Finite Group Databasebeta

← C113×#18894 #43286914

Subgroups — C113×#18894 #43286914

Order 28928.

1022 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
1C113×#3501C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic, complemented
3C113×#3208C211yesmaximal, characteristic, complemented
4C2×#459×C113C211yesmaximal, characteristic
5C113×#1627C214yesmaximal, complemented
6C113×#1622C214yesmaximal, complemented
7C113×#1542C211yesmaximal, characteristic, complemented
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C22×D8×C113—21no—
11#554×C113—21no—
12#554×C113—22no—
13#554×C113—22no—
14#554×C113C2212yescomplemented
15D4×Q8×C113—21no—
16D4×Q8×C113C2212yescomplemented
17#544×C113—21no—
18#543×C113—22no—
19#533×C113C2211yescharacteristic
20#533×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×C22⋊Q8×C113—22no—
23#518×C113—21no—
24C2×C4×D4×C113C2211yescharacteristic
25#492×C113—21no—
26#492×C113C2212yescomplemented
27#486×C113—21no—
28#486×C113C2212yescomplemented
29#460×C113—22no—
30#460×C113C2214yescomplemented
31#459×C113—22no—
32#459×C113C2214yes—
33#450×C113—22no—
34#450×C113—22no—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#102×C113—21no—
39#333×C113C2212yescomplemented
40#332×C113C2212yescomplemented
41Q8⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yescomplemented
43C22×Q8×C113—22no—
44C22×D4×C113—21no—
45C22×D4×C113—21no—
46C22×D4×C113—21no—
47C22×D4×C113D411yescharacteristic
48C23×C4×C113—21no—
49C2×SD16×C113—24no—
50C2×SD16×C113—24no—
51C2×D8×C113—24no—
52C2×D8×C113—44no—
53C22×C8×C113—21no—
54C4⋊Q8×C113—22no—
55C4⋊Q8×C113—22no—
56C4⋊Q8×C113D411yescharacteristic
57C4⋊Q8×C113D411yescharacteristic
58C4⋊Q8×C113C2311yescharacteristic
59C4⋊Q8×C113C2311yescharacteristic
60#127×C113—21no—
61#127×C113—21no—
62#127×C113—21no—
63#127×C113C2312yes—
64#125×C113—22no—
65#125×C113—22no—
66#125×C113—21no—
67#125×C113—21no—
68C22⋊Q8×C113—24no—
69C22⋊Q8×C113—24no—
70C22⋊Q8×C113—24no—
71C22⋊Q8×C113—24no—
72C22⋊Q8×C113—22no—
73C22⋊Q8×C113—24no—
74C22⋊Q8×C113—21no—
75C22⋊Q8×C113—21no—
76C22⋊Q8×C113—22no—
77C22⋊Q8×C113—24no—
78C22⋊Q8×C113D412yes—
79C22⋊Q8×C113D412yes—
80C4×Q8×C113—21no—
81C4×Q8×C113—21no—
82C4×Q8×C113D412yes—
83C4×Q8×C113C2312yes—
84C4×D4×C113—22no—
85C4×D4×C113—22no—
86C4×D4×C113—22no—
87C4×D4×C113—22no—
88C4×D4×C113—21no—
89C4×D4×C113—21no—
90C4×D4×C113D412yes—
91C4×D4×C113C2312yes—
92#117×C113—21no—
93#117×C113—21no—
94C2×C4⋊C4×C113—24no—
95C2×C4⋊C4×C113—22no—
96C2×C4⋊C4×C113D411yescharacteristic
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—21no—
99C2×C42×C113C2311yescharacteristic
100C4⋊C8×C113—21no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113C2312yes—
103C4⋊C8×C113C2312yes—
104#102×C113—24no—
105#102×C113—24no—
106#102×C113—24no—
107C22⋊C8×C113—21no—
108C22⋊C8×C113—21no—
109C4×C8×C113—21no—
110C4×C8×C113C2312yes—
111C24×C113—21no—
112C24×C113—41no—
113C2×Q8×C113—24no—
114C2×Q8×C113—21no—
115C2×Q8×C113—21no—
116C2×Q8×C113—84no—
117C2×Q8×C113C2×D412yes—
118C2×Q8×C113C2×D412yes—
119C2×D4×C113—21no—
120C2×D4×C113—22no—
121C2×D4×C113—22no—
122C2×D4×C113—22no—
123C2×D4×C113—22no—
124C2×D4×C113—41no—
125C2×D4×C113—41no—
126C2×D4×C113—41no—
127C2×D4×C113—42no—
128C2×D4×C113—42no—
129C2×D4×C113—82no—
130C2×D4×C113—82no—
131C2×D4×C113SD1614yescomplemented
132C2×D4×C113C2×D412yes—
133C22×C4×C113—24no—
134C22×C4×C113—24no—
135C22×C4×C113—21no—
136C22×C4×C113—22no—
137C22×C4×C113—22no—
138C22×C4×C113—82no—
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142SD16×C113—84no—
143SD16×C113—84no—
144D8×C113—48no—
145C2×C8×C113—22no—
146C2×C8×C113—22no—
147C2×C8×C113—22no—
148C2×C8×C113—42no—
149C4⋊C4×C113—24no—
150C4⋊C4×C113—24no—
151C4⋊C4×C113—24no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—21no—
155C4⋊C4×C113—21no—
156C4⋊C4×C113—21no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—22no—
159C4⋊C4×C113—21no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113C2×D412yes—
164C4⋊C4×C113C2×D412yes—
165C4⋊C4×C113C2×D412yes—
166C22⋊C4×C113—24no—
