—
81H(5,𝔽2)×C113—21no—
82H(5,𝔽2)×C113—22no—
83H(5,𝔽2)×C113—41no—
84H(5,𝔽2)×C113—41no—
85H(5,𝔽2)×C113D412yescomplemented
86C2×#41×C113—22no—
87C2×#41×C113—22no—
88C2×#41×C113—21no—
89C2×#41×C113—21no—
90C2×#41×C113—21no—
91C2×#41×C113—21no—
92C2×#41×C113—41no—
93C2×#41×C113—41no—
94C2×#41×C113C2311yescharacteristic
95C2×#41×C113C2311yescharacteristic
96C2×#41×C113C2311yescharacteristic
97C2×#41×C113C2311yescharacteristic
98C2×#41×C113C2311yescharacteristic
99C22×Q8×C113—21no—
100C22×Q8×C113—21no—
101C22×Q8×C113C2311yescharacteristic
102C22×D4×C113—21no—
103C22×D4×C113—21no—
104C22×D4×C113—41no—
105C22×D4×C113C2311yescharacteristic
106#137×C113—24no—
107#137×C113—24no—
108#137×C113—24no—
109#137×C113—24no—
110#137×C113—22no—
111#137×C113—22no—
112#137×C113—21no—
113#137×C113—22no—
114#137×C113—21no—
115#137×C113—21no—
116#137×C113—21no—
117#137×C113—21no—
118#137×C113—21no—
119#137×C113—21no—
120#137×C113—21no—
121#137×C113—22no—
122#137×C113D412yes—
123#137×C113D412yescomplemented
124AGL(1,ℤ/8)×C113—24no—
125AGL(1,ℤ/8)×C113—24no—
126AGL(1,ℤ/8)×C113—24no—
127AGL(1,ℤ/8)×C113—24no—
128AGL(1,ℤ/8)×C113—22no—
129AGL(1,ℤ/8)×C113—22no—
130AGL(1,ℤ/8)×C113—21no—
131AGL(1,ℤ/8)×C113—22no—
132AGL(1,ℤ/8)×C113—21no—
133AGL(1,ℤ/8)×C113—21no—
134AGL(1,ℤ/8)×C113—21no—
135AGL(1,ℤ/8)×C113—21no—
136AGL(1,ℤ/8)×C113—21no—
137AGL(1,ℤ/8)×C113—21no—
138AGL(1,ℤ/8)×C113—21no—
139AGL(1,ℤ/8)×C113—22no—
140AGL(1,ℤ/8)×C113D412yes—
141AGL(1,ℤ/8)×C113D412yescomplemented
142#135×C113—24no—
143#135×C113—24no—
144#135×C113—24no—
145#135×C113—24no—
146#135×C113—22no—
147#135×C113—22no—
148#135×C113—22no—
149#135×C113—22no—
150#135×C113—41no—
151C2×Q16×C113—24no—
152C2×Q16×C113—21no—
153C2×Q16×C113D412yescomplemented
154C2×SD16×C113—24no—
155C2×SD16×C113—24no—
156C2×SD16×C113—21no—
157C2×SD16×C113—21no—
158C2×SD16×C113—22no—
159C2×SD16×C113—22no—
160C2×SD16×C113—41no—
161C2×SD16×C113D412yes—
162C2×SD16×C113D412yescomplemented
163C2×D8×C113—24no—
164C2×D8×C113—21no—
165C2×D8×C113D412yes—
166#131×C113—22no—
167#131×C113—22no—
168#131×C113—22no—
169#131×C113—22no—
170C2×M16×C113—22no—
171C2×M16×C113—22no—
172C2×M16×C113C2311yescharacteristic
173C2×M16×C113C2311yescharacteristic
174C2×M16×C113C2311yescharacteristic
175C2×M16×C113C2311yescharacteristic
176C2×M16×C113C2311yescharacteristic
177C22×C8×C113C2311yescharacteristic
178C4⋊Q8×C113—21no—
179#127×C113—21no—
180#124×C113—21no—
181#124×C113—21no—
182#123×C113—41no—
183C22⋊Q8×C113—22no—
184#121×C113—22no—
185#120×C113—41no—
186#117×C113C2311yescharacteristic
187#117×C113C2311yescharacteristic
188#104×C113—22no—
189#104×C113—22no—
190#104×C113—22no—
191#104×C113—22no—
192#103×C113—21no—
193#103×C113—21no—
194#103×C113—22no—
195#102×C113—21no—
196#102×C113—21no—
197#102×C113—22no—
198#101×C113—22no—
199#100×C113—22no—
200#99×C113—41no—
201C22⋊C8×C113—22no—
202C22⋊C8×C113—22no—
203C22⋊C8×C113—41no—
