Finite Group Databasebeta

← C113×#13422 #43281442

Subgroups — C113×#13422 #43281442

Order 28928.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2669C211yesmaximal, characteristic
2C2×#353×C113C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C113C211yesmaximal, characteristic, complemented
4C113×#1889C211yesmaximal, characteristic, complemented
5C113×#1887C211yesmaximal, characteristic, complemented
6C113×#1867C211yesmaximal, characteristic, complemented
7C113×#1390C211yesmaximal, characteristic, complemented
8C2×#127×C113C2211yescharacteristic
9C2×#121×C113—21no—
10C2×#120×C113—21no—
11C2×#120×C113C2211yescharacteristic
12#518×C113C2211yescharacteristic
13#418×C113—21no—
14C2×#100×C113C2211yescharacteristic
15C2×#99×C113C2211yescharacteristic
16C2×#99×C113C2211yescharacteristic
17#394×C113—21no—
18#392×C113—21no—
19#392×C113—21no—
20#388×C113—21no—
21#386×C113C2211yescharacteristic
22#385×C113—21no—
23#379×C113—21no—
24#353×C113—22no—
25AΣL(1,𝔽16)×C113—22no—
26#342×C113—21no—
27#342×C113—21no—
28#339×C113—21no—
29C25×C113D411yescharacteristic
30C22×D4×C113—21no—
31C22×D4×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113—21no—
34C22×D4×C113—21no—
35C22×D4×C113D411yescharacteristic
36C22×D4×C113C2311yescharacteristic
37C23×C4×C113D411yescharacteristic
38C2×M16×C113—21no—
39#127×C113—21no—
40#127×C113—21no—
41#127×C113—21no—
42#127×C113—21no—
43#121×C113—44no—
44#120×C113—21no—
45#120×C113—21no—
46#120×C113—21no—
47#120×C113—21no—
48#120×C113—44no—
49C4×D4×C113—41no—
50C4×D4×C113—41no—
51#117×C113—21no—
52C2×C4⋊C4×C113—21no—
53C2×C4⋊C4×C113—41no—
54C2×C22⋊C4×C113—21no—
55C2×C22⋊C4×C113—21no—
56C2×C22⋊C4×C113—21no—
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—21no—
59C2×C22⋊C4×C113—21no—
60C2×C22⋊C4×C113—21no—
61C2×C22⋊C4×C113—21no—
62C2×C22⋊C4×C113—21no—
63C2×C22⋊C4×C113—21no—
64C2×C22⋊C4×C113—41no—
65C2×C22⋊C4×C113—41no—
66C2×C22⋊C4×C113D411yescharacteristic
67C2×C22⋊C4×C113D411yescharacteristic
68C2×C42×C113D411yescharacteristic
69#102×C113—41no—
70#102×C113—41no—
71#100×C113—21no—
72#100×C113—21no—
73#99×C113—21no—
74#99×C113—21no—
75#99×C113—21no—
76#99×C113D412yescomplemented
77#95×C113—21no—
78#95×C113—21no—
79#95×C113—41no—
80C24×C113—21no—
81C24×C113—21no—
82C24×C113—21no—
83C24×C113—21no—
84C24×C113—41no—
85C24×C113—42no—
86C24×C113—41no—
87C24×C113—81no—
88C24×C113C2×D411yescharacteristic
89C24×C113C2×D411yescharacteristic
90C2×D4×C113—21no—
91C2×D4×C113—21no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—42no—
97C2×D4×C113—42no—
98C2×D4×C113—42no—
99C2×D4×C113—42no—
100C2×D4×C113—42no—
101C2×D4×C113—42no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113—41no—
105C2×D4×C113—41no—
106C2×D4×C113—41no—
107C2×D4×C113—41no—
108C2×D4×C113—81no—
109C2×D4×C113—81no—
110C2×D4×C113—81no—
111C2×D4×C113—81no—
112C2×D4×C113—81no—
113C2×D4×C113—81no—
114C2×D4×C113C2×D411yescharacteristic
115C2×D4×C113#4111yescharacteristic
116C2×D4×C113#4111yescharacteristic
117C2×D4×C113#4111yescharacteristic
118C22×C4×C113—21no—
119C22×C4×C113—21no—
120C22×C4×C113—21no—
121C22×C4×C113—21no—
122C22×C4×C113—21no—
123C22×C4×C113—21no—
124C22×C4×C113—21no—
125C22×C4×C113—21no—
126C22×C4×C113—42no—
