Finite Group Databasebeta

← C113×#13080 #43281100

Subgroups — C113×#13080 #43281100

Order 28928.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C113C211yesmaximal, characteristic
2C113×#2405C211yesmaximal, characteristic
3C2×#352×C113C212yesmaximal, complemented
4C113×#1781C211yesmaximal, characteristic
5C113×#1390C212yesmaximal, complemented
6C23×D4×C113C2211yescharacteristic
7C22×M16×C113—21no—
8C2×#123×C113C411yescharacteristic, complemented
9C2×#123×C113C2211yescharacteristic
10C22×C22⋊C4×C113C411yescharacteristic, complemented
11C2×#100×C113—21no—
12C2×#100×C113—24no—
13C2×#100×C113C2212yes—
14C2×#99×C113—21no—
15C2×#99×C113C2212yes—
16#394×C113—21no—
17#394×C113—21no—
18#386×C113C411yescharacteristic, complemented
19#386×C113C2211yescharacteristic
20#385×C113—21no—
21#379×C113—21no—
22#379×C113—21no—
23#379×C113C411yescharacteristic, complemented
24#352×C113—24no—
25C25×C113C2×C411yescharacteristic
26C25×C113D411yescharacteristic
27C22×D4×C113—22no—
28C22×D4×C113—22no—
29C22×D4×C113—42no—
30C22×D4×C113—41no—
31C22×D4×C113—41no—
32C22×D4×C113C2×C411yescharacteristic
33C22×D4×C113D411yescharacteristic
34C22×D4×C113D411yescharacteristic
35C22×D4×C113C2311yescharacteristic
36C23×C4×C113C2×C411yescharacteristic
37C23×C4×C113C2×C411yescharacteristic
38C23×C4×C113D411yescharacteristic
39C2×M16×C113—24no—
40C2×M16×C113—22no—
41C2×M16×C113—41no—
42C2×M16×C113—42no—
43C22×C8×C113—41no—
44#123×C113—22no—
45#123×C113—22no—
46#123×C113—42no—
47C2×C4⋊C4×C113—21no—
48C2×C4⋊C4×C113—21no—
49C2×C22⋊C4×C113—21no—
50C2×C22⋊C4×C113—21no—
51C2×C22⋊C4×C113—21no—
52C2×C22⋊C4×C113—21no—
53C2×C22⋊C4×C113—21no—
54C2×C22⋊C4×C113—22no—
55C2×C22⋊C4×C113—21no—
56C2×C22⋊C4×C113—21no—
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—41no—
59C2×C22⋊C4×C113—41no—
60C2×C22⋊C4×C113—41no—
61C2×C22⋊C4×C113—41no—
62C2×C22⋊C4×C113C2×C411yescharacteristic
63C2×C22⋊C4×C113C2×C411yescharacteristic
64#100×C113—24no—
65#100×C113—22no—
66#100×C113D414yes—
67#99×C113—22no—
68#99×C113—22no—
69#99×C113—42no—
70#95×C113—21no—
71#95×C113—21no—
72C24×C113—21no—
73C24×C113—21no—
74C24×C113—21no—
75C24×C113—21no—
76C24×C113—22no—
77C24×C113—22no—
78C24×C113—41no—
79C24×C113—41no—
80C24×C113—42no—
81C24×C113—42no—
82C24×C113—81no—
83C24×C113—81no—
84C24×C113C22⋊C411yescharacteristic
85C24×C113C22⋊C411yescharacteristic
86C24×C113C22⋊C411yescharacteristic
87C24×C113C22×C411yescharacteristic
88C24×C113C2×D411yescharacteristic
89C2×D4×C113—22no—
90C2×D4×C113—22no—
91C2×D4×C113—22no—
92C2×D4×C113—22no—
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—41no—
96C2×D4×C113—41no—
97C2×D4×C113—41no—
98C2×D4×C113—41no—
99C2×D4×C113—41no—
100C2×D4×C113—41no—
101C2×D4×C113—44no—
102C2×D4×C113—44no—
103C2×D4×C113—44no—
104C2×D4×C113—44no—
105C2×D4×C113C2×D412yes—
106C2×D4×C113#4112yes—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113—22no—
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113—21no—
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113—21no—
116C22×C4×C113—22no—
117C22×C4×C113—41no—
118C22×C4×C113—41no—
119C22×C4×C113—41no—
120C22×C4×C113—42no—
