Finite Group Databasebeta

← C113×#24031 #43292051

Subgroups — C113×#24031 #43292051

Order 28928.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3488C211yesmaximal, characteristic
2C113×#3093C211yesmaximal, characteristic, complemented
3C113×#2896C211yesmaximal, characteristic, complemented
4C113×#2500C211yesmaximal, characteristic, complemented
5C113×#2040C211yesmaximal, characteristic, complemented
6C113×#2039C211yesmaximal, characteristic, complemented
7C113×#2037C211yesmaximal, characteristic, complemented
8C113×#2037C211yesmaximal, characteristic, complemented
9C113×#1900C211yesmaximal, characteristic, complemented
10C113×#1871C211yesmaximal, characteristic, complemented
11C113×#1860C211yesmaximal, characteristic, complemented
12C113×#1859C211yesmaximal, characteristic, complemented
13C113×#1792C211yesmaximal, characteristic, complemented
14C113×#1792C211yesmaximal, characteristic, complemented
15C113×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic, complemented
19#550×C113—21no—
20#548×C113—21no—
21#546×C113—21no—
22#546×C113—22no—
23D42×C113—22no—
24D42×C113—21no—
25#537×C113—21no—
26#537×C113C2211yescharacteristic
27#535×C113—21no—
28#535×C113C2211yescharacteristic
29#525×C113—21no—
30#525×C113C2211yescharacteristic
31C2×#121×C113—21no—
32C2×#121×C113C2211yescharacteristic
33#520×C113C2211yescharacteristic
34C2×#117×C113C2211yescharacteristic, complemented
35#485×C113—21no—
36#485×C113—21no—
37#482×C113—21no—
38#482×C113—21no—
39#428×C113C2211yescharacteristic, complemented
40#428×C113C2211yescharacteristic, complemented
41C2×#104×C113C2211yescharacteristic
42C2×#104×C113C2211yescharacteristic
43C2×#104×C113C2211yescharacteristic, complemented
44C2×#104×C113C2211yescharacteristic, complemented
45C2×#104×C113C2211yescharacteristic, complemented
46C2×#104×C113C2211yescharacteristic, complemented
47#419×C113—21no—
48#418×C113—21no—
49#417×C113C2211yescharacteristic
50#417×C113C2211yescharacteristic
51#417×C113C2211yescharacteristic, complemented
52#417×C113C2211yescharacteristic, complemented
53#417×C113C2211yescharacteristic, complemented
54#417×C113C2211yescharacteristic, complemented
55#416×C113—21no—
56#416×C113—21no—
57C2×#100×C113C2211yescharacteristic, complemented
58C2×#100×C113C2211yescharacteristic, complemented
59#407×C113C2211yescharacteristic, complemented
60#394×C113—22no—
61#390×C113C2211yescharacteristic, complemented
62#390×C113C2211yescharacteristic, complemented
63#388×C113—22no—
64#384×C113C2211yescharacteristic, complemented
65#382×C113C2211yescharacteristic, complemented
66C4×C22⋊C4×C113C2211yescharacteristic, complemented
67#343×C113C2211yescharacteristic, complemented
68#343×C113C2211yescharacteristic, complemented
69#339×C113C2211yescharacteristic, complemented
70#339×C113C2211yescharacteristic, complemented
71H(5,𝔽2)×C113—22no—
72H(5,𝔽2)×C113—22no—
73H(5,𝔽2)×C113—41no—
74H(5,𝔽2)×C113—41no—
75C2×#41×C113—21no—
76C2×#41×C113—21no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—22no—
80C2×#41×C113—22no—
81C2×#41×C113—41no—
82C2×#41×C113—41no—
83C2×#41×C113D411yescharacteristic
84C2×#41×C113D411yescharacteristic
85C2×#41×C113C2311yescharacteristic
86C2×#41×C113C2311yescharacteristic
87C2×#41×C113C2311yescharacteristic
88C22×Q8×C113D411yescharacteristic
89C22×D4×C113—21no—
90C22×D4×C113—22no—
91C22×D4×C113—22no—
92C22×D4×C113—21no—
