Finite Group Databasebeta

← C113×#18914 #43286934

Subgroups — C113×#18914 #43286934

Order 28928.

954 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3502C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic
3C113×#3208C211yesmaximal, characteristic
4C2×#460×C113C211yesmaximal, characteristic
5C113×#1626C214yesmaximal, complemented
6C113×#1623C214yesmaximal, complemented
7C113×#1542C211yesmaximal, characteristic, complemented
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10C22×SD16×C113—21no—
11Q82×C113—21no—
12Q82×C113C2212yescomplemented
13#557×C113—21no—
14#557×C113—22no—
15#557×C113—22no—
16#557×C113C2212yescomplemented
17#544×C113—22no—
18#544×C113—21no—
19#533×C113—22no—
20#533×C113C2211yescharacteristic
21#533×C113C2211yescharacteristic
22C2×#127×C113C2211yescharacteristic
23#519×C113—21no—
24C2×C4×Q8×C113C2211yescharacteristic
25#492×C113—21no—
26#492×C113C2212yes—
27#486×C113—21no—
28#486×C113C2212yes—
29#460×C113—22no—
30#460×C113—22no—
31#460×C113C2214yes—
32#460×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
42Q8⋊C8×C113C2214yescomplemented
43C22×Q8×C113D411yescharacteristic
44C22×D4×C113—21no—
45C22×D4×C113—21no—
46C22×D4×C113—21no—
47C2×SD16×C113—24no—
48C2×SD16×C113—24no—
49C2×SD16×C113—24no—
50C2×SD16×C113—44no—
51C22×C8×C113—21no—
52C4⋊Q8×C113—24no—
53C4⋊Q8×C113—22no—
54C4⋊Q8×C113—22no—
55C4⋊Q8×C113—24no—
56C4⋊Q8×C113—22no—
57C4⋊Q8×C113—22no—
58C4⋊Q8×C113D411yescharacteristic
59C4⋊Q8×C113D411yescharacteristic
60C4⋊Q8×C113C2311yescharacteristic
61C4⋊Q8×C113C2311yescharacteristic
62#127×C113—21no—
63#127×C113—21no—
64#127×C113—21no—
65#127×C113C2312yes—
66#125×C113—24no—
67#125×C113—24no—
68#125×C113—22no—
69#125×C113—24no—
70#125×C113—22no—
71#125×C113—21no—
72#125×C113—21no—
73C22⋊Q8×C113—24no—
74C22⋊Q8×C113—21no—
75C22⋊Q8×C113—21no—
76C22⋊Q8×C113D412yes—
77C22⋊Q8×C113D412yes—
78C4×Q8×C113—22no—
79C4×Q8×C113—22no—
80C4×Q8×C113—24no—
81C4×Q8×C113—22no—
82C4×Q8×C113—22no—
83C4×Q8×C113—22no—
84C4×Q8×C113—22no—
85C4×Q8×C113—21no—
86C4×Q8×C113—21no—
87C4×Q8×C113—21no—
88C4×Q8×C113—21no—
89C4×Q8×C113D412yes—
90C4×Q8×C113D412yes—
91C4×Q8×C113C2312yes—
92C4×Q8×C113C2312yes—
93#117×C113—24no—
94#117×C113—21no—
95#117×C113—21no—
96C2×C4⋊C4×C113—21no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C42×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—41no—
112C2×Q8×C113—24no—
113C2×Q8×C113—21no—
114C2×Q8×C113—21no—
115C2×Q8×C113—22no—
116C2×Q8×C113—21no—
117C2×Q8×C113SD1614yescomplemented
118C2×Q8×C113C2×D412yes—
119C2×Q8×C113C2×D412yes—
120C2×Q8×C113C2×D412yes—
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—
131C22×C4×C113—21no—
132C22×C4×C113—21no—
133C22×C4×C113C2×D411yescharacteristic
134C22×C4×C113C2×D411yescharacteristic
135C22×C4×C113C2×D411yescharacteristic
136SD16×C113—48no—
137SD16×C113—84no—
138SD16×C113—84no—
139C2×C8×C113—22no—
140C2×C8×C113—22no—
141C2×C8×C113—22no—
142C2×C8×C113—42no—
143C4⋊C4×C113—24no—
144C4⋊C4×C113—24no—
145C4⋊C4×C113—24no—
146C4⋊C4×C113—24no—
147C4⋊C4×C113—24no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—21no—
151C4⋊C4×C113—21no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—21no—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—21no—
159C4⋊C4×C113—21no—
160C4⋊C4×C113—22no—
161C4⋊C4×C113C2×D412yes—
162C4⋊C4×C113C2×D412yes—
163C4⋊C4×C113C2×D412yes—
164C22⋊C4×C113—22no—
165C22⋊C4×C113—22no—
166C42×C113—24no—
167C42×C113—24no—
168C42×C113—22no—
169C42×C113—22no—
170C42×C113—22no—
171C42×C113—22no—
172C42×C113C2×D411yescharacteristic
173C42×C113C2×D411yescharacteristic
174C42×C113C2×D411yescharacteristic
