Finite Group Databasebeta

← C113×#18905 #43286925

Subgroups — C113×#18905 #43286925

Order 28928.

926 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3501C211yesmaximal, characteristic
2C113×#3230C211yesmaximal, characteristic, complemented
3C113×#3209C211yesmaximal, characteristic, complemented
4C2×#474×C113C211yesmaximal, characteristic
5C113×#1649C214yesmaximal, complemented
6C113×#1644C214yesmaximal, complemented
7C113×#1542C211yesmaximal, characteristic, complemented
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic
10#554×C113—21no—
11#554×C113—22no—
12#554×C113—22no—
13#554×C113C2212yes—
14D4×Q8×C113—21no—
15D4×Q8×C113C2212yes—
16#544×C113—21no—
17#543×C113—22no—
18#533×C113C2211yescharacteristic
19#533×C113C2211yescharacteristic
20C2×C4⋊Q8×C113C2211yescharacteristic
21C2×C22⋊Q8×C113—22no—
22#518×C113—21no—
23C2×C4×D4×C113C2211yescharacteristic
24#500×C113C2212yescomplemented
25#494×C113—21no—
26#487×C113—21no—
27#487×C113C2212yescomplemented
28#484×C113—22no—
29#477×C113—22no—
30#474×C113—22no—
31#474×C113C2214yes—
32#462×C113C2214yescomplemented
33#451×C113—22no—
34#431×C113C2211yescharacteristic
35#431×C113C2211yescharacteristic
36C2×#107×C113—21no—
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#102×C113—21no—
39#333×C113C2212yescomplemented
40#332×C113C2212yescomplemented
41Q8⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yes—
43C22×Q8×C113—22no—
44C22×Q8×C113—21no—
45C22×D4×C113D411yescharacteristic
46C23×C4×C113—21no—
47C2×Q16×C113—24no—
48C22×C8×C113—21no—
49C4⋊Q8×C113—22no—
50C4⋊Q8×C113—22no—
51C4⋊Q8×C113—21no—
52C4⋊Q8×C113—21no—
53C4⋊Q8×C113—21no—
54C4⋊Q8×C113D411yescharacteristic
55C4⋊Q8×C113D411yescharacteristic
56C4⋊Q8×C113C2312yes—
57C4⋊Q8×C113C2311yescharacteristic
58C4⋊Q8×C113C2311yescharacteristic
59#125×C113—22no—
60#125×C113—22no—
61#125×C113—21no—
62#125×C113—21no—
63C22⋊Q8×C113—24no—
64C22⋊Q8×C113—24no—
65C22⋊Q8×C113—24no—
66C22⋊Q8×C113—24no—
67C22⋊Q8×C113—22no—
68C22⋊Q8×C113—24no—
69C22⋊Q8×C113—21no—
70C22⋊Q8×C113—21no—
71C22⋊Q8×C113—22no—
72C22⋊Q8×C113—24no—
73C22⋊Q8×C113D412yes—
74C22⋊Q8×C113D412yes—
75C4×Q8×C113—21no—
76C4×Q8×C113—21no—
77C4×Q8×C113D412yes—
78C4×Q8×C113C2312yes—
79C4×D4×C113—22no—
80C4×D4×C113—22no—
81C4×D4×C113—22no—
82C4×D4×C113—22no—
83C4×D4×C113—21no—
84C4×D4×C113—21no—
85C4×D4×C113D412yes—
86C4×D4×C113C2312yes—
87#117×C113—21no—
88#117×C113—21no—
89C2×C4⋊C4×C113—24no—
90C2×C4⋊C4×C113—22no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113D411yescharacteristic
94C2×C22⋊C4×C113—24no—
95C2×C22⋊C4×C113—21no—
96C2×C42×C113C2311yescharacteristic
97#107×C113—24no—
98#107×C113—24no—
99C4⋊C8×C113—21no—
100C4⋊C8×C113—21no—
101C4⋊C8×C113C2312yes—
102C4⋊C8×C113C2312yes—
103#103×C113—24no—
104#103×C113—24no—
105#102×C113—24no—
106C22⋊C8×C113—21no—
107C22⋊C8×C113—21no—
108C4×C8×C113—21no—
109C4×C8×C113C2312yes—
110C24×C113—21no—
111C2×Q8×C113—24no—
112C2×Q8×C113—21no—
113C2×Q8×C113—21no—
114C2×Q8×C113—22no—
115C2×Q8×C113—41no—
116C2×Q8×C113—82no—
117C2×Q8×C113—84no—
118C2×Q8×C113C2×D412yes—
119C2×Q8×C113C2×D412yes—
120C2×D4×C113—21no—
121C2×D4×C113—22no—
122C2×D4×C113Q1614yescomplemented
123C2×D4×C113C2×D412yes—
124C22×C4×C113—24no—
125C22×C4×C113—24no—
126C22×C4×C113—21no—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—41no—
130C22×C4×C113—82no—
131C22×C4×C113C2×D411yescharacteristic
132C22×C4×C113C2×D411yescharacteristic
133C22×C4×C113C2×D411yescharacteristic
134Q16×C113—84no—
135C2×C8×C113—22no—
136C2×C8×C113—22no—
137C2×C8×C113—22no—
138C2×C8×C113—42no—
139C4⋊C4×C113—24no—
140C4⋊C4×C113—24no—
141C4⋊C4×C113—24no—
142C4⋊C4×C113—22no—
143C4⋊C4×C113—22no—
144C4⋊C4×C113—21no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—21no—
