Finite Group Databasebeta

← C113×#24471 #43292491

Subgroups — C113×#24471 #43292491

Order 28928.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×#421×C113C211yesmaximal, characteristic, complemented
6C113×#2620C211yesmaximal, characteristic, complemented
7C113×#2039C211yesmaximal, characteristic, complemented
8C113×#2037C211yesmaximal, characteristic, complemented
9C113×#2007C211yesmaximal, characteristic, complemented
10C113×#2004C211yesmaximal, characteristic, complemented
11C113×#1900C211yesmaximal, characteristic, complemented
12C113×#1897C211yesmaximal, characteristic, complemented
13C113×#1882C211yesmaximal, characteristic, complemented
14C113×#1859C211yesmaximal, 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
39C2×#117×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
50#421×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#396×C113—22no—
65#394×C113—22no—
66#391×C113C2211yescharacteristic, complemented
67#390×C113C2211yescharacteristic, complemented
68#384×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×C113C2311yescharacteristic
102#137×C113—22no—
103#137×C113—22no—
104#137×C113—22no—
105#137×C113—41no—
106#137×C113—41no—
107#137×C113—41no—
108C2×Q16×C113—21no—
109C2×Q16×C113—21no—
110C2×Q16×C113—21no—
111C2×SD16×C113—21no—
112C2×SD16×C113—21no—
113C2×SD16×C113—21no—
114C2×M16×C113—21no—
115C2×M16×C113—22no—
116C2×M16×C113—41no—
117C2×M16×C113C2311yescharacteristic
118C2×M16×C113C2311yescharacteristic
119C2×M16×C113C2311yescharacteristic
120C2×M16×C113C2311yescharacteristic
121C22×C8×C113—21no—
122#127×C113—22no—
123#127×C113—21no—
124#124×C113—22no—
125#124×C113—21no—
126#124×C113—22no—
127#124×C113—41no—
128#123×C113—22no—
129#123×C113—21no—
130C22⋊Q8×C113—22no—
131C22⋊Q8×C113—21no—
132C22⋊Q8×C113—21no—
133C22⋊Q8×C113—21no—
134C22⋊Q8×C113—21no—
135C22⋊Q8×C113—21no—
136C22⋊Q8×C113—21no—
137C22⋊Q8×C113D411yescharacteristic
138C22⋊Q8×C113D411yescharacteristic
139#121×C113—22no—
140#121×C113—22no—
141#121×C113—22no—
142#121×C113—22no—
143#121×C113—22no—
144#121×C113—21no—
145#121×C113—21no—
146#121×C113—21no—
147#121×C113—21no—
148#121×C113—21no—
149#121×C113—21no—
150#121×C113—22no—
151#121×C113—21no—
152#121×C113—21no—
153#121×C113D411yescharacteristic
154#121×C113D411yescharacteristic
155#120×C113—22no—
156#120×C113—22no—
157#120×C113—22no—
158#120×C113—21no—
159#120×C113—22no—
160C4×Q8×C113—21no—
161C4×D4×C113—22no—
162C4×D4×C113—22no—
163C4×D4×C113—21no—
164C4×D4×C113—22no—
165C4×D4×C113—21no—
166C4×D4×C113—21no—
167#117×C113—21no—
168#117×C113—22no—
169#117×C113—41no—
170#117×C113C2311yescharacteristic
171C2×C4⋊C4×C113—21no—
172C2×C4⋊C4×C113—21no—
173C2×C4⋊C4×C113—21no—
174C2×C4⋊C4×C113—22no—
175C2×C4⋊C4×C113C2311yescharacteristic
176C2×C4⋊C4×C113C2311yescharacteristic
177C2×C22⋊C4×C113—22no—
178C2×C22⋊C4×C113—21no—
179C2×C22⋊C4×C113—21no—
180C2×C22⋊C4×C113—22no—
181C2×C22⋊C4×C113—22no—
182C2×C22⋊C4×C113D412yes—
183C2×C42×C113C2311yescharacteristic
184C2×C42×C113C2311yescharacteristic
185#107×C113—21no—
186#106×C113—21no—
187#104×C113—22no—
188#104×C113—22no—
189#104×C113—22no—
190#104×C113—22no—
191#104×C113—41no—
192#104×C113D414yescomplemented
193#103×C113—21no—
194#103×C113—21no—
195#103×C113—21no—
196#103×C113—21no—
