Finite Group Databasebeta

← C113×#18922 #43286942

Subgroups — C113×#18922 #43286942

Order 28928.

1142 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3497C211yesmaximal, characteristic
2C113×#3226C211yesmaximal, characteristic, complemented
3C113×#3226C211yesmaximal, characteristic, complemented
4C2×#462×C113C211yesmaximal, characteristic, complemented
5C113×#1649C214yesmaximal, complemented
6C113×#1641C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10C2×2−1+4×C113—21no—
11C22×Q16×C113—21no—
12#550×C113—21no—
13#550×C113C2212yes—
14D4×Q8×C113—21no—
15D4×Q8×C113C2212yes—
16#548×C113—22no—
17#548×C113—22no—
18#537×C113—22no—
19#537×C113—21no—
20#532×C113—22no—
21#532×C113C2211yescharacteristic
22#532×C113C2211yescharacteristic
23C2×C4⋊Q8×C113C2211yescharacteristic
24C2×C4×Q8×C113C2211yescharacteristic
25#500×C113—21no—
26#500×C113C2212yes—
27#486×C113—21no—
28#486×C113C2212yes—
29#480×C113—22no—
30#480×C113—22no—
31#474×C113—22no—
32#474×C113C2214yes—
33#462×C113—22no—
34#462×C113C2214yes—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#103×C113—21no—
39#332×C113C2212yes—
40#331×C113C2212yes—
41Q8⋊C8×C113C2214yes—
42D4⋊C8×C113C2214yes—
432−1+4×C113—44no—
442−1+4×C113—44no—
45C2×#41×C113—24no—
46C2×#41×C113—22no—
47C2×#41×C113—22no—
48C2×#41×C113—21no—
49C2×#41×C113—21no—
50C22×Q8×C113—22no—
51C22×Q8×C113—22no—
52C22×Q8×C113—21no—
53C22×Q8×C113D411yescharacteristic
54C2×Q16×C113—24no—
55C2×Q16×C113—44no—
56C22×C8×C113—21no—
57C4⋊Q8×C113—22no—
58C4⋊Q8×C113—21no—
59C4⋊Q8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113D411yescharacteristic
62C4⋊Q8×C113C2312yes—
63C4⋊Q8×C113C2311yescharacteristic
64#127×C113—22no—
65#127×C113D411yescharacteristic
66#127×C113C2311yescharacteristic
67#124×C113—24no—
68#124×C113—21no—
69#124×C113—21no—
70C22⋊Q8×C113—22no—
71C22⋊Q8×C113—24no—
72C22⋊Q8×C113—22no—
73C22⋊Q8×C113—24no—
74#121×C113—24no—
75#121×C113—22no—
76#121×C113—24no—
77#121×C113—24no—
78#121×C113—21no—
79#121×C113—21no—
80#121×C113—22no—
81#121×C113D412yes—
82#121×C113D412yes—
83C4×Q8×C113—21no—
84C4×Q8×C113—21no—
85C4×Q8×C113D412yes—
86C4×Q8×C113C2312yes—
87C4×D4×C113—24no—
88C4×D4×C113—22no—
89C4×D4×C113—22no—
90C4×D4×C113—21no—
91C4×D4×C113—21no—
92C4×D4×C113D412yes—
93C4×D4×C113C2312yes—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113—21no—
96C2×C4⋊C4×C113—21no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C42×C113—21no—
99C2×C42×C113C2311yescharacteristic
100#107×C113—24no—
101#107×C113—24no—
102C4⋊C8×C113—21no—
103C4⋊C8×C113—21no—
104C4⋊C8×C113C2312yes—
105C4⋊C8×C113C2312yes—
106#103×C113—24no—
107#102×C113—24no—
108#102×C113—24no—
109C22⋊C8×C113—21no—
110C22⋊C8×C113—21no—
111C4×C8×C113—21no—
112C4×C8×C113C2312yes—
113#41×C113—416no—
114#41×C113—44no—
115#41×C113—48no—
116#41×C113—44no—
117#41×C113—42no—
118#41×C113—42no—
119#41×C113—42no—
120#41×C113—42no—
121C2×Q8×C113—24no—
122C2×Q8×C113—21no—
123C2×Q8×C113—21no—
124C2×Q8×C113—22no—
125C2×Q8×C113—21no—
126C2×Q8×C113—22no—
127C2×Q8×C113—44no—
128C2×Q8×C113—48no—
129C2×Q8×C113—44no—
130C2×Q8×C113—41no—
131C2×Q8×C113—42no—
132C2×Q8×C113—42no—
133C2×Q8×C113D814yes—
134C2×Q8×C113C2×D412yes—
