Finite Group Databasebeta

← C113×#8977 #43276997

Subgroups — C113×#8977 #43276997

Order 28928.

764 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C113C211yesmaximal, characteristic
2D4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
3C113×#1982C211yesmaximal, characteristic, complemented
4C113×#1957C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C113C211yesmaximal, characteristic, complemented
6C113×#1296C211yesmaximal, characteristic, complemented
7C113×#1279C211yesmaximal, characteristic, complemented
8C22×D8×C113—21no—
9C2×#127×C113C2211yescharacteristic
10C2×C4×D4×C113—21no—
11C2×C4×D4×C113C2211yescharacteristic
12C22×C4⋊C4×C113—21no—
13#459×C113—22no—
14#459×C113C414yescomplemented
15C2×C4⋊C8×C113C2211yescharacteristic
16C2×C4⋊C8×C113C2211yescharacteristic
17C2×#102×C113—21no—
18C2×#102×C113—22no—
19C2×#102×C113—21no—
20C2×#102×C113—21no—
21C2×C4×C8×C113C2211yescharacteristic
22#389×C113—21no—
23#385×C113—22no—
24#384×C113C2211yescharacteristic
25#380×C113—21no—
26C4×C4⋊C4×C113C2211yescharacteristic
27D4⋊C8×C113—22no—
28C22×D4×C113—21no—
29C22×D4×C113—21no—
30C22×D4×C113—21no—
31C22×D4×C113D411yescharacteristic
32C23×C4×C113—21no—
33C23×C4×C113—22no—
34C2×D8×C113—24no—
35C2×D8×C113—42no—
36C2×D8×C113—42no—
37C22×C8×C113—21no—
38C22×C8×C113—21no—
39C22×C8×C113—21no—
40#127×C113—21no—
41#127×C113—21no—
42#127×C113—21no—
43#127×C113C2×C412yescomplemented
44C4×D4×C113—21no—
45C4×D4×C113—21no—
46C4×D4×C113—42no—
47C4×D4×C113—42no—
48C4×D4×C113C2×C412yes—
49C4×D4×C113D412yes—
50C2×C4⋊C4×C113—22no—
51C2×C4⋊C4×C113—21no—
52C2×C4⋊C4×C113—21no—
53C2×C4⋊C4×C113—42no—
54C2×C4⋊C4×C113—42no—
55C2×C4⋊C4×C113D411yescharacteristic
56C2×C4⋊C4×C113D411yescharacteristic
57C2×C4⋊C4×C113D411yescharacteristic
58C2×C4⋊C4×C113D412yes—
59C2×C22⋊C4×C113—21no—
60C2×C22⋊C4×C113—22no—
61C2×C42×C113—21no—
62C2×C42×C113C2311yescharacteristic
63C4⋊C8×C113—21no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113—21no—
66C4⋊C8×C113C2×C412yescomplemented
67#102×C113—24no—
68#102×C113—42no—
69#102×C113—44no—
70#102×C113—42no—
71C4×C8×C113—21no—
72C4×C8×C113—21no—
73#95×C113—22no—
74#95×C113—21no—
75C24×C113—21no—
76C24×C113—41no—
77C2×D4×C113—22no—
78C2×D4×C113—22no—
79C2×D4×C113—22no—
80C2×D4×C113—21no—
81C2×D4×C113—21no—
82C2×D4×C113—21no—
83C2×D4×C113—42no—
84C2×D4×C113—42no—
85C2×D4×C113—41no—
86C2×D4×C113—41no—
87C2×D4×C113—41no—
88C2×D4×C113—41no—
89C2×D4×C113—41no—
90C2×D4×C113—41no—
91C2×D4×C113—41no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113C22⋊C412yes—
97C2×D4×C113D812yes—
98C2×D4×C113SD1612yes—
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—22no—
102C22×C4×C113—22no—
103C22×C4×C113—21no—
104C22×C4×C113—22no—
105C22×C4×C113—44no—
106C22×C4×C113—41no—
107C22×C4×C113—41no—
108C22×C4×C113—41no—
109C22×C4×C113—41no—
110C22×C4×C113—44no—
111C22×C4×C113—82no—
112C22×C4×C113C2×D411yescharacteristic
113C22×C4×C113C2×D411yescharacteristic
114C22×C4×C113C2×D411yescharacteristic
115D8×C113—48no—
116C2×C8×C113—22no—
117C2×C8×C113—22no—
118C2×C8×C113—41no—
119C2×C8×C113—41no—
120C2×C8×C113—41no—
121C2×C8×C113—41no—
122C2×C8×C113—41no—
123C2×C8×C113—41no—
124C2×C8×C113—41no—
125C4⋊C4×C113—21no—
126C4⋊C4×C113—21no—
127C4⋊C4×C113—21no—
128C4⋊C4×C113—21no—
129C4⋊C4×C113—42no—
130C4⋊C4×C113—44no—
131C4⋊C4×C113—41no—
132C4⋊C4×C113—41no—
133C4⋊C4×C113—41no—
134C4⋊C4×C113—41no—
135C4⋊C4×C113C22⋊C412yes—
136C4⋊C4×C113D812yescomplemented
137C22⋊C4×C113—22no—
138C22⋊C4×C113—22no—
139C22⋊C4×C113—44no—
140C42×C113—41no—
141C42×C113—41no—
142C42×C113C22×C411yescharacteristic
143C42×C113C2×D411yescharacteristic
144C42×C113#4111yescharacteristic
145C42×C113#4111yescharacteristic
146C23×C113—22no—
147C23×C113—22no—
148C23×C113—22no—
149C23×C113—41no—
150C23×C113—41no—
151C23×C113—41no—
152C23×C113—41no—
153C23×C113—42no—
154C23×C113—81no—
155C23×C113—81no—
156C23×C113—81no—
157C23×C113—81no—
158C23×C113—81no—
159C23×C113—81no—
160C23×C113#12011yescharacteristic
