Finite Group Databasebeta

← C113×#26102 #43294122

Subgroups — C113×#26102 #43294122

Order 28928.

708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2552C211yesmaximal, characteristic, complemented
2C113×#2357C211yesmaximal, characteristic
3C113×#2094C211yesmaximal, characteristic
4C113×#2093C211yesmaximal, characteristic
5C113×#2067C211yesmaximal, characteristic
6C113×#2065C211yesmaximal, characteristic
7C113×#1949C211yesmaximal, characteristic, complemented
8C113×#1948C211yesmaximal, characteristic, complemented
9C113×#1947C211yesmaximal, characteristic, complemented
10C113×#1940C211yesmaximal, characteristic, complemented
11C113×#1921C211yesmaximal, characteristic, complemented
12C113×#1919C211yesmaximal, characteristic, complemented
13C113×#1847C211yesmaximal, characteristic, complemented
14C113×#1802C211yesmaximal, characteristic
15C113×#1762C211yesmaximal, characteristic
16C2×#125×C113—21no—
17C2×C4×D4×C113C2211yescharacteristic
18C2×#107×C113C2211yescharacteristic
19C2×#107×C113C2211yescharacteristic
20C2×#107×C113C2211yescharacteristic
21C2×#106×C113C2211yescharacteristic
22C2×#106×C113C2211yescharacteristic
23C2×#106×C113C2211yescharacteristic
24C2×C4⋊C8×C113C2211yescharacteristic
25C2×C4⋊C8×C113C2211yescharacteristic
26C2×C4⋊C8×C113C2211yescharacteristic
27C2×#102×C113C2211yescharacteristic
28C2×#102×C113C2211yescharacteristic
29C2×#102×C113C2211yescharacteristic
30C2×#102×C113C2211yescharacteristic
31C2×#97×C113C2211yescharacteristic
32#398×C113—21no—
33#398×C113—21no—
34#390×C113C2211yescharacteristic
35#390×C113C2211yescharacteristic
36#389×C113—21no—
37#389×C113C2211yescharacteristic
38#389×C113C2211yescharacteristic
39#388×C113—21no—
40#388×C113—21no—
41#384×C113C2211yescharacteristic
42#384×C113C2211yescharacteristic
43#384×C113C2211yescharacteristic
44#382×C113C2211yescharacteristic
45#381×C113—21no—
46C4×C4⋊C4×C113C2211yescharacteristic
47C4×C4⋊C4×C113C2211yescharacteristic
48C4×C4⋊C4×C113C2211yescharacteristic
49C4×C4⋊C4×C113C2211yescharacteristic
50C4×C22⋊C4×C113—21no—
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×D4×C113C2311yescharacteristic
60C23×C4×C113—21no—
61C22×C8×C113C2311yescharacteristic
62C22×C8×C113C2311yescharacteristic
63C22×C8×C113C2311yescharacteristic
64C22×C8×C113C2311yescharacteristic
65#125×C113—44no—
66C4×D4×C113—22no—
67C4×D4×C113Q814yes—
68C2×C4⋊C4×C113—21no—
69C2×C4⋊C4×C113—21no—
70C2×C4⋊C4×C113—21no—
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×C113D411yescharacteristic
77C2×C4⋊C4×C113D411yescharacteristic
78C2×C4⋊C4×C113C2311yescharacteristic
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×C22⋊C4×C113—21no—
86C2×C22⋊C4×C113—21no—
87C2×C22⋊C4×C113—21no—
88C2×C22⋊C4×C113—21no—
89C2×C22⋊C4×C113—21no—
90C2×C42×C113—21no—
91C2×C42×C113—21no—
92C2×C42×C113—21no—
93C2×C42×C113C2311yescharacteristic
94C2×C42×C113C2311yescharacteristic
95C2×C42×C113C2311yescharacteristic
96#107×C113—22no—
97#107×C113—41no—
98#107×C113—41no—
99#106×C113—22no—
100#106×C113—41no—
101#106×C113—41no—
102C4⋊C8×C113—22no—
103C4⋊C8×C113—22no—
104C4⋊C8×C113—22no—
105#102×C113—22no—
106#102×C113—22no—
107#102×C113—41no—
108#102×C113—41no—
