Finite Group Databasebeta

← C113×#25073 #43293093

Subgroups — C113×#25073 #43293093

Order 28928.

716 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2538C211yesmaximal, characteristic
2C113×#2355C211yesmaximal, characteristic, complemented
3C113×#2094C211yesmaximal, characteristic
4C113×#2092C211yesmaximal, characteristic
5C113×#2085C211yesmaximal, characteristic, complemented
6C113×#2084C211yesmaximal, characteristic, complemented
7C113×#1985C211yesmaximal, characteristic, complemented
8C113×#1948C211yesmaximal, characteristic, complemented
9C113×#1926C211yesmaximal, characteristic
10C113×#1925C211yesmaximal, characteristic
11C113×#1920C211yesmaximal, characteristic, complemented
12C113×#1918C211yesmaximal, characteristic, complemented
13C113×#1847C211yesmaximal, characteristic, complemented
14C113×#1804C211yesmaximal, characteristic
15C113×#1762C211yesmaximal, characteristic
16C2×C22⋊Q8×C113—21no—
17C2×C4×Q8×C113C2211yescharacteristic
18C2×C4×D4×C113C2211yescharacteristic
19C2×#107×C113C2211yescharacteristic
20C2×#107×C113C2211yescharacteristic
21C2×#106×C113C2211yescharacteristic
22C2×#106×C113C2211yescharacteristic
23C2×#106×C113C2211yescharacteristic
24C2×#106×C113C2211yescharacteristic
25C2×C4⋊C8×C113C2211yescharacteristic
26C2×#102×C113C2211yescharacteristic
27C2×#102×C113C2211yescharacteristic
28C2×#102×C113C2211yescharacteristic
29C2×#102×C113C2211yescharacteristic
30C2×#97×C113C2211yescharacteristic
31#396×C113—21no—
32#396×C113—21no—
33#391×C113—21no—
34#390×C113C2211yescharacteristic
35#390×C113C2211yescharacteristic
36#389×C113C2211yescharacteristic
37#389×C113C2211yescharacteristic
38#387×C113—21no—
39#387×C113—21no—
40#384×C113C2211yescharacteristic
41#384×C113C2211yescharacteristic
42#382×C113C2211yescharacteristic
43#382×C113C2211yescharacteristic
44#380×C113—21no—
45C4×C4⋊C4×C113—21no—
46C4×C4⋊C4×C113C2211yescharacteristic
47C4×C4⋊C4×C113C2211yescharacteristic
48C4×C4⋊C4×C113C2211yescharacteristic
49#340×C113C2211yescharacteristic
50#340×C113C2211yescharacteristic
51#340×C113C2211yescharacteristic
52#340×C113C2211yescharacteristic
53#340×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#336×C113C2211yescharacteristic
56#336×C113C2211yescharacteristic
57#336×C113C2211yescharacteristic
58#336×C113C2211yescharacteristic
59C22×Q8×C113D411yescharacteristic
60C22×D4×C113C2311yescharacteristic
61C23×C4×C113—21no—
62C22×C8×C113C2311yescharacteristic
63C22×C8×C113C2311yescharacteristic
64C22×C8×C113C2311yescharacteristic
65C22×C8×C113C2311yescharacteristic
66C22⋊Q8×C113—44no—
67C4×Q8×C113—22no—
68C4×Q8×C113—22no—
69C4×D4×C113—22no—
70C4×D4×C113—22no—
71C2×C4⋊C4×C113—21no—
72C2×C4⋊C4×C113—21no—
73C2×C4⋊C4×C113—21no—
74C2×C4⋊C4×C113—21no—
75C2×C4⋊C4×C113—21no—
76C2×C4⋊C4×C113—21no—
77C2×C4⋊C4×C113D411yescharacteristic
78C2×C4⋊C4×C113D411yescharacteristic
79C2×C4⋊C4×C113D411yescharacteristic
80C2×C4⋊C4×C113C2311yescharacteristic
81C2×C4⋊C4×C113C2311yescharacteristic
82C2×C4⋊C4×C113C2311yescharacteristic
83C2×C4⋊C4×C113C2311yescharacteristic
84C2×C4⋊C4×C113C2311yescharacteristic
85C2×C4⋊C4×C113C2311yescharacteristic
86C2×C4⋊C4×C113C2311yescharacteristic
87C2×C22⋊C4×C113—21no—
88C2×C22⋊C4×C113—21no—
89C2×C22⋊C4×C113—21no—
90C2×C22⋊C4×C113—21no—
91C2×C22⋊C4×C113—21no—
92C2×C42×C113—21no—
93C2×C42×C113—21no—
94C2×C42×C113—21no—
95C2×C42×C113C2311yescharacteristic
96C2×C42×C113C2311yescharacteristic
97C2×C42×C113C2311yescharacteristic
98#107×C113—22no—
99#107×C113—41no—
