Finite Group Databasebeta

← C113×#8534 #43276554

Subgroups — C113×#8534 #43276554

Order 28928.

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 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×#1898C214yesmaximal, complemented
3C113×#1781C211yesmaximal, characteristic, complemented
4C113×#1438C211yesmaximal, 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×C113C412yescomplemented
12#525×C113—21no—
13C2×#120×C113—21no—
14C2×#120×C113C2212yes—
15#518×C113C411yescharacteristic, complemented
16C22×C22⋊C4×C113—21no—
17C22×C22⋊C4×C113C2212yescomplemented
18C2×#99×C113—21no—
19C2×#99×C113—21no—
20C2×#99×C113—24no—
21#379×C113C2212yescomplemented
22C2×#95×C113—21no—
23#342×C113—24no—
24C25×C113D411yescharacteristic
25C25×C113C2311yescharacteristic
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—24no—
33C22×D4×C113—22no—
34C22×D4×C113—42no—
35C22×D4×C113—42no—
36C22×D4×C113C2×C411yescharacteristic
37C22×D4×C113C2×C411yescharacteristic
38C22×D4×C113C2×C412yes—
39C22×D4×C113D411yescharacteristic
40C22×D4×C113D411yescharacteristic
41C22×D4×C113D414yes—
42C23×C4×C113—22no—
43C23×C4×C113D411yescharacteristic
44#127×C113—22no—
45#124×C113—22no—
46#123×C113—22no—
47#123×C113—22no—
48#123×C113—22no—
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—22no—
60#120×C113—24no—
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—24no—
67C2×C22⋊C4×C113—24no—
68C2×C22⋊C4×C113—22no—
69C2×C22⋊C4×C113—44no—
70C2×C22⋊C4×C113—44no—
71C2×C22⋊C4×C113—42no—
72C2×C22⋊C4×C113C2×C412yes—
73C2×C22⋊C4×C113D414yes—
74#99×C113—48no—
75#99×C113—42no—
76#99×C113—42no—
77#95×C113—42no—
78C24×C113—21no—
79C24×C113—22no—
80C24×C113—22no—
81C24×C113—42no—
82C24×C113—41no—
83C24×C113—41no—
84C24×C113—41no—
85C24×C113—42no—
86C24×C113—42no—
87C24×C113—42no—
88C24×C113C22⋊C411yescharacteristic
89C24×C113C22⋊C411yescharacteristic
90C24×C113C22⋊C412yescomplemented
91C24×C113C22×C411yescharacteristic
92C24×C113C2×D411yescharacteristic
93C24×C113C2×D414yes—
94C24×C113C2×D411yescharacteristic
95#41×C113—42no—
96#41×C113—48no—
97#41×C113—42no—
98C2×Q8×C113—21no—
99C2×D4×C113—22no—
100C2×D4×C113—22no—
101C2×D4×C113—22no—
102C2×D4×C113—21no—
103C2×D4×C113—22no—
104C2×D4×C113—22no—
105C2×D4×C113—22no—
106C2×D4×C113—22no—
107C2×D4×C113—24no—
108C2×D4×C113—22no—
109C2×D4×C113—22no—
110C2×D4×C113—24no—
111C2×D4×C113—24no—
112C2×D4×C113—22no—
113C2×D4×C113—22no—
114C2×D4×C113—41no—
115C2×D4×C113—41no—
116C2×D4×C113—41no—
117C2×D4×C113—41no—
118C2×D4×C113—416no—
119C2×D4×C113—48no—
120C2×D4×C113—42no—
121C2×D4×C113—42no—
122C2×D4×C113—42no—
123C2×D4×C113—42no—
124C2×D4×C113—44no—
125C2×D4×C113—44no—
126C2×D4×C113—82no—
127C2×D4×C113—82no—
128C22×C4×C113—21no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—24no—
134C22×C4×C113—41no—
135C22×C4×C113—42no—
136C22×C4×C113—42no—
137C22×C4×C113—42no—
138C22×C4×C113—42no—
139C22×C4×C113—42no—
140C22×C4×C113—42no—
141C22×C4×C113—42no—
142C22×C4×C113C22⋊C411yescharacteristic
143C22×C4×C113C22⋊C411yescharacteristic
144C22×C4×C113C22⋊C414yescomplemented
145C22×C4×C113C22⋊C412yescomplemented
146C4⋊C4×C113—22no—
147C4⋊C4×C113—24no—
148C22⋊C4×C113—22no—
149C22⋊C4×C113—24no—
150C22⋊C4×C113—24no—
151C22⋊C4×C113—22no—
152C22⋊C4×C113—22no—
153C22⋊C4×C113—24no—
154C22⋊C4×C113—24no—
155C22⋊C4×C113—28no—
156C22⋊C4×C113—44no—
157C22⋊C4×C113—48no—