127C22×C4×C113—41no—
128C22×C4×C113—41no—
129C22×C4×C113—41no—
130C22×C4×C113C2×D411yescharacteristic
131M16×C113—41no—
132M16×C113—41no—
133C2×C8×C113—41no—
134C4⋊C4×C113—21no—
135C4⋊C4×C113—21no—
136C4⋊C4×C113—42no—
137C4⋊C4×C113—82no—
138C22⋊C4×C113—24no—
139C22⋊C4×C113—22no—
140C22⋊C4×C113—21no—
141C22⋊C4×C113—21no—
142C22⋊C4×C113—42no—
143C22⋊C4×C113—42no—
144C22⋊C4×C113—42no—
145C22⋊C4×C113—41no—
146C22⋊C4×C113—41no—
147C22⋊C4×C113—41no—
148C22⋊C4×C113—41no—
149C22⋊C4×C113—41no—
150C22⋊C4×C113—41no—
151C22⋊C4×C113—41no—
152C22⋊C4×C113—41no—
153C22⋊C4×C113—41no—
154C22⋊C4×C113—81no—
155C22⋊C4×C113—82no—
156C22⋊C4×C113—82no—
157C42×C113—21no—
158C42×C113—21no—
159C42×C113—41no—
160C23×C113—21no—
161C23×C113—21no—
162C23×C113—21no—
163C23×C113—21no—
164C23×C113—22no—
165C23×C113—41no—
166C23×C113—41no—
167C23×C113—41no—
168C23×C113—41no—
169C23×C113—41no—
170C23×C113—41no—
171C23×C113—41no—
172C23×C113—42no—
173C23×C113—41no—
174C23×C113—41no—
175C23×C113—41no—
176C23×C113—41no—
177C23×C113—42no—
178C23×C113—42no—
179C23×C113—41no—
180C23×C113—41no—
181C23×C113—41no—
182C23×C113—41no—
183C23×C113—41no—
184C23×C113—41no—
185C23×C113—81no—
186C23×C113—82no—
187C23×C113—81no—
188C23×C113—82no—
189C23×C113—84no—
190C23×C113—81no—
191C23×C113#12011yescharacteristic
192C23×C113#12111yescharacteristic
193C23×C113#12111yescharacteristic
194C23×C113#12311yescharacteristic
195C23×C113#12411yescharacteristic
196D4×C113—41no—
197D4×C113—41no—
198D4×C113—41no—
199D4×C113—41no—
200D4×C113—42no—
201D4×C113—81no—
202D4×C113—82no—
203D4×C113—82no—
204D4×C113—82no—
205D4×C113—82no—
206D4×C113—84no—
207D4×C113—82no—
208D4×C113—82no—
209D4×C113—84no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—41no—
215C2×C4×C113—41no—
216C2×C4×C113—41no—
217C2×C4×C113—41no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
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—81no—
229C2×C4×C113—81no—
230C2×C4×C113—81no—
231C2×C4×C113—81no—
232C2×C4×C113—81no—
233C2×C4×C113—81no—
234C2×C4×C113—81no—
235C2×C4×C113—81no—
236C2×C4×C113—81no—
237C2×C4×C113—81no—
238C2×C4×C113#12111yescharacteristic
239C2×C4×C113#12311yescharacteristic
240C8×C113—81no—
241C22×C113—21no—
242C22×C113—21no—
243C22×C113—21no—
244C22×C113—21no—
245C22×C113—21no—
246C22×C113—21no—
247C22×C113—41no—
248C22×C113—41no—
249C22×C113—41no—
250C22×C113—41no—
251C22×C113—42no—
252C22×C113—42no—
253C22×C113—41no—
254C22×C113—41no—
255C22×C113—41no—
256C22×C113—41no—
257C22×C113—44no—
258C22×C113—42no—
259C22×C113—81no—
260C22×C113—81no—
261C22×C113—81no—
262C22×C113—81no—
263C22×C113—81no—
264C22×C113—81no—
265C22×C113—81no—
266C22×C113—81no—
267C22×C113—82no—
268C22×C113—82no—
269C22×C113—82no—
270C22×C113—81no—
271C22×C113—81no—
272C22×C113—81no—
273C22×C113—81no—
274C22×C113—81no—
275C22×C113#39411yescharacteristic
276C22×C113B(4,𝔽2)11yescharacteristic
277C22×C113#45811yescharacteristic
278C4×C113—21no—
279C4×C113—21no—
280C4×C113—42no—
281C4×C113—42no—
282C4×C113—81no—
283C4×C113—81no—
284C4×C113—82no—
285C4×C113—81no—
286C4×C113—81no—
287C4×C113—161no—
288#13422C11311yesmaximal, characteristic, direct product factor, Sylow
289C2×C113—21no—
290C2×C113—21no—
291C2×C113—41no—
