Finite Group Databasebeta

← C113×#24467 #43292487

Subgroups — C113×#24467 #43292487

Order 28928.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3488C211yesmaximal, characteristic
2C113×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C113C211yesmaximal, characteristic, complemented
4C113×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C113C211yesmaximal, characteristic, complemented
6C113×#2850C211yesmaximal, characteristic, complemented
7C113×#2040C211yesmaximal, characteristic, complemented
8C113×#2037C211yesmaximal, characteristic, complemented
9C113×#2007C211yesmaximal, characteristic, complemented
10C113×#2004C211yesmaximal, characteristic, complemented
11C113×#1900C211yesmaximal, characteristic, complemented
12C113×#1896C211yesmaximal, characteristic, complemented
13C113×#1882C211yesmaximal, characteristic, complemented
14C113×#1860C211yesmaximal, characteristic, complemented
15C113×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C2×#137×C113C2211yescharacteristic
19C2×#137×C113C2211yescharacteristic, complemented
20C2×#137×C113C2211yescharacteristic, complemented
21C22×M16×C113C2211yescharacteristic, complemented
22#550×C113—21no—
23#548×C113—21no—
24#546×C113—21no—
25#546×C113—22no—
26D42×C113—22no—
27D42×C113—21no—
28#537×C113—21no—
29#537×C113C2211yescharacteristic
30#535×C113—21no—
31#535×C113C2211yescharacteristic
32C2×#124×C113C2211yescharacteristic, complemented
33#525×C113—21no—
34#525×C113C2211yescharacteristic
35C2×C22⋊Q8×C113C2211yescharacteristic, complemented
36C2×#121×C113—21no—
37C2×#121×C113C2211yescharacteristic
38#520×C113C2211yescharacteristic
39C22×C42×C113C2211yescharacteristic, complemented
40#470×C113—21no—
41#468×C113—21no—
42#467×C113—21no—
43#465×C113—21no—
44#455×C113—24no—
45#452×C113—21no—
46#452×C113—21no—
47#451×C113—21no—
48#450×C113—21no—
49#428×C113C2211yescharacteristic, complemented
50C2×#104×C113—24no—
51C2×#104×C113C2211yescharacteristic
52C2×#104×C113C2211yescharacteristic
53C2×#104×C113C2211yescharacteristic, complemented
54C2×#104×C113C2211yescharacteristic, complemented
55C2×#104×C113C2211yescharacteristic, complemented
56C2×#104×C113C2211yescharacteristic, complemented
57#419×C113C2211yescharacteristic, complemented
58#417×C113C2211yescharacteristic
59#417×C113C2211yescharacteristic, complemented
60#417×C113C2211yescharacteristic, complemented
61C2×#100×C113C2211yescharacteristic, complemented
62C2×#100×C113C2211yescharacteristic, complemented
63#407×C113C2211yescharacteristic, complemented
64#391×C113C2211yescharacteristic, complemented
65#390×C113C2211yescharacteristic, complemented
66#388×C113—22no—
67#386×C113—22no—
68#382×C113C2211yescharacteristic, complemented
69#343×C113C2211yescharacteristic, complemented
70#343×C113C2211yescharacteristic, complemented
71#339×C113C2211yescharacteristic, complemented
72#339×C113C2211yescharacteristic, complemented
73H(5,𝔽2)×C113—22no—
74H(5,𝔽2)×C113—22no—
75H(5,𝔽2)×C113—41no—
76H(5,𝔽2)×C113—41no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—22no—
