Finite Group Databasebeta

← C113×#18626 #43286646

Subgroups — C113×#18626 #43286646

Order 28928.

1088 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3511C211yesmaximal, characteristic, complemented
2C113×#3205C211yesmaximal, characteristic, complemented
3C2×#492×C113C211yesmaximal, characteristic, complemented
4C113×#3038C211yesmaximal, characteristic, complemented
5C113×#1624C214yesmaximal, complemented
6C113×#1622C214yesmaximal, complemented
7C113×#1548C211yesmaximal, characteristic, complemented
8C113×#1492C211yesmaximal, characteristic, complemented
9C113×#1476C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C113—21no—
11C22×SD16×C113—22no—
12#556×C113—21no—
13#555×C113C2212yescomplemented
14#554×C113C2212yescomplemented
15#553×C113—22no—
16#548×C113—22no—
17#547×C113—21no—
18#542×C113—22no—
19#537×C113—21no—
20#533×C113—21no—
21#532×C113—21no—
22#532×C113C2211yescharacteristic
23C2×C4⋊Q8×C113C2211yescharacteristic
24C2×#127×C113C2211yescharacteristic
25#520×C113—21no—
26C4×#41×C113C2211yescharacteristic
27#493×C113—21no—
28#492×C113—22no—
29#492×C113C2214yes—
30#486×C113—21no—
31#460×C113—21no—
32#460×C113C2212yes—
33#459×C113—21no—
34#459×C113C2214yes—
35#459×C113C2212yes—
36#447×C113—22no—
37#431×C113C2211yescharacteristic
38#423×C113C2211yescharacteristic
39#418×C113—21no—
40C2×C4×C8×C113C2211yescharacteristic
41#333×C113C2214yescomplemented
42Q8⋊C8×C113C2212yescomplemented
43D4⋊C8×C113C2214yescomplemented
44D4⋊C8×C113C2212yescomplemented
45C2×#41×C113—22no—
46C2×#41×C113—21no—
47C2×#41×C113D411yescharacteristic
48C22×Q8×C113D412yes—
49C22×D4×C113—21no—
50C22×D4×C113—21no—
51C22×D4×C113—21no—
52AGL(1,ℤ/8)×C113—44no—
53C2×SD16×C113—28no—
54C2×SD16×C113—22no—
55C2×SD16×C113—48no—
56C2×D8×C113—22no—
57C2×D8×C113—24no—
58C2×M16×C113—21no—
59C22×C8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113—21no—
62C4⋊Q8×C113D412yes—
63C4⋊Q8×C113D411yescharacteristic
64C4⋊Q8×C113C2312yes—
65#127×C113—21no—
66#127×C113—21no—
67#127×C113—21no—
68#127×C113D411yescharacteristic
69#127×C113C2312yes—
70#126×C113—24no—
71#125×C113—22no—
72#124×C113—22no—
73#124×C113—24no—
74#124×C113—21no—
75#123×C113—24no—
76C22⋊Q8×C113—22no—
77C22⋊Q8×C113—22no—
78C22⋊Q8×C113—22no—
79C22⋊Q8×C113—24no—
80#121×C113—22no—
81#121×C113—24no—
82#121×C113—22no—
83#121×C113—22no—
84#121×C113—21no—
85#121×C113D412yes—
86C4×Q8×C113—22no—
87C4×Q8×C113—22no—
88C4×Q8×C113D411yescharacteristic
89C4×Q8×C113C2311yescharacteristic
90C4×D4×C113—22no—
91C4×D4×C113—24no—
92C4×D4×C113—22no—
93C4×D4×C113—21no—
94C4×D4×C113—21no—
95C4×D4×C113—21no—
96C4×D4×C113D411yescharacteristic
97C4×D4×C113C2311yescharacteristic
98C4×D4×C113C2312yes—
99#117×C113—22no—
100#117×C113—22no—
101#117×C113—21no—
102#117×C113D411yescharacteristic
103C2×C4⋊C4×C113—21no—
104C2×C4⋊C4×C113—21no—
105C2×C4⋊C4×C113—22no—
106C2×C42×C113—21no—
107C2×C42×C113C2311yescharacteristic
108C4⋊C8×C113—21no—
109C4⋊C8×C113C2312yes—
110C4⋊C8×C113C2312yes—
111#102×C113—22no—
112#102×C113—22no—
113#102×C113—24no—
114C22⋊C8×C113—21no—
115C4×C8×C113—21no—
116C4×C8×C113—21no—
117C4×C8×C113C2312yes—
118C24×C113—41no—
119#41×C113—22no—
120#41×C113—22no—
121#41×C113—42no—
122#41×C113—42no—
123#41×C113—84no—