121C22×C4×C113—81no—
122C22×C4×C113C22⋊C411yescharacteristic
123C22×C4×C113C2×D411yescharacteristic
124M16×C113—24no—
125M16×C113—44no—
126M16×C113—42no—
127C2×C8×C113—44no—
128C2×C8×C113—42no—
129C4⋊C4×C113—42no—
130C4⋊C4×C113—41no—
131C4⋊C4×C113—41no—
132C22⋊C4×C113—22no—
133C22⋊C4×C113—42no—
134C22⋊C4×C113—42no—
135C22⋊C4×C113—42no—
136C22⋊C4×C113—41no—
137C22⋊C4×C113—41no—
138C22⋊C4×C113—42no—
139C22⋊C4×C113—41no—
140C22⋊C4×C113—42no—
141C22⋊C4×C113—42no—
142C22⋊C4×C113—81no—
143C22⋊C4×C113—81no—
144C22⋊C4×C113—81no—
145C22⋊C4×C113—82no—
146C22⋊C4×C113—82no—
147C23×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—21no—
159C23×C113—21no—
160C23×C113—41no—
161C23×C113—42no—
162C23×C113—42no—
163C23×C113—42no—
164C23×C113—42no—
165C23×C113—41no—
166C23×C113—41no—
167C23×C113—41no—
168C23×C113—41no—
169C23×C113—41no—
170C23×C113—41no—
171C23×C113—42no—
172C23×C113—42no—
173C23×C113—41no—
174C23×C113—41no—
175C23×C113—42no—
176C23×C113—42no—
177C23×C113—81no—
178C23×C113—81no—
179C23×C113—81no—
180C23×C113—81no—
181C23×C113—84no—
182C23×C113—84no—
183C23×C113—84no—
184C23×C113—84no—
185C23×C113#9911yescharacteristic
186C23×C113#9911yescharacteristic
187C23×C113C2×C22⋊C411yescharacteristic
188C23×C113C4×D412yes—
189C23×C113#12112yes—
190D4×C113—42no—
191D4×C113—42no—
192D4×C113—44no—
193D4×C113—44no—
194D4×C113—42no—
195D4×C113—42no—
196C2×C4×C113—22no—
197C2×C4×C113—22no—
198C2×C4×C113—22no—
199C2×C4×C113—22no—
200C2×C4×C113—21no—
201C2×C4×C113—21no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—41no—
205C2×C4×C113—41no—
206C2×C4×C113—41no—
207C2×C4×C113—41no—
208C2×C4×C113—41no—
209C2×C4×C113—41no—
210C2×C4×C113—41no—
211C2×C4×C113—41no—
212C2×C4×C113—41no—
213C2×C4×C113—41no—
214C2×C4×C113—41no—
215C2×C4×C113—41no—
216C2×C4×C113—82no—
217C2×C4×C113—82no—
218C2×C4×C113—82no—
219C2×C4×C113—82no—
220C2×C4×C113—82no—
221C2×C4×C113#9912yes—
222C2×C4×C113#12011yescharacteristic
223C2×C4×C113#12311yescharacteristic
224C8×C113—44no—
225C22×C113—21no—
226C22×C113—21no—
227C22×C113—21no—
228C22×C113—21no—
229C22×C113—21no—
230C22×C113—21no—
231C22×C113—21no—
232C22×C113—22no—
233C22×C113—22no—
234C22×C113—42no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113—42no—
238C22×C113—42no—
239C22×C113—42no—
240C22×C113—41no—
241C22×C113—41no—
242C22×C113—41no—
243C22×C113—41no—
244C22×C113—41no—
245C22×C113—41no—
246C22×C113—41no—
247C22×C113—41no—
248C22×C113—41no—
249C22×C113—41no—
250C22×C113—81no—
251C22×C113—84no—
252C22×C113—84no—
253C22×C113—81no—
254C22×C113—81no—
255C22×C113—81no—
256C22×C113—84no—
257C22×C113—84no—
258C22×C113#35212yescomplemented
259C22×C113#38611yescharacteristic
260C22×C113C2×#9911yescharacteristic
261C22×C113C2×#9911yescharacteristic
262C4×C113—21no—
263C4×C113—22no—
264C4×C113—21no—
265C4×C113—81no—
266C4×C113—81no—
267C4×C113—81no—
268C4×C113—81no—
269C4×C113—162no—
270#13080C11311yesmaximal, characteristic, direct product factor, Sylow
271C2×C113—21no—
272C2×C113—21no—
273C2×C113—22no—
274C2×C113—42no—
275C2×C113—41no—
276C2×C113—42no—
277C2×C113—81no—
278C2×C113—81no—
279C2×C113#189811yescharacteristic