82C2×#41×C113—22no—
83C2×#41×C113—41no—
84C2×#41×C113—41no—
85C2×#41×C113D411yescharacteristic
86C2×#41×C113D411yescharacteristic
87C2×#41×C113C2311yescharacteristic
88C2×#41×C113C2311yescharacteristic
89C2×#41×C113C2311yescharacteristic
90C22×Q8×C113D411yescharacteristic
91C22×Q8×C113C2311yescharacteristic
92C22×D4×C113—21no—
93C22×D4×C113—22no—
94C22×D4×C113—22no—
95C22×D4×C113—21no—
96C22×D4×C113—21no—
97C22×D4×C113D411yescharacteristic
98C22×D4×C113D412yes—
99C22×D4×C113C2311yescharacteristic
100C23×C4×C113—21no—
101C23×C4×C113—21no—
102C23×C4×C113C2311yescharacteristic
103#137×C113—22no—
104#137×C113—22no—
105#137×C113—22no—
106#137×C113—41no—
107#137×C113—41no—
108#137×C113—41no—
109C2×Q16×C113—21no—
110C2×Q16×C113—21no—
111C2×Q16×C113—21no—
112C2×SD16×C113—21no—
113C2×SD16×C113—21no—
114C2×SD16×C113—21no—
115C2×M16×C113—21no—
116C2×M16×C113—22no—
117C2×M16×C113—41no—
118C2×M16×C113C2311yescharacteristic
119C2×M16×C113C2311yescharacteristic
120C2×M16×C113C2311yescharacteristic
121C2×M16×C113C2311yescharacteristic
122C22×C8×C113—21no—
123#127×C113—22no—
124#127×C113—21no—
125#124×C113—22no—
126#124×C113—21no—
127#124×C113—22no—
128#124×C113—41no—
129#123×C113—22no—
130#123×C113—21no—
131C22⋊Q8×C113—22no—
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—22no—
141#121×C113—22no—
142#121×C113—22no—
143#121×C113—22no—
144#121×C113—22no—
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—22no—
152#121×C113—21no—
153#121×C113—21no—
154#121×C113D411yescharacteristic
155#121×C113D411yescharacteristic
156#120×C113—22no—
157#120×C113—22no—
158#120×C113—22no—
159#120×C113—21no—
160#120×C113—22no—
161C4×Q8×C113—21no—
162C4×D4×C113—22no—
163C4×D4×C113—22no—
164C4×D4×C113—21no—
165C4×D4×C113—22no—
166C4×D4×C113—21no—
167C4×D4×C113—21no—
168#117×C113—21no—
169#117×C113C2311yescharacteristic
170C2×C4⋊C4×C113—21no—
171C2×C4⋊C4×C113—21no—
172C2×C4⋊C4×C113C2311yescharacteristic
173C2×C4⋊C4×C113C2311yescharacteristic
174C2×C22⋊C4×C113—22no—
175C2×C22⋊C4×C113—21no—
176C2×C22⋊C4×C113—22no—
177C2×C22⋊C4×C113—22no—
178C2×C22⋊C4×C113D412yes—
179C2×C42×C113—22no—
180C2×C42×C113—21no—
181C2×C42×C113—41no—
182C2×C42×C113C2311yescharacteristic
183C2×C42×C113C2311yescharacteristic
184#107×C113—21no—
185#106×C113—21no—
186#104×C113—22no—
187#104×C113—22no—
188#104×C113—22no—
189#104×C113—22no—
190#104×C113—41no—
191#104×C113D414yescomplemented
192#103×C113—21no—
193#103×C113—21no—
194#103×C113—21no—
195#103×C113—21no—
196#103×C113—21no—
197#102×C113—21no—
198#102×C113—21no—
199#102×C113—21no—
200#100×C113—22no—
201#100×C113—41no—
202C22⋊C8×C113—21no—
203C22⋊C8×C113—21no—
204#95×C113—22no—
205#95×C113—22no—
206C24×C113—22no—
207C24×C113—21no—
208C24×C113C2×D411yescharacteristic
209C24×C113C2×D412yes—
210#41×C113—21no—
211#41×C113—21no—
212#41×C113—22no—
213#41×C113—22no—
214#41×C113—21no—
215#41×C113—21no—
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—42no—
223#41×C113—42no—
224#41×C113—41no—
225#41×C113—41no—
226#41×C113—42no—