167C22⋊C4×C113—24no—
168C22⋊C4×C113—22no—
169C22⋊C4×C113—22no—
170C22⋊C4×C113—22no—
171C22⋊C4×C113—22no—
172C42×C113—22no—
173C42×C113—22no—
174C42×C113C2×D411yescharacteristic
175C42×C113C2×D411yescharacteristic
176C42×C113C2×D411yescharacteristic
177C42×C113C2411yescharacteristic
178C23×C113—22no—
179C23×C113—24no—
180C23×C113—42no—
181C23×C113—81no—
182C23×C113—81no—
183C23×C113—82no—
184C23×C113—82no—
185C23×C113—82no—
186C23×C113#12011yescharacteristic
187Q8×C113—24no—
188Q8×C113—42no—
189Q8×C113—42no—
190Q8×C113—81no—
191Q8×C113—84no—
192D4×C113—22no—
193D4×C113—24no—
194D4×C113—44no—
195D4×C113—42no—
196D4×C113—42no—
197D4×C113—44no—
198D4×C113—82no—
199D4×C113—82no—
200D4×C113—82no—
201D4×C113C2×SD1614yes—
202C2×C4×C113—22no—
203C2×C4×C113—22no—
204C2×C4×C113—22no—
205C2×C4×C113—22no—
206C2×C4×C113—22no—
207C2×C4×C113—22no—
208C2×C4×C113—41no—
209C2×C4×C113—44no—
210C2×C4×C113—82no—
211C2×C4×C113—81no—
212C2×C4×C113—84no—
213C2×C4×C113—84no—
214C2×C4×C113#12011yescharacteristic
215C2×C4×C113#12011yescharacteristic
216C2×C4×C113#12011yescharacteristic
217C2×C4×C113C2×SD1612yes—
218C2×C4×C113#13712yes—
219C2×C4×C113C22×D411yescharacteristic
220C2×C4×C113C22×D411yescharacteristic
221C2×C4×C113C22×D411yescharacteristic
222C8×C113—42no—
223C8×C113—42no—
224C8×C113—42no—
225C22×C113—21no—
226C22×C113—21no—
227C22×C113—24no—
228C22×C113—42no—
229C22×C113—42no—
230C22×C113—84no—
231C22×C113—82no—
232C22×C113—82no—
233C22×C113—82no—
234C22×C113—164no—
235C22×C113#44812yes—
236C22×C113C2×#12011yescharacteristic
237C4×C113—21no—
238C4×C113—21no—
239C4×C113—21no—
240C4×C113—42no—
241C4×C113—42no—
242C4×C113—42no—
243C4×C113—42no—
244C4×C113—42no—
245C4×C113#44812yes—
246C4×C113C22×SD1611yescharacteristic
247C4×C113C2×#13711yescharacteristic
248C4×C113#57612yes—
249#18894C11311yesmaximal, characteristic, direct product factor, Sylow
250C2×C113—22no—
251C2×C113—44no—
252C2×C113—162no—
253C2×C113C2×#44811yescharacteristic
254C2×C113#300811yescharacteristic
255C2×C113#302111yescharacteristic
256#3501C2×C11311yescharacteristic, complemented
257#3208C2×C11311yescharacteristic, complemented
258#3208C2×C11311yescharacteristic, complemented
259C2×#459C2×C11311yescharacteristic
260#1627C2×C11314yescomplemented
261#1622C2×C11314yescomplemented
262#1542C2×C11311yescharacteristic, complemented
263#1481C2×C11311yescharacteristic, complemented
264#1478C2×C11311yescharacteristic, complemented
265C113#1889411yescharacteristic, direct product factor, Sylow
266C22×D8—21no—
267#554—21no—
268#554—22no—
269#554—22no—
270#554C22×C11312yescomplemented
271D4×Q8—21no—
272D4×Q8C22×C11312yescomplemented
273#544—21no—
274#543—22no—
275#533C22×C11311yescharacteristic
276#533C22×C11311yescharacteristic
277C2×#127C22×C11311yescharacteristic
278C2×C22⋊Q8—22no—
279#518—21no—
280C2×C4×D4C22×C11311yescharacteristic
281#492—21no—
282#492C22×C11312yescomplemented
283#486—21no—
284#486C22×C11312yescomplemented
285#460—22no—
286#460C22×C11314yescomplemented
287#459—22no—
288#459C22×C11314yes—
289#450—22no—
290#450—22no—
291#431C22×C11311yescharacteristic
292#431C22×C11311yescharacteristic
293C2×C4⋊C8C22×C11311yescharacteristic
294C2×#102—21no—
295#333C22×C11312yescomplemented
296#332C22×C11312yescomplemented
297Q8⋊C8C22×C11314yescomplemented
298D4⋊C8C22×C11314yescomplemented
299C22×Q8—22no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4D4×C11311yescharacteristic
304C23×C4—21no—
305C2×SD16—24no—
306C2×SD16—24no—
307C2×D8—24no—
308C2×D8—44no—
309C22×C8—21no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8D4×C11311yescharacteristic
313C4⋊Q8D4×C11311yescharacteristic
314C4⋊Q8C23×C11311yescharacteristic
315C4⋊Q8C23×C11311yescharacteristic
316#127—21no—
317#127—21no—
318#127—21no—
319#127C23×C11312yes—
320#125—22no—
321#125—22no—
322#125—21no—
323#125—21no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8D4×C11312yes—
335C22⋊Q8D4×C11312yes—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8D4×C11312yes—