147C4⋊C4×C113—21no—
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—22no—
155C4⋊C4×C113—41no—
156C4⋊C4×C113—41no—
157C4⋊C4×C113C2×D412yes—
158C4⋊C4×C113C2×D412yes—
159C4⋊C4×C113C2×D412yes—
160C22⋊C4×C113—24no—
161C22⋊C4×C113—24no—
162C22⋊C4×C113—22no—
163C22⋊C4×C113—22no—
164C22⋊C4×C113—22no—
165C22⋊C4×C113—22no—
166C42×C113—22no—
167C42×C113—22no—
168C42×C113C2×D411yescharacteristic
169C42×C113C2×D411yescharacteristic
170C42×C113C2×D411yescharacteristic
171C42×C113C2411yescharacteristic
172C23×C113—22no—
173C23×C113—24no—
174C23×C113—81no—
175C23×C113—81no—
176C23×C113#12011yescharacteristic
177Q8×C113—24no—
178Q8×C113—42no—
179Q8×C113—42no—
180Q8×C113—44no—
181Q8×C113—81no—
182Q8×C113—82no—
183Q8×C113—84no—
184D4×C113—22no—
185D4×C113—24no—
186D4×C113C2×Q1614yes—
187C2×C4×C113—22no—
188C2×C4×C113—22no—
189C2×C4×C113—22no—
190C2×C4×C113—22no—
191C2×C4×C113—22no—
192C2×C4×C113—22no—
193C2×C4×C113—41no—
194C2×C4×C113—44no—
195C2×C4×C113—42no—
196C2×C4×C113—82no—
197C2×C4×C113—81no—
198C2×C4×C113—84no—
199C2×C4×C113—84no—
200C2×C4×C113—82no—
201C2×C4×C113#12011yescharacteristic
202C2×C4×C113#12011yescharacteristic
203C2×C4×C113#12011yescharacteristic
204C2×C4×C113C2×Q1612yes—
205C2×C4×C113#13712yes—
206C2×C4×C113C22×D411yescharacteristic
207C2×C4×C113C22×D411yescharacteristic
208C2×C4×C113C22×D411yescharacteristic
209C8×C113—42no—
210C8×C113—42no—
211C8×C113—42no—
212C22×C113—21no—
213C22×C113—21no—
214C22×C113—24no—
215C22×C113—42no—
216C22×C113—42no—
217C22×C113—84no—
218C22×C113#45112yes—
219C22×C113C2×#12011yescharacteristic
220C4×C113—21no—
221C4×C113—21no—
222C4×C113—21no—
223C4×C113—42no—
224C4×C113—42no—
225C4×C113—42no—
226C4×C113—42no—
227C4×C113—42no—
228C4×C113—82no—
229C4×C113#45112yes—
230C4×C113C22×Q1611yescharacteristic
231C4×C113C2×#13711yescharacteristic
232C4×C113#57612yes—
233#18905C11311yesmaximal, characteristic, direct product factor, Sylow
234C2×C113—22no—
235C2×C113—44no—
236C2×C113C2×#45111yescharacteristic
237C2×C113#300811yescharacteristic
238C2×C113#302211yescharacteristic
239#3501C2×C11311yescharacteristic
240#3230C2×C11311yescharacteristic, complemented
241#3209C2×C11311yescharacteristic, complemented
242C2×#474C2×C11311yescharacteristic
243#1649C2×C11314yescomplemented
244#1644C2×C11314yescomplemented
245#1542C2×C11311yescharacteristic, complemented
246#1481C2×C11311yescharacteristic, complemented
247#1478C2×C11311yescharacteristic
248C113#1890511yescharacteristic, direct product factor, Sylow
249#554—21no—
250#554—22no—
251#554—22no—
252#554C22×C11312yes—
253D4×Q8—21no—
254D4×Q8C22×C11312yes—
255#544—21no—
256#543—22no—
257#533C22×C11311yescharacteristic
258#533C22×C11311yescharacteristic
259C2×C4⋊Q8C22×C11311yescharacteristic
260C2×C22⋊Q8—22no—
261#518—21no—
262C2×C4×D4C22×C11311yescharacteristic
263#500C22×C11312yescomplemented
264#494—21no—
265#487—21no—
266#487C22×C11312yescomplemented
267#484—22no—
268#477—22no—
269#474—22no—
270#474C22×C11314yes—
271#462C22×C11314yescomplemented
272#451—22no—
273#431C22×C11311yescharacteristic
274#431C22×C11311yescharacteristic
275C2×#107—21no—
276C2×C4⋊C8C22×C11311yescharacteristic
277C2×#102—21no—
278#333C22×C11312yescomplemented
279#332C22×C11312yescomplemented
280Q8⋊C8C22×C11314yescomplemented
281D4⋊C8C22×C11314yes—
282C22×Q8—22no—
283C22×Q8—21no—
284C22×D4D4×C11311yescharacteristic
285C23×C4—21no—
286C2×Q16—24no—
287C22×C8—21no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8D4×C11311yescharacteristic
294C4⋊Q8D4×C11311yescharacteristic
295C4⋊Q8C23×C11312yes—
296C4⋊Q8C23×C11311yescharacteristic
297C4⋊Q8C23×C11311yescharacteristic
298#125—22no—
299#125—22no—
300#125—21no—
