Finite Group Databasebeta

← C113×#10735 #43278755

Subgroups — C113×#10735 #43278755

Order 28928.

3062 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C113C211yesmaximal, characteristic
2C2×#379×C113C211yesmaximal, characteristic
3C2×#379×C113C211yesmaximal, characteristic
4C2×#342×C113C214yesmaximal, complemented
5C26×C113C2211yescharacteristic
6C24×C4×C113—21no—
7C22×C22⋊C4×C113—21no—
8C22×C22⋊C4×C113—22no—
9C22×C22⋊C4×C113—28no—
10C22×C22⋊C4×C113—22no—
11C22×C22⋊C4×C113C414yescomplemented
12C22×C22⋊C4×C113C414yescomplemented
13C22×C22⋊C4×C113C2212yes—
14C22×C22⋊C4×C113C2212yes—
15C22×C22⋊C4×C113C2212yes—
16#379×C113—22no—
17#379×C113—21no—
18#379×C113—22no—
19#379×C113—21no—
20#379×C113C414yescomplemented
21#342×C113—28no—
22C25×C113—24no—
23C25×C113—24no—
24C25×C113—48no—
25C25×C113C2×C412yes—
26C25×C113C2×C412yes—
27C25×C113C2×C412yes—
28C25×C113D411yescharacteristic
29C25×C113D412yes—
30C25×C113D412yes—
31C25×C113D411yescharacteristic
32C25×C113Q812yes—
33C25×C113C2311yescharacteristic
34C23×C4×C113—28no—
35C23×C4×C113—24no—
36C23×C4×C113—22no—
37C23×C4×C113—22no—
38C23×C4×C113—48no—
39C23×C4×C113C2×C414yescomplemented
40C2×C22⋊C4×C113—28no—
41C2×C22⋊C4×C113—216no—
42C2×C22⋊C4×C113—24no—
43C2×C22⋊C4×C113—24no—
44C2×C22⋊C4×C113—22no—
45C2×C22⋊C4×C113—216no—
46C2×C22⋊C4×C113—24no—
47C2×C22⋊C4×C113—24no—
48C2×C22⋊C4×C113—28no—
49C2×C22⋊C4×C113—24no—
50C2×C22⋊C4×C113—24no—
51C2×C22⋊C4×C113—24no—
52C2×C22⋊C4×C113—22no—
53C2×C22⋊C4×C113—22no—
54C2×C22⋊C4×C113—22no—
55C2×C22⋊C4×C113—24no—
56C2×C22⋊C4×C113—48no—
57C2×C22⋊C4×C113—48no—
58C2×C22⋊C4×C113C2×C414yes—
59C2×C22⋊C4×C113C2×C414yescomplemented
60C2×C22⋊C4×C113D418yes—
61C24×C113—28no—
62C24×C113—22no—
63C24×C113—22no—
64C24×C113—28no—
65C24×C113—28no—
66C24×C113—24no—
67C24×C113—24no—
68C24×C113—28no—
69C24×C113—28no—
70C24×C113—24no—
71C24×C113—22no—
72C24×C113—28no—
73C24×C113—28no—
74C24×C113—24no—
75C24×C113—22no—
76C24×C113—48no—
77C24×C113—48no—
78C24×C113—44no—
79C24×C113—48no—
80C24×C113—44no—
81C24×C113—44no—
82C24×C113—48no—
83C24×C113—44no—
84C24×C113—432no—
85C24×C113—432no—
86C24×C113C4214yes—
87C24×C113C22⋊C412yes—
88C24×C113C22⋊C412yes—
89C24×C113C22⋊C414yes—
90C24×C113C22⋊C412yes—
91C24×C113C22⋊C412yes—
92C24×C113C4⋊C412yes—
93C24×C113C4⋊C414yes—
94C24×C113C4⋊C414yes—
95C24×C113C4⋊C412yes—
96C24×C113C22×C411yescharacteristic
97C24×C113C22×C411yescharacteristic
98C24×C113C22×C411yescharacteristic
99C24×C113C2×D411yescharacteristic
100C24×C113C2×D411yescharacteristic
101C24×C113C2×D411yescharacteristic
102C24×C113C2×D414yes—
103C24×C113C2×Q811yescharacteristic
104C24×C113#4114yes—
105C22×C4×C113—216no—
106C22×C4×C113—24no—
107C22×C4×C113—28no—
108C22×C4×C113—24no—
109C22×C4×C113—24no—
110C22×C4×C113—28no—
111C22×C4×C113—432no—
112C22×C4×C113—416no—
113C22×C4×C113—48no—
114C22×C4×C113—48no—
115C22×C4×C113—44no—
116C22×C4×C113—48no—
117C22⋊C4×C113—216no—
118C22⋊C4×C113—24no—