100#106×C113—22no—
101#106×C113—41no—
102#106×C113—41no—
103#106×C113—41no—
104C4⋊C8×C113—22no—
105#102×C113—22no—
106#102×C113—41no—
107#102×C113—41no—
108#102×C113Q814yescomplemented
109#97×C113—22no—
110#95×C113—21no—
111#95×C113—21no—
112#95×C113—21no—
113#95×C113—21no—
114#95×C113—21no—
115#95×C113—21no—
116#95×C113—21no—
117#95×C113—21no—
118#95×C113—21no—
119C24×C113—21no—
120C2×Q8×C113—22no—
121C2×Q8×C113—22no—
122C2×Q8×C113—41no—
123C2×D4×C113—21no—
124C2×D4×C113—21no—
125C2×D4×C113—21no—
126C2×D4×C113—21no—
127C2×D4×C113—21no—
128C2×D4×C113C2×Q812yes—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—21no—
132C22×C4×C113—21no—
133C22×C4×C113—21no—
134C22×C4×C113—21no—
135C22×C4×C113—21no—
136C22×C4×C113—42no—
137C22×C4×C113—42no—
138C22×C4×C113—42no—
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142C22×C4×C113C2×D411yescharacteristic
143C22×C4×C113C2×D411yescharacteristic
144C22×C4×C113C2×D411yescharacteristic
145C22×C4×C113C2411yescharacteristic
146C2×C8×C113—21no—
147C2×C8×C113—21no—
148C2×C8×C113—21no—
149C2×C8×C113—21no—
150C2×C8×C113—21no—
151C2×C8×C113—21no—
152C2×C8×C113—21no—
153C2×C8×C113—21no—
154C2×C8×C113—21no—
155C2×C8×C113—21no—
156C2×C8×C113C2×Q812yes—
157C2×C8×C113#4112yes—
158C4⋊C4×C113—22no—
159C4⋊C4×C113—22no—
160C4⋊C4×C113—22no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—21no—
163C4⋊C4×C113—21no—
164C4⋊C4×C113—21no—
165C4⋊C4×C113—21no—
166C4⋊C4×C113—21no—
167C4⋊C4×C113—21no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—21no—
170C4⋊C4×C113—21no—
171C4⋊C4×C113—21no—
172C4⋊C4×C113—21no—
173C4⋊C4×C113—21no—
174C4⋊C4×C113—42no—
175C4⋊C4×C113—42no—
176C4⋊C4×C113—42no—
177C4⋊C4×C113—42no—
178C4⋊C4×C113—81no—
179C4⋊C4×C113—81no—
180C4⋊C4×C113C2×Q812yes—
181C22⋊C4×C113—42no—
182C22⋊C4×C113—42no—
183C22⋊C4×C113—42no—
184C22⋊C4×C113—81no—
185C22⋊C4×C113—81no—
186C42×C113—21no—
187C42×C113—21no—
188C42×C113—21no—
189C42×C113—21no—
190C42×C113—42no—
191C42×C113—81no—
192C42×C113—81no—
193C42×C113#4112yes—
194C42×C113#4112yes—
195C23×C113—22no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—41no—
200C23×C113—41no—
201C23×C113—41no—
202C23×C113C22×D411yescharacteristic
203Q8×C113—44no—
204D4×C113—22no—
205D4×C113—22no—
206D4×C113—41no—
207D4×C113—41no—
208C2×C4×C113—21no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113—21no—
213C2×C4×C113—21no—
214C2×C4×C113—21no—
215C2×C4×C113—21no—
216C2×C4×C113—21no—
217C2×C4×C113—22no—
218C2×C4×C113—21no—
219C2×C4×C113—21no—
220C2×C4×C113—21no—
221C2×C4×C113—21no—
222C2×C4×C113—21no—
223C2×C4×C113—21no—
224C2×C4×C113—41no—
225C2×C4×C113—41no—
226C2×C4×C113—41no—
227C2×C4×C113—41no—
228C2×C4×C113—41no—
229C2×C4×C113—41no—
230C2×C4×C113—41no—
231C2×C4×C113—41no—
232C2×C4×C113—41no—
233C2×C4×C113—41no—
234C2×C4×C113—41no—
235C2×C4×C113—41no—
236C2×C4×C113—41no—
237C2×C4×C113—41no—
238C2×C4×C113—41no—
239C2×C4×C113—41no—
240C2×C4×C113—41no—
241C2×C4×C113—41no—
242C2×C4×C113—41no—
243C2×C4×C113—41no—
244C2×C4×C113—84no—
245C2×C4×C113#12312yes—
246C2×C4×C113#12312yes—
247C2×C4×C113AGL(1,ℤ/8)12yes—
248C2×C4×C113C22×Q811yescharacteristic
249C2×C4×C113C2×#4111yescharacteristic
250C2×C4×C113C2×#4111yescharacteristic
251C2×C4×C113C2×#4111yescharacteristic
252C2×C4×C113H(5,𝔽2)11yescharacteristic
253C2×C4×C1132−1+411yescharacteristic
254C8×C113—22no—
255C8×C113—22no—
256C8×C113—41no—
257C8×C113—41no—
258C22×C113—42no—
259C22×C113—42no—
260C22×C113—42no—
261C22×C113—81no—
262C22×C113—81no—
263C22×C113—81no—
264C22×C113—81no—