280C2×C113C2×#35211yescharacteristic
281C2×C113#212111yescharacteristic
282C22×#100C2×C11311yescharacteristic
283#2405C2×C11311yescharacteristic
284C2×#352C2×C11312yescomplemented
285#1781C2×C11311yescharacteristic
286#1390C2×C11312yescomplemented
287C113#1308011yescharacteristic, direct product factor, Sylow
288C23×D4C22×C11311yescharacteristic
289C22×M16—21no—
290C2×#123C4×C11311yescharacteristic, complemented
291C2×#123C22×C11311yescharacteristic
292C22×C22⋊C4C4×C11311yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C11312yes—
296C2×#99—21no—
297C2×#99C22×C11312yes—
298#394—21no—
299#394—21no—
300#386C4×C11311yescharacteristic, complemented
301#386C22×C11311yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C11311yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C11311yescharacteristic
308C25D4×C11311yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C11311yescharacteristic
315C22×D4D4×C11311yescharacteristic
316C22×D4D4×C11311yescharacteristic
317C22×D4C23×C11311yescharacteristic
318C23×C4C2×C4×C11311yescharacteristic
319C23×C4C2×C4×C11311yescharacteristic
320C23×C4D4×C11311yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C11311yescharacteristic
345C2×C22⋊C4C2×C4×C11311yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C11314yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C11311yescharacteristic
367C24C22⋊C4×C11311yescharacteristic
368C24C22⋊C4×C11311yescharacteristic
369C24C22×C4×C11311yescharacteristic
370C24C2×D4×C11311yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C11312yes—
388C2×D4#41×C11312yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C11311yescharacteristic
405C22×C4C2×D4×C11311yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C11311yescharacteristic
468C23#99×C11311yescharacteristic
469C23C2×C22⋊C4×C11311yescharacteristic
470C23C4×D4×C11312yes—
471C23#121×C11312yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C11312yes—
504C2×C4#120×C11311yescharacteristic
505C2×C4#123×C11311yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C11312yescomplemented
541C22#386×C11311yescharacteristic
542C22C2×#99×C11311yescharacteristic
543C22C2×#99×C11311yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C113×#189811yescharacteristic
561C2C2×#352×C11311yescharacteristic
562C2C113×#212111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#99
commutatorC24C22×C4×C113
Frattini, cosocleC22×D4C23×C113
prime radicalC23×D4×C113C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C24×C113 ◁ C23×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C113C2semidirect
5. C113×#1390C2semidirect
8. C2×#123×C113C4semidirect
10. C22×C22⋊C4×C113C4semidirect
18. #386×C113C4semidirect
23. #379×C113C4semidirect
258. C22×C113#352semidirect
270. #13080C113direct (N × H)
284. C2×#352C2×C113semidirect
286. #1390C2×C113semidirect
287. C113#13080direct (N × H)
290. C2×#123C4×C113semidirect
292. C22×C22⋊C4C4×C113semidirect
300. #386C4×C113semidirect
305. #379C4×C113semidirect
540. C22#352×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1132
C113×#24052
C2×#352×C1132
C113×#17812
C113×#13902
#13080113