204C24×C113—21no—
205C24×C113—41no—
206#41×C113—21no—
207#41×C113—21no—
208#41×C113—21no—
209#41×C113—21no—
210#41×C113—24no—
211#41×C113—24no—
212#41×C113—22no—
213#41×C113—22no—
214#41×C113—22no—
215#41×C113—22no—
216#41×C113—21no—
217#41×C113—21no—
218#41×C113—21no—
219#41×C113—21no—
220#41×C113—21no—
221#41×C113—21no—
222#41×C113—21no—
223#41×C113—21no—
224#41×C113—21no—
225#41×C113—21no—
226#41×C113—21no—
227#41×C113—21no—
228#41×C113—42no—
229#41×C113—42no—
230#41×C113—42no—
231#41×C113—42no—
232#41×C113—42no—
233#41×C113—44no—
234#41×C113—42no—
235#41×C113—42no—
236#41×C113—42no—
237#41×C113—41no—
238#41×C113—41no—
239#41×C113—44no—
240#41×C113—42no—
241#41×C113—42no—
242#41×C113C2×D412yes—
243#41×C113C2×D412yes—
244#41×C113C2×D412yes—
245#41×C113C2×D412yes—
246C2×Q8×C113—21no—
247C2×Q8×C113—24no—
248C2×Q8×C113—22no—
249C2×Q8×C113—22no—
250C2×Q8×C113—21no—
251C2×Q8×C113—21no—
252C2×Q8×C113—21no—
253C2×Q8×C113—21no—
254C2×Q8×C113—41no—
255C2×Q8×C113—42no—
256C2×Q8×C113—42no—
257C2×Q8×C113—41no—
258C2×Q8×C113—42no—
259C2×Q8×C113C2×D412yes—
260C2×Q8×C113C2×D411yescharacteristic
261C2×Q8×C113C2×D411yescharacteristic
262C2×Q8×C113C2×D411yescharacteristic
263C2×Q8×C113C2×D411yescharacteristic
264C2×Q8×C113C2×D411yescharacteristic
265C2×D4×C113—21no—
266C2×D4×C113—21no—
267C2×D4×C113—24no—
268C2×D4×C113—22no—
269C2×D4×C113—22no—
270C2×D4×C113—21no—
271C2×D4×C113—21no—
272C2×D4×C113—21no—
273C2×D4×C113—21no—
274C2×D4×C113—21no—
275C2×D4×C113—21no—
276C2×D4×C113—21no—
277C2×D4×C113—21no—
278C2×D4×C113—42no—
279C2×D4×C113—41no—
280C2×D4×C113—41no—
281C2×D4×C113—42no—
282C2×D4×C113—42no—
283C2×D4×C113—41no—
284C2×D4×C113—44no—
285C2×D4×C113—42no—
286C2×D4×C113—42no—
287C2×D4×C113—44no—
288C2×D4×C113—41no—
289C2×D4×C113—42no—
290C2×D4×C113—42no—
291C2×D4×C113C2×D412yes—
292C2×D4×C113C2×D411yescharacteristic
293C2×D4×C113C2×D411yescharacteristic
294C2×D4×C113C2×D411yescharacteristic
295C2×D4×C113C2×D411yescharacteristic
296C2×D4×C113C2×D411yescharacteristic
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—41no—
304C22×C4×C113—42no—
305C22×C4×C113—41no—
306C22×C4×C113—41no—
307C22×C4×C113C2411yescharacteristic
308Q16×C113—24no—
309Q16×C113—22no—
310Q16×C113—22no—
311Q16×C113—22no—
312Q16×C113—24no—
313Q16×C113—22no—
314Q16×C113—41no—
315SD16×C113—24no—
316SD16×C113—22no—
317SD16×C113—24no—
318SD16×C113—22no—
319SD16×C113—22no—
320SD16×C113—22no—
321SD16×C113—22no—
322SD16×C113—24no—
323SD16×C113—22no—
324SD16×C113—22no—
325SD16×C113—24no—
326SD16×C113—22no—
327SD16×C113—44no—
328SD16×C113—41no—
329SD16×C113—41no—
330D8×C113—24no—
331D8×C113—22no—
332D8×C113—22no—
333D8×C113—22no—
334D8×C113—24no—
335D8×C113—22no—
336D8×C113—41no—
337M16×C113—24no—
338M16×C113—24no—
339M16×C113—21no—
340M16×C113—21no—
341M16×C113—21no—
342M16×C113—21no—
343M16×C113—21no—
344M16×C113—21no—
345M16×C113—21no—
346M16×C113—21no—