339C4×Q8C23×C11312yes—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C11312yes—
347C4×D4C23×C11312yes—
348#117—21no—
349#117—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4D4×C11311yescharacteristic
353C2×C22⋊C4—24no—
354C2×C22⋊C4—21no—
355C2×C42C23×C11311yescharacteristic
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8C23×C11312yes—
359C4⋊C8C23×C11312yes—
360#102—24no—
361#102—24no—
362#102—24no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C4×C8—21no—
366C4×C8C23×C11312yes—
367C24—21no—
368C24—41no—
369C2×Q8—24no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—84no—
373C2×Q8C2×D4×C11312yes—
374C2×Q8C2×D4×C11312yes—
375C2×D4—21no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—82no—
386C2×D4—82no—
387C2×D4SD16×C11314yescomplemented
388C2×D4C2×D4×C11312yes—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—82no—
395C22×C4C2×D4×C11311yescharacteristic
396C22×C4C2×D4×C11311yescharacteristic
397C22×C4C2×D4×C11311yescharacteristic
398SD16—84no—
399SD16—84no—
400D8—48no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—42no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4C2×D4×C11312yes—
420C4⋊C4C2×D4×C11312yes—
421C4⋊C4C2×D4×C11312yes—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C42—22no—
429C42—22no—
430C42C2×D4×C11311yescharacteristic
431C42C2×D4×C11311yescharacteristic
432C42C2×D4×C11311yescharacteristic
433C42C24×C11311yescharacteristic
434C23—22no—
435C23—24no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23—82no—
440C23—82no—
441C23—82no—
442C23#120×C11311yescharacteristic
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—81no—
447Q8—84no—
448D4—22no—
449D4—24no—
450D4—44no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—82no—
455D4—82no—
456D4—82no—
457D4C2×SD16×C11314yes—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—44no—
466C2×C4—82no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4#120×C11311yescharacteristic
471C2×C4#120×C11311yescharacteristic
472C2×C4#120×C11311yescharacteristic
473C2×C4C2×SD16×C11312yes—
474C2×C4#137×C11312yes—
475C2×C4C22×D4×C11311yescharacteristic
476C2×C4C22×D4×C11311yescharacteristic
477C2×C4C22×D4×C11311yescharacteristic
478C8—42no—
479C8—42no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—24no—
484C22—42no—
485C22—42no—
486C22—84no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—164no—
491C22#448×C11312yes—
492C22C2×#120×C11311yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4#448×C11312yes—
502C4C22×SD16×C11311yescharacteristic
503C4C2×#137×C11311yescharacteristic
504C4#576×C11312yes—
505C2—22no—
506C2—44no—
507C2—162no—
508C2C2×#448×C11311yescharacteristic
509C2C113×#300811yescharacteristic
510C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC2×#459×C113C2
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×#3501C2semidirect
2. C113×#3208C2semidirect
3. C113×#3208C2semidirect
5. C113×#1627C2semidirect
6. C113×#1622C2semidirect
7. C113×#1542C2semidirect
8. C113×#1481C2semidirect
9. C113×#1478C2semidirect
14. #554×C113C22semidirect
16. D4×Q8×C113C22semidirect
26. #492×C113C22semidirect
28. #486×C113C22semidirect
30. #460×C113C22semidirect
39. #333×C113C22semidirect
40. #332×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
42. D4⋊C8×C113C22semidirect
131. C2×D4×C113SD16semidirect
249. #18894C113direct (N × H)
256. #3501C2×C113semidirect
257. #3208C2×C113semidirect
258. #3208C2×C113semidirect
260. #1627C2×C113semidirect
261. #1622C2×C113semidirect
262. #1542C2×C113semidirect
263. #1481C2×C113semidirect
264. #1478C2×C113semidirect
265. C113#18894direct (N × H)
270. #554C22×C113semidirect
272. D4×Q8C22×C113semidirect
282. #492C22×C113semidirect
284. #486C22×C113semidirect
286. #460C22×C113semidirect
295. #333C22×C113semidirect
296. #332C22×C113semidirect
297. Q8⋊C8C22×C113semidirect
298. D4⋊C8C22×C113semidirect
387. C2×D4SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35012
C113×#32082
C2×#459×C1132
C113×#16272
C113×#16222
C113×#15422
C113×#14812
C113×#14782
#18894113