93C22×D4×C113—21no—
94C22×D4×C113D411yescharacteristic
95C22×D4×C113D412yes—
96C22×D4×C113C2311yescharacteristic
97C23×C4×C113—21no—
98C23×C4×C113C2311yescharacteristic
99C2×M16×C113—21no—
100C2×M16×C113—41no—
101C2×M16×C113—41no—
102C2×M16×C113C2311yescharacteristic
103C2×M16×C113C2311yescharacteristic
104C2×M16×C113C2311yescharacteristic
105C2×M16×C113C2311yescharacteristic
106C22×C8×C113—21no—
107#127×C113—22no—
108#127×C113—21no—
109#124×C113—22no—
110#124×C113—21no—
111#123×C113—22no—
112#123×C113—21no—
113C22⋊Q8×C113—22no—
114C22⋊Q8×C113—21no—
115C22⋊Q8×C113—21no—
116C22⋊Q8×C113D411yescharacteristic
117C22⋊Q8×C113D411yescharacteristic
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—22no—
121#121×C113—22no—
122#121×C113—22no—
123#121×C113—21no—
124#121×C113—21no—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113—21no—
129#121×C113—22no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113D411yescharacteristic
133#121×C113D411yescharacteristic
134#120×C113—22no—
135#120×C113—22no—
136#120×C113—22no—
137#120×C113—21no—
138#120×C113—22no—
139C4×Q8×C113—21no—
140C4×D4×C113—22no—
141C4×D4×C113—22no—
142C4×D4×C113—21no—
143C4×D4×C113—22no—
144C4×D4×C113—21no—
145C4×D4×C113—21no—
146#117×C113—21no—
147#117×C113—21no—
148#117×C113—21no—
149#117×C113—21no—
150#117×C113—21no—
151#117×C113C2311yescharacteristic
152C2×C4⋊C4×C113—21no—
153C2×C4⋊C4×C113—22no—
154C2×C4⋊C4×C113C2311yescharacteristic
155C2×C4⋊C4×C113C2311yescharacteristic
156C2×C4⋊C4×C113C2311yescharacteristic
157C2×C22⋊C4×C113—22no—
158C2×C22⋊C4×C113—21no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—22no—
161C2×C22⋊C4×C113—22no—
162C2×C22⋊C4×C113D412yes—
163C2×C42×C113—21no—
164C2×C42×C113C2311yescharacteristic
165C2×C42×C113C2311yescharacteristic
166#107×C113—21no—
167#107×C113—21no—
168#106×C113—21no—
169#106×C113—21no—
170#104×C113—22no—
171#104×C113—22no—
172#104×C113—41no—
173#104×C113—41no—
174#104×C113—41no—
175#104×C113—41no—
176#103×C113—21no—
177#103×C113—21no—
178#103×C113—21no—
179#103×C113—21no—
180#103×C113—21no—
181#103×C113—21no—
182#102×C113—21no—
183#102×C113—21no—
184#102×C113—21no—
185#102×C113—21no—
186#102×C113—21no—
187#102×C113—21no—
188#100×C113—41no—
189#100×C113—41no—
190C22⋊C8×C113—21no—
191C22⋊C8×C113—21no—
192#95×C113—21no—
193#95×C113—22no—
194C24×C113—22no—
195C24×C113—21no—
196C24×C113C2×D412yes—
197C24×C113C2×D411yescharacteristic
198#41×C113—21no—
199#41×C113—21no—
200#41×C113—22no—
201#41×C113—22no—
202#41×C113—21no—
203#41×C113—21no—
204#41×C113—21no—
205#41×C113—21no—
206#41×C113—21no—
207#41×C113—21no—
208#41×C113—21no—
209#41×C113—21no—
210#41×C113—42no—
211#41×C113—42no—
212#41×C113—41no—
213#41×C113—41no—
214#41×C113—42no—
215#41×C113—42no—
216#41×C113—42no—
217#41×C113—42no—
218#41×C113—42no—
219#41×C113—42no—
220#41×C113#4112yes—
221#41×C113#4112yes—
222C2×Q8×C113—21no—
223C2×Q8×C113—22no—
224C2×Q8×C113—41no—
225C2×Q8×C113C2×D411yescharacteristic
226C2×Q8×C113C2×D411yescharacteristic
227C2×Q8×C113C2×D411yescharacteristic
228C2×D4×C113—21no—
229C2×D4×C113—22no—
230C2×D4×C113—22no—
231C2×D4×C113—22no—
232C2×D4×C113—22no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—21no—
238C2×D4×C113—22no—
239C2×D4×C113—22no—
240C2×D4×C113—22no—
241C2×D4×C113—21no—
242C2×D4×C113—22no—
243C2×D4×C113—21no—
244C2×D4×C113—21no—
245C2×D4×C113—21no—
246C2×D4×C113—21no—