265C22×C113C2×#12311yescharacteristic
266C22×C113D4×Q811yescharacteristic
267C22×C113#55011yescharacteristic
268C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C113#57511yescharacteristic
270C22×C113#57711yescharacteristic
271C22×C113#57711yescharacteristic
272C4×C113—22no—
273C4×C113—22no—
274C4×C113—22no—
275C4×C113—41no—
276C4×C113—41no—
277C4×C113—41no—
278C4×C113—42no—
279C4×C113—81no—
280C4×C113—81no—
281C4×C113—81no—
282C4×C113—81no—
283C4×C113—81no—
284C4×C113—81no—
285C4×C113#53311yescharacteristic
286C4×C113#54211yescharacteristic
287C4×C113#55211yescharacteristic
288C4×C113#55411yescharacteristic
289#25073C11311yesmaximal, characteristic, direct product factor, Sylow
290C2×C113—82no—
291C2×C113#242311yescharacteristic
292C2×C113#309411yescharacteristic
293C2×C113#309911yescharacteristic
294C2×C113#338411yescharacteristic
295C2×C113#338811yescharacteristic
296C2×C113#339711yescharacteristic
297C2×C113#340111yescharacteristic
298#2538C2×C11311yescharacteristic
299#2355C2×C11311yescharacteristic, complemented
300#2094C2×C11311yescharacteristic
301#2092C2×C11311yescharacteristic
302#2085C2×C11311yescharacteristic, complemented
303#2084C2×C11311yescharacteristic, complemented
304#1985C2×C11311yescharacteristic, complemented
305#1948C2×C11311yescharacteristic, complemented
306#1926C2×C11311yescharacteristic
307#1925C2×C11311yescharacteristic
308#1920C2×C11311yescharacteristic, complemented
309#1918C2×C11311yescharacteristic, complemented
310#1847C2×C11311yescharacteristic, complemented
311#1804C2×C11311yescharacteristic
312#1762C2×C11311yescharacteristic
313C113#2507311yescharacteristic, direct product factor, Sylow
314C2×C22⋊Q8—21no—
315C2×C4×Q8C22×C11311yescharacteristic
316C2×C4×D4C22×C11311yescharacteristic
317C2×#107C22×C11311yescharacteristic
318C2×#107C22×C11311yescharacteristic
319C2×#106C22×C11311yescharacteristic
320C2×#106C22×C11311yescharacteristic
321C2×#106C22×C11311yescharacteristic
322C2×#106C22×C11311yescharacteristic
323C2×C4⋊C8C22×C11311yescharacteristic
324C2×#102C22×C11311yescharacteristic
325C2×#102C22×C11311yescharacteristic
326C2×#102C22×C11311yescharacteristic
327C2×#102C22×C11311yescharacteristic
328C2×#97C22×C11311yescharacteristic
329#396—21no—
330#396—21no—
331#391—21no—
332#390C22×C11311yescharacteristic
333#390C22×C11311yescharacteristic
334#389C22×C11311yescharacteristic
335#389C22×C11311yescharacteristic
336#387—21no—
337#387—21no—
338#384C22×C11311yescharacteristic
339#384C22×C11311yescharacteristic
340#382C22×C11311yescharacteristic
341#382C22×C11311yescharacteristic
342#380—21no—
343C4×C4⋊C4—21no—
344C4×C4⋊C4C22×C11311yescharacteristic
345C4×C4⋊C4C22×C11311yescharacteristic
346C4×C4⋊C4C22×C11311yescharacteristic
347#340C22×C11311yescharacteristic
348#340C22×C11311yescharacteristic
349#340C22×C11311yescharacteristic
350#340C22×C11311yescharacteristic
351#340C22×C11311yescharacteristic
352#340C22×C11311yescharacteristic
353#336C22×C11311yescharacteristic
354#336C22×C11311yescharacteristic
355#336C22×C11311yescharacteristic
356#336C22×C11311yescharacteristic
357C22×Q8D4×C11311yescharacteristic
358C22×D4C23×C11311yescharacteristic
359C23×C4—21no—
360C22×C8C23×C11311yescharacteristic
361C22×C8C23×C11311yescharacteristic
362C22×C8C23×C11311yescharacteristic
363C22×C8C23×C11311yescharacteristic
364C22⋊Q8—44no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×D4—22no—
368C4×D4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C11311yescharacteristic