175C42×C113C2411yescharacteristic
176C23×C113—42no—
177C23×C113—82no—
178C23×C113—82no—
179C23×C113—82no—
180C23×C113#12011yescharacteristic
181Q8×C113—22no—
182Q8×C113—24no—
183Q8×C113—24no—
184Q8×C113—42no—
185Q8×C113—42no—
186Q8×C113—81no—
187Q8×C113—84no—
188Q8×C113C2×SD1614yes—
189D4×C113—44no—
190D4×C113—42no—
191D4×C113—42no—
192D4×C113—44no—
193D4×C113—82no—
194D4×C113—82no—
195D4×C113—82no—
196C2×C4×C113—22no—
197C2×C4×C113—24no—
198C2×C4×C113—22no—
199C2×C4×C113—22no—
200C2×C4×C113—22no—
201C2×C4×C113—22no—
202C2×C4×C113—22no—
203C2×C4×C113—22no—
204C2×C4×C113—41no—
205C2×C4×C113—81no—
206C2×C4×C113#12011yescharacteristic
207C2×C4×C113#12011yescharacteristic
208C2×C4×C113#12011yescharacteristic
209C2×C4×C113C2×SD1612yes—
210C2×C4×C113#13712yes—
211C2×C4×C113C22×D411yescharacteristic
212C2×C4×C113C22×D411yescharacteristic
213C2×C4×C113C22×D411yescharacteristic
214C8×C113—42no—
215C8×C113—42no—
216C8×C113—42no—
217C22×C113—21no—
218C22×C113—21no—
219C22×C113—82no—
220C22×C113—82no—
221C22×C113—82no—
222C22×C113—164no—
223C22×C113#44812yes—
224C22×C113C2×#12011yescharacteristic
225C4×C113—24no—
226C4×C113—21no—
227C4×C113—21no—
228C4×C113—21no—
229C4×C113—42no—
230C4×C113—42no—
231C4×C113—42no—
232C4×C113—42no—
233C4×C113—42no—
234C4×C113#44812yes—
235C4×C113C22×SD1611yescharacteristic
236C4×C113C2×#13711yescharacteristic
237C4×C113#57712yes—
238#18914C11311yesmaximal, characteristic, direct product factor, Sylow
239C2×C113—22no—
240C2×C113—162no—
241C2×C113C2×#44811yescharacteristic
242C2×C113#301011yescharacteristic
243C2×C113#302111yescharacteristic
244#3502C2×C11311yescharacteristic, complemented
245#3208C2×C11311yescharacteristic
246#3208C2×C11311yescharacteristic
247C2×#460C2×C11311yescharacteristic
248#1626C2×C11314yescomplemented
249#1623C2×C11314yescomplemented
250#1542C2×C11311yescharacteristic, complemented
251#1481C2×C11311yescharacteristic, complemented
252#1479C2×C11311yescharacteristic, complemented
253C113#1891411yescharacteristic, direct product factor, Sylow
254C22×SD16—21no—
255Q82—21no—
256Q82C22×C11312yescomplemented
257#557—21no—
258#557—22no—
259#557—22no—
260#557C22×C11312yescomplemented
261#544—22no—
262#544—21no—
263#533—22no—
264#533C22×C11311yescharacteristic
265#533C22×C11311yescharacteristic
266C2×#127C22×C11311yescharacteristic
267#519—21no—
268C2×C4×Q8C22×C11311yescharacteristic
269#492—21no—
270#492C22×C11312yes—
271#486—21no—
272#486C22×C11312yes—
273#460—22no—
274#460—22no—
275#460C22×C11314yes—
276#460C22×C11314yes—
277#450—22no—
278#450—22no—
279#431C22×C11311yescharacteristic
280#431C22×C11311yescharacteristic
281C2×C4⋊C8C22×C11311yescharacteristic
282C2×#102—21no—
283#333C22×C11312yescomplemented
284#332C22×C11312yescomplemented
285Q8⋊C8C22×C11314yescomplemented
286Q8⋊C8C22×C11314yescomplemented
287C22×Q8D4×C11311yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C2×SD16—24no—
292C2×SD16—24no—
293C2×SD16—24no—
294C2×SD16—44no—
295C22×C8—21no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—24no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8D4×C11311yescharacteristic
303C4⋊Q8D4×C11311yescharacteristic
304C4⋊Q8C23×C11311yescharacteristic
305C4⋊Q8C23×C11311yescharacteristic
306#127—21no—
307#127—21no—
308#127—21no—
309#127C23×C11312yes—
310#125—24no—
311#125—24no—
312#125—22no—
313#125—24no—
314#125—22no—
315#125—21no—
316#125—21no—
317C22⋊Q8—24no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8D4×C11312yes—
321C22⋊Q8D4×C11312yes—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—24no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8D4×C11312yes—