227#41×C113—42no—
228#41×C113—42no—
229#41×C113—42no—
230#41×C113—42no—
231#41×C113—42no—
232#41×C113C2×D412yes—
233#41×C113#4112yes—
234C2×Q8×C113—21no—
235C2×Q8×C113—22no—
236C2×Q8×C113—21no—
237C2×Q8×C113—21no—
238C2×Q8×C113—21no—
239C2×Q8×C113—21no—
240C2×Q8×C113—21no—
241C2×Q8×C113—21no—
242C2×Q8×C113—41no—
243C2×Q8×C113C2×D411yescharacteristic
244C2×Q8×C113C2×D411yescharacteristic
245C2×Q8×C113C2×D411yescharacteristic
246C2×D4×C113—21no—
247C2×D4×C113—22no—
248C2×D4×C113—22no—
249C2×D4×C113—22no—
250C2×D4×C113—22no—
251C2×D4×C113—21no—
252C2×D4×C113—21no—
253C2×D4×C113—21no—
254C2×D4×C113—21no—
255C2×D4×C113—21no—
256C2×D4×C113—22no—
257C2×D4×C113—22no—
258C2×D4×C113—22no—
259C2×D4×C113—21no—
260C2×D4×C113—22no—
261C2×D4×C113—21no—
262C2×D4×C113—21no—
263C2×D4×C113—21no—
264C2×D4×C113—21no—
265C2×D4×C113—21no—
266C2×D4×C113—21no—
267C2×D4×C113—21no—
268C2×D4×C113—41no—
269C2×D4×C113—42no—
270C2×D4×C113—42no—
271C2×D4×C113—42no—
272C2×D4×C113—42no—
273C2×D4×C113—44no—
274C2×D4×C113—44no—
275C2×D4×C113—42no—
276C2×D4×C113—42no—
277C2×D4×C113—44no—
278C2×D4×C113—84no—
279C2×D4×C113C2×D411yescharacteristic
280C2×D4×C113C2×D411yescharacteristic
281C2×D4×C113C2×D411yescharacteristic
282C22×C4×C113—21no—
283C22×C4×C113—21no—
284C22×C4×C113—21no—
285C22×C4×C113—21no—
286C22×C4×C113—21no—
287C22×C4×C113—22no—
288C22×C4×C113—21no—
289C22×C4×C113—21no—
290C22×C4×C113—21no—
291C22×C4×C113—22no—
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—42no—
299C22×C4×C113—42no—
300C22×C4×C113—42no—
301C22×C4×C113—42no—
302C22×C4×C113—42no—
303C22×C4×C113C2×D411yescharacteristic
304C22×C4×C113C2×D411yescharacteristic
305C22×C4×C113C2×D411yescharacteristic
306C22×C4×C113C2×D411yescharacteristic
307C22×C4×C113C2×D411yescharacteristic
308C22×C4×C113C2×D412yes—
309C22×C4×C113C2411yescharacteristic
310Q16×C113—42no—
311Q16×C113—42no—
312Q16×C113—42no—
313SD16×C113—42no—
314SD16×C113—42no—
315SD16×C113—42no—
316M16×C113—21no—
317M16×C113—21no—
318M16×C113—21no—
319M16×C113—21no—
320M16×C113—21no—
321M16×C113—21no—
322M16×C113—21no—
323M16×C113—42no—
324M16×C113C2×D412yescomplemented
325C2×C8×C113—21no—
326C2×C8×C113—21no—
327C2×C8×C113—21no—
328C2×C8×C113—21no—
329C2×C8×C113—42no—
330C4⋊C4×C113—22no—
331C4⋊C4×C113—22no—
332C4⋊C4×C113—21no—
333C4⋊C4×C113—21no—
334C4⋊C4×C113—21no—
335C4⋊C4×C113—21no—
336C4⋊C4×C113—21no—
337C4⋊C4×C113—21no—
338C4⋊C4×C113—41no—
339C4⋊C4×C113—41no—
340C4⋊C4×C113C2×D411yescharacteristic
341C4⋊C4×C113C2×D411yescharacteristic
342C22⋊C4×C113—22no—
343C22⋊C4×C113—22no—
344C22⋊C4×C113—22no—
345C22⋊C4×C113—22no—
346C22⋊C4×C113—22no—
347C22⋊C4×C113—21no—
348C22⋊C4×C113—21no—
349C22⋊C4×C113—21no—
350C22⋊C4×C113—21no—
351C22⋊C4×C113—22no—
352C22⋊C4×C113—22no—
353C22⋊C4×C113—21no—
354C22⋊C4×C113—44no—
355C22⋊C4×C113—44no—
356C22⋊C4×C113—41no—
357C22⋊C4×C113—41no—
358C42×C113—22no—
359C42×C113—21no—
360C42×C113—21no—
361C42×C113—21no—
362C42×C113—21no—
363C42×C113—42no—
364C42×C113C2×D412yescomplemented
365C23×C113—21no—
366C23×C113—21no—