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×C113D411yescharacteristic
118#95×C113D411yescharacteristic
119C24×C113—21no—
120C2×D4×C113—21no—
121C2×D4×C113—21no—
122C2×D4×C113—21no—
123C2×D4×C113—21no—
124C2×D4×C113—21no—
125C2×D4×C113C2×Q812yes—
126C22×C4×C113—21no—
127C22×C4×C113—24no—
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—81no—
135C22×C4×C113—81no—
136C22×C4×C113C2×D411yescharacteristic
137C22×C4×C113C2×D411yescharacteristic
138C22×C4×C113C2×D411yescharacteristic
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142C22×C4×C113C2411yescharacteristic
143C2×C8×C113—21no—
144C2×C8×C113—21no—
145C2×C8×C113—21no—
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#4112yes—
154C2×C8×C113#4112yes—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—21no—
159C4⋊C4×C113—21no—
160C4⋊C4×C113—21no—
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—42no—
171C4⋊C4×C113—42no—
172C4⋊C4×C113—42no—
173C4⋊C4×C113—42no—
174C4⋊C4×C113—42no—
175C4⋊C4×C113—81no—
176C4⋊C4×C113—81no—
177C4⋊C4×C113—81no—
178C4⋊C4×C113C2×Q812yes—
179C22⋊C4×C113—24no—
180C22⋊C4×C113—42no—
181C22⋊C4×C113—42no—
182C22⋊C4×C113—81no—
183C22⋊C4×C113—81no—
184C42×C113—21no—
185C42×C113—21no—
186C42×C113—21no—
187C42×C113—21no—
188C42×C113—42no—
189C42×C113—81no—
190C42×C113—81no—
191C42×C113C2×Q812yes—
192C42×C113#4112yes—
193C23×C113—22no—
194C23×C113—41no—
195C23×C113—41no—
196C23×C113—41no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—41no—
200C23×C113C22×D411yescharacteristic
201D4×C113—22no—
202D4×C113—22no—
203D4×C113—41no—
204D4×C113—41no—
205C2×C4×C113—21no—
206C2×C4×C113—21no—
207C2×C4×C113—21no—
208C2×C4×C113—21no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113—21no—
213C2×C4×C113—22no—
214C2×C4×C113—21no—
215C2×C4×C113—21no—
216C2×C4×C113—21no—
217C2×C4×C113—21no—
218C2×C4×C113—21no—
219C2×C4×C113—21no—
220C2×C4×C113—41no—
221C2×C4×C113—41no—
222C2×C4×C113—41no—
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—84no—
241C2×C4×C113C22⋊Q812yes—
242C2×C4×C113C22⋊Q812yes—
243C2×C4×C113AGL(1,ℤ/8)12yes—
244C2×C4×C113#13712yes—
245C2×C4×C113C22×Q811yescharacteristic
246C2×C4×C113C2×#4111yescharacteristic
247C2×C4×C113C2×#4111yescharacteristic
248C2×C4×C113C2×#4111yescharacteristic
249C2×C4×C113H(5,𝔽2)11yescharacteristic
250C2×C4×C1132−1+411yescharacteristic
251C8×C113—22no—
252C8×C113—22no—
253C8×C113—41no—
254C8×C113—41no—
255C22×C113—42no—
256C22×C113—42no—
257C22×C113—42no—
258C22×C113—81no—
259C22×C113—81no—
260C22×C113—81no—
261C22×C113—81no—
262C22×C113C2×C22⋊Q811yescharacteristic
263C22×C113#54711yescharacteristic
264C22×C113#55011yescharacteristic
265C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C113C2×#13711yescharacteristic
267C22×C113#57611yescharacteristic
268C22×C113#57711yescharacteristic
269C4×C113—22no—
270C4×C113—22no—
271C4×C113—22no—
272C4×C113—22no—
273C4×C113—42no—
274C4×C113—41no—
275C4×C113—41no—
276C4×C113—81no—
277C4×C113—81no—
278C4×C113—81no—
279C4×C113—81no—
280C4×C113—81no—
281C4×C113—81no—
282C4×C113#53311yescharacteristic
283C4×C113#54411yescharacteristic
284C4×C113#55211yescharacteristic
285C4×C113#55311yescharacteristic
286#26102C11311yesmaximal, characteristic, direct product factor, Sylow
