Finite Group Databasebeta

← C113×#25594 #43293614

Subgroups — C113×#25594 #43293614

Order 28928.

1050 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3509C211yesmaximal, characteristic, complemented
2C113×#3140C211yesmaximal, characteristic, complemented
3C113×#3040C211yesmaximal, characteristic
4C113×#2658C211yesmaximal, characteristic, complemented
5C113×#2005C212yesmaximal, complemented
6C113×#2003C212yesmaximal
7C113×#1995C211yesmaximal, characteristic, complemented
8C113×#1966C211yesmaximal, characteristic, complemented
9C113×#1888C212yesmaximal, complemented
10C113×#1886C212yesmaximal, complemented
11C113×#1759C211yesmaximal, characteristic, complemented
12C2×#137×C113C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
14#557×C113—22no—
15#556×C113—22no—
16#552×C113—24no—
17#541×C113—22no—
18#536×C113C2212yes—
19#533×C113—22no—
20#533×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2212yes—
22C2×C4⋊Q8×C113C2211yescharacteristic
23C2×#124×C113C2212yes—
24C2×#124×C113C2211yescharacteristic
25#519×C113C2212yes—
26C4×#41×C113C2211yescharacteristic
27#489×C113—22no—
28#488×C113—22no—
29#464×C113—22no—
30#463×C113—22no—
31#423×C113C2211yescharacteristic
32C2×#104×C113C2212yes—
33#419×C113C2212yes—
34#419×C113C2211yescharacteristic
35#418×C113C2212yes—
36#418×C113C2211yescharacteristic
37C2×#101×C113C2212yes—
38C2×#101×C113C2212yes—
39C4×M16×C113C2211yescharacteristic
40#399×C113—24no—
41#376×C113C2211yescharacteristic
42#339×C113C2212yes—
43#339×C113C2212yes—
44#339×C113C2212yes—
45C2×#41×C113C2311yescharacteristic
46C22×Q8×C113C2311yescharacteristic
47C22×Q8×C113C2312yes—
48C22×D4×C113C2311yescharacteristic
49#137×C113—42no—
50AGL(1,ℤ/8)×C113—42no—
51C2×Q16×C113—21no—
52C2×SD16×C113—21no—
53C2×SD16×C113—21no—
54C2×D8×C113—21no—
55C2×M16×C113C2311yescharacteristic
56C2×M16×C113C2311yescharacteristic
57C2×M16×C113C2312yes—
58C4⋊Q8×C113—22no—
59C4⋊Q8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113—22no—
62C4⋊Q8×C113—24no—
63C4⋊Q8×C113—42no—
64C4⋊Q8×C113D412yes—
65#126×C113—28no—
66#125×C113—24no—
67#125×C113—28no—
68#125×C113D412yes—
69#124×C113—22no—
70#124×C113—22no—
71#124×C113—21no—
72#124×C113—21no—
73#124×C113—24no—
74#124×C113—42no—
75#123×C113—24no—
76C22⋊Q8×C113—24no—
77C22⋊Q8×C113—22no—
78C22⋊Q8×C113—24no—
79C4×Q8×C113—24no—
80C4×Q8×C113—24no—
81C4×Q8×C113—24no—
82C4×Q8×C113—22no—
83C4×Q8×C113D412yes—
84C4×D4×C113—22no—
85C4×D4×C113D412yes—
86#117×C113—24no—
87#117×C113—24no—
88#117×C113—21no—
89#117×C113C2311yescharacteristic
90#117×C113C2312yes—
91C2×C4⋊C4×C113—24no—
92C2×C4⋊C4×C113D414yes—
93C2×C22⋊C4×C113—24no—
94C2×C22⋊C4×C113—22no—
95C2×C42×C113—21no—
96C2×C42×C113C2312yes—
97C2×C42×C113C2311yescharacteristic
98C4⋊C8×C113—22no—
99#104×C113—24no—
100#103×C113—22no—
101#103×C113—24no—
102#102×C113—22no—
103#102×C113—24no—
104#101×C113—42no—
105#101×C113—42no—
106#97×C113—21no—
107C4×C8×C113—21no—
108#95×C113—22no—
109C24×C113—21no—
110#41×C113—22no—
111#41×C113—22no—
112C2×Q8×C113—22no—
113C2×Q8×C113—22no—
114C2×Q8×C113—22no—
115C2×Q8×C113—22no—
116C2×Q8×C113—22no—
117C2×Q8×C113—22no—
118C2×Q8×C113—22no—
119C2×Q8×C113—21no—
120C2×Q8×C113—21no—
121C2×Q8×C113—22no—
122C2×Q8×C113—22no—
123C2×Q8×C113C2×D411yescharacteristic
124C2×D4×C113—21no—
125C2×D4×C113—21no—
126C2×D4×C113—21no—
127C2×D4×C113—22no—
128C2×D4×C113—22no—
129C2×D4×C113C2×D411yescharacteristic
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—21no—
133C22×C4×C113—21no—
134C22×C4×C113C2×D414yes—
135C22×C4×C113C2×D412yes—
136C22×C4×C113C2411yescharacteristic
137Q16×C113—42no—
138SD16×C113—42no—
139SD16×C113—42no—
140D8×C113—42no—
141M16×C113—22no—
142M16×C113—22no—
143M16×C113—22no—
144M16×C113—22no—
145C2×C8×C113—22no—
