Finite Group Databasebeta

← C113×#27103 #43295123

Subgroups — C113×#27103 #43295123

Order 28928.

706 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2496C211yesmaximal, characteristic
2C113×#2362C211yesmaximal, characteristic
3C113×#2088C211yesmaximal, characteristic, complemented
4C113×#2083C211yesmaximal, characteristic, complemented
5C113×#2036C211yesmaximal, characteristic
6C113×#2036C211yesmaximal, characteristic
7C113×#1933C211yesmaximal, characteristic, complemented
8C113×#1927C211yesmaximal, characteristic, complemented
9C113×#1923C211yesmaximal, characteristic
10C113×#1918C211yesmaximal, characteristic, complemented
11C113×#1863C211yesmaximal, characteristic, complemented
12C113×#1854C211yesmaximal, characteristic
13C113×#1825C211yesmaximal, characteristic
14C113×#1803C211yesmaximal, characteristic, complemented
15C4×#107×C113C211yesmaximal, characteristic, complemented
16C2×#126×C113—21no—
17C2×C22⋊Q8×C113C2211yescharacteristic
18C2×C4×Q8×C113C2211yescharacteristic
19C2×#117×C113C2211yescharacteristic
20C2×#107×C113C2211yescharacteristic
21C2×#107×C113C2211yescharacteristic
22C2×#107×C113C2211yescharacteristic
23C2×#106×C113C2211yescharacteristic
24C2×C4⋊C8×C113C2211yescharacteristic
25C2×#103×C113C2211yescharacteristic
26C2×#103×C113C2211yescharacteristic
27C2×#103×C113C2211yescharacteristic
28C2×#103×C113C2211yescharacteristic
29C2×C22⋊C8×C113C2211yescharacteristic
30C2×C22⋊C8×C113C2211yescharacteristic
31C2×C4×C8×C113C2211yescharacteristic
32#400×C113—21no—
33#397×C113—21no—
34#391×C113C2211yescharacteristic
35#389×C113C2211yescharacteristic
36#389×C113C2211yescharacteristic
37#389×C113C2211yescharacteristic
38#388×C113—21no—
39#388×C113—21no—
40#387×C113—21no—
41#387×C113—21no—
42#384×C113C2211yescharacteristic
43#380×C113C2211yescharacteristic
44#380×C113C2211yescharacteristic
45C4×C4⋊C4×C113—21no—
46C4×C4⋊C4×C113C2211yescharacteristic
47C4×C4⋊C4×C113C2211yescharacteristic
48C4×C22⋊C4×C113C2211yescharacteristic
49#340×C113C2211yescharacteristic
50#340×C113C2211yescharacteristic
51#340×C113C2211yescharacteristic
52#340×C113C2211yescharacteristic
53#340×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#336×C113C2211yescharacteristic
58#336×C113C2211yescharacteristic
59C22×Q8×C113C2311yescharacteristic
60C23×C4×C113C2311yescharacteristic
61C22×C8×C113C2311yescharacteristic
62C22×C8×C113C2311yescharacteristic
63C22×C8×C113C2311yescharacteristic
64C22×C8×C113C2311yescharacteristic
65#126×C113—44no—
66C22⋊Q8×C113—22no—
67C22⋊Q8×C113—22no—
68C4×Q8×C113—22no—
69C4×Q8×C113—41no—
70#117×C113—22no—
71#117×C113—41no—
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×C113—21no—
78C2×C4⋊C4×C113—21no—
79C2×C4⋊C4×C113C2311yescharacteristic
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×C22⋊C4×C113—21no—
87C2×C22⋊C4×C113—21no—
88C2×C22⋊C4×C113—21no—
89C2×C22⋊C4×C113—21no—
90C2×C22⋊C4×C113D411yescharacteristic
91C2×C22⋊C4×C113D411yescharacteristic
92C2×C42×C113—21no—
93C2×C42×C113—21no—
94C2×C42×C113—21no—
95C2×C42×C113—21no—
96C2×C42×C113C2311yescharacteristic
97C2×C42×C113C2311yescharacteristic
98#107×C113—22no—
99#107×C113—22no—
100#107×C113—22no—
101#106×C113—41no—