197#103×C113—21no—
198#102×C113—21no—
199#102×C113—21no—
200#102×C113—21no—
201#100×C113—22no—
202#100×C113—41no—
203C22⋊C8×C113—21no—
204C22⋊C8×C113—21no—
205#95×C113—22no—
206C24×C113—22no—
207C24×C113—21no—
208C24×C113C2×D412yes—
209C24×C113C2×D411yescharacteristic
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—82no—
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—22no—
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—42no—
299C22×C4×C113—42no—
300C22×C4×C113C2×D411yescharacteristic
301C22×C4×C113C2×D411yescharacteristic
302C22×C4×C113C2×D411yescharacteristic
303C22×C4×C113C2×D411yescharacteristic
304C22×C4×C113C2×D411yescharacteristic
305C22×C4×C113C2×D412yes—
306C22×C4×C113C2411yescharacteristic
307Q16×C113—42no—
308Q16×C113—42no—
309Q16×C113—42no—
310SD16×C113—42no—
311SD16×C113—42no—
312SD16×C113—42no—
313M16×C113—21no—
314M16×C113—21no—
315M16×C113—21no—
316M16×C113—21no—
317M16×C113—21no—
318M16×C113—21no—
319M16×C113—21no—
320M16×C113—42no—
321M16×C113C2×D412yescomplemented
322C2×C8×C113—21no—
323C2×C8×C113—21no—
324C2×C8×C113—21no—
325C2×C8×C113—21no—
326C2×C8×C113—42no—
327C4⋊C4×C113—22no—
328C4⋊C4×C113—22no—
329C4⋊C4×C113—21no—
330C4⋊C4×C113—21no—
331C4⋊C4×C113—21no—
332C4⋊C4×C113—21no—
333C4⋊C4×C113—21no—
334C4⋊C4×C113—21no—
335C4⋊C4×C113—42no—
336C4⋊C4×C113—41no—
337C4⋊C4×C113—41no—
338C4⋊C4×C113—82no—
339C4⋊C4×C113C2×D411yescharacteristic
340C4⋊C4×C113C2×D411yescharacteristic
341C22⋊C4×C113—22no—
342C22⋊C4×C113—22no—
343C22⋊C4×C113—22no—
344C22⋊C4×C113—22no—
345C22⋊C4×C113—22no—
346C22⋊C4×C113—21no—
347C22⋊C4×C113—21no—
348C22⋊C4×C113—21no—
349C22⋊C4×C113—21no—
350C22⋊C4×C113—22no—
351C22⋊C4×C113—22no—
352C22⋊C4×C113—21no—
353C22⋊C4×C113—42no—
354C22⋊C4×C113—44no—
355C22⋊C4×C113—41no—
356C22⋊C4×C113—41no—
357C22⋊C4×C113—82no—
358C42×C113—22no—
359C42×C113—21no—
360C42×C113—21no—
361C42×C113—21no—
362C42×C113—21no—
363C42×C113C2×D412yescomplemented
364C23×C113—21no—
365C23×C113—21no—
366C23×C113—21no—
367C23×C113—22no—
368C23×C113—21no—
369C23×C113—21no—
370C23×C113—22no—
371C23×C113—22no—
372C23×C113—41no—
373C23×C113—41no—
374C23×C113—42no—
375C23×C113—42no—
376C23×C113—44no—
377C23×C113—42no—
378C23×C113—42no—
379C23×C113—81no—
380C23×C113—82no—
381C23×C113—82no—
382C23×C113#12011yescharacteristic
383C23×C113#12011yescharacteristic
384C23×C113C22×D411yescharacteristic
385Q8×C113—21no—
386Q8×C113—21no—
387Q8×C113—21no—
388Q8×C113—21no—
389Q8×C113—21no—
390Q8×C113—42no—
391Q8×C113—41no—
392Q8×C113—41no—
393Q8×C113—41no—
394Q8×C113—41no—
395Q8×C113#12112yes—
396D4×C113—22no—
397D4×C113—22no—
398D4×C113—21no—
399D4×C113—21no—
400D4×C113—21no—
401D4×C113—21no—
402D4×C113—21no—
403D4×C113—42no—
404D4×C113—42no—
405D4×C113—44no—
406D4×C113—42no—
407D4×C113—44no—
408D4×C113—44no—
409D4×C113—42no—
410D4×C113—41no—
411D4×C113—41no—
412D4×C113—41no—
413D4×C113—41no—
414D4×C113—41no—
415D4×C113—41no—
416D4×C113—41no—
417D4×C113—41no—
418D4×C113—81no—
419D4×C113—82no—
420D4×C113—82no—
421D4×C113—82no—
422D4×C113—82no—
423D4×C113#12112yes—
424C2×C4×C113—21no—
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—22no—
434C2×C4×C113—21no—
435C2×C4×C113—21no—
436C2×C4×C113—22no—
437C2×C4×C113—21no—
438C2×C4×C113—22no—
439C2×C4×C113—21no—
440C2×C4×C113—21no—