287C2×C113—82no—
288C2×C113#244111yescharacteristic
289C2×C113#307911yescharacteristic
290C2×C113#308111yescharacteristic
291C2×C113#334511yescharacteristic
292C2×C113#334611yescharacteristic
293C2×C113#339911yescharacteristic
294C2×C113#340011yescharacteristic
295#2552C2×C11311yescharacteristic, complemented
296#2357C2×C11311yescharacteristic
297#2094C2×C11311yescharacteristic
298#2093C2×C11311yescharacteristic
299#2067C2×C11311yescharacteristic
300#2065C2×C11311yescharacteristic
301#1949C2×C11311yescharacteristic, complemented
302#1948C2×C11311yescharacteristic, complemented
303#1947C2×C11311yescharacteristic, complemented
304#1940C2×C11311yescharacteristic, complemented
305#1921C2×C11311yescharacteristic, complemented
306#1919C2×C11311yescharacteristic, complemented
307#1847C2×C11311yescharacteristic, complemented
308#1802C2×C11311yescharacteristic
309#1762C2×C11311yescharacteristic
310C113#2610211yescharacteristic, direct product factor, Sylow
311C2×#125—21no—
312C2×C4×D4C22×C11311yescharacteristic
313C2×#107C22×C11311yescharacteristic
314C2×#107C22×C11311yescharacteristic
315C2×#107C22×C11311yescharacteristic
316C2×#106C22×C11311yescharacteristic
317C2×#106C22×C11311yescharacteristic
318C2×#106C22×C11311yescharacteristic
319C2×C4⋊C8C22×C11311yescharacteristic
320C2×C4⋊C8C22×C11311yescharacteristic
321C2×C4⋊C8C22×C11311yescharacteristic
322C2×#102C22×C11311yescharacteristic
323C2×#102C22×C11311yescharacteristic
324C2×#102C22×C11311yescharacteristic
325C2×#102C22×C11311yescharacteristic
326C2×#97C22×C11311yescharacteristic
327#398—21no—
328#398—21no—
329#390C22×C11311yescharacteristic
330#390C22×C11311yescharacteristic
331#389—21no—
332#389C22×C11311yescharacteristic
333#389C22×C11311yescharacteristic
334#388—21no—
335#388—21no—
336#384C22×C11311yescharacteristic
337#384C22×C11311yescharacteristic
338#384C22×C11311yescharacteristic
339#382C22×C11311yescharacteristic
340#381—21no—
341C4×C4⋊C4C22×C11311yescharacteristic
342C4×C4⋊C4C22×C11311yescharacteristic
343C4×C4⋊C4C22×C11311yescharacteristic
344C4×C4⋊C4C22×C11311yescharacteristic
345C4×C22⋊C4—21no—
346#340C22×C11311yescharacteristic
347#340C22×C11311yescharacteristic
348#340C22×C11311yescharacteristic
349#340C22×C11311yescharacteristic
350#340C22×C11311yescharacteristic
351#340C22×C11311yescharacteristic
352#336C22×C11311yescharacteristic
353#336C22×C11311yescharacteristic
354C22×D4C23×C11311yescharacteristic
355C23×C4—21no—
356C22×C8C23×C11311yescharacteristic
357C22×C8C23×C11311yescharacteristic
358C22×C8C23×C11311yescharacteristic
359C22×C8C23×C11311yescharacteristic
360#125—44no—
361C4×D4—22no—
362C4×D4Q8×C11314yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C11311yescharacteristic
372C2×C4⋊C4D4×C11311yescharacteristic
373C2×C4⋊C4C23×C11311yescharacteristic
374C2×C4⋊C4C23×C11311yescharacteristic
375C2×C4⋊C4C23×C11311yescharacteristic
376C2×C4⋊C4C23×C11311yescharacteristic
377C2×C4⋊C4C23×C11311yescharacteristic
378C2×C4⋊C4C23×C11311yescharacteristic
379C2×C4⋊C4C23×C11311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42C23×C11311yescharacteristic
389C2×C42C23×C11311yescharacteristic