119C22⋊C4×C113—28no—
120C22⋊C4×C113—28no—
121C22⋊C4×C113—416no—
122C22⋊C4×C113—48no—
123C22⋊C4×C113—48no—
124C22⋊C4×C113—42no—
125C22⋊C4×C113—42no—
126C22⋊C4×C113—44no—
127C22⋊C4×C113—42no—
128C22⋊C4×C113—42no—
129C22⋊C4×C113C22⋊C418yescomplemented
130C23×C113—216no—
131C23×C113—216no—
132C23×C113—28no—
133C23×C113—28no—
134C23×C113—22no—
135C23×C113—22no—
136C23×C113—24no—
137C23×C113—24no—
138C23×C113—24no—
139C23×C113—24no—
140C23×C113—24no—
141C23×C113—24no—
142C23×C113—28no—
143C23×C113—28no—
144C23×C113—28no—
145C23×C113—28no—
146C23×C113—28no—
147C23×C113—22no—
148C23×C113—28no—
149C23×C113—22no—
150C23×C113—28no—
151C23×C113—24no—
152C23×C113—28no—
153C23×C113—24no—
154C23×C113—24no—
155C23×C113—24no—
156C23×C113—44no—
157C23×C113—44no—
158C23×C113—44no—
159C23×C113—44no—
160C23×C113—44no—
161C23×C113—44no—
162C23×C113—42no—
163C23×C113—42no—
164C23×C113—48no—
165C23×C113—42no—
166C23×C113—42no—
167C23×C113—48no—
168C23×C113—432no—
169C23×C113—432no—
170C23×C113—416no—
171C23×C113—416no—
172C23×C113—416no—
173C23×C113—432no—
174C23×C113—432no—
175C23×C113—416no—
176C23×C113—48no—
177C23×C113—48no—
178C23×C113#9514yes—
179C23×C113#9514yes—
180C23×C113#9918yes—
181C23×C113C2×C4211yescharacteristic
182C23×C113C2×C22⋊C411yescharacteristic
183C23×C113C2×C22⋊C411yescharacteristic
184C23×C113C2×C22⋊C412yes—
185C23×C113C2×C22⋊C411yescharacteristic
186C23×C113C2×C4⋊C411yescharacteristic
187C23×C113C2×C4⋊C411yescharacteristic
188C23×C113C2×C4⋊C411yescharacteristic
189C23×C113#11712yes—
190C23×C113C4×D414yes—
191C23×C113C4×D414yes—
192C23×C113#12012yes—
193C23×C113#12012yes—
194C23×C113#12114yes—
195C23×C113C22⋊Q814yes—
196C23×C113#12312yes—
197C23×C113#12312yes—
198C2×C4×C113—28no—
199C2×C4×C113—432no—
200C2×C4×C113—416no—
201C2×C4×C113—48no—
202C2×C4×C113—48no—
203C2×C4×C113—44no—
204C2×C4×C113—44no—
205C2×C4×C113—48no—
206C2×C4×C113—88no—
207C2×C4×C113—88no—
208C22×C113—28no—
209C22×C113—28no—
210C22×C113—216no—
211C22×C113—24no—
212C22×C113—28no—
213C22×C113—28no—
214C22×C113—216no—
215C22×C113—24no—
216C22×C113—24no—
217C22×C113—22no—
218C22×C113—22no—
219C22×C113—24no—
220C22×C113—22no—
221C22×C113—22no—
222C22×C113—22no—
223C22×C113—22no—
224C22×C113—24no—
225C22×C113—24no—
226C22×C113—24no—
227C22×C113—42no—
228C22×C113—42no—
229C22×C113—44no—
230C22×C113—42no—
231C22×C113—44no—
232C22×C113—42no—
233C22×C113—416no—
234C22×C113—416no—
235C22×C113—416no—
236C22×C113—416no—
237C22×C113—44no—
238C22×C113—44no—
239C22×C113—48no—
240C22×C113—48no—
241C22×C113#34218yescomplemented
242C22×C113C2×#9511yescharacteristic
243C22×C113C4×C22⋊C412yes—
244C22×C113#37911yescharacteristic
245C22×C113#38012yes—
246C22×C113#38111yescharacteristic
247C22×C113#38512yes—
248C22×C113#38512yes—
249C22×C113#38612yes—
250C22×C113#38612yes—
251C22×C113C2×#9914yes—
252C4×C113—48no—
253C4×C113—84no—
254C4×C113—84no—
255#10735C11311yesmaximal, characteristic, direct product factor, Sylow