347M16×C113C2×D412yes—
348M16×C113C2×D412yes—
349C2×C8×C113—24no—
350C2×C8×C113—24no—
351C2×C8×C113—21no—
352C2×C8×C113—21no—
353C2×C8×C113—21no—
354C2×C8×C113—21no—
355C2×C8×C113—21no—
356C2×C8×C113—21no—
357C2×C8×C113C2×D412yes—
358C2×C8×C113C2×D412yes—
359C4⋊C4×C113—21no—
360C4⋊C4×C113—21no—
361C4⋊C4×C113—42no—
362C22⋊C4×C113—21no—
363C22⋊C4×C113—21no—
364C22⋊C4×C113—42no—
365C22⋊C4×C113—42no—
366C42×C113—21no—
367C42×C113—21no—
368C23×C113—21no—
369C23×C113—21no—
370C23×C113—21no—
371C23×C113—21no—
372C23×C113—21no—
373C23×C113—22no—
374C23×C113—42no—
375C23×C113—44no—
376C23×C113—41no—
377C23×C113—41no—
378C23×C113—161no—
379C23×C113—162no—
380C23×C113H(5,𝔽2)11yescharacteristic
381Q8×C113—21no—
382Q8×C113—21no—
383Q8×C113—21no—
384Q8×C113—21no—
385Q8×C113—22no—
386Q8×C113—21no—
387Q8×C113—21no—
388Q8×C113—22no—
389Q8×C113—21no—
390Q8×C113—21no—
391Q8×C113—42no—
392Q8×C113—44no—
393Q8×C113—41no—
394Q8×C113—41no—
395Q8×C113#12012yes—
396Q8×C113#12012yes—
397D4×C113—22no—
398D4×C113—22no—
399D4×C113—22no—
400D4×C113—22no—
401D4×C113—21no—
402D4×C113—21no—
403D4×C113—22no—
404D4×C113—21no—
405D4×C113—21no—
406D4×C113—21no—
407D4×C113—21no—
408D4×C113—21no—
409D4×C113—21no—
410D4×C113—22no—
411D4×C113—42no—
412D4×C113—42no—
413D4×C113—44no—
414D4×C113—42no—
415D4×C113—44no—
416D4×C113—44no—
417D4×C113—41no—
418D4×C113—41no—
419D4×C113—41no—
420D4×C113—41no—
421D4×C113—41no—
422D4×C113—41no—
423D4×C113—41no—
424D4×C113—41no—
425D4×C113—162no—
426D4×C113#12012yes—
427D4×C113#12012yes—
428C2×C4×C113—21no—
429C2×C4×C113—21no—
430C2×C4×C113—22no—
431C2×C4×C113—22no—
432C2×C4×C113—22no—
433C2×C4×C113—22no—
434C2×C4×C113—21no—
435C2×C4×C113—21no—
436C2×C4×C113—22no—
437C2×C4×C113—21no—
438C2×C4×C113—42no—
439C2×C4×C113—42no—
440C2×C4×C113—42no—
441C2×C4×C113—44no—
442C2×C4×C113—44no—
443C2×C4×C113—44no—
444C2×C4×C113—41no—
445C2×C4×C113—41no—
446C2×C4×C113—41no—
447C2×C4×C113—41no—
448C2×C4×C113—41no—
449C2×C4×C113—41no—
450C2×C4×C113—41no—
451C2×C4×C113—41no—
452C2×C4×C113—41no—
453C2×C4×C113—41no—
454C2×C4×C113C22×D411yescharacteristic
455C2×C4×C113C22×D411yescharacteristic
456C2×C4×C113C22×D411yescharacteristic
457C2×C4×C113C22×D411yescharacteristic
458C2×C4×C113C22×D411yescharacteristic
459C2×C4×C113H(5,𝔽2)11yescharacteristic
460C8×C113—22no—
461C8×C113—22no—
462C8×C113—22no—
463C8×C113—22no—
464C8×C113—41no—
465C8×C113—41no—
466C22×C113—22no—
467C22×C113—22no—
468C22×C113—41no—
469C22×C113—42no—
470C22×C113—42no—
471C22×C113—41no—
472C22×C113—41no—
473C22×C113—41no—
474C22×C113—42no—
475C22×C113—81no—
476C22×C113—81no—
477C22×C113—82no—
478C22×C113—81no—
479C22×C113—82no—
480C22×C113—161no—
481C22×C113—162no—
482C22×C113—164no—
483C22×C113#53411yescharacteristic
484C22×C113D4211yescharacteristic
485C22×C113D4211yescharacteristic
486C4×C113—22no—
487C4×C113—22no—
488C4×C113—41no—
489C4×C113—41no—
490C4×C113—41no—