158C22⋊C4×C113—42no—
159C22⋊C4×C113—42no—
160C22⋊C4×C113—44no—
161C22⋊C4×C113—44no—
162C42×C113—22no—
163C23×C113—21no—
164C23×C113—21no—
165C23×C113—22no—
166C23×C113—22no—
167C23×C113—21no—
168C23×C113—21no—
169C23×C113—21no—
170C23×C113—21no—
171C23×C113—21no—
172C23×C113—21no—
173C23×C113—24no—
174C23×C113—24no—
175C23×C113—21no—
176C23×C113—22no—
177C23×C113—21no—
178C23×C113—21no—
179C23×C113—44no—
180C23×C113—42no—
181C23×C113—44no—
182C23×C113—42no—
183C23×C113—44no—
184C23×C113—42no—
185C23×C113—42no—
186C23×C113—42no—
187C23×C113—44no—
188C23×C113—42no—
189C23×C113—42no—
190C23×C113—42no—
191C23×C113—44no—
192C23×C113—42no—
193C23×C113—42no—
194C23×C113—82no—
195C23×C113—81no—
196C23×C113—82no—
197C23×C113—82no—
198C23×C113—81no—
199C23×C113—81no—
200C23×C113—82no—
201C23×C113—81no—
202C23×C113—81no—
203C23×C113—81no—
204C23×C113—82no—
205C23×C113#9912yescomplemented
206C23×C113C2×C22⋊C412yes—
207C23×C113C2×C22⋊C411yescharacteristic
208C23×C113#12012yes—
209C23×C113#12012yes—
210Q8×C113—42no—
211D4×C113—28no—
212D4×C113—44no—
213D4×C113—42no—
214D4×C113—44no—
215D4×C113—44no—
216D4×C113—44no—
217D4×C113—44no—
218D4×C113—42no—
219D4×C113—42no—
220D4×C113—44no—
221D4×C113—44no—
222D4×C113—84no—
223D4×C113—84no—
224C2×C4×C113—21no—
225C2×C4×C113—21no—
226C2×C4×C113—24no—
227C2×C4×C113—22no—
228C2×C4×C113—21no—
229C2×C4×C113—21no—
230C2×C4×C113—21no—
231C2×C4×C113—44no—
232C2×C4×C113—44no—
233C2×C4×C113—42no—
234C2×C4×C113—44no—
235C2×C4×C113—42no—
236C2×C4×C113—44no—
237C2×C4×C113—44no—
238C2×C4×C113—44no—
239C2×C4×C113—82no—
240C2×C4×C113—82no—
241C2×C4×C113—82no—
242C2×C4×C113—82no—
243C2×C4×C113—82no—
244C2×C4×C113—82no—
245C2×C4×C113—84no—
246C2×C4×C113#9912yescomplemented
247C22×C113—21no—
248C22×C113—22no—
249C22×C113—21no—
250C22×C113—22no—
251C22×C113—21no—
252C22×C113—21no—
253C22×C113—22no—
254C22×C113—22no—
255C22×C113—22no—
256C22×C113—22no—
257C22×C113—22no—
258C22×C113—22no—
259C22×C113—24no—
260C22×C113—24no—
261C22×C113—42no—
262C22×C113—42no—
263C22×C113—42no—
264C22×C113—42no—
265C22×C113—41no—
266C22×C113—44no—
267C22×C113—42no—
268C22×C113—84no—
269C22×C113—81no—
270C22×C113—81no—
271C22×C113—81no—
272C22×C113—81no—
273C22×C113—81no—
274C22×C113—84no—
275C22×C113—84no—
276C22×C113—84no—
277C22×C113—81no—
278C22×C113—162no—
279C22×C113—162no—
280C22×C113#37911yescharacteristic
281C22×C113C2×#9911yescharacteristic
282C22×C113C2×#9911yescharacteristic
283C22×C113B(4,𝔽2)12yes—
284C22×C113#45812yes—
285C4×C113—22no—
286C4×C113—41no—
287C4×C113—42no—
288C4×C113—44no—
289C4×C113—84no—
290C4×C113—162no—
291#8534C11311yesmaximal, characteristic, direct product factor, Sylow
292C2×C113—22no—
293C2×C113—21no—
294C2×C113—21no—
295C2×C113—22no—
296C2×C113—42no—
297C2×C113—42no—
298C2×C113—42no—
299C2×C113—81no—
300C2×C113—82no—
301C2×C113#178111yescharacteristic
302C2×C113#179012yes—
303#3484C2×C11311yescharacteristic
304#1898C2×C11314yescomplemented
305#1781C2×C11311yescharacteristic, complemented
306#1438C2×C11311yescharacteristic, complemented
307C113#853411yescharacteristic, direct product factor, Sylow
308C2×H(5,𝔽2)C4×C11311yescharacteristic, complemented
309C23×D4C22×C11311yescharacteristic
310#546—24no—
311D42—24no—
312#535—21no—
313#534—21no—
314#534C4×C11312yescomplemented
315#525—21no—
316C2×#120—21no—
317C2×#120C22×C11312yes—