102C4⋊C8×C113—41no—
103#103×C113—22no—
104#103×C113—22no—
105#103×C113—22no—
106#103×C113—41no—
107C22⋊C8×C113—22no—
108C22⋊C8×C113—41no—
109C4×C8×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—
119#95×C113D411yescharacteristic
120#95×C113D411yescharacteristic
121C24×C113C2×D411yescharacteristic
122C2×Q8×C113—21no—
123C2×Q8×C113—21no—
124C2×Q8×C113—21no—
125C2×Q8×C113—21no—
126C2×Q8×C113—21no—
127C2×Q8×C113#4112yes—
128C22×C4×C113—21no—
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—21no—
137C22×C4×C113—21no—
138C22×C4×C113—21no—
139C22×C4×C113—21no—
140C22×C4×C113—21no—
141C22×C4×C113—21no—
142C22×C4×C113C2×D411yescharacteristic
143C22×C4×C113C2×D411yescharacteristic
144C22×C4×C113C2×D411yescharacteristic
145C22×C4×C113C2×D411yescharacteristic
146C22×C4×C113C2×D411yescharacteristic
147C22×C4×C113C2411yescharacteristic
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×C113—21no—
157C2×C8×C113—21no—
158C2×C8×C113—21no—
159C2×C8×C113#4112yes—
160C4⋊C4×C113—24no—
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—42no—
174C4⋊C4×C113—42no—
175C4⋊C4×C113—42no—
176C4⋊C4×C113—42no—
177C4⋊C4×C113—42no—
178C4⋊C4×C113—42no—
179C4⋊C4×C113#4112yes—
180C4⋊C4×C113#4112yes—
181C22⋊C4×C113—24no—
182C22⋊C4×C113—22no—
183C22⋊C4×C113—22no—
184C22⋊C4×C113—42no—
185C22⋊C4×C113—42no—
186C22⋊C4×C113—42no—
187C42×C113—21no—
188C42×C113—21no—
189C42×C113—21no—
190C42×C113—21no—
191C42×C113—42no—
192C42×C113—42no—
193C42×C113—42no—
194C42×C113—42no—
195C23×C113—21no—
196C23×C113—21no—
197C23×C113—21no—
198C23×C113—21no—
199C23×C113—21no—
200C23×C113—21no—
201C23×C113—21no—
202C23×C113C22×D411yescharacteristic
203Q8×C113—22no—
204Q8×C113—22no—
205Q8×C113—41no—
206Q8×C113—41no—
207C2×C4×C113—21no—
208C2×C4×C113—21no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—22no—
212C2×C4×C113—22no—
213C2×C4×C113—21no—
214C2×C4×C113—21no—
215C2×C4×C113—22no—
216C2×C4×C113—21no—
217C2×C4×C113—21no—
218C2×C4×C113—21no—
219C2×C4×C113—21no—
220C2×C4×C113—21no—
221C2×C4×C113—21no—
222C2×C4×C113—21no—
223C2×C4×C113—41no—
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—41no—
245C2×C4×C113—41no—
246C2×C4×C113—41no—
247C2×C4×C113—41no—
248C2×C4×C113#13512yes—
249C2×C4×C113AGL(1,ℤ/8)12yes—
250C2×C4×C113C2×#4111yescharacteristic
251C2×C4×C113C2×#4111yescharacteristic
252C2×C4×C113C2×#4111yescharacteristic
253C2×C4×C113C2×#4111yescharacteristic
254C2×C4×C113H(5,𝔽2)11yescharacteristic
255C2×C4×C1132−1+411yescharacteristic
256C8×C113—22no—
257C8×C113—41no—
258C8×C113—41no—
259C8×C113—41no—
260C22×C113—41no—
261C22×C113—41no—
262C22×C113—41no—
263C22×C113—41no—
264C22×C113—41no—
265C22×C113—41no—
266C22×C113—41no—
267C22×C113#52511yescharacteristic
268C22×C113#54611yescharacteristic
269C22×C113#54711yescharacteristic
270C22×C113C2×#13511yescharacteristic
271C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C113#57811yescharacteristic
273C22×C113#57811yescharacteristic
274C4×C113—22no—
275C4×C113—22no—
276C4×C113—41no—
277C4×C113—42no—
278C4×C113—41no—
279C4×C113—42no—
280C4×C113—41no—
281C4×C113—42no—
282C4×C113—81no—
283C4×C113—81no—
284C4×C113—81no—
285C4×C113—81no—
286C4×C113—81no—
287C4×C113#52911yescharacteristic