247C2×D4×C113—21no—
248C2×D4×C113—21no—
249C2×D4×C113—21no—
250C2×D4×C113—41no—
251C2×D4×C113—42no—
252C2×D4×C113—42no—
253C2×D4×C113—42no—
254C2×D4×C113—42no—
255C2×D4×C113—44no—
256C2×D4×C113—44no—
257C2×D4×C113—42no—
258C2×D4×C113—42no—
259C2×D4×C113—82no—
260C2×D4×C113—84no—
261C2×D4×C113C2×D411yescharacteristic
262C2×D4×C113C2×D411yescharacteristic
263C2×D4×C113C2×D411yescharacteristic
264C22×C4×C113—21no—
265C22×C4×C113—21no—
266C22×C4×C113—21no—
267C22×C4×C113—21no—
268C22×C4×C113—21no—
269C22×C4×C113—22no—
270C22×C4×C113—21no—
271C22×C4×C113—21no—
272C22×C4×C113—22no—
273C22×C4×C113—21no—
274C22×C4×C113—21no—
275C22×C4×C113—21no—
276C22×C4×C113—21no—
277C22×C4×C113—21no—
278C22×C4×C113—21no—
279C22×C4×C113—21no—
280C22×C4×C113—42no—
281C22×C4×C113—42no—
282C22×C4×C113C2×D411yescharacteristic
283C22×C4×C113C2×D411yescharacteristic
284C22×C4×C113C2×D411yescharacteristic
285C22×C4×C113C2×D411yescharacteristic
286C22×C4×C113C2×D411yescharacteristic
287C22×C4×C113C2×D412yes—
288C22×C4×C113C2411yescharacteristic
289M16×C113—21no—
290M16×C113—21no—
291M16×C113—21no—
292M16×C113—21no—
293M16×C113—21no—
294M16×C113—21no—
295M16×C113—21no—
296M16×C113—21no—
297M16×C113—42no—
298C2×C8×C113—21no—
299C2×C8×C113—21no—
300C2×C8×C113—21no—
301C2×C8×C113—21no—
302C2×C8×C113—42no—
303C4⋊C4×C113—22no—
304C4⋊C4×C113—22no—
305C4⋊C4×C113—21no—
306C4⋊C4×C113—21no—
307C4⋊C4×C113—21no—
308C4⋊C4×C113—21no—
309C4⋊C4×C113—21no—
310C4⋊C4×C113—21no—
311C4⋊C4×C113—21no—
312C4⋊C4×C113—21no—
313C4⋊C4×C113—82no—
314C4⋊C4×C113C2×D411yescharacteristic
315C4⋊C4×C113C2×D411yescharacteristic
316C22⋊C4×C113—22no—
317C22⋊C4×C113—22no—
318C22⋊C4×C113—22no—
319C22⋊C4×C113—22no—
320C22⋊C4×C113—22no—
321C22⋊C4×C113—21no—
322C22⋊C4×C113—21no—
323C22⋊C4×C113—21no—
324C22⋊C4×C113—21no—
325C22⋊C4×C113—22no—
326C22⋊C4×C113—22no—
327C22⋊C4×C113—21no—
328C22⋊C4×C113—42no—
329C22⋊C4×C113—44no—
330C22⋊C4×C113—41no—
331C22⋊C4×C113—41no—
332C22⋊C4×C113—82no—
333C42×C113—22no—
334C42×C113—21no—
335C42×C113—21no—
336C42×C113—21no—
337C42×C113—21no—
338C42×C113—21no—
339C42×C113—41no—
340C42×C113—41no—
341C23×C113—21no—
342C23×C113—21no—
343C23×C113—21no—
344C23×C113—22no—
345C23×C113—21no—
346C23×C113—21no—
347C23×C113—22no—
348C23×C113—22no—
349C23×C113—41no—
350C23×C113—41no—
351C23×C113—42no—
352C23×C113—42no—
353C23×C113—44no—
354C23×C113—42no—
355C23×C113—42no—
356C23×C113—81no—
357C23×C113—82no—
358C23×C113—82no—
359C23×C113#12011yescharacteristic
360C23×C113#12011yescharacteristic
361C23×C113C22×D411yescharacteristic
362Q8×C113—21no—
363Q8×C113—21no—
364Q8×C113—21no—
365Q8×C113—21no—
366Q8×C113—21no—
367Q8×C113—42no—
368Q8×C113#12312yes—
369D4×C113—22no—
370D4×C113—22no—
371D4×C113—21no—
372D4×C113—21no—
373D4×C113—21no—
374D4×C113—21no—
375D4×C113—21no—
376D4×C113—42no—
377D4×C113—42no—
378D4×C113—44no—
379D4×C113—42no—
380D4×C113—44no—
381D4×C113—44no—
382D4×C113—42no—
383D4×C113—41no—
384D4×C113—41no—
385D4×C113—41no—
386D4×C113—41no—
387D4×C113—41no—
388D4×C113—41no—
389D4×C113—41no—
390D4×C113—41no—
391D4×C113—81no—
392D4×C113—82no—
393D4×C113—82no—
394D4×C113—82no—
395D4×C113—82no—
396D4×C113#12312yes—
397C2×C4×C113—21no—
398C2×C4×C113—21no—
399C2×C4×C113—21no—
400C2×C4×C113—21no—
401C2×C4×C113—21no—
402C2×C4×C113—21no—
403C2×C4×C113—21no—
404C2×C4×C113—21no—
405C2×C4×C113—21no—
406C2×C4×C113—21no—
407C2×C4×C113—21no—