491C4×C113—42no—
492C4×C113—81no—
493C4×C113—81no—
494C4×C113C2×#12011yescharacteristic
495C4×C113C2×#12011yescharacteristic
496C4×C113D4211yescharacteristic
497C4×C113D4211yescharacteristic
498#23894C11311yesmaximal, characteristic, direct product factor, Sylow
499C2×C113—21no—
500C2×C113—21no—
501C2×C113—21no—
502C2×C113—42no—
503C2×C113—42no—
504C2×C113—81no—
505C2×C113—81no—
506C2×C113—82no—
507C2×C113—81no—
508C2×C113#240311yescharacteristic
509#3586C2×C11311yescharacteristic, complemented
510#3585C2×C11311yescharacteristic, complemented
511#3020C2×C11311yescharacteristic, complemented
512#3019C2×C11311yescharacteristic, complemented
513#3010C2×C11311yescharacteristic, complemented
514#3009C2×C11311yescharacteristic, complemented
515#2019C2×C11311yescharacteristic, complemented
516#2017C2×C11311yescharacteristic, complemented
517#2009C2×C11311yescharacteristic, complemented
518#2008C2×C11311yescharacteristic, complemented
519#1903C2×C11311yescharacteristic, complemented
520#1902C2×C11311yescharacteristic, complemented
521#1881C2×C11311yescharacteristic, complemented
522#1881C2×C11311yescharacteristic, complemented
523#1794C2×C11311yescharacteristic, complemented
524C113#2389411yescharacteristic, direct product factor, Sylow
525#585C22×C11311yescharacteristic
526C2×2−1+4C22×C11311yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C11311yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C11311yescharacteristic
539#575C22×C11311yescharacteristic
540#575C22×C11311yescharacteristic
541#575C22×C11311yescharacteristic, complemented
542#575C22×C11311yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C11311yescharacteristic
545C2×#137C22×C11311yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
548C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
549C22×SD16C22×C11311yescharacteristic, complemented
550#568C22×C11311yescharacteristic
551#568C22×C11311yescharacteristic, complemented
552#536C22×C11311yescharacteristic, complemented
553#535C22×C11311yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C11311yescharacteristic
563#421C22×C11311yescharacteristic, complemented
564#421C22×C11311yescharacteristic, complemented
565#421C22×C11311yescharacteristic, complemented
566#419C22×C11311yescharacteristic, complemented
567#418C22×C11311yescharacteristic, complemented
568#416C22×C11311yescharacteristic
569#416C22×C11311yescharacteristic, complemented
570C2×#101C22×C11311yescharacteristic, complemented
571C2×#100C22×C11311yescharacteristic, complemented
572#410C22×C11311yescharacteristic, complemented
573#408C22×C11311yescharacteristic, complemented
574#408C22×C11311yescharacteristic, complemented
575#408C22×C11311yescharacteristic, complemented
576#344C22×C11311yescharacteristic, complemented
577#344C22×C11311yescharacteristic, complemented
578#341C22×C11311yescharacteristic, complemented