288C4×C113#54211yescharacteristic
289C4×C113#55211yescharacteristic
290C4×C113#55311yescharacteristic
291#27103C11311yesmaximal, characteristic, direct product factor, Sylow
292C2×C113—81no—
293C2×C113#246811yescharacteristic
294C2×C113#310611yescharacteristic
295C2×C113#312711yescharacteristic
296C2×C113#330011yescharacteristic
297C2×C113#333011yescharacteristic
298C2×C113#334211yescharacteristic
299C2×C113#334311yescharacteristic
300#2496C2×C11311yescharacteristic
301#2362C2×C11311yescharacteristic
302#2088C2×C11311yescharacteristic, complemented
303#2083C2×C11311yescharacteristic, complemented
304#2036C2×C11311yescharacteristic
305#2036C2×C11311yescharacteristic
306#1933C2×C11311yescharacteristic, complemented
307#1927C2×C11311yescharacteristic, complemented
308#1923C2×C11311yescharacteristic
309#1918C2×C11311yescharacteristic, complemented
310#1863C2×C11311yescharacteristic, complemented
311#1854C2×C11311yescharacteristic
312#1825C2×C11311yescharacteristic
313#1803C2×C11311yescharacteristic, complemented
314C4×#107C2×C11311yescharacteristic, complemented
315C113#2710311yescharacteristic, direct product factor, Sylow
316C2×#126—21no—
317C2×C22⋊Q8C22×C11311yescharacteristic
318C2×C4×Q8C22×C11311yescharacteristic
319C2×#117C22×C11311yescharacteristic
320C2×#107C22×C11311yescharacteristic
321C2×#107C22×C11311yescharacteristic
322C2×#107C22×C11311yescharacteristic
323C2×#106C22×C11311yescharacteristic
324C2×C4⋊C8C22×C11311yescharacteristic
325C2×#103C22×C11311yescharacteristic
326C2×#103C22×C11311yescharacteristic
327C2×#103C22×C11311yescharacteristic
328C2×#103C22×C11311yescharacteristic
329C2×C22⋊C8C22×C11311yescharacteristic
330C2×C22⋊C8C22×C11311yescharacteristic
331C2×C4×C8C22×C11311yescharacteristic
332#400—21no—
333#397—21no—
334#391C22×C11311yescharacteristic
335#389C22×C11311yescharacteristic
336#389C22×C11311yescharacteristic
337#389C22×C11311yescharacteristic
338#388—21no—
339#388—21no—
340#387—21no—
341#387—21no—
342#384C22×C11311yescharacteristic
343#380C22×C11311yescharacteristic
344#380C22×C11311yescharacteristic
345C4×C4⋊C4—21no—
346C4×C4⋊C4C22×C11311yescharacteristic
347C4×C4⋊C4C22×C11311yescharacteristic
348C4×C22⋊C4C22×C11311yescharacteristic
349#340C22×C11311yescharacteristic
350#340C22×C11311yescharacteristic
351#340C22×C11311yescharacteristic
352#340C22×C11311yescharacteristic
353#340C22×C11311yescharacteristic
354#340C22×C11311yescharacteristic
355#340C22×C11311yescharacteristic
356#340C22×C11311yescharacteristic
357#336C22×C11311yescharacteristic
358#336C22×C11311yescharacteristic
359C22×Q8C23×C11311yescharacteristic
360C23×C4C23×C11311yescharacteristic
361C22×C8C23×C11311yescharacteristic
362C22×C8C23×C11311yescharacteristic
363C22×C8C23×C11311yescharacteristic
364C22×C8C23×C11311yescharacteristic
365#126—44no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C4×Q8—22no—
369C4×Q8—41no—
370#117—22no—
371#117—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
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×C4⋊C4C23×C11311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4D4×C11311yescharacteristic
391C2×C22⋊C4D4×C11311yescharacteristic