367C23×C113—21no—
368C23×C113—22no—
369C23×C113—22no—
370C23×C113—21no—
371C23×C113—21no—
372C23×C113—22no—
373C23×C113—22no—
374C23×C113—41no—
375C23×C113—42no—
376C23×C113—44no—
377C23×C113—42no—
378C23×C113—42no—
379C23×C113—42no—
380C23×C113—81no—
381C23×C113—82no—
382C23×C113—82no—
383C23×C113#12011yescharacteristic
384C23×C113#12011yescharacteristic
385C23×C113C22×D411yescharacteristic
386Q8×C113—21no—
387Q8×C113—21no—
388Q8×C113—21no—
389Q8×C113—21no—
390Q8×C113—21no—
391Q8×C113—42no—
392Q8×C113—41no—
393Q8×C113—41no—
394Q8×C113—41no—
395Q8×C113—41no—
396Q8×C113#12112yes—
397D4×C113—22no—
398D4×C113—22no—
399D4×C113—21no—
400D4×C113—21no—
401D4×C113—21no—
402D4×C113—21no—
403D4×C113—21no—
404D4×C113—42no—
405D4×C113—42no—
406D4×C113—44no—
407D4×C113—42no—
408D4×C113—44no—
409D4×C113—41no—
410D4×C113—41no—
411D4×C113—41no—
412D4×C113—41no—
413D4×C113—44no—
414D4×C113—42no—
415D4×C113—41no—
416D4×C113—41no—
417D4×C113—41no—
418D4×C113—41no—
419D4×C113—81no—
420D4×C113—82no—
421D4×C113—82no—
422D4×C113—82no—
423D4×C113—82no—
424D4×C113#12112yes—
425C2×C4×C113—21no—
426C2×C4×C113—21no—
427C2×C4×C113—21no—
428C2×C4×C113—21no—
429C2×C4×C113—21no—
430C2×C4×C113—21no—
431C2×C4×C113—21no—
432C2×C4×C113—21no—
433C2×C4×C113—21no—
434C2×C4×C113—22no—
435C2×C4×C113—21no—
436C2×C4×C113—21no—
437C2×C4×C113—22no—
438C2×C4×C113—22no—
439C2×C4×C113—21no—
440C2×C4×C113—22no—
441C2×C4×C113—21no—
442C2×C4×C113—21no—
443C2×C4×C113—21no—
444C2×C4×C113—22no—
445C2×C4×C113—42no—
446C2×C4×C113—42no—
447C2×C4×C113—42no—
448C2×C4×C113—44no—
449C2×C4×C113—41no—
450C2×C4×C113—41no—
451C2×C4×C113—41no—
452C2×C4×C113—48no—
453C2×C4×C113—41no—
454C2×C4×C113—41no—
455C2×C4×C113—41no—
456C2×C4×C113—41no—
457C2×C4×C113—41no—
458C2×C4×C113—42no—
459C2×C4×C113—42no—
460C2×C4×C113—41no—
461C2×C4×C113—41no—
462C2×C4×C113—41no—
463C2×C4×C113—41no—
464C2×C4×C113—82no—
465C2×C4×C113#12011yescharacteristic
466C2×C4×C113#12011yescharacteristic
467C2×C4×C113C22×D411yescharacteristic
468C2×C4×C113C22×D411yescharacteristic
469C2×C4×C113C22×D411yescharacteristic
470C2×C4×C113C2×#4111yescharacteristic
471C2×C4×C113H(5,𝔽2)11yescharacteristic
472C2×C4×C113H(5,𝔽2)11yescharacteristic
473C8×C113—22no—
474C8×C113—41no—
475C8×C113—41no—
476C8×C113—41no—
477C22×C113—21no—
478C22×C113—21no—
479C22×C113—21no—
480C22×C113—21no—
481C22×C113—21no—
482C22×C113—22no—
483C22×C113—21no—
484C22×C113—21no—
485C22×C113—42no—
486C22×C113—42no—
487C22×C113—41no—
488C22×C113—41no—
489C22×C113—41no—
490C22×C113—41no—
491C22×C113—42no—
492C22×C113—42no—
493C22×C113—41no—
494C22×C113—41no—
495C22×C113—41no—
496C22×C113—42no—
497C22×C113—41no—
498C22×C113—84no—
499C22×C113—82no—
500C22×C113—82no—
501C22×C113—164no—
502C22×C113#45512yescomplemented
503C22×C113C2×#12011yescharacteristic
504C22×C113D4211yescharacteristic
505C22×C113#54611yescharacteristic
506C4×C113—21no—
507C4×C113—21no—
508C4×C113—22no—
509C4×C113—42no—
510C4×C113—42no—
511C4×C113—41no—
512C4×C113—41no—
513C4×C113—42no—
514C4×C113—41no—