441C2×C4×C113—21no—
442C2×C4×C113—22no—
443C2×C4×C113—42no—
444C2×C4×C113—42no—
445C2×C4×C113—42no—
446C2×C4×C113—44no—
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—42no—
454C2×C4×C113—41no—
455C2×C4×C113—42no—
456C2×C4×C113—41no—
457C2×C4×C113—41no—
458C2×C4×C113—41no—
459C2×C4×C113—41no—
460C2×C4×C113—41no—
461C2×C4×C113—41no—
462C2×C4×C113—82no—
463C2×C4×C113#12011yescharacteristic
464C2×C4×C113#12011yescharacteristic
465C2×C4×C113C22×D411yescharacteristic
466C2×C4×C113C22×D411yescharacteristic
467C2×C4×C113C22×D411yescharacteristic
468C2×C4×C113C2×#4111yescharacteristic
469C2×C4×C113H(5,𝔽2)11yescharacteristic
470C2×C4×C113H(5,𝔽2)11yescharacteristic
471C8×C113—22no—
472C8×C113—41no—
473C8×C113—41no—
474C8×C113—41no—
475C22×C113—21no—
476C22×C113—21no—
477C22×C113—21no—
478C22×C113—21no—
479C22×C113—22no—
480C22×C113—21no—
481C22×C113—21no—
482C22×C113—21no—
483C22×C113—21no—
484C22×C113—41no—
485C22×C113—41no—
486C22×C113—41no—
487C22×C113—41no—
488C22×C113—42no—
489C22×C113—42no—
490C22×C113—41no—
491C22×C113—41no—
492C22×C113—41no—
493C22×C113—42no—
494C22×C113—41no—
495C22×C113—81no—
496C22×C113—81no—
497C22×C113—82no—
498C22×C113—82no—
499C22×C113—84no—
500C22×C113—164no—
501C22×C113C2×#12011yescharacteristic
502C22×C113D4211yescharacteristic
503C22×C113#54611yescharacteristic
504C4×C113—21no—
505C4×C113—21no—
506C4×C113—22no—
507C4×C113—42no—
508C4×C113—41no—
509C4×C113—41no—
510C4×C113—42no—
511C4×C113—41no—
512C4×C113—41no—
513C4×C113—81no—
514C4×C113—81no—
515C4×C113—81no—
516C4×C113C2×#12111yescharacteristic
517C4×C113#53411yescharacteristic
518C4×C113D4211yescharacteristic
519C4×C113#54611yescharacteristic
520#24471C11311yesmaximal, characteristic, direct product factor, Sylow
521C2×C113—21no—
522C2×C113—21no—
523C2×C113—41no—
524C2×C113—41no—
525C2×C113—42no—
526C2×C113—81no—
527C2×C113—82no—
528C2×C113—81no—
529C2×C113#241011yescharacteristic
530C2×C113#301911yescharacteristic
531C2×C113#302211yescharacteristic
532#3488C2×C11311yescharacteristic
533#3056C2×C11311yescharacteristic, complemented
534C2×#455C2×C11311yescharacteristic, complemented
535#3007C2×C11311yescharacteristic, complemented
536C2×#421C2×C11311yescharacteristic, complemented
537#2620C2×C11311yescharacteristic, complemented
538#2039C2×C11311yescharacteristic, complemented
539#2037C2×C11311yescharacteristic, complemented
540#2007C2×C11311yescharacteristic, complemented
541#2004C2×C11311yescharacteristic, complemented
542#1900C2×C11311yescharacteristic, complemented
543#1897C2×C11311yescharacteristic, complemented
544#1882C2×C11311yescharacteristic, complemented
545#1859C2×C11311yescharacteristic, complemented
546#1792C2×C11311yescharacteristic, complemented
547C113#2447111yescharacteristic, direct product factor, Sylow
548C2×H(5,𝔽2)C22×C11311yescharacteristic
549C22×#41C22×C11311yescharacteristic
550C2×#137C22×C11311yescharacteristic
551C2×#137C22×C11311yescharacteristic, complemented
552C2×#137C22×C11311yescharacteristic, complemented
553C22×M16C22×C11311yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C11311yescharacteristic
562#535—21no—
563#535C22×C11311yescharacteristic
564C2×#124C22×C11311yescharacteristic, complemented
565#525—21no—
566#525C22×C11311yescharacteristic
