Finite Group Databasebeta

← C113×#13093 #43281113

Subgroups — C113×#13093 #43281113

Order 28928.

752 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#413×C113C211yesmaximal, characteristic, complemented
2C113×#2431C211yesmaximal, characteristic
3C2×#355×C113C212yesmaximal, complemented
4C113×#1785C211yesmaximal, characteristic, complemented
5C113×#1394C212yesmaximal, complemented
6C22×#41×C113C2211yescharacteristic
7C22×M16×C113—21no—
8C2×#127×C113C411yescharacteristic
9C2×#124×C113C2211yescharacteristic
10C2×#121×C113C411yescharacteristic
11#413×C113—24no—
12C2×#101×C113C2212yes—
13C2×#101×C113C2212yes—
14C2×#100×C113—21no—
15C2×#100×C113—21no—
16#407×C113—21no—
17#392×C113—21no—
18#392×C113—21no—
19#391×C113C2211yescharacteristic
20#390×C113C411yescharacteristic
21#386×C113—21no—
22#386×C113—21no—
23C4×C22⋊C4×C113C411yescharacteristic
24#355×C113—24no—
25C2×#41×C113—22no—
26C2×#41×C113—22no—
27C2×#41×C113—41no—
28C2×#41×C113—41no—
29C2×#41×C113—42no—
30C22×Q8×C113C2311yescharacteristic
31C22×D4×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113—21no—
34C22×D4×C113C2×C411yescharacteristic
35C22×D4×C113C2×C411yescharacteristic
36C22×D4×C113D411yescharacteristic
37C22×D4×C113D411yescharacteristic
38C23×C4×C113C2×C411yescharacteristic
39C23×C4×C113D411yescharacteristic
40C23×C4×C113D411yescharacteristic
41C2×M16×C113—24no—
42C2×M16×C113—22no—
43C2×M16×C113—22no—
44C2×M16×C113—42no—
45C2×M16×C113—41no—
46C22×C8×C113—41no—
47#127×C113—42no—
48#124×C113—22no—
49#124×C113—22no—
50#121×C113—41no—
51#121×C113—41no—
52C2×C4⋊C4×C113C2×C411yescharacteristic
53C2×C22⋊C4×C113—21no—
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×C42×C113C2×C411yescharacteristic
60C2×C42×C113C2×C411yescharacteristic
61#101×C113—22no—
62#101×C113—22no—
63#101×C113—22no—
64#101×C113D414yescomplemented
65#100×C113—24no—
66#100×C113—42no—
67C22⋊C8×C113—41no—
68C22⋊C8×C113—41no—
69#95×C113—21no—
70#95×C113—21no—
71#95×C113—21no—
72C24×C113—21no—
73C24×C113C22⋊C411yescharacteristic
74C24×C113C22⋊C411yescharacteristic
75C24×C113C22⋊C411yescharacteristic
76#41×C113—44no—
77#41×C113—44no—
78#41×C113—44no—
79#41×C113—44no—
80C2×Q8×C113—41no—
81C2×Q8×C113—41no—
82C2×Q8×C113C2×D412yes—
83C2×Q8×C113#4112yes—
84C2×D4×C113—22no—
85C2×D4×C113—22no—
86C2×D4×C113—22no—
87C2×D4×C113—22no—
88C2×D4×C113—21no—
89C2×D4×C113—22no—
90C2×D4×C113—21no—
91C2×D4×C113—41no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—41no—
97C2×D4×C113—42no—
98C2×D4×C113—42no—
99C2×D4×C113—42no—
100C2×D4×C113—42no—
101C2×D4×C113—42no—
102C2×D4×C113—81no—
103C2×D4×C113—81no—
104C2×D4×C113—81no—
105C2×D4×C113—81no—
106C22×C4×C113—22no—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113—21no—
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—22no—
118C22×C4×C113—21no—
119C22×C4×C113—21no—
120C22×C4×C113—41no—
121C22×C4×C113—41no—
122C22×C4×C113C22⋊C411yescharacteristic
123C22×C4×C113C22×C411yescharacteristic
124C22×C4×C113C2×D411yescharacteristic
125C22×C4×C113C2×D411yescharacteristic
126M16×C113—24no—
127M16×C113—44no—
128M16×C113—42no—
129M16×C113—42no—
130M16×C113—42no—
131C2×C8×C113—44no—
132C2×C8×C113—42no—
133C2×C8×C113—42no—
134C4⋊C4×C113—41no—
135C22⋊C4×C113—42no—
136C22⋊C4×C113—41no—
137C22⋊C4×C113—41no—
138C22⋊C4×C113—41no—
139C22⋊C4×C113—42no—