124C2×Q8×C113—21no—
125C2×Q8×C113—22no—
126C2×Q8×C113—44no—
127C2×Q8×C113C2×D411yescharacteristic
128C2×Q8×C113C2×D414yes—
129C2×D4×C113—21no—
130C2×D4×C113—22no—
131C2×D4×C113—24no—
132C2×D4×C113—21no—
133C2×D4×C113—21no—
134C2×D4×C113—22no—
135C2×D4×C113—22no—
136C2×D4×C113—22no—
137C2×D4×C113—44no—
138C2×D4×C113—41no—
139C2×D4×C113—41no—
140C2×D4×C113—41no—
141C2×D4×C113—42no—
142C2×D4×C113—42no—
143C2×D4×C113—82no—
144C2×D4×C113C2×D412yes—
145C2×D4×C113C2×D411yescharacteristic
146C22×C4×C113—24no—
147C22×C4×C113—22no—
148C22×C4×C113—21no—
149C22×C4×C113—21no—
150C22×C4×C113—21no—
151C22×C4×C113—22no—
152C22×C4×C113C2×D411yescharacteristic
153C22×C4×C113C2×D411yescharacteristic
154C22×C4×C113C2×D411yescharacteristic
155SD16×C113—416no—
156SD16×C113—44no—
157D8×C113—44no—
158D8×C113—84no—
159M16×C113—42no—
160C2×C8×C113—24no—
161C2×C8×C113—22no—
162C2×C8×C113—22no—
163C2×C8×C113—22no—
164C4⋊C4×C113—24no—
165C4⋊C4×C113—24no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—22no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—21no—
170C4⋊C4×C113—22no—
171C4⋊C4×C113—22no—
172C4⋊C4×C113—21no—
173C4⋊C4×C113C2×D411yescharacteristic
174C4⋊C4×C113C2×D411yescharacteristic
175C4⋊C4×C113C2×D412yes—
176C22⋊C4×C113—24no—
177C22⋊C4×C113—24no—
178C22⋊C4×C113—24no—
179C22⋊C4×C113—21no—
180C22⋊C4×C113—21no—
181C22⋊C4×C113—22no—
182C22⋊C4×C113—21no—
183C22⋊C4×C113—22no—
184C42×C113—24no—
185C42×C113—21no—
186C42×C113—21no—
187C42×C113—21no—
188C42×C113C2×D411yescharacteristic
189C42×C113C2×D411yescharacteristic
190C42×C113C2×D411yescharacteristic
191C42×C113C2411yescharacteristic
192C23×C113—21no—
193C23×C113—22no—
194C23×C113—42no—
195C23×C113—82no—
196C23×C113—82no—
197C23×C113—82no—
198C23×C113#12011yescharacteristic
199Q8×C113—21no—
200Q8×C113—21no—
201Q8×C113—44no—
202Q8×C113—42no—
203Q8×C113—44no—
204D4×C113—21no—
205D4×C113—21no—
206D4×C113—24no—
207D4×C113—44no—
208D4×C113—42no—
209D4×C113—44no—
210D4×C113—42no—
211D4×C113—42no—
212D4×C113—44no—
213D4×C113—42no—
214D4×C113—42no—
215D4×C113—82no—
216D4×C113—84no—
217D4×C113—82no—
218D4×C113—82no—
219C2×C4×C113—22no—
220C2×C4×C113—22no—
221C2×C4×C113—21no—
222C2×C4×C113—21no—
223C2×C4×C113—22no—
224C2×C4×C113—21no—
225C2×C4×C113—24no—
226C2×C4×C113—42no—
227C2×C4×C113—42no—
228C2×C4×C113—42no—
229C2×C4×C113—42no—
230C2×C4×C113—42no—
231C2×C4×C113—82no—
232C2×C4×C113—84no—
233C2×C4×C113#12011yescharacteristic
234C2×C4×C113#12011yescharacteristic
235C2×C4×C113#12011yescharacteristic
236C2×C4×C113#13512yes—
237C2×C4×C113AGL(1,ℤ/8)12yes—
238C2×C4×C113C22×D411yescharacteristic
239C2×C4×C113C22×D411yescharacteristic
240C2×C4×C113C22×D411yescharacteristic
241C8×C113—24no—
242C8×C113—42no—
243C8×C113—42no—
244C22×C113—21no—
245C22×C113—21no—
246C22×C113—41no—
247C22×C113—42no—
248C22×C113—41no—
249C22×C113—42no—
250C22×C113—41no—
251C22×C113—42no—
252C22×C113—82no—
253C22×C113—82no—
254C22×C113—82no—
255C22×C113—164no—
256C22×C113#44912yes—
257C22×C113C2×#12011yescharacteristic
258C4×C113—21no—
259C4×C113—21no—
260C4×C113—41no—
261C4×C113—42no—
262C4×C113—41no—
263C4×C113—41no—
264C4×C113—44no—
265C4×C113#44912yes—
266C4×C113#45312yes—
267C4×C113C2×#13511yescharacteristic