567C2×C22⋊Q8C22×C11311yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C11311yescharacteristic
570#520C22×C11311yescharacteristic
571C2×#117C22×C11311yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C11311yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C11311yescharacteristic
584C2×#104C22×C11311yescharacteristic
585C2×#104C22×C11311yescharacteristic, complemented
586C2×#104C22×C11311yescharacteristic, complemented
587C2×#104C22×C11311yescharacteristic, complemented
588C2×#104C22×C11311yescharacteristic, complemented
589#419C22×C11311yescharacteristic, complemented
590#417C22×C11311yescharacteristic
591#417C22×C11311yescharacteristic, complemented
592#417C22×C11311yescharacteristic, complemented
593C2×#100C22×C11311yescharacteristic, complemented
594C2×#100C22×C11311yescharacteristic, complemented
595#407C22×C11311yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C11311yescharacteristic, complemented
599#390C22×C11311yescharacteristic, complemented
600#384C22×C11311yescharacteristic, complemented
601#343C22×C11311yescharacteristic, complemented
602#343C22×C11311yescharacteristic, complemented
603#339C22×C11311yescharacteristic, complemented
604#339C22×C11311yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C11311yescharacteristic
618C2×#41D4×C11311yescharacteristic
619C2×#41C23×C11311yescharacteristic
620C2×#41C23×C11311yescharacteristic
621C2×#41C23×C11311yescharacteristic
622C22×Q8D4×C11311yescharacteristic
623C22×Q8C23×C11311yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C11311yescharacteristic
630C22×D4D4×C11312yes—
631C22×D4C23×C11311yescharacteristic
632C23×C4—21no—
633C23×C4C23×C11311yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C11311yescharacteristic
650C2×M16C23×C11311yescharacteristic
651C2×M16C23×C11311yescharacteristic
652C2×M16C23×C11311yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C11311yescharacteristic
670C22⋊Q8D4×C11311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C11311yescharacteristic
686#121D4×C11311yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C11311yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C11311yescharacteristic
708C2×C4⋊C4C23×C11311yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C11312yes—
715C2×C42C23×C11311yescharacteristic
716C2×C42C23×C11311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C11314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C11312yes—
741C24C2×D4×C11311yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C11312yes—
765#41#41×C11312yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C11311yescharacteristic
776C2×Q8C2×D4×C11311yescharacteristic
777C2×Q8C2×D4×C11311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C11311yescharacteristic
812C2×D4C2×D4×C11311yescharacteristic
813C2×D4C2×D4×C11311yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C11311yescharacteristic
833C22×C4C2×D4×C11311yescharacteristic
834C22×C4C2×D4×C11311yescharacteristic
835C22×C4C2×D4×C11311yescharacteristic
836C22×C4C2×D4×C11311yescharacteristic
837C22×C4C2×D4×C11312yes—
838C22×C4C24×C11311yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C11312yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C11311yescharacteristic