146C2×C8×C113—21no—
147C2×C8×C113—21no—
148C4⋊C4×C113—28no—
149C4⋊C4×C113—28no—
150C4⋊C4×C113—24no—
151C4⋊C4×C113—24no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—24no—
155C4⋊C4×C113—48no—
156C4⋊C4×C113C2×D412yes—
157C4⋊C4×C113C2×D414yes—
158C22⋊C4×C113—28no—
159C22⋊C4×C113—21no—
160C22⋊C4×C113—22no—
161C22⋊C4×C113—22no—
162C22⋊C4×C113—48no—
163C22⋊C4×C113—42no—
164C22⋊C4×C113—42no—
165C42×C113—28no—
166C42×C113—22no—
167C42×C113—21no—
168C42×C113—22no—
169C42×C113—22no—
170C42×C113C2×D411yescharacteristic
171C42×C113C2×D411yescharacteristic
172C42×C113C2×D412yes—
173C42×C113#4114yes—
174C23×C113—21no—
175C23×C113—44no—
176C23×C113—41no—
177C23×C113—42no—
178C23×C113C22×D411yescharacteristic
179Q8×C113—21no—
180Q8×C113—21no—
181Q8×C113—44no—
182Q8×C113—42no—
183Q8×C113—42no—
184Q8×C113—42no—
185Q8×C113—42no—
186Q8×C113—41no—
187Q8×C113—41no—
188Q8×C113—42no—
189D4×C113—21no—
190D4×C113—21no—
191D4×C113—42no—
192D4×C113—41no—
193D4×C113—41no—
194D4×C113—42no—
195C2×C4×C113—22no—
196C2×C4×C113—24no—
197C2×C4×C113—24no—
198C2×C4×C113—21no—
199C2×C4×C113—24no—
200C2×C4×C113—24no—
201C2×C4×C113—24no—
202C2×C4×C113—42no—
203C2×C4×C113—44no—
204C2×C4×C113—44no—
205C2×C4×C113—42no—
206C2×C4×C113—41no—
207C2×C4×C113—42no—
208C2×C4×C113#12012yes—
209C2×C4×C113#12012yes—
210C2×C4×C113C22×D411yescharacteristic
211C2×C4×C113C22×D411yescharacteristic
212C2×C4×C113C2×#4112yes—
213C2×C4×C113H(5,𝔽2)12yes—
214C8×C113—41no—
215C8×C113—41no—
216C8×C113—42no—
217C22×C113—22no—
218C22×C113—41no—
219C22×C113—42no—
220C22×C113—84no—
221C22×C113—81no—
222C22×C113—82no—
223C22×C113C2×#12011yescharacteristic
224C22×C113#54612yes—
225C4×C113—22no—
226C4×C113—22no—
227C4×C113—44no—
228C4×C113—44no—
229C4×C113—41no—
230C4×C113—42no—
231C4×C113—44no—
232C4×C113—81no—
233C4×C113#53211yescharacteristic
234C4×C113#53511yescharacteristic
235C4×C113#55012yes—
236#25594C11311yesmaximal, characteristic, direct product factor, Sylow
237C2×C113—22no—
238C2×C113—81no—
239C2×C113—161no—
240C2×C113#243111yescharacteristic
241C2×C113#302012yes—
242#3509C2×C11311yescharacteristic, complemented
243#3140C2×C11311yescharacteristic, complemented
244#3040C2×C11311yescharacteristic
245#2658C2×C11311yescharacteristic, complemented
246#2005C2×C11312yescomplemented
247#2003C2×C11312yes—
248#1995C2×C11311yescharacteristic, complemented
249#1966C2×C11311yescharacteristic, complemented
250#1888C2×C11312yescomplemented
251#1886C2×C11312yescomplemented
252#1759C2×C11311yescharacteristic, complemented
253C113#2559411yescharacteristic, direct product factor, Sylow
254C2×#137C22×C11311yescharacteristic
255C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
256#557—22no—
257#556—22no—
258#552—24no—
259#541—22no—
260#536C22×C11312yes—
261#533—22no—
262#533C22×C11311yescharacteristic
263C2×C4⋊Q8C22×C11312yes—
264C2×C4⋊Q8C22×C11311yescharacteristic
265C2×#124C22×C11311yescharacteristic
266C2×#124C22×C11312yes—
267#519C22×C11312yes—
268C4×#41C22×C11311yescharacteristic
269#489—22no—
270#488—22no—
271#464—22no—
272#463—22no—
273#423C22×C11311yescharacteristic
274C2×#104C22×C11312yes—
275#419C22×C11312yes—
276#419C22×C11311yescharacteristic
277#418C22×C11312yes—
278#418C22×C11311yescharacteristic
279C2×#101C22×C11312yes—
280C2×#101C22×C11312yes—
281C4×M16C22×C11311yescharacteristic
282#399—24no—
283#376C22×C11311yescharacteristic
284#339C22×C11312yes—
285#339C22×C11312yes—
286#339C22×C11312yes—
287C2×#41C23×C11311yescharacteristic
288C22×Q8C23×C11311yescharacteristic
289C22×Q8C23×C11312yes—
290C22×D4C23×C11311yescharacteristic
291#137—42no—
292AGL(1,ℤ/8)—42no—
293C2×Q16—21no—
294C2×SD16—21no—
295C2×SD16—21no—
296C2×D8—21no—
297C2×M16C23×C11311yescharacteristic