161D4×C113—22no—
162D4×C113—22no—
163D4×C113—22no—
164D4×C113—44no—
165D4×C113—42no—
166D4×C113—42no—
167D4×C113—42no—
168D4×C113—42no—
169D4×C113—82no—
170D4×C113—81no—
171D4×C113—81no—
172D4×C113—81no—
173D4×C113—81no—
174D4×C113#10214yescomplemented
175C2×C4×C113—21no—
176C2×C4×C113—21no—
177C2×C4×C113—22no—
178C2×C4×C113—22no—
179C2×C4×C113—41no—
180C2×C4×C113—41no—
181C2×C4×C113—41no—
182C2×C4×C113—41no—
183C2×C4×C113—42no—
184C2×C4×C113—42no—
185C2×C4×C113—42no—
186C2×C4×C113—42no—
187C2×C4×C113—41no—
188C2×C4×C113—42no—
189C2×C4×C113—42no—
190C2×C4×C113—41no—
191C2×C4×C113—42no—
192C2×C4×C113—41no—
193C2×C4×C113—88no—
194C2×C4×C113C2×C22⋊C411yescharacteristic
195C2×C4×C113C4×D411yescharacteristic
196C2×C4×C113C4×D411yescharacteristic
197C2×C4×C113#12111yescharacteristic
198C2×C4×C113#12111yescharacteristic
199C2×C4×C113#12311yescharacteristic
200C2×C4×C113C2×D811yescharacteristic
201C2×C4×C113C2×D811yescharacteristic
202C2×C4×C113C2×SD1611yescharacteristic
203C2×C4×C113#13511yescharacteristic
204C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C113#13711yescharacteristic
208C8×C113—42no—
209C8×C113—42no—
210C8×C113—81no—
211C22×C113—24no—
212C22×C113—42no—
213C22×C113—42no—
214C22×C113—42no—
215C22×C113—42no—
216C22×C113—42no—
217C22×C113—42no—
218C22×C113—82no—
219C22×C113—82no—
220C22×C113—82no—
221C22×C113—161no—
222C22×C113—161no—
223C22×C113—161no—
224C22×C113—161no—
225C22×C113#38611yescharacteristic
226C22×C113#44711yescharacteristic
227C22×C113#44711yescharacteristic
228C22×C113#44811yescharacteristic
229C22×C113#44911yescharacteristic
230C22×C113#45311yescharacteristic
231C22×C113#45411yescharacteristic
232C4×C113—21no—
233C4×C113—21no—
234C4×C113—42no—
235C4×C113—42no—
236C4×C113—82no—
237C4×C113—81no—
238C4×C113C2×#10211yescharacteristic
239C4×C113#41711yescharacteristic
240C4×C113C4×D811yescharacteristic
241C4×C113#44211yescharacteristic
242C4×C113#45911yescharacteristic
243C4×C113#46311yescharacteristic
244C4×C113#48011yescharacteristic
245C4×C113#48111yescharacteristic
246#8977C11311yesmaximal, characteristic, direct product factor, Sylow
247C2×C113—44no—
248C2×C113—162no—
249C2×C113#161911yescharacteristic
250C2×C113#162211yescharacteristic
251C2×C113#162511yescharacteristic
252C2×C113#162711yescharacteristic
253C2×C113#187411yescharacteristic
254C2×C113#187911yescharacteristic
255C2×C113#188311yescharacteristic
256C2×#459C2×C11311yescharacteristic
257D4×C4⋊C4C2×C11311yescharacteristic, complemented
258#1982C2×C11311yescharacteristic, complemented
259#1957C2×C11311yescharacteristic, complemented
260C2×D4⋊C8C2×C11311yescharacteristic, complemented
261#1296C2×C11311yescharacteristic, complemented
262#1279C2×C11311yescharacteristic, complemented
263C113#897711yescharacteristic, direct product factor, Sylow
264C22×D8—21no—
265C2×#127C22×C11311yescharacteristic
266C2×C4×D4—21no—
267C2×C4×D4C22×C11311yescharacteristic
268C22×C4⋊C4—21no—
269#459—22no—
270#459C4×C11314yescomplemented
271C2×C4⋊C8C22×C11311yescharacteristic
272C2×C4⋊C8C22×C11311yescharacteristic
273C2×#102—21no—
274C2×#102—22no—
275C2×#102—21no—
276C2×#102—21no—
277C2×C4×C8C22×C11311yescharacteristic
278#389—21no—
279#385—22no—
280#384C22×C11311yescharacteristic
281#380—21no—
282C4×C4⋊C4C22×C11311yescharacteristic
283D4⋊C8—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4D4×C11311yescharacteristic
288C23×C4—21no—
289C23×C4—22no—
290C2×D8—24no—
291C2×D8—42no—
292C2×D8—42no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296#127—21no—
297#127—21no—
298#127—21no—
299#127C2×C4×C11312yescomplemented
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4C2×C4×C11312yes—
305C4×D4D4×C11312yes—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4D4×C11311yescharacteristic
312C2×C4⋊C4D4×C11311yescharacteristic
313C2×C4⋊C4D4×C11311yescharacteristic
314C2×C4⋊C4D4×C11312yes—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C42—21no—