301#125—21no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—24no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8D4×C11312yes—
313C22⋊Q8D4×C11312yes—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C11312yes—
317C4×Q8C23×C11312yes—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4D4×C11312yes—
325C4×D4C23×C11312yes—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4D4×C11311yescharacteristic
333C2×C22⋊C4—24no—
334C2×C22⋊C4—21no—
335C2×C42C23×C11311yescharacteristic
336#107—24no—
337#107—24no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8C23×C11312yes—
341C4⋊C8C23×C11312yes—
342#103—24no—
343#103—24no—
344#102—24no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C4×C8—21no—
348C4×C8C23×C11312yes—
349C24—21no—
350C2×Q8—24no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—82no—
356C2×Q8—84no—
357C2×Q8C2×D4×C11312yes—
358C2×Q8C2×D4×C11312yes—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4Q16×C11314yescomplemented
362C2×D4C2×D4×C11312yes—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4—82no—
370C22×C4C2×D4×C11311yescharacteristic
371C22×C4C2×D4×C11311yescharacteristic
372C22×C4C2×D4×C11311yescharacteristic
373Q16—84no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—42no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C11312yes—
397C4⋊C4C2×D4×C11312yes—
398C4⋊C4C2×D4×C11312yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C42—22no—
406C42—22no—
407C42C2×D4×C11311yescharacteristic
408C42C2×D4×C11311yescharacteristic
409C42C2×D4×C11311yescharacteristic
410C42C24×C11311yescharacteristic
411C23—22no—
412C23—24no—
413C23—81no—
414C23—81no—
415C23#120×C11311yescharacteristic
416Q8—24no—
417Q8—42no—
418Q8—42no—
419Q8—44no—
420Q8—81no—
421Q8—82no—
422Q8—84no—
423D4—22no—
424D4—24no—
425D4C2×Q16×C11314yes—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—82no—
436C2×C4—81no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4—82no—
440C2×C4#120×C11311yescharacteristic
441C2×C4#120×C11311yescharacteristic
442C2×C4#120×C11311yescharacteristic
443C2×C4C2×Q16×C11312yes—
444C2×C4#137×C11312yes—
445C2×C4C22×D4×C11311yescharacteristic
446C2×C4C22×D4×C11311yescharacteristic
447C2×C4C22×D4×C11311yescharacteristic
448C8—42no—
449C8—42no—
450C8—42no—
451C22—21no—
452C22—21no—
453C22—24no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22#451×C11312yes—
458C22C2×#120×C11311yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—82no—
468C4#451×C11312yes—
469C4C22×Q16×C11311yescharacteristic
470C4C2×#137×C11311yescharacteristic
471C4#576×C11312yes—
472C2—22no—
473C2—44no—
474C2C2×#451×C11311yescharacteristic
475C2C113×#300811yescharacteristic
476C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC22×D4×C113D4
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
2. C113×#3230C2semidirect
3. C113×#3209C2semidirect
5. C113×#1649C2semidirect
6. C113×#1644C2semidirect
7. C113×#1542C2semidirect
8. C113×#1481C2semidirect
24. #500×C113C22semidirect
27. #487×C113C22semidirect
32. #462×C113C22semidirect
39. #333×C113C22semidirect
40. #332×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
122. C2×D4×C113Q16semidirect
233. #18905C113direct (N × H)
240. #3230C2×C113semidirect
241. #3209C2×C113semidirect
243. #1649C2×C113semidirect
244. #1644C2×C113semidirect
245. #1542C2×C113semidirect
246. #1481C2×C113semidirect
248. C113#18905direct (N × H)
263. #500C22×C113semidirect
266. #487C22×C113semidirect
271. #462C22×C113semidirect
278. #333C22×C113semidirect
279. #332C22×C113semidirect
280. Q8⋊C8C22×C113semidirect
361. C2×D4Q16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35012
C113×#32302
C113×#32092
C2×#474×C1132
C113×#16492
C113×#16442
C113×#15422
C113×#14812
C113×#14782
#18905113