268C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C113#57712yes—
270#18626C11311yesmaximal, characteristic, direct product factor, Sylow
271C2×C113—22no—
272C2×C113—81no—
273C2×C113—82no—
274C2×C113—162no—
275C2×C113C2×#44911yescharacteristic
276C2×C113#301011yescharacteristic
277C2×C113C2×#45311yescharacteristic
278#3511C2×C11311yescharacteristic, complemented
279#3205C2×C11311yescharacteristic, complemented
280C2×#492C2×C11311yescharacteristic, complemented
281#3038C2×C11311yescharacteristic, complemented
282#1624C2×C11314yescomplemented
283#1622C2×C11314yescomplemented
284#1548C2×C11311yescharacteristic, complemented
285#1492C2×C11311yescharacteristic, complemented
286#1476C2×C11311yescharacteristic, complemented
287C113#1862611yescharacteristic, direct product factor, Sylow
288C2×AGL(1,ℤ/8)—21no—
289C22×SD16—22no—
290#556—21no—
291#555C22×C11312yescomplemented
292#554C22×C11312yescomplemented
293#553—22no—
294#548—22no—
295#547—21no—
296#542—22no—
297#537—21no—
298#533—21no—
299#532—21no—
300#532C22×C11311yescharacteristic
301C2×C4⋊Q8C22×C11311yescharacteristic
302C2×#127C22×C11311yescharacteristic
303#520—21no—
304C4×#41C22×C11311yescharacteristic
305#493—21no—
306#492—22no—
307#492C22×C11314yes—
308#486—21no—
309#460—21no—
310#460C22×C11312yes—
311#459—21no—
312#459C22×C11314yes—
313#459C22×C11312yes—
314#447—22no—
315#431C22×C11311yescharacteristic
316#423C22×C11311yescharacteristic
317#418—21no—
318C2×C4×C8C22×C11311yescharacteristic
319#333C22×C11314yescomplemented
320Q8⋊C8C22×C11312yescomplemented
321D4⋊C8C22×C11314yescomplemented
322D4⋊C8C22×C11312yescomplemented
323C2×#41—22no—
324C2×#41—21no—
325C2×#41D4×C11311yescharacteristic
326C22×Q8D4×C11312yes—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330AGL(1,ℤ/8)—44no—
331C2×SD16—28no—
332C2×SD16—22no—
333C2×SD16—48no—
334C2×D8—22no—
335C2×D8—24no—
336C2×M16—21no—
337C22×C8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8D4×C11312yes—
341C4⋊Q8D4×C11311yescharacteristic
342C4⋊Q8C23×C11312yes—
343#127—21no—
344#127—21no—
345#127—21no—
346#127D4×C11311yescharacteristic
347#127C23×C11312yes—
348#126—24no—
349#125—22no—
350#124—22no—
351#124—24no—
352#124—21no—
353#123—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—24no—
358#121—22no—
359#121—24no—
360#121—22no—
361#121—22no—
362#121—21no—
363#121D4×C11312yes—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8D4×C11311yescharacteristic
367C4×Q8C23×C11311yescharacteristic
368C4×D4—22no—
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4D4×C11311yescharacteristic
375C4×D4C23×C11311yescharacteristic
376C4×D4C23×C11312yes—
377#117—22no—
378#117—22no—
379#117—21no—
380#117D4×C11311yescharacteristic
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C42—21no—
385C2×C42C23×C11311yescharacteristic
386C4⋊C8—21no—
387C4⋊C8C23×C11312yes—
388C4⋊C8C23×C11312yes—
389#102—22no—
390#102—22no—
391#102—24no—
392C22⋊C8—21no—
393C4×C8—21no—
394C4×C8—21no—
395C4×C8C23×C11312yes—
396C24—41no—
397#41—22no—
398#41—22no—
399#41—42no—
400#41—42no—
401#41—84no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—44no—
405C2×Q8C2×D4×C11311yescharacteristic