579#338C22×C11311yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C11312yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C11312yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C11311yescharacteristic
604C2×#41C23×C11311yescharacteristic
605C2×#41C23×C11311yescharacteristic
606C2×#41C23×C11311yescharacteristic
607C2×#41C23×C11311yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C11311yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C11311yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C11312yes—
632#137D4×C11312yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C11312yes—
650AGL(1,ℤ/8)D4×C11312yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C11312yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C11312yes—
671C2×SD16D4×C11312yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C11312yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C11311yescharacteristic
682C2×M16C23×C11311yescharacteristic
683C2×M16C23×C11311yescharacteristic
684C2×M16C23×C11311yescharacteristic
685C2×M16C23×C11311yescharacteristic
686C22×C8C23×C11311yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C11311yescharacteristic
696#117C23×C11311yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C11312yes—
752#41C2×D4×C11312yes—
753#41C2×D4×C11312yes—
754#41C2×D4×C11312yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C11312yes—
769C2×Q8C2×D4×C11311yescharacteristic
770C2×Q8C2×D4×C11311yescharacteristic
771C2×Q8C2×D4×C11311yescharacteristic
772C2×Q8C2×D4×C11311yescharacteristic
773C2×Q8C2×D4×C11311yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C11312yes—
801C2×D4C2×D4×C11311yescharacteristic
802C2×D4C2×D4×C11311yescharacteristic
803C2×D4C2×D4×C11311yescharacteristic
804C2×D4C2×D4×C11311yescharacteristic
805C2×D4C2×D4×C11311yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C11311yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C11312yes—
857M16C2×D4×C11312yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C11312yes—
867C2×C8C2×D4×C11312yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C11311yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C11312yes—
905Q8#120×C11312yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C11312yes—
936D4#120×C11312yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C11311yescharacteristic
964C2×C4C22×D4×C11311yescharacteristic
965C2×C4C22×D4×C11311yescharacteristic
966C2×C4C22×D4×C11311yescharacteristic
967C2×C4C22×D4×C11311yescharacteristic
968C2×C4H(5,𝔽2)×C11311yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C11311yescharacteristic
993C22D42×C11311yescharacteristic
994C22D42×C11311yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C11311yescharacteristic
1004C4C2×#120×C11311yescharacteristic
1005C4D42×C11311yescharacteristic
1006C4D42×C11311yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C113×#240311yescharacteristic
subgroupG/H
