Finite Group Databasebeta

← C113×#12705 #43280725

Subgroups — C113×#12705 #43280725

Order 28928.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3484C211yesmaximal, characteristic
2C113×#2121C214yesmaximal, complemented
3C113×#1783C211yesmaximal, characteristic, complemented
4C113×#1781C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C113C411yescharacteristic, complemented
6C23×D4×C113C2211yescharacteristic
7#546×C113—24no—
8D42×C113—24no—
9#535×C113—21no—
10#534×C113—21no—
11#534×C113C2212yes—
12#525×C113—21no—
13C2×#120×C113—21no—
14C2×#120×C113C412yescomplemented
15#518×C113C411yescharacteristic, complemented
16C2×#100×C113—21no—
17C2×#100×C113C2212yescomplemented
18C2×#99×C113—21no—
19C2×#99×C113C2212yescomplemented
20#407×C113—21no—
21#379×C113—21no—
22#352×C113—24no—
23AΣL(1,𝔽16)×C113—24no—
24C25×C113C2×C411yescharacteristic
25C25×C113D411yescharacteristic
26H(5,𝔽2)×C113—42no—
27H(5,𝔽2)×C113—42no—
28C2×#41×C113—21no—
29C2×#41×C113—22no—
30C22×D4×C113—21no—
31C22×D4×C113—22no—
32C22×D4×C113—22no—
33C22×D4×C113—22no—
34C22×D4×C113—24no—
35C22×D4×C113—42no—
36C22×D4×C113—42no—
37C22×D4×C113C2×C411yescharacteristic
38C22×D4×C113C2×C412yes—
39C22×D4×C113D411yescharacteristic
40C22×D4×C113D411yescharacteristic
41C22×D4×C113C2311yescharacteristic
42C23×C4×C113D411yescharacteristic
43C2×M16×C113—22no—
44#127×C113—22no—
45#124×C113—22no—
46#123×C113—22no—
47#123×C113—22no—
48#123×C113D414yes—
49C22⋊Q8×C113—22no—
50#121×C113—22no—
51#121×C113—24no—
52#121×C113—24no—
53#121×C113—24no—
54#120×C113—24no—
55#120×C113—22no—
56#120×C113—22no—
57#120×C113—22no—
58#120×C113—22no—
59#120×C113—24no—
60#120×C113D414yes—
61C4×D4×C113—24no—
62C4×D4×C113—24no—
63#117×C113—21no—
64C2×C22⋊C4×C113—22no—
65C2×C22⋊C4×C113—21no—
66C2×C22⋊C4×C113—22no—
67C2×C22⋊C4×C113—22no—
68C2×C22⋊C4×C113—42no—
69C2×C22⋊C4×C113C2×C412yes—
70#100×C113—24no—
71#100×C113—42no—
72#99×C113—24no—
73#99×C113—42no—
74C22⋊C8×C113—42no—
75C24×C113—21no—
76C24×C113—22no—
77C24×C113—22no—
78C24×C113—22no—
79C24×C113—41no—
80C24×C113—41no—
81C24×C113—41no—
82C24×C113—82no—
83C24×C113—82no—
84C24×C113C22⋊C411yescharacteristic
85C24×C113C22⋊C411yescharacteristic
86C24×C113C22⋊C411yescharacteristic
87C24×C113C22⋊C412yescomplemented
88C24×C113C22×C411yescharacteristic
89C24×C113C2×D411yescharacteristic
90#41×C113—42no—
91#41×C113—48no—
92#41×C113—42no—
93C2×Q8×C113—21no—
94C2×D4×C113—22no—
95C2×D4×C113—22no—
96C2×D4×C113—24no—
97C2×D4×C113—22no—
98C2×D4×C113—21no—
99C2×D4×C113—22no—
100C2×D4×C113—22no—
101C2×D4×C113—22no—
102C2×D4×C113—22no—
103C2×D4×C113—24no—
104C2×D4×C113—24no—
105C2×D4×C113—22no—
106C2×D4×C113—22no—
107C2×D4×C113—22no—
108C2×D4×C113—41no—
109C2×D4×C113—41no—
110C2×D4×C113—41no—
111C2×D4×C113—41no—
112C2×D4×C113—416no—
113C2×D4×C113—48no—
114C2×D4×C113—42no—
115C2×D4×C113—42no—
116C2×D4×C113—42no—
117C2×D4×C113—42no—
118C2×D4×C113—84no—
119C2×D4×C113—84no—
120C2×D4×C113C2×D414yes—
121C22×C4×C113—21no—
122C22×C4×C113—22no—
123C22×C4×C113—22no—
124C22×C4×C113—22no—