872C4⋊C4C2×D4×C11311yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C11312yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C11311yescharacteristic
915C23#120×C11311yescharacteristic
916C23C22×D4×C11311yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C11312yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C11312yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C11311yescharacteristic
996C2×C4#120×C11311yescharacteristic
997C2×C4C22×D4×C11311yescharacteristic
998C2×C4C22×D4×C11311yescharacteristic
999C2×C4C22×D4×C11311yescharacteristic
1000C2×C4C2×#41×C11311yescharacteristic
1001C2×C4H(5,𝔽2)×C11311yescharacteristic
1002C2×C4H(5,𝔽2)×C11311yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C11311yescharacteristic
1034C22D42×C11311yescharacteristic
1035C22#546×C11311yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C11311yescharacteristic
1049C4#534×C11311yescharacteristic
1050C4D42×C11311yescharacteristic
1051C4#546×C11311yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C113×#241011yescharacteristic
1061C2C113×#301911yescharacteristic
1062C2C113×#302211yescharacteristic
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. C2×#421×C113C2semidirect
6. C113×#2620C2semidirect
7. C113×#2039C2semidirect
8. C113×#2037C2semidirect
9. C113×#2007C2semidirect
10. C113×#2004C2semidirect
11. C113×#1900C2semidirect
12. C113×#1897C2semidirect
13. C113×#1882C2semidirect
14. C113×#1859C2semidirect
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. C2×#117×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
66. #391×C113C22semidirect
67. #390×C113C22semidirect
68. #384×C113C22semidirect
69. #343×C113C22semidirect
70. #343×C113C22semidirect
71. #339×C113C22semidirect
72. #339×C113C22semidirect
192. #104×C113D4semidirect
321. M16×C113C2×D4semidirect
363. C42×C113C2×D4semidirect
520. #24471C113direct (N × H)
533. #3056C2×C113semidirect
534. C2×#455C2×C113semidirect
535. #3007C2×C113semidirect
536. C2×#421C2×C113semidirect
537. #2620C2×C113semidirect
538. #2039C2×C113semidirect
539. #2037C2×C113semidirect
540. #2007C2×C113semidirect
541. #2004C2×C113semidirect
542. #1900C2×C113semidirect
543. #1897C2×C113semidirect
544. #1882C2×C113semidirect
545. #1859C2×C113semidirect
546. #1792C2×C113semidirect
547. C113#24471direct (N × H)
551. C2×#137C22×C113semidirect
552. C2×#137C22×C113semidirect
553. C22×M16C22×C113semidirect
564. C2×#124C22×C113semidirect
567. C2×C22⋊Q8C22×C113semidirect
571. C2×#117C22×C113semidirect
581. #428C22×C113semidirect
585. C2×#104C22×C113semidirect
586. C2×#104C22×C113semidirect
587. C2×#104C22×C113semidirect
588. C2×#104C22×C113semidirect
589. #419C22×C113semidirect
591. #417C22×C113semidirect
592. #417C22×C113semidirect
593. C2×#100C22×C113semidirect
594. C2×#100C22×C113semidirect
595. #407C22×C113semidirect
598. #391C22×C113semidirect
599. #390C22×C113semidirect
600. #384C22×C113semidirect
601. #343C22×C113semidirect
602. #343C22×C113semidirect
603. #339C22×C113semidirect
604. #339C22×C113semidirect
724. #104D4×C113semidirect
853. M16C2×D4×C113semidirect
895. C42C2×D4×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
C2×#421×C1132
C113×#26202
C113×#20392
C113×#20372
C113×#20072
C113×#20042
C113×#19002
C113×#18972
C113×#18822
C113×#18592
C113×#17922
#24471113