334C4×Q8D4×C11312yes—
335C4×Q8C23×C11312yes—
336C4×Q8C23×C11312yes—
337#117—24no—
338#117—21no—
339#117—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4D4×C11311yescharacteristic
342C2×C42—21no—
343C2×C42C23×C11311yescharacteristic
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8C23×C11312yes—
347C4⋊C8C23×C11312yes—
348#102—24no—
349#102—24no—
350#102—24no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C4×C8—21no—
354C4×C8C23×C11312yes—
355C24—41no—
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8SD16×C11314yescomplemented
362C2×Q8C2×D4×C11312yes—
363C2×Q8C2×D4×C11312yes—
364C2×Q8C2×D4×C11312yes—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—82no—
374C2×D4—82no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4C2×D4×C11311yescharacteristic
378C22×C4C2×D4×C11311yescharacteristic
379C22×C4C2×D4×C11311yescharacteristic
380SD16—48no—
381SD16—84no—
382SD16—84no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—42no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4C2×D4×C11312yes—
406C4⋊C4C2×D4×C11312yes—
407C4⋊C4C2×D4×C11312yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C42—24no—
411C42—24no—
412C42—22no—
413C42—22no—
414C42—22no—
415C42—22no—
416C42C2×D4×C11311yescharacteristic
417C42C2×D4×C11311yescharacteristic
418C42C2×D4×C11311yescharacteristic
419C42C24×C11311yescharacteristic
420C23—42no—
421C23—82no—
422C23—82no—
423C23—82no—
424C23#120×C11311yescharacteristic
425Q8—22no—
426Q8—24no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—81no—
431Q8—84no—
432Q8C2×SD16×C11314yes—
433D4—44no—
434D4—42no—
435D4—42no—
436D4—44no—
437D4—82no—
438D4—82no—
439D4—82no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4#120×C11311yescharacteristic
451C2×C4#120×C11311yescharacteristic
452C2×C4#120×C11311yescharacteristic
453C2×C4C2×SD16×C11312yes—
454C2×C4#137×C11312yes—
455C2×C4C22×D4×C11311yescharacteristic
456C2×C4C22×D4×C11311yescharacteristic
457C2×C4C22×D4×C11311yescharacteristic
458C8—42no—
459C8—42no—
460C8—42no—
461C22—21no—
462C22—21no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—164no—
467C22#448×C11312yes—
468C22C2×#120×C11311yescharacteristic
469C4—24no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—42no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4#448×C11312yes—
479C4C22×SD16×C11311yescharacteristic
480C4C2×#137×C11311yescharacteristic
481C4#577×C11312yes—
482C2—22no—
483C2—162no—
484C2C2×#448×C11311yescharacteristic
485C2C113×#301011yescharacteristic
486C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC2×#127×C113C22
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×#3502C2semidirect
5. C113×#1626C2semidirect
6. C113×#1623C2semidirect
7. C113×#1542C2semidirect
8. C113×#1481C2semidirect
9. C113×#1479C2semidirect
12. Q82×C113C22semidirect
16. #557×C113C22semidirect
39. #333×C113C22semidirect
40. #332×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
42. Q8⋊C8×C113C22semidirect
117. C2×Q8×C113SD16semidirect
238. #18914C113direct (N × H)
244. #3502C2×C113semidirect
248. #1626C2×C113semidirect
249. #1623C2×C113semidirect
250. #1542C2×C113semidirect
251. #1481C2×C113semidirect
252. #1479C2×C113semidirect
253. C113#18914direct (N × H)
256. Q82C22×C113semidirect
260. #557C22×C113semidirect
283. #333C22×C113semidirect
284. #332C22×C113semidirect
285. Q8⋊C8C22×C113semidirect
286. Q8⋊C8C22×C113semidirect
361. C2×Q8SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35022
C113×#32082
C2×#460×C1132
C113×#16262
C113×#16232
C113×#15422
C113×#14812
C113×#14792
#18914113