298C2×M16C23×C11311yescharacteristic
299C2×M16C23×C11312yes—
300C4⋊Q8—22no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—22no—
304C4⋊Q8—24no—
305C4⋊Q8—42no—
306C4⋊Q8D4×C11312yes—
307#126—28no—
308#125—24no—
309#125—28no—
310#125D4×C11312yes—
311#124—22no—
312#124—22no—
313#124—21no—
314#124—21no—
315#124—24no—
316#124—42no—
317#123—24no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C22⋊Q8—24no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8—22no—
325C4×Q8D4×C11312yes—
326C4×D4—22no—
327C4×D4D4×C11312yes—
328#117—24no—
329#117—24no—
330#117—21no—
331#117C23×C11311yescharacteristic
332#117C23×C11312yes—
333C2×C4⋊C4—24no—
334C2×C4⋊C4D4×C11314yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C42—21no—
338C2×C42C23×C11312yes—
339C2×C42C23×C11311yescharacteristic
340C4⋊C8—22no—
341#104—24no—
342#103—22no—
343#103—24no—
344#102—22no—
345#102—24no—
346#101—42no—
347#101—42no—
348#97—21no—
349C4×C8—21no—
350#95—22no—
351C24—21no—
352#41—22no—
353#41—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8C2×D4×C11311yescharacteristic
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4C2×D4×C11311yescharacteristic
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4C2×D4×C11314yes—
377C22×C4C2×D4×C11312yes—
378C22×C4C24×C11311yescharacteristic
379Q16—42no—
380SD16—42no—
381SD16—42no—
382D8—42no—
383M16—22no—
384M16—22no—
385M16—22no—
386M16—22no—
387C2×C8—22no—
388C2×C8—21no—
389C2×C8—21no—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—48no—
398C4⋊C4C2×D4×C11312yes—
399C4⋊C4C2×D4×C11314yes—
400C22⋊C4—28no—
401C22⋊C4—21no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—48no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C42—28no—
408C42—22no—
409C42—21no—
410C42—22no—
411C42—22no—
412C42C2×D4×C11311yescharacteristic
413C42C2×D4×C11311yescharacteristic
414C42C2×D4×C11312yes—
415C42#41×C11314yes—
416C23—21no—
417C23—44no—
418C23—41no—
419C23—42no—
420C23C22×D4×C11311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—44no—
424Q8—42no—
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—41no—
429Q8—41no—
430Q8—42no—
431D4—21no—
432D4—21no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—42no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4#120×C11312yes—
451C2×C4#120×C11312yes—
452C2×C4C22×D4×C11311yescharacteristic
453C2×C4C22×D4×C11311yescharacteristic
454C2×C4C2×#41×C11312yes—
455C2×C4H(5,𝔽2)×C11312yes—
456C8—41no—
457C8—41no—
458C8—42no—
459C22—22no—
460C22—41no—
461C22—42no—
462C22—84no—
463C22—81no—
464C22—82no—
465C22C2×#120×C11311yescharacteristic
466C22#546×C11312yes—
467C4—22no—
468C4—22no—
469C4—44no—
470C4—44no—
471C4—41no—
472C4—42no—
473C4—44no—
474C4—81no—
475C4#532×C11311yescharacteristic
476C4#535×C11311yescharacteristic
477C4#550×C11312yes—
478C2—22no—
479C2—81no—
480C2—161no—
481C2C113×#243111yescharacteristic
482C2C113×#302012yes—
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×AGL(1,ℤ/8)×C113C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3509C2semidirect
2. C113×#3140C2semidirect
4. C113×#2658C2semidirect
5. C113×#2005C2semidirect
7. C113×#1995C2semidirect
8. C113×#1966C2semidirect
9. C113×#1888C2semidirect
10. C113×#1886C2semidirect
11. C113×#1759C2semidirect
236. #25594C113direct (N × H)
242. #3509C2×C113semidirect
243. #3140C2×C113semidirect
245. #2658C2×C113semidirect
246. #2005C2×C113semidirect
248. #1995C2×C113semidirect
249. #1966C2×C113semidirect
250. #1888C2×C113semidirect
251. #1886C2×C113semidirect
252. #1759C2×C113semidirect
253. C113#25594direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35092
C113×#31402
C113×#30402
C113×#26582
C113×#20052
C113×#20032
C113×#19952
C113×#19662
C113×#18882
C113×#18862
C113×#17592
#25594113