256C2×C113—21no—
257C2×C113—22no—
258C2×C113—28no—
259C2×C113—21no—
260C2×C113—22no—
261C2×C113—22no—
262C2×C113—22no—
263C2×C113—22no—
264C2×C113—44no—
265C2×C113C22⋊#9511yescharacteristic
266C2×C113C2×#34212yes—
267C2×C113#189814yes—
268C23×C22⋊C4C2×C11311yescharacteristic
269C2×#379C2×C11311yescharacteristic
270C2×#379C2×C11311yescharacteristic
271C2×#342C2×C11314yescomplemented
272C113#1073511yescharacteristic, direct product factor, Sylow
273C26C22×C11311yescharacteristic
274C24×C4—21no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—22no—
277C22×C22⋊C4—28no—
278C22×C22⋊C4—22no—
279C22×C22⋊C4C4×C11314yescomplemented
280C22×C22⋊C4C4×C11314yescomplemented
281C22×C22⋊C4C22×C11312yes—
282C22×C22⋊C4C22×C11312yes—
283C22×C22⋊C4C22×C11312yes—
284#379—22no—
285#379—21no—
286#379—22no—
287#379—21no—
288#379C4×C11314yescomplemented
289#342—28no—
290C25—24no—
291C25—24no—
292C25—48no—
293C25C2×C4×C11312yes—
294C25C2×C4×C11312yes—
295C25C2×C4×C11312yes—
296C25D4×C11311yescharacteristic
297C25D4×C11312yes—
298C25D4×C11311yescharacteristic
299C25D4×C11312yes—
300C25Q8×C11312yes—
301C25C23×C11311yescharacteristic
302C23×C4—28no—
303C23×C4—24no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—48no—
307C23×C4C2×C4×C11314yescomplemented
308C2×C22⋊C4—28no—
309C2×C22⋊C4—216no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—216no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—48no—
326C2×C22⋊C4C2×C4×C11314yes—
327C2×C22⋊C4C2×C4×C11314yescomplemented
328C2×C22⋊C4D4×C11318yes—
329C24—28no—
330C24—22no—
331C24—22no—
332C24—28no—
333C24—28no—
334C24—24no—
335C24—24no—
336C24—28no—
337C24—28no—
338C24—24no—
339C24—22no—
340C24—28no—
341C24—28no—
342C24—24no—
343C24—22no—
344C24—48no—
345C24—48no—
346C24—44no—
347C24—48no—
348C24—44no—
349C24—44no—
350C24—48no—
351C24—44no—
352C24—432no—
353C24—432no—
354C24C42×C11314yes—
355C24C22⋊C4×C11312yes—
356C24C22⋊C4×C11312yes—
357C24C22⋊C4×C11314yes—
358C24C22⋊C4×C11312yes—
359C24C22⋊C4×C11312yes—
360C24C4⋊C4×C11312yes—
361C24C4⋊C4×C11314yes—
362C24C4⋊C4×C11314yes—
363C24C4⋊C4×C11312yes—
364C24C22×C4×C11311yescharacteristic
365C24C22×C4×C11311yescharacteristic
366C24C22×C4×C11311yescharacteristic
367C24C2×D4×C11311yescharacteristic
368C24C2×D4×C11311yescharacteristic
369C24C2×D4×C11311yescharacteristic
370C24C2×D4×C11314yes—
371C24C2×Q8×C11311yescharacteristic
372C24#41×C11314yes—
373C22×C4—216no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—28no—
379C22×C4—432no—
380C22×C4—416no—
381C22×C4—48no—
382C22×C4—48no—
383C22×C4—44no—
384C22×C4—48no—
385C22⋊C4—216no—
386C22⋊C4—24no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C22⋊C4—416no—
390C22⋊C4—48no—
391C22⋊C4—48no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—44no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4C22⋊C4×C11318yescomplemented
398C23—216no—
399C23—216no—
400C23—28no—
401C23—28no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—24no—