140C22⋊C4×C113—41no—
141C22⋊C4×C113—81no—
142C22⋊C4×C113—81no—
143C42×C113—22no—
144C42×C113—41no—
145C23×C113—21no—
146C23×C113—21no—
147C23×C113—21no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—21no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—41no—
154C23×C113—41no—
155C23×C113—41no—
156C23×C113—41no—
157C23×C113—41no—
158C23×C113—41no—
159C23×C113—41no—
160C23×C113—41no—
161C23×C113—41no—
162C23×C113—41no—
163C23×C113—41no—
164C23×C113—41no—
165C23×C113—41no—
166C23×C113#9912yes—
167C23×C113C2×C22⋊C411yescharacteristic
168Q8×C113—42no—
169Q8×C113—42no—
170D4×C113—44no—
171D4×C113—44no—
172D4×C113—42no—
173D4×C113—42no—
174D4×C113—82no—
175D4×C113—84no—
176D4×C113—84no—
177D4×C113—84no—
178C2×C4×C113—22no—
179C2×C4×C113—22no—
180C2×C4×C113—22no—
181C2×C4×C113—22no—
182C2×C4×C113—21no—
183C2×C4×C113—21no—
184C2×C4×C113—21no—
185C2×C4×C113—21no—
186C2×C4×C113—21no—
187C2×C4×C113—21no—
188C2×C4×C113—21no—
189C2×C4×C113—21no—
190C2×C4×C113—22no—
191C2×C4×C113—42no—
192C2×C4×C113—42no—
193C2×C4×C113—42no—
194C2×C4×C113—42no—
195C2×C4×C113—41no—
196C2×C4×C113—41no—
197C2×C4×C113—41no—
198C2×C4×C113—41no—
199C2×C4×C113—41no—
200C2×C4×C113—41no—
201C2×C4×C113—41no—
202C2×C4×C113—41no—
203C2×C4×C113#9911yescharacteristic
204C2×C4×C113#9911yescharacteristic
205C2×C4×C113C4×D412yes—
206C2×C4×C113#12011yescharacteristic
207C2×C4×C113#12112yes—
208C2×C4×C113#12311yescharacteristic
209C8×C113—44no—
210C8×C113—82no—
211C22×C113—21no—
212C22×C113—21no—
213C22×C113—22no—
214C22×C113—42no—
215C22×C113—42no—
216C22×C113—41no—
217C22×C113—41no—
218C22×C113—41no—
219C22×C113—41no—
220C22×C113—41no—
221C22×C113—41no—
222C22×C113—41no—
223C22×C113—41no—
224C22×C113—81no—
225C22×C113—81no—
226C22×C113—81no—
227C22×C113—81no—
228C22×C113—81no—
229C22×C113—81no—
230C22×C113—81no—
231C22×C113—81no—
232C22×C113—81no—
233C22×C113—81no—
234C22×C113—81no—
235C22×C113#38611yescharacteristic
236C22×C113C2×#9911yescharacteristic
237C22×C113C2×#9911yescharacteristic
238C4×C113—21no—
239C4×C113—22no—
240C4×C113—21no—
241C4×C113—21no—
242C4×C113—21no—
243C4×C113—22no—
244C4×C113—42no—
245C4×C113—81no—
246C4×C113—81no—
247#13093C11311yesmaximal, characteristic, direct product factor, Sylow
248C2×C113—21no—
249C2×C113—21no—
250C2×C113—42no—
251C2×C113—81no—
252C2×C113—81no—
253C2×C113—161no—
254C2×C113#189811yescharacteristic
255C2×C113#213211yescharacteristic
256C2×C113#213411yescharacteristic
257C2×#413C2×C11311yescharacteristic, complemented
258#2431C2×C11311yescharacteristic
259C2×#355C2×C11312yescomplemented
260#1785C2×C11311yescharacteristic, complemented
261#1394C2×C11312yescomplemented
262C113#1309311yescharacteristic, direct product factor, Sylow
263C22×#41C22×C11311yescharacteristic
264C22×M16—21no—
265C2×#127C4×C11311yescharacteristic
266C2×#124C22×C11311yescharacteristic
267C2×#121C4×C11311yescharacteristic
268#413—24no—
269C2×#101C22×C11312yes—
270C2×#101C22×C11312yes—
271C2×#100—21no—
272C2×#100—21no—
273#407—21no—
274#392—21no—
275#392—21no—
276#391C22×C11311yescharacteristic
277#390C4×C11311yescharacteristic
278#386—21no—
279#386—21no—
280C4×C22⋊C4C4×C11311yescharacteristic
281#355—24no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—41no—
285C2×#41—41no—
286C2×#41—42no—
287C22×Q8C23×C11311yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×C4×C11311yescharacteristic