515C4×C113—41no—
516C4×C113—81no—
517C4×C113—81no—
518C4×C113C2×#12111yescharacteristic
519C4×C113#53411yescharacteristic
520C4×C113D4211yescharacteristic
521C4×C113#54611yescharacteristic
522#24467C11311yesmaximal, characteristic, direct product factor, Sylow
523C2×C113—21no—
524C2×C113—21no—
525C2×C113—22no—
526C2×C113—41no—
527C2×C113—42no—
528C2×C113—81no—
529C2×C113—82no—
530C2×C113—81no—
531C2×C113#241011yescharacteristic
532C2×C113C2×#45511yescharacteristic
533C2×C113#301811yescharacteristic
534#3488C2×C11311yescharacteristic
535#3056C2×C11311yescharacteristic, complemented
536C2×#455C2×C11311yescharacteristic, complemented
537#3007C2×C11311yescharacteristic, complemented
538C22×#104C2×C11311yescharacteristic, complemented
539#2850C2×C11311yescharacteristic, complemented
540#2040C2×C11311yescharacteristic, complemented
541#2037C2×C11311yescharacteristic, complemented
542#2007C2×C11311yescharacteristic, complemented
543#2004C2×C11311yescharacteristic, complemented
544#1900C2×C11311yescharacteristic, complemented
545#1896C2×C11311yescharacteristic, complemented
546#1882C2×C11311yescharacteristic, complemented
547#1860C2×C11311yescharacteristic, complemented
548#1792C2×C11311yescharacteristic, complemented
549C113#2446711yescharacteristic, direct product factor, Sylow
550C2×H(5,𝔽2)C22×C11311yescharacteristic
551C22×#41C22×C11311yescharacteristic
552C2×#137C22×C11311yescharacteristic
553C2×#137C22×C11311yescharacteristic, complemented
554C2×#137C22×C11311yescharacteristic, complemented
555C22×M16C22×C11311yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C11311yescharacteristic
564#535—21no—
565#535C22×C11311yescharacteristic
566C2×#124C22×C11311yescharacteristic, complemented
567#525—21no—
568#525C22×C11311yescharacteristic
569C2×C22⋊Q8C22×C11311yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C11311yescharacteristic
572#520C22×C11311yescharacteristic
573C22×C42C22×C11311yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C11311yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C11311yescharacteristic
586C2×#104C22×C11311yescharacteristic
587C2×#104C22×C11311yescharacteristic, complemented
588C2×#104C22×C11311yescharacteristic, complemented
589C2×#104C22×C11311yescharacteristic, complemented
590C2×#104C22×C11311yescharacteristic, complemented
591#419C22×C11311yescharacteristic, complemented
592#417C22×C11311yescharacteristic
593#417C22×C11311yescharacteristic, complemented
594#417C22×C11311yescharacteristic, complemented
595C2×#100C22×C11311yescharacteristic, complemented
596C2×#100C22×C11311yescharacteristic, complemented
597#407C22×C11311yescharacteristic, complemented
598#391C22×C11311yescharacteristic, complemented
599#390C22×C11311yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C11311yescharacteristic, complemented
603#343C22×C11311yescharacteristic, complemented
604#343C22×C11311yescharacteristic, complemented
605#339C22×C11311yescharacteristic, complemented
606#339C22×C11311yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C11311yescharacteristic