125C22×C4×C113—22no—
126C22×C4×C113—22no—
127C22×C4×C113—41no—
128C22×C4×C113—42no—
129C22×C4×C113C22⋊C411yescharacteristic
130C22×C4×C113C22⋊C412yescomplemented
131C22×C4×C113C2×D411yescharacteristic
132M16×C113—42no—
133M16×C113—42no—
134C2×C8×C113—42no—
135C4⋊C4×C113—22no—
136C4⋊C4×C113—24no—
137C22⋊C4×C113—24no—
138C22⋊C4×C113—22no—
139C22⋊C4×C113—24no—
140C22⋊C4×C113—22no—
141C22⋊C4×C113—24no—
142C22⋊C4×C113—24no—
143C22⋊C4×C113—42no—
144C22⋊C4×C113—42no—
145C22⋊C4×C113—84no—
146C22⋊C4×C113C22⋊C414yescomplemented
147C42×C113—22no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—21no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—21no—
154C23×C113—21no—
155C23×C113—21no—
156C23×C113—21no—
157C23×C113—21no—
158C23×C113—22no—
159C23×C113—21no—
160C23×C113—21no—
161C23×C113—42no—
162C23×C113—44no—
163C23×C113—44no—
164C23×C113—44no—
165C23×C113—44no—
166C23×C113—44no—
167C23×C113—42no—
168C23×C113—42no—
169C23×C113—82no—
170C23×C113—82no—
171C23×C113—82no—
172C23×C113—81no—
173C23×C113—81no—
174C23×C113—81no—
175C23×C113—81no—
176C23×C113—82no—
177C23×C113—82no—
178C23×C113—82no—
179C23×C113—82no—
180C23×C113—82no—
181C23×C113—82no—
182C23×C113—82no—
183C23×C113—82no—
184C23×C113#9912yes—
185C23×C113C2×C22⋊C412yes—
186C23×C113C2×C22⋊C411yescharacteristic
187C23×C113#12012yes—
188Q8×C113—42no—
189D4×C113—28no—
190D4×C113—44no—
191D4×C113—44no—
192D4×C113—44no—
193D4×C113—42no—
194D4×C113—44no—
195D4×C113—44no—
196D4×C113—48no—
197D4×C113—42no—
198D4×C113—42no—
199D4×C113—84no—
200D4×C113—84no—
201C2×C4×C113—21no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—21no—
205C2×C4×C113—24no—
206C2×C4×C113—22no—
207C2×C4×C113—44no—
208C2×C4×C113—44no—
209C2×C4×C113—42no—
210C2×C4×C113—42no—
211C2×C4×C113—82no—
212C2×C4×C113—82no—
213C2×C4×C113—82no—
214C2×C4×C113—84no—
215C2×C4×C113#9912yes—
216C2×C4×C113#12012yes—
217C8×C113—82no—
218C22×C113—22no—
219C22×C113—22no—
220C22×C113—22no—
221C22×C113—22no—
222C22×C113—22no—
223C22×C113—22no—
224C22×C113—41no—
225C22×C113—42no—
226C22×C113—42no—
227C22×C113—42no—
228C22×C113—42no—
229C22×C113—42no—
230C22×C113—41no—
231C22×C113—41no—
232C22×C113—41no—
233C22×C113—44no—
234C22×C113—42no—
235C22×C113—41no—
236C22×C113—42no—
237C22×C113—41no—
238C22×C113—81no—
239C22×C113—81no—
240C22×C113—81no—
241C22×C113—81no—
242C22×C113—81no—
243C22×C113—81no—
244C22×C113—88no—
245C22×C113—88no—
246C22×C113—162no—
247C22×C113—162no—
248C22×C113#37911yescharacteristic
249C22×C113C2×#9911yescharacteristic
250C22×C113C2×#9911yescharacteristic
251C4×C113—22no—
252C4×C113—22no—
253C4×C113—44no—
254C4×C113—42no—
255C4×C113—162no—
256#12705C11311yesmaximal, characteristic, direct product factor, Sylow
257C2×C113—21no—
258C2×C113—21no—
259C2×C113—21no—
260C2×C113—42no—
261C2×C113—42no—
262C2×C113—42no—
263C2×C113—42no—
264C2×C113—81no—
265C2×C113—82no—
266C2×C113#178111yescharacteristic
267#3484C2×C11311yescharacteristic
268#2121C2×C11314yescomplemented
269#1783C2×C11311yescharacteristic, complemented