292C22×D4C2×C4×C11311yescharacteristic
293C22×D4D4×C11311yescharacteristic
294C22×D4D4×C11311yescharacteristic
295C23×C4C2×C4×C11311yescharacteristic
296C23×C4D4×C11311yescharacteristic
297C23×C4D4×C11311yescharacteristic
298C2×M16—24no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—42no—
302C2×M16—41no—
303C22×C8—41no—
304#127—42no—
305#124—22no—
306#124—22no—
307#121—41no—
308#121—41no—
309C2×C4⋊C4C2×C4×C11311yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C42C2×C4×C11311yescharacteristic
317C2×C42C2×C4×C11311yescharacteristic
318#101—22no—
319#101—22no—
320#101—22no—
321#101D4×C11314yescomplemented
322#100—24no—
323#100—42no—
324C22⋊C8—41no—
325C22⋊C8—41no—
326#95—21no—
327#95—21no—
328#95—21no—
329C24—21no—
330C24C22⋊C4×C11311yescharacteristic
331C24C22⋊C4×C11311yescharacteristic
332C24C22⋊C4×C11311yescharacteristic
333#41—44no—
334#41—44no—
335#41—44no—
336#41—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8C2×D4×C11312yes—
340C2×Q8#41×C11312yes—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—22no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—81no—
360C2×D4—81no—
361C2×D4—81no—
362C2×D4—81no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4C22⋊C4×C11311yescharacteristic
380C22×C4C22×C4×C11311yescharacteristic
381C22×C4C2×D4×C11311yescharacteristic
382C22×C4C2×D4×C11311yescharacteristic
383M16—24no—
384M16—44no—
385M16—42no—
386M16—42no—
387M16—42no—
388C2×C8—44no—
389C2×C8—42no—
390C2×C8—42no—
391C4⋊C4—41no—
392C22⋊C4—42no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—42no—
397C22⋊C4—41no—
398C22⋊C4—81no—
399C22⋊C4—81no—
400C42—22no—
401C42—41no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23#99×C11312yes—
424C23C2×C22⋊C4×C11311yescharacteristic
425Q8—42no—
426Q8—42no—
427D4—44no—
428D4—44no—
429D4—42no—
430D4—42no—
431D4—82no—
432D4—84no—
433D4—84no—
434D4—84no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4#99×C11311yescharacteristic
461C2×C4#99×C11311yescharacteristic
462C2×C4C4×D4×C11312yes—
463C2×C4#120×C11311yescharacteristic
464C2×C4#121×C11312yes—
465C2×C4#123×C11311yescharacteristic
466C8—44no—
467C8—82no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22#386×C11311yescharacteristic
493C22C2×#99×C11311yescharacteristic
494C22C2×#99×C11311yescharacteristic
495C4—21no—
496C4—22no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—42no—
502C4—81no—
503C4—81no—
504C2—21no—
505C2—21no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—161no—
510C2C113×#189811yescharacteristic
511C2C113×#213211yescharacteristic
512C2C113×#213411yescharacteristic
subgroupG/H
center, socleC22×C113C2×#99
commutatorC22×C4C22×C4×C113
Frattini, cosocleC22×Q8C23×C113
prime radicalC113×#2431C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ C22×#41×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#413×C113C2semidirect
3. C2×#355×C113C2semidirect
4. C113×#1785C2semidirect
5. C113×#1394C2semidirect
64. #101×C113D4semidirect
247. #13093C113direct (N × H)
257. C2×#413C2×C113semidirect
259. C2×#355C2×C113semidirect
260. #1785C2×C113semidirect
261. #1394C2×C113semidirect
262. C113#13093direct (N × H)
321. #101D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#413×C1132
C113×#24312
C2×#355×C1132
C113×#17852
C113×#13942
#13093113