620C2×#41D4×C11311yescharacteristic
621C2×#41C23×C11311yescharacteristic
622C2×#41C23×C11311yescharacteristic
623C2×#41C23×C11311yescharacteristic
624C22×Q8D4×C11311yescharacteristic
625C22×Q8C23×C11311yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C11311yescharacteristic
632C22×D4D4×C11312yes—
633C22×D4C23×C11311yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C11311yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C11311yescharacteristic
653C2×M16C23×C11311yescharacteristic
654C2×M16C23×C11311yescharacteristic
655C2×M16C23×C11311yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C11311yescharacteristic
673C22⋊Q8D4×C11311yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C11311yescharacteristic
689#121D4×C11311yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C11311yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C11311yescharacteristic
707C2×C4⋊C4C23×C11311yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C11312yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C11311yescharacteristic
717C2×C42C23×C11311yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C11314yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C11311yescharacteristic
743C24C2×D4×C11312yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C11312yes—
767#41#41×C11312yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C11311yescharacteristic
778C2×Q8C2×D4×C11311yescharacteristic
779C2×Q8C2×D4×C11311yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C11311yescharacteristic
814C2×D4C2×D4×C11311yescharacteristic
815C2×D4C2×D4×C11311yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C11311yescharacteristic
838C22×C4C2×D4×C11311yescharacteristic
839C22×C4C2×D4×C11311yescharacteristic
840C22×C4C2×D4×C11311yescharacteristic
841C22×C4C2×D4×C11311yescharacteristic
842C22×C4C2×D4×C11312yes—
843C22×C4C24×C11311yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C11312yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C11311yescharacteristic
875C4⋊C4C2×D4×C11311yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C11312yescomplemented
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C11311yescharacteristic
918C23#120×C11311yescharacteristic
919C23C22×D4×C11311yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C11312yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C11312yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C11311yescharacteristic
1000C2×C4#120×C11311yescharacteristic
1001C2×C4C22×D4×C11311yescharacteristic
1002C2×C4C22×D4×C11311yescharacteristic
1003C2×C4C22×D4×C11311yescharacteristic
1004C2×C4C2×#41×C11311yescharacteristic
1005C2×C4H(5,𝔽2)×C11311yescharacteristic
1006C2×C4H(5,𝔽2)×C11311yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C11312yescomplemented
1037C22C2×#120×C11311yescharacteristic
1038C22D42×C11311yescharacteristic
1039C22#546×C11311yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C11311yescharacteristic
1053C4#534×C11311yescharacteristic