270#1781C2×C11311yescharacteristic, complemented
271C113#1270511yescharacteristic, direct product factor, Sylow
272C2×H(5,𝔽2)C4×C11311yescharacteristic, complemented
273C23×D4C22×C11311yescharacteristic
274#546—24no—
275D42—24no—
276#535—21no—
277#534—21no—
278#534C22×C11312yes—
279#525—21no—
280C2×#120—21no—
281C2×#120C4×C11312yescomplemented
282#518C4×C11311yescharacteristic, complemented
283C2×#100—21no—
284C2×#100C22×C11312yescomplemented
285C2×#99—21no—
286C2×#99C22×C11312yescomplemented
287#407—21no—
288#379—21no—
289#352—24no—
290AΣL(1,𝔽16)—24no—
291C25C2×C4×C11311yescharacteristic
292C25D4×C11311yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C11311yescharacteristic
305C22×D4C2×C4×C11312yes—
306C22×D4D4×C11311yescharacteristic
307C22×D4D4×C11311yescharacteristic
308C22×D4C23×C11311yescharacteristic
309C23×C4D4×C11311yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C11314yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C11314yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C11312yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C11311yescharacteristic
352C24C22⋊C4×C11311yescharacteristic
353C24C22⋊C4×C11311yescharacteristic
354C24C22⋊C4×C11312yescomplemented
355C24C22×C4×C11311yescharacteristic
356C24C2×D4×C11311yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C11314yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C11311yescharacteristic
397C22×C4C22⋊C4×C11312yescomplemented
398C22×C4C2×D4×C11311yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C11314yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C11312yes—
452C23C2×C22⋊C4×C11312yes—
453C23C2×C22⋊C4×C11311yescharacteristic
454C23#120×C11312yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C11312yes—
483C2×C4#120×C11312yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22#379×C11311yescharacteristic
516C22C2×#99×C11311yescharacteristic
517C22C2×#99×C11311yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2C113×#178111yescharacteristic
subgroupG/H
center, socleC2×C113#1781
commutatorC24C22×C4×C113
Frattini, cosocleC22×D4C23×C113
prime radicalC113×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C23×C113 ◁ C23×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2121C2semidirect
3. C113×#1783C2semidirect
4. C113×#1781C2semidirect
5. C2×H(5,𝔽2)×C113C4semidirect
14. C2×#120×C113C4semidirect
15. #518×C113C4semidirect
17. C2×#100×C113C22semidirect
19. C2×#99×C113C22semidirect
87. C24×C113C22⋊C4semidirect
130. C22×C4×C113C22⋊C4semidirect
146. C22⋊C4×C113C22⋊C4semidirect
256. #12705C113direct (N × H)
268. #2121C2×C113semidirect
269. #1783C2×C113semidirect
270. #1781C2×C113semidirect
271. C113#12705direct (N × H)
272. C2×H(5,𝔽2)C4×C113semidirect
281. C2×#120C4×C113semidirect
282. #518C4×C113semidirect
284. C2×#100C22×C113semidirect
286. C2×#99C22×C113semidirect
354. C24C22⋊C4×C113semidirect
397. C22×C4C22⋊C4×C113semidirect
413. C22⋊C4C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C113×#21212
C113×#17832
C113×#17812
#12705113