408C2×C4×C113—22no—
409C2×C4×C113—22no—
410C2×C4×C113—22no—
411C2×C4×C113—21no—
412C2×C4×C113—22no—
413C2×C4×C113—21no—
414C2×C4×C113—21no—
415C2×C4×C113—21no—
416C2×C4×C113—42no—
417C2×C4×C113—42no—
418C2×C4×C113—42no—
419C2×C4×C113—44no—
420C2×C4×C113—41no—
421C2×C4×C113—41no—
422C2×C4×C113—41no—
423C2×C4×C113—41no—
424C2×C4×C113—41no—
425C2×C4×C113—41no—
426C2×C4×C113—42no—
427C2×C4×C113—41no—
428C2×C4×C113—42no—
429C2×C4×C113—41no—
430C2×C4×C113—42no—
431C2×C4×C113—41no—
432C2×C4×C113—41no—
433C2×C4×C113—41no—
434C2×C4×C113—82no—
435C2×C4×C113#12011yescharacteristic
436C2×C4×C113#12011yescharacteristic
437C2×C4×C113C22×D411yescharacteristic
438C2×C4×C113C22×D411yescharacteristic
439C2×C4×C113C2×#4111yescharacteristic
440C2×C4×C113C2×#4111yescharacteristic
441C2×C4×C113H(5,𝔽2)11yescharacteristic
442C2×C4×C113H(5,𝔽2)11yescharacteristic
443C8×C113—41no—
444C8×C113—41no—
445C8×C113—41no—
446C8×C113—41no—
447C22×C113—21no—
448C22×C113—21no—
449C22×C113—21no—
450C22×C113—21no—
451C22×C113—22no—
452C22×C113—21no—
453C22×C113—21no—
454C22×C113—21no—
455C22×C113—21no—
456C22×C113—41no—
457C22×C113—41no—
458C22×C113—41no—
459C22×C113—41no—
460C22×C113—42no—
461C22×C113—41no—
462C22×C113—42no—
463C22×C113—41no—
464C22×C113—42no—
465C22×C113—41no—
466C22×C113—41no—
467C22×C113—81no—
468C22×C113—81no—
469C22×C113—82no—
470C22×C113—82no—
471C22×C113—84no—
472C22×C113—164no—
473C22×C113C2×#12011yescharacteristic
474C22×C113#54611yescharacteristic
475C22×C113#54611yescharacteristic
476C4×C113—21no—
477C4×C113—21no—
478C4×C113—22no—
479C4×C113—42no—
480C4×C113—41no—
481C4×C113—41no—
482C4×C113—41no—
483C4×C113—42no—
484C4×C113—41no—
485C4×C113—81no—
486C4×C113—81no—
487C4×C113—81no—
488C4×C113C2×#12311yescharacteristic
489C4×C113#53411yescharacteristic
490C4×C113#54611yescharacteristic
491C4×C113#54611yescharacteristic
492#24031C11311yesmaximal, characteristic, direct product factor, Sylow
493C2×C113—21no—
494C2×C113—21no—
495C2×C113—41no—
496C2×C113—41no—
497C2×C113—42no—
498C2×C113—81no—
499C2×C113—82no—
500C2×C113—81no—
501C2×C113#240511yescharacteristic
502C2×C113#301811yescharacteristic
503C2×C113#301911yescharacteristic
504#3488C2×C11311yescharacteristic
505#3093C2×C11311yescharacteristic, complemented
506#2896C2×C11311yescharacteristic, complemented
507#2500C2×C11311yescharacteristic, complemented
508#2040C2×C11311yescharacteristic, complemented
509#2039C2×C11311yescharacteristic, complemented
510#2037C2×C11311yescharacteristic, complemented
511#2037C2×C11311yescharacteristic, complemented
512#1900C2×C11311yescharacteristic, complemented
513#1871C2×C11311yescharacteristic, complemented
514#1860C2×C11311yescharacteristic, complemented
515#1859C2×C11311yescharacteristic, complemented
516#1792C2×C11311yescharacteristic, complemented
517#1792C2×C11311yescharacteristic, complemented
518#1789C2×C11311yescharacteristic, complemented
519C113#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C11311yescharacteristic
521C22×#41C22×C11311yescharacteristic
522C22×M16C22×C11311yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C11311yescharacteristic
531#535—21no—
532#535C22×C11311yescharacteristic
533#525—21no—
534#525C22×C11311yescharacteristic
535C2×#121—21no—
536C2×#121C22×C11311yescharacteristic
537#520C22×C11311yescharacteristic