318#518C4×C11311yescharacteristic, complemented
319C22×C22⋊C4—21no—
320C22×C22⋊C4C22×C11312yescomplemented
321C2×#99—24no—
322C2×#99—21no—
323C2×#99—21no—
324#379C22×C11312yescomplemented
325C2×#95—21no—
326#342—24no—
327C25D4×C11311yescharacteristic
328C25C23×C11311yescharacteristic
329H(5,𝔽2)—42no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×C4×C11311yescharacteristic
340C22×D4C2×C4×C11311yescharacteristic
341C22×D4C2×C4×C11312yes—
342C22×D4D4×C11311yescharacteristic
343C22×D4D4×C11311yescharacteristic
344C22×D4D4×C11314yes—
345C23×C4—22no—
346C23×C4D4×C11311yescharacteristic
347#127—22no—
348#124—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352C22⋊Q8—22no—
353#121—22no—
354#121—24no—
355#121—24no—
356#121—24no—
357#120—24no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—22no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C2×C4×C11312yes—
376C2×C22⋊C4D4×C11314yes—
377#99—48no—
378#99—42no—
379#99—42no—
380#95—42no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊C4×C11311yescharacteristic
392C24C22⋊C4×C11311yescharacteristic
393C24C22⋊C4×C11312yescomplemented
394C24C22×C4×C11311yescharacteristic
395C24C2×D4×C11311yescharacteristic
396C24C2×D4×C11314yes—
397C24C2×D4×C11311yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C22⋊C4×C11311yescharacteristic
446C22×C4C22⋊C4×C11311yescharacteristic
447C22×C4C22⋊C4×C11314yescomplemented
448C22×C4C22⋊C4×C11312yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—28no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—21no—
479C23—22no—
480C23—21no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#99×C11312yescomplemented
509C23C2×C22⋊C4×C11312yes—
510C23C2×C22⋊C4×C11311yescharacteristic
511C23#120×C11312yes—
512C23#120×C11312yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—84no—
549C2×C4#99×C11312yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22#379×C11311yescharacteristic
584C22C2×#99×C11311yescharacteristic
585C22C2×#99×C11311yescharacteristic
586C22B(4,𝔽2)×C11312yes—
587C22#458×C11312yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—84no—
593C4—162no—
594C2—22no—
595C2—21no—
596C2—21no—
597C2—22no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2C113×#178111yescharacteristic
604C2C113×#179012yes—
subgroupG/H
center, socleC22×C113#379
commutatorC24C22×C4×C113
Frattini, cosocleC25C23×C113
prime radicalC113×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1898C2semidirect
3. C113×#1781C2semidirect
4. C113×#1438C2semidirect
5. C2×H(5,𝔽2)×C113C4semidirect
11. #534×C113C4semidirect
15. #518×C113C4semidirect
17. C22×C22⋊C4×C113C22semidirect
21. #379×C113C22semidirect
90. C24×C113C22⋊C4semidirect
144. C22×C4×C113C22⋊C4semidirect
145. C22×C4×C113C22⋊C4semidirect
205. C23×C113#99semidirect
246. C2×C4×C113#99semidirect
291. #8534C113direct (N × H)
304. #1898C2×C113semidirect
305. #1781C2×C113semidirect
306. #1438C2×C113semidirect
307. C113#8534direct (N × H)
308. C2×H(5,𝔽2)C4×C113semidirect
314. #534C4×C113semidirect
318. #518C4×C113semidirect
320. C22×C22⋊C4C22×C113semidirect
324. #379C22×C113semidirect
393. C24C22⋊C4×C113semidirect
447. C22×C4C22⋊C4×C113semidirect
448. C22×C4C22⋊C4×C113semidirect
508. C23#99×C113semidirect
549. C2×C4#99×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C113×#18982
C113×#17812
C113×#14382
#8534113