406C2×Q8C2×D4×C11314yes—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—44no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4C2×D4×C11312yes—
423C2×D4C2×D4×C11311yescharacteristic
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4C2×D4×C11311yescharacteristic
431C22×C4C2×D4×C11311yescharacteristic
432C22×C4C2×D4×C11311yescharacteristic
433SD16—416no—
434SD16—44no—
435D8—44no—
436D8—84no—
437M16—42no—
438C2×C8—24no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4C2×D4×C11311yescharacteristic
452C4⋊C4C2×D4×C11311yescharacteristic
453C4⋊C4C2×D4×C11312yes—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—22no—
460C22⋊C4—21no—
461C22⋊C4—22no—
462C42—24no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42C2×D4×C11311yescharacteristic
467C42C2×D4×C11311yescharacteristic
468C42C2×D4×C11311yescharacteristic
469C42C24×C11311yescharacteristic
470C23—21no—
471C23—22no—
472C23—42no—
473C23—82no—
474C23—82no—
475C23—82no—
476C23#120×C11311yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—44no—
480Q8—42no—
481Q8—44no—
482D4—21no—
483D4—21no—
484D4—24no—
485D4—44no—
486D4—42no—
487D4—44no—
488D4—42no—
489D4—42no—
490D4—44no—
491D4—42no—
492D4—42no—
493D4—82no—
494D4—84no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—84no—
511C2×C4#120×C11311yescharacteristic
512C2×C4#120×C11311yescharacteristic
513C2×C4#120×C11311yescharacteristic
514C2×C4#135×C11312yes—
515C2×C4AGL(1,ℤ/8)×C11312yes—
516C2×C4C22×D4×C11311yescharacteristic
517C2×C4C22×D4×C11311yescharacteristic
518C2×C4C22×D4×C11311yescharacteristic
519C8—24no—
520C8—42no—
521C8—42no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—42no—
526C22—41no—
527C22—42no—
528C22—41no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—164no—
534C22#449×C11312yes—
535C22C2×#120×C11311yescharacteristic
536C4—21no—
537C4—21no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4—41no—
542C4—44no—
543C4#449×C11312yes—
544C4#453×C11312yes—
545C4C2×#135×C11311yescharacteristic
546C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
547C4#577×C11312yes—
548C2—22no—
549C2—81no—
550C2—82no—
551C2—162no—
552C2C2×#449×C11311yescharacteristic
553C2C113×#301011yescharacteristic
554C2C2×#453×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3511C2semidirect
2. C113×#3205C2semidirect
3. C2×#492×C113C2semidirect
4. C113×#3038C2semidirect
5. C113×#1624C2semidirect
6. C113×#1622C2semidirect
7. C113×#1548C2semidirect
8. C113×#1492C2semidirect
9. C113×#1476C2semidirect
13. #555×C113C22semidirect
14. #554×C113C22semidirect
41. #333×C113C22semidirect
42. Q8⋊C8×C113C22semidirect
43. D4⋊C8×C113C22semidirect
44. D4⋊C8×C113C22semidirect
270. #18626C113direct (N × H)
278. #3511C2×C113semidirect
279. #3205C2×C113semidirect
280. C2×#492C2×C113semidirect
281. #3038C2×C113semidirect
282. #1624C2×C113semidirect
283. #1622C2×C113semidirect
284. #1548C2×C113semidirect
285. #1492C2×C113semidirect
286. #1476C2×C113semidirect
287. C113#18626direct (N × H)
291. #555C22×C113semidirect
292. #554C22×C113semidirect
319. #333C22×C113semidirect
320. Q8⋊C8C22×C113semidirect
321. D4⋊C8C22×C113semidirect
322. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35112
C113×#32052
C2×#492×C1132
C113×#30382
C113×#16242
C113×#16222
C113×#15482
C113×#14922
C113×#14762
#18626113