408C23—24no—
409C23—24no—
410C23—28no—
411C23—28no—
412C23—28no—
413C23—28no—
414C23—28no—
415C23—22no—
416C23—28no—
417C23—22no—
418C23—28no—
419C23—24no—
420C23—28no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—42no—
431C23—42no—
432C23—48no—
433C23—42no—
434C23—42no—
435C23—48no—
436C23—432no—
437C23—432no—
438C23—416no—
439C23—416no—
440C23—416no—
441C23—432no—
442C23—432no—
443C23—416no—
444C23—48no—
445C23—48no—
446C23#95×C11314yes—
447C23#95×C11314yes—
448C23#99×C11318yes—
449C23C2×C42×C11311yescharacteristic
450C23C2×C22⋊C4×C11311yescharacteristic
451C23C2×C22⋊C4×C11311yescharacteristic
452C23C2×C22⋊C4×C11312yes—
453C23C2×C22⋊C4×C11311yescharacteristic
454C23C2×C4⋊C4×C11311yescharacteristic
455C23C2×C4⋊C4×C11311yescharacteristic
456C23C2×C4⋊C4×C11311yescharacteristic
457C23#117×C11312yes—
458C23C4×D4×C11314yes—
459C23C4×D4×C11314yes—
460C23#120×C11312yes—
461C23#120×C11312yes—
462C23#121×C11314yes—
463C23C22⋊Q8×C11314yes—
464C23#123×C11312yes—
465C23#123×C11312yes—
466C2×C4—28no—
467C2×C4—432no—
468C2×C4—416no—
469C2×C4—48no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—88no—
475C2×C4—88no—
476C22—28no—
477C22—28no—
478C22—216no—
479C22—24no—
480C22—28no—
481C22—28no—
482C22—216no—
483C22—24no—
484C22—24no—
485C22—22no—
486C22—22no—
487C22—24no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—42no—
499C22—44no—
500C22—42no—
501C22—416no—
502C22—416no—
503C22—416no—
504C22—416no—
505C22—44no—
506C22—44no—
507C22—48no—
508C22—48no—
509C22#342×C11318yescomplemented
510C22C2×#95×C11311yescharacteristic
511C22C4×C22⋊C4×C11312yes—
512C22#379×C11311yescharacteristic
513C22#380×C11312yes—
514C22#381×C11311yescharacteristic
515C22#385×C11312yes—
516C22#385×C11312yes—
517C22#386×C11312yes—
518C22#386×C11312yes—
519C22C2×#99×C11314yes—
520C4—48no—
521C4—84no—
522C4—84no—
523C2—21no—
524C2—22no—
525C2—28no—
526C2—21no—
527C2—22no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2—44no—
532C2C113×C22⋊#9511yescharacteristic
533C2C2×#342×C11312yes—
534C2C113×#189814yes—
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC23C2×C42×C113
Frattini, cosocleC25C23×C113
prime radicalC26×C113C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C26×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#342×C113C2semidirect
11. C22×C22⋊C4×C113C4semidirect
12. C22×C22⋊C4×C113C4semidirect
20. #379×C113C4semidirect
39. C23×C4×C113C2×C4semidirect
59. C2×C22⋊C4×C113C2×C4semidirect
129. C22⋊C4×C113C22⋊C4semidirect
241. C22×C113#342semidirect
255. #10735C113direct (N × H)
271. C2×#342C2×C113semidirect
272. C113#10735direct (N × H)
279. C22×C22⋊C4C4×C113semidirect
280. C22×C22⋊C4C4×C113semidirect
288. #379C4×C113semidirect
307. C23×C4C2×C4×C113semidirect
327. C2×C22⋊C4C2×C4×C113semidirect
397. C22⋊C4C22⋊C4×C113semidirect
509. C22#342×C113semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1132
C2×#379×C1132
C2×#342×C1132
#10735113