538C2×#117C22×C11311yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C11311yescharacteristic, complemented
544#428C22×C11311yescharacteristic, complemented
545C2×#104C22×C11311yescharacteristic
546C2×#104C22×C11311yescharacteristic
547C2×#104C22×C11311yescharacteristic, complemented
548C2×#104C22×C11311yescharacteristic, complemented
549C2×#104C22×C11311yescharacteristic, complemented
550C2×#104C22×C11311yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C11311yescharacteristic
554#417C22×C11311yescharacteristic
555#417C22×C11311yescharacteristic, complemented
556#417C22×C11311yescharacteristic, complemented
557#417C22×C11311yescharacteristic, complemented
558#417C22×C11311yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C11311yescharacteristic, complemented
562C2×#100C22×C11311yescharacteristic, complemented
563#407C22×C11311yescharacteristic, complemented
564#394—22no—
565#390C22×C11311yescharacteristic, complemented
566#390C22×C11311yescharacteristic, complemented
567#388—22no—
568#384C22×C11311yescharacteristic, complemented
569#382C22×C11311yescharacteristic, complemented
570C4×C22⋊C4C22×C11311yescharacteristic, complemented
571#343C22×C11311yescharacteristic, complemented
572#343C22×C11311yescharacteristic, complemented
573#339C22×C11311yescharacteristic, complemented
574#339C22×C11311yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C11311yescharacteristic
588C2×#41D4×C11311yescharacteristic
589C2×#41C23×C11311yescharacteristic
590C2×#41C23×C11311yescharacteristic
591C2×#41C23×C11311yescharacteristic
592C22×Q8D4×C11311yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C11311yescharacteristic
599C22×D4D4×C11312yes—
600C22×D4C23×C11311yescharacteristic
601C23×C4—21no—
602C23×C4C23×C11311yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C11311yescharacteristic
607C2×M16C23×C11311yescharacteristic
608C2×M16C23×C11311yescharacteristic
609C2×M16C23×C11311yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C11311yescharacteristic
621C22⋊Q8D4×C11311yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C11311yescharacteristic
637#121D4×C11311yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C11311yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C11311yescharacteristic
659C2×C4⋊C4C23×C11311yescharacteristic
660C2×C4⋊C4C23×C11311yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C11312yes—
667C2×C42—21no—
668C2×C42C23×C11311yescharacteristic
669C2×C42C23×C11311yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C11312yes—
701C24C2×D4×C11311yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C11312yes—
725#41#41×C11312yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C11311yescharacteristic
730C2×Q8C2×D4×C11311yescharacteristic
731C2×Q8C2×D4×C11311yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C11311yescharacteristic
766C2×D4C2×D4×C11311yescharacteristic
767C2×D4C2×D4×C11311yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C11311yescharacteristic
787C22×C4C2×D4×C11311yescharacteristic
788C22×C4C2×D4×C11311yescharacteristic
789C22×C4C2×D4×C11311yescharacteristic
790C22×C4C2×D4×C11311yescharacteristic
791C22×C4C2×D4×C11312yes—
792C22×C4C24×C11311yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C11311yescharacteristic
819C4⋊C4C2×D4×C11311yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C11311yescharacteristic
864C23#120×C11311yescharacteristic