1054C4D42×C11311yescharacteristic
1055C4#546×C11311yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C113×#241011yescharacteristic
1065C2C2×#455×C11311yescharacteristic
1066C2C113×#301811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3488C2
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
2. C113×#3056C2semidirect
3. C2×#455×C113C2semidirect
4. C113×#3007C2semidirect
5. C22×#104×C113C2semidirect
6. C113×#2850C2semidirect
7. C113×#2040C2semidirect
8. C113×#2037C2semidirect
9. C113×#2007C2semidirect
10. C113×#2004C2semidirect
11. C113×#1900C2semidirect
12. C113×#1896C2semidirect
13. C113×#1882C2semidirect
14. C113×#1860C2semidirect
15. C113×#1792C2semidirect
19. C2×#137×C113C22semidirect
20. C2×#137×C113C22semidirect
21. C22×M16×C113C22semidirect
32. C2×#124×C113C22semidirect
35. C2×C22⋊Q8×C113C22semidirect
39. C22×C42×C113C22semidirect
49. #428×C113C22semidirect
53. C2×#104×C113C22semidirect
54. C2×#104×C113C22semidirect
55. C2×#104×C113C22semidirect
56. C2×#104×C113C22semidirect
57. #419×C113C22semidirect
59. #417×C113C22semidirect
60. #417×C113C22semidirect
61. C2×#100×C113C22semidirect
62. C2×#100×C113C22semidirect
63. #407×C113C22semidirect
64. #391×C113C22semidirect
65. #390×C113C22semidirect
68. #382×C113C22semidirect
69. #343×C113C22semidirect
70. #343×C113C22semidirect
71. #339×C113C22semidirect
72. #339×C113C22semidirect
191. #104×C113D4semidirect
324. M16×C113C2×D4semidirect
364. C42×C113C2×D4semidirect
502. C22×C113#455semidirect
522. #24467C113direct (N × H)
535. #3056C2×C113semidirect
536. C2×#455C2×C113semidirect
537. #3007C2×C113semidirect
538. C22×#104C2×C113semidirect
539. #2850C2×C113semidirect
540. #2040C2×C113semidirect
541. #2037C2×C113semidirect
542. #2007C2×C113semidirect
543. #2004C2×C113semidirect
544. #1900C2×C113semidirect
545. #1896C2×C113semidirect
546. #1882C2×C113semidirect
547. #1860C2×C113semidirect
548. #1792C2×C113semidirect
549. C113#24467direct (N × H)
553. C2×#137C22×C113semidirect
554. C2×#137C22×C113semidirect
555. C22×M16C22×C113semidirect
566. C2×#124C22×C113semidirect
569. C2×C22⋊Q8C22×C113semidirect
573. C22×C42C22×C113semidirect
583. #428C22×C113semidirect
587. C2×#104C22×C113semidirect
588. C2×#104C22×C113semidirect
589. C2×#104C22×C113semidirect
590. C2×#104C22×C113semidirect
591. #419C22×C113semidirect
593. #417C22×C113semidirect
594. #417C22×C113semidirect
595. C2×#100C22×C113semidirect
596. C2×#100C22×C113semidirect
597. #407C22×C113semidirect
598. #391C22×C113semidirect
599. #390C22×C113semidirect
602. #382C22×C113semidirect
603. #343C22×C113semidirect
604. #343C22×C113semidirect
605. #339C22×C113semidirect
606. #339C22×C113semidirect
725. #104D4×C113semidirect
858. M16C2×D4×C113semidirect
898. C42C2×D4×C113semidirect
1036. C22#455×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34882
C113×#30562
C2×#455×C1132
C113×#30072
C22×#104×C1132
C113×#28502
C113×#20402
C113×#20372
C113×#20072
C113×#20042
C113×#19002
C113×#18962
C113×#18822
C113×#18602
C113×#17922
#24467113