292C2×C113—41no—
293C2×C113—41no—
294C2×C113—41no—
295C2×C113—82no—
296C2×C113—161no—
297C2×C113#204411yescharacteristic
298C2×C113#219611yescharacteristic
299C2×C113#220011yescharacteristic
300#2669C2×C11311yescharacteristic
301C2×#353C2×C11311yescharacteristic, complemented
302C2×AΣL(1,𝔽16)C2×C11311yescharacteristic, complemented
303#1889C2×C11311yescharacteristic, complemented
304#1887C2×C11311yescharacteristic, complemented
305#1867C2×C11311yescharacteristic, complemented
306#1390C2×C11311yescharacteristic, complemented
307C113#1342211yescharacteristic, direct product factor, Sylow
308C2×#127C22×C11311yescharacteristic
309C2×#121—21no—
310C2×#120—21no—
311C2×#120C22×C11311yescharacteristic
312#518C22×C11311yescharacteristic
313#418—21no—
314C2×#100C22×C11311yescharacteristic
315C2×#99C22×C11311yescharacteristic
316C2×#99C22×C11311yescharacteristic
317#394—21no—
318#392—21no—
319#392—21no—
320#388—21no—
321#386C22×C11311yescharacteristic
322#385—21no—
323#379—21no—
324#353—22no—
325AΣL(1,𝔽16)—22no—
326#342—21no—
327#342—21no—
328#339—21no—
329C25D4×C11311yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C11311yescharacteristic
336C22×D4C23×C11311yescharacteristic
337C23×C4D4×C11311yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C11311yescharacteristic
367C2×C22⋊C4D4×C11311yescharacteristic
368C2×C42D4×C11311yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C11312yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C11311yescharacteristic
389C24C2×D4×C11311yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C11311yescharacteristic
415C2×D4#41×C11311yescharacteristic
416C2×D4#41×C11311yescharacteristic
417C2×D4#41×C11311yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C11311yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C11311yescharacteristic
492C23#121×C11311yescharacteristic
493C23#121×C11311yescharacteristic
494C23#123×C11311yescharacteristic
495C23#124×C11311yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
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—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C11311yescharacteristic
539C2×C4#123×C11311yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#394×C11311yescharacteristic
576C22B(4,𝔽2)×C11311yescharacteristic
577C22#458×C11311yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2C113×#204411yescharacteristic
597C2C113×#219611yescharacteristic
598C2C113×#220011yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C113
prime radicalC113×#2669C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C22×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C113C2semidirect
3. C2×AΣL(1,𝔽16)×C113C2semidirect
4. C113×#1889C2semidirect
5. C113×#1887C2semidirect
6. C113×#1867C2semidirect
7. C113×#1390C2semidirect
76. #99×C113D4semidirect
288. #13422C113direct (N × H)
301. C2×#353C2×C113semidirect
302. C2×AΣL(1,𝔽16)C2×C113semidirect
303. #1889C2×C113semidirect
304. #1887C2×C113semidirect
305. #1867C2×C113semidirect
306. #1390C2×C113semidirect
307. C113#13422direct (N × H)
376. #99D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#26692
C2×#353×C1132
C2×AΣL(1,𝔽16)×C1132
C113×#18892
C113×#18872
C113×#18672
C113×#13902
#13422113