318C2×C42C23×C11311yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8C2×C4×C11312yescomplemented
323#102—24no—
324#102—42no—
325#102—44no—
326#102—42no—
327C4×C8—21no—
328C4×C8—21no—
329#95—22no—
330#95—21no—
331C24—21no—
332C24—41no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4C22⋊C4×C11312yes—
353C2×D4D8×C11312yes—
354C2×D4SD16×C11312yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—44no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4C2×D4×C11311yescharacteristic
369C22×C4C2×D4×C11311yescharacteristic
370C22×C4C2×D4×C11311yescharacteristic
371D8—48no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—41no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—42no—
386C4⋊C4—44no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C22⋊C4×C11312yes—
392C4⋊C4D8×C11312yescomplemented
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—44no—
396C42—41no—
397C42—41no—
398C42C22×C4×C11311yescharacteristic
399C42C2×D4×C11311yescharacteristic
400C42#41×C11311yescharacteristic
401C42#41×C11311yescharacteristic
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23#120×C11311yescharacteristic
417D4—22no—
418D4—22no—
419D4—22no—
420D4—44no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—82no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4#102×C11314yescomplemented
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—88no—
450C2×C4C2×C22⋊C4×C11311yescharacteristic
451C2×C4C4×D4×C11311yescharacteristic
452C2×C4C4×D4×C11311yescharacteristic
453C2×C4#121×C11311yescharacteristic
454C2×C4#121×C11311yescharacteristic
455C2×C4#123×C11311yescharacteristic
456C2×C4C2×D8×C11311yescharacteristic
457C2×C4C2×D8×C11311yescharacteristic
458C2×C4C2×SD16×C11311yescharacteristic
459C2×C4#135×C11311yescharacteristic
460C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
461C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
462C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
463C2×C4#137×C11311yescharacteristic
464C8—42no—
465C8—42no—
466C8—81no—
467C22—24no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—161no—
478C22—161no—
479C22—161no—
480C22—161no—
481C22#386×C11311yescharacteristic
482C22#447×C11311yescharacteristic
483C22#447×C11311yescharacteristic
484C22#448×C11311yescharacteristic
485C22#449×C11311yescharacteristic
486C22#453×C11311yescharacteristic
487C22#454×C11311yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—82no—
493C4—81no—
494C4C2×#102×C11311yescharacteristic
495C4#417×C11311yescharacteristic
496C4C4×D8×C11311yescharacteristic
497C4#442×C11311yescharacteristic
498C4#459×C11311yescharacteristic
499C4#463×C11311yescharacteristic
500C4#480×C11311yescharacteristic
501C4#481×C11311yescharacteristic
502C2—44no—
503C2—162no—
504C2C113×#161911yescharacteristic
505C2C113×#162211yescharacteristic
506C2C113×#162511yescharacteristic
507C2C113×#162711yescharacteristic
508C2C113×#187411yescharacteristic
509C2C113×#187911yescharacteristic
510C2C113×#188311yescharacteristic
subgroupG/H
center, socleC23×C113#120
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC2×#459×C113C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊C4×C113C2semidirect
3. C113×#1982C2semidirect
4. C113×#1957C2semidirect
5. C2×D4⋊C8×C113C2semidirect
6. C113×#1296C2semidirect
7. C113×#1279C2semidirect
14. #459×C113C4semidirect
43. #127×C113C2×C4semidirect
66. C4⋊C8×C113C2×C4semidirect
136. C4⋊C4×C113D8semidirect
174. D4×C113#102semidirect
246. #8977C113direct (N × H)
257. D4×C4⋊C4C2×C113semidirect
258. #1982C2×C113semidirect
259. #1957C2×C113semidirect
260. C2×D4⋊C8C2×C113semidirect
261. #1296C2×C113semidirect
262. #1279C2×C113semidirect
263. C113#8977direct (N × H)
270. #459C4×C113semidirect
299. #127C2×C4×C113semidirect
322. C4⋊C8C2×C4×C113semidirect
392. C4⋊C4D8×C113semidirect
430. D4#102×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1132
D4×C4⋊C4×C1132
C113×#19822
C113×#19572
C2×D4⋊C8×C1132
C113×#12962
C113×#12792
#8977113