865C23C22×D4×C11311yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C11312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C11312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C11311yescharacteristic
940C2×C4#120×C11311yescharacteristic
941C2×C4C22×D4×C11311yescharacteristic
942C2×C4C22×D4×C11311yescharacteristic
943C2×C4C2×#41×C11311yescharacteristic
944C2×C4C2×#41×C11311yescharacteristic
945C2×C4H(5,𝔽2)×C11311yescharacteristic
946C2×C4H(5,𝔽2)×C11311yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C11311yescharacteristic
978C22#546×C11311yescharacteristic
979C22#546×C11311yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C11311yescharacteristic
993C4#534×C11311yescharacteristic
994C4#546×C11311yescharacteristic
995C4#546×C11311yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C113×#240511yescharacteristic
1005C2C113×#301811yescharacteristic
1006C2C113×#301911yescharacteristic
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×#3093C2semidirect
3. C113×#2896C2semidirect
4. C113×#2500C2semidirect
5. C113×#2040C2semidirect
6. C113×#2039C2semidirect
7. C113×#2037C2semidirect
8. C113×#2037C2semidirect
9. C113×#1900C2semidirect
10. C113×#1871C2semidirect
11. C113×#1860C2semidirect
12. C113×#1859C2semidirect
13. C113×#1792C2semidirect
14. C113×#1792C2semidirect
15. C113×#1789C2semidirect
18. C22×M16×C113C22semidirect
34. C2×#117×C113C22semidirect
39. #428×C113C22semidirect
40. #428×C113C22semidirect
43. C2×#104×C113C22semidirect
44. C2×#104×C113C22semidirect
45. C2×#104×C113C22semidirect
46. C2×#104×C113C22semidirect
51. #417×C113C22semidirect
52. #417×C113C22semidirect
53. #417×C113C22semidirect
54. #417×C113C22semidirect
57. C2×#100×C113C22semidirect
58. C2×#100×C113C22semidirect
59. #407×C113C22semidirect
61. #390×C113C22semidirect
62. #390×C113C22semidirect
64. #384×C113C22semidirect
65. #382×C113C22semidirect
66. C4×C22⋊C4×C113C22semidirect
67. #343×C113C22semidirect
68. #343×C113C22semidirect
69. #339×C113C22semidirect
70. #339×C113C22semidirect
492. #24031C113direct (N × H)
505. #3093C2×C113semidirect
506. #2896C2×C113semidirect
507. #2500C2×C113semidirect
508. #2040C2×C113semidirect
509. #2039C2×C113semidirect
510. #2037C2×C113semidirect
511. #2037C2×C113semidirect
512. #1900C2×C113semidirect
513. #1871C2×C113semidirect
514. #1860C2×C113semidirect
515. #1859C2×C113semidirect
516. #1792C2×C113semidirect
517. #1792C2×C113semidirect
518. #1789C2×C113semidirect
519. C113#24031direct (N × H)
522. C22×M16C22×C113semidirect
538. C2×#117C22×C113semidirect
543. #428C22×C113semidirect
544. #428C22×C113semidirect
547. C2×#104C22×C113semidirect
548. C2×#104C22×C113semidirect
549. C2×#104C22×C113semidirect
550. C2×#104C22×C113semidirect
555. #417C22×C113semidirect
556. #417C22×C113semidirect
557. #417C22×C113semidirect
558. #417C22×C113semidirect
561. C2×#100C22×C113semidirect
562. C2×#100C22×C113semidirect
563. #407C22×C113semidirect
565. #390C22×C113semidirect
566. #390C22×C113semidirect
568. #384C22×C113semidirect
569. #382C22×C113semidirect
570. C4×C22⋊C4C22×C113semidirect
571. #343C22×C113semidirect
572. #343C22×C113semidirect
573. #339C22×C113semidirect
574. #339C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34882
C113×#30932
C113×#28962
C113×#25002
C113×#20402
C113×#20392
C113×#20372
C113×#19002
C113×#18712
C113×#18602
C113×#18592
C113×#17922
C113×#17892
#24031113