390C2×C42C23×C11311yescharacteristic
391#107—22no—
392#107—41no—
393#107—41no—
394#106—22no—
395#106—41no—
396#106—41no—
397C4⋊C8—22no—
398C4⋊C8—22no—
399C4⋊C8—22no—
400#102—22no—
401#102—22no—
402#102—41no—
403#102—41no—
404#97—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95D4×C11311yescharacteristic
413#95D4×C11311yescharacteristic
414C24—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4C2×Q8×C11312yes—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4C2×D4×C11311yescharacteristic
432C22×C4C2×D4×C11311yescharacteristic
433C22×C4C2×D4×C11311yescharacteristic
434C22×C4C2×D4×C11311yescharacteristic
435C22×C4C2×D4×C11311yescharacteristic
436C22×C4C2×D4×C11311yescharacteristic
437C22×C4C24×C11311yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8#41×C11312yes—
449C2×C8#41×C11312yes—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4C2×Q8×C11312yes—
474C22⋊C4—24no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—42no—
484C42—81no—
485C42—81no—
486C42C2×Q8×C11312yes—
487C42#41×C11312yes—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C22×D4×C11311yescharacteristic
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
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—84no—
536C2×C4C22⋊Q8×C11312yes—
537C2×C4C22⋊Q8×C11312yes—
538C2×C4AGL(1,ℤ/8)×C11312yes—
539C2×C4#137×C11312yes—
540C2×C4C22×Q8×C11311yescharacteristic
541C2×C4C2×#41×C11311yescharacteristic
542C2×C4C2×#41×C11311yescharacteristic
543C2×C4C2×#41×C11311yescharacteristic
544C2×C4H(5,𝔽2)×C11311yescharacteristic
545C2×C42−1+4×C11311yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C22⋊Q8×C11311yescharacteristic
558C22#547×C11311yescharacteristic
559C22#550×C11311yescharacteristic
560C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
561C22C2×#137×C11311yescharacteristic
562C22#576×C11311yescharacteristic
563C22#577×C11311yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C11311yescharacteristic
578C4#544×C11311yescharacteristic
579C4#552×C11311yescharacteristic
580C4#553×C11311yescharacteristic
581C2—82no—
582C2C113×#244111yescharacteristic
583C2C113×#307911yescharacteristic
584C2C113×#308111yescharacteristic
585C2C113×#334511yescharacteristic
586C2C113×#334611yescharacteristic
587C2C113×#339911yescharacteristic
588C2C113×#340011yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC22×D4×C113C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C4⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#2552C2semidirect
7. C113×#1949C2semidirect
8. C113×#1948C2semidirect
9. C113×#1947C2semidirect
10. C113×#1940C2semidirect
11. C113×#1921C2semidirect
12. C113×#1919C2semidirect
13. C113×#1847C2semidirect
286. #26102C113direct (N × H)
295. #2552C2×C113semidirect
301. #1949C2×C113semidirect
302. #1948C2×C113semidirect
303. #1947C2×C113semidirect
304. #1940C2×C113semidirect
305. #1921C2×C113semidirect
306. #1919C2×C113semidirect
307. #1847C2×C113semidirect
310. C113#26102direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#25522
C113×#23572
C113×#20942
C113×#20932
C113×#20672
C113×#20652
C113×#19492
C113×#19482
C113×#19472
C113×#19402
C113×#19212
C113×#19192
C113×#18472
C113×#18022
C113×#17622
#26102113