376C2×C4⋊C4D4×C11311yescharacteristic
377C2×C4⋊C4D4×C11311yescharacteristic
378C2×C4⋊C4C23×C11311yescharacteristic
379C2×C4⋊C4C23×C11311yescharacteristic
380C2×C4⋊C4C23×C11311yescharacteristic
381C2×C4⋊C4C23×C11311yescharacteristic
382C2×C4⋊C4C23×C11311yescharacteristic
383C2×C4⋊C4C23×C11311yescharacteristic
384C2×C4⋊C4C23×C11311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C11311yescharacteristic
394C2×C42C23×C11311yescharacteristic
395C2×C42C23×C11311yescharacteristic
396#107—22no—
397#107—41no—
398#106—22no—
399#106—41no—
400#106—41no—
401#106—41no—
402C4⋊C8—22no—
403#102—22no—
404#102—41no—
405#102—41no—
406#102Q8×C11314yescomplemented
407#97—22no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417C24—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×Q8×C11312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4C2×D4×C11311yescharacteristic
438C22×C4C2×D4×C11311yescharacteristic
439C22×C4C2×D4×C11311yescharacteristic
440C22×C4C2×D4×C11311yescharacteristic
441C22×C4C2×D4×C11311yescharacteristic
442C22×C4C2×D4×C11311yescharacteristic
443C22×C4C24×C11311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8C2×Q8×C11312yes—
455C2×C8#41×C11312yes—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4C2×Q8×C11312yes—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—81no—
490C42—81no—
491C42#41×C11312yes—
492C42#41×C11312yes—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×D4×C11311yescharacteristic
501Q8—44no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4#123×C11312yes—
544C2×C4#123×C11312yes—
545C2×C4AGL(1,ℤ/8)×C11312yes—
546C2×C4C22×Q8×C11311yescharacteristic
547C2×C4C2×#41×C11311yescharacteristic
548C2×C4C2×#41×C11311yescharacteristic
549C2×C4C2×#41×C11311yescharacteristic
550C2×C4H(5,𝔽2)×C11311yescharacteristic
551C2×C42−1+4×C11311yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×#123×C11311yescharacteristic
564C22D4×Q8×C11311yescharacteristic
565C22#550×C11311yescharacteristic
566C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
567C22#575×C11311yescharacteristic
568C22#577×C11311yescharacteristic
569C22#577×C11311yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4#533×C11311yescharacteristic
584C4#542×C11311yescharacteristic
585C4#552×C11311yescharacteristic
586C4#554×C11311yescharacteristic
587C2—82no—
588C2C113×#242311yescharacteristic
589C2C113×#309411yescharacteristic
590C2C113×#309911yescharacteristic
591C2C113×#338411yescharacteristic
592C2C113×#338811yescharacteristic
593C2C113×#339711yescharacteristic
594C2C113×#340111yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC22×D4×C113C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×Q8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2355C2semidirect
5. C113×#2085C2semidirect
6. C113×#2084C2semidirect
7. C113×#1985C2semidirect
8. C113×#1948C2semidirect
11. C113×#1920C2semidirect
12. C113×#1918C2semidirect
13. C113×#1847C2semidirect
108. #102×C113Q8semidirect
289. #25073C113direct (N × H)
299. #2355C2×C113semidirect
302. #2085C2×C113semidirect
303. #2084C2×C113semidirect
304. #1985C2×C113semidirect
305. #1948C2×C113semidirect
308. #1920C2×C113semidirect
309. #1918C2×C113semidirect
310. #1847C2×C113semidirect
313. C113#25073direct (N × H)
406. #102Q8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#25382
C113×#23552
C113×#20942
C113×#20922
C113×#20852
C113×#20842
C113×#19852
C113×#19482
C113×#19262
C113×#19252
C113×#19202
C113×#19182
C113×#18472
C113×#18042
C113×#17622
#25073113