center, socleC2×C113#2403
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3586C2semidirect
2. C113×#3585C2semidirect
3. C113×#3020C2semidirect
4. C113×#3019C2semidirect
5. C113×#3010C2semidirect
6. C113×#3009C2semidirect
7. C113×#2019C2semidirect
8. C113×#2017C2semidirect
9. C113×#2009C2semidirect
10. C113×#2008C2semidirect
11. C113×#1903C2semidirect
12. C113×#1902C2semidirect
13. C113×#1881C2semidirect
14. C113×#1881C2semidirect
15. C113×#1794C2semidirect
17. C2×2−1+4×C113C22semidirect
32. #575×C113C22semidirect
33. #575×C113C22semidirect
36. C2×#137×C113C22semidirect
40. C22×SD16×C113C22semidirect
42. #568×C113C22semidirect
43. #536×C113C22semidirect
44. #535×C113C22semidirect
54. #421×C113C22semidirect
55. #421×C113C22semidirect
56. #421×C113C22semidirect
57. #419×C113C22semidirect
58. #418×C113C22semidirect
60. #416×C113C22semidirect
61. C2×#101×C113C22semidirect
62. C2×#100×C113C22semidirect
63. #410×C113C22semidirect
64. #408×C113C22semidirect
65. #408×C113C22semidirect
66. #408×C113C22semidirect
67. #344×C113C22semidirect
68. #344×C113C22semidirect
69. #341×C113C22semidirect
70. #338×C113C22semidirect
77. 2−1+4×C113D4semidirect
85. H(5,𝔽2)×C113D4semidirect
123. #137×C113D4semidirect
141. AGL(1,ℤ/8)×C113D4semidirect
153. C2×Q16×C113D4semidirect
162. C2×SD16×C113D4semidirect
498. #23894C113direct (N × H)
509. #3586C2×C113semidirect
510. #3585C2×C113semidirect
511. #3020C2×C113semidirect
512. #3019C2×C113semidirect
513. #3010C2×C113semidirect
514. #3009C2×C113semidirect
515. #2019C2×C113semidirect
516. #2017C2×C113semidirect
517. #2009C2×C113semidirect
518. #2008C2×C113semidirect
519. #1903C2×C113semidirect
520. #1902C2×C113semidirect
521. #1881C2×C113semidirect
522. #1881C2×C113semidirect
523. #1794C2×C113semidirect
524. C113#23894direct (N × H)
526. C2×2−1+4C22×C113semidirect
541. #575C22×C113semidirect
542. #575C22×C113semidirect
545. C2×#137C22×C113semidirect
549. C22×SD16C22×C113semidirect
551. #568C22×C113semidirect
552. #536C22×C113semidirect
553. #535C22×C113semidirect
563. #421C22×C113semidirect
564. #421C22×C113semidirect
565. #421C22×C113semidirect
566. #419C22×C113semidirect
567. #418C22×C113semidirect
569. #416C22×C113semidirect
570. C2×#101C22×C113semidirect
571. C2×#100C22×C113semidirect
572. #410C22×C113semidirect
573. #408C22×C113semidirect
574. #408C22×C113semidirect
575. #408C22×C113semidirect
576. #344C22×C113semidirect
577. #344C22×C113semidirect
578. #341C22×C113semidirect
579. #338C22×C113semidirect
586. 2−1+4D4×C113semidirect
594. H(5,𝔽2)D4×C113semidirect
632. #137D4×C113semidirect
650. AGL(1,ℤ/8)D4×C113semidirect
662. C2×Q16D4×C113semidirect
671. C2×SD16D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35862
C113×#35852
C113×#30202
C113×#30192
C113×#30102
C113×#30092
C113×#20192
C113×#20172
C113×#20092
C113×#20082
C113×#19032
C113×#19022
C113×#18812
C113×#17942
#23894113