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42C23×C11311yescharacteristic
397C2×C42C23×C11311yescharacteristic
398#107—22no—
399#107—22no—
400#107—22no—
401#106—41no—
402C4⋊C8—41no—
403#103—22no—
404#103—22no—
405#103—22no—
406#103—41no—
407C22⋊C8—22no—
408C22⋊C8—41no—
409C4×C8—22no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95D4×C11311yescharacteristic
420#95D4×C11311yescharacteristic
421C24C2×D4×C11311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8#41×C11312yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4C2×D4×C11311yescharacteristic
443C22×C4C2×D4×C11311yescharacteristic
444C22×C4C2×D4×C11311yescharacteristic
445C22×C4C2×D4×C11311yescharacteristic
446C22×C4C2×D4×C11311yescharacteristic
447C22×C4C24×C11311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8#41×C11312yes—
460C4⋊C4—24no—
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—21no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4#41×C11312yes—
480C4⋊C4#41×C11312yes—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—42no—
493C42—42no—
494C42—42no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22×D4×C11311yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
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—21no—
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—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4#135×C11312yes—
549C2×C4AGL(1,ℤ/8)×C11312yes—
550C2×C4C2×#41×C11311yescharacteristic
551C2×C4C2×#41×C11311yescharacteristic
552C2×C4C2×#41×C11311yescharacteristic
553C2×C4C2×#41×C11311yescharacteristic
554C2×C4H(5,𝔽2)×C11311yescharacteristic
555C2×C42−1+4×C11311yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#525×C11311yescharacteristic
568C22#546×C11311yescharacteristic
569C22#547×C11311yescharacteristic
570C22C2×#135×C11311yescharacteristic
571C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
572C22#578×C11311yescharacteristic
573C22#578×C11311yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4#529×C11311yescharacteristic
588C4#542×C11311yescharacteristic
589C4#552×C11311yescharacteristic
590C4#553×C11311yescharacteristic
591C2—81no—
592C2C113×#246811yescharacteristic
593C2C113×#310611yescharacteristic
594C2C113×#312711yescharacteristic
595C2C113×#330011yescharacteristic
596C2C113×#333011yescharacteristic
597C2C113×#334211yescharacteristic
598C2C113×#334311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC24×C113C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#2088C2semidirect
4. C113×#2083C2semidirect
7. C113×#1933C2semidirect
8. C113×#1927C2semidirect
10. C113×#1918C2semidirect
11. C113×#1863C2semidirect
14. C113×#1803C2semidirect
15. C4×#107×C113C2semidirect
291. #27103C113direct (N × H)
302. #2088C2×C113semidirect
303. #2083C2×C113semidirect
306. #1933C2×C113semidirect
307. #1927C2×C113semidirect
309. #1918C2×C113semidirect
310. #1863C2×C113semidirect
313. #1803C2×C113semidirect
314. C4×#107C2×C113semidirect
315. C113#27103direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#24962
C113×#23622
C113×#20882
C113×#20832
C113×#20362
C113×#19332
C113×#19272
C113×#19232
C113×#19182
C113×#18632
C113×#18542
C113×#18252
C113×#18032
C4×#107×C1132
#27103113