135C2×D4×C113—24no—
136C2×D4×C113—22no—
137C2×D4×C113—22no—
138C2×D4×C113—24no—
139C2×D4×C113—21no—
140C2×D4×C113—21no—
141C2×D4×C113—21no—
142C2×D4×C113—21no—
143C2×D4×C113C2×D412yes—
144C2×D4×C113C2×D412yes—
145C22×C4×C113—21no—
146C22×C4×C113—24no—
147C22×C4×C113—24no—
148C22×C4×C113—21no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—41no—
152C22×C4×C113C2×D411yescharacteristic
153C22×C4×C113C2×D411yescharacteristic
154C22×C4×C113C2×D411yescharacteristic
155Q16×C113—48no—
156C2×C8×C113—22no—
157C2×C8×C113—22no—
158C2×C8×C113—22no—
159C2×C8×C113—42no—
160C4⋊C4×C113—24no—
161C4⋊C4×C113—22no—
162C4⋊C4×C113—21no—
163C4⋊C4×C113—21no—
164C4⋊C4×C113—22no—
165C4⋊C4×C113—21no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—22no—
168C4⋊C4×C113—41no—
169C4⋊C4×C113—41no—
170C4⋊C4×C113C2×D412yes—
171C4⋊C4×C113C2×D412yes—
172C4⋊C4×C113C2×D412yes—
173C22⋊C4×C113—24no—
174C22⋊C4×C113—24no—
175C22⋊C4×C113—22no—
176C22⋊C4×C113—22no—
177C22⋊C4×C113—22no—
178C22⋊C4×C113—22no—
179C42×C113—22no—
180C42×C113—22no—
181C42×C113C2×D411yescharacteristic
182C42×C113C2×D411yescharacteristic
183C42×C113C2×D411yescharacteristic
184C42×C113C2411yescharacteristic
185C23×C113—22no—
186C23×C113—22no—
187C23×C113#12011yescharacteristic
188Q8×C113—22no—
189Q8×C113—24no—
190Q8×C113—48no—
191Q8×C113—41no—
192Q8×C113—41no—
193Q8×C113—42no—
194Q8×C113—42no—
195Q8×C113—42no—
196Q8×C113—82no—
197Q8×C113C2×D814yes—
198D4×C113—24no—
199D4×C113—42no—
200D4×C113—48no—
201D4×C113—44no—
202D4×C113—44no—
203D4×C113—41no—
204D4×C113—41no—
205D4×C113—42no—
206D4×C113—42no—
207D4×C113—81no—
208D4×C113—84no—
209C2×C4×C113—22no—
210C2×C4×C113—24no—
211C2×C4×C113—22no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—41no—
216C2×C4×C113—48no—
217C2×C4×C113—48no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—44no—
221C2×C4×C113—42no—
222C2×C4×C113—81no—
223C2×C4×C113—82no—
224C2×C4×C113#12011yescharacteristic
225C2×C4×C113#12011yescharacteristic
226C2×C4×C113#12011yescharacteristic
227C2×C4×C113C2×D812yes—
228C2×C4×C113AGL(1,ℤ/8)12yes—
229C2×C4×C113C22×D411yescharacteristic
230C2×C4×C113C22×D411yescharacteristic
231C2×C4×C113C22×D411yescharacteristic
232C8×C113—42no—
233C8×C113—42no—
234C8×C113—42no—
235C22×C113—21no—
236C22×C113—21no—
237C22×C113—42no—
238C22×C113—42no—
239C22×C113—42no—
240C22×C113—42no—
241C22×C113—42no—
242C22×C113—42no—
243C22×C113#44712yes—
244C22×C113C2×#12011yescharacteristic
245C4×C113—24no—
246C4×C113—21no—
247C4×C113—21no—
248C4×C113—21no—
249C4×C113—42no—
250C4×C113—42no—
251C4×C113—42no—
252C4×C113—82no—
253C4×C113#44712yes—
254C4×C113C22×D811yescharacteristic
255C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
256C4×C113#57812yes—
257#18922C11311yesmaximal, characteristic, direct product factor, Sylow
258C2×C113—22no—
259C2×C113—82no—
260C2×C113—82no—
261C2×C113C2×#44711yescharacteristic
262C2×C113#301111yescharacteristic
263C2×C113#302211yescharacteristic
264#3497C2×C11311yescharacteristic
265#3226C2×C11311yescharacteristic, complemented
266#3226C2×C11311yescharacteristic, complemented
267C2×#462C2×C11311yescharacteristic, complemented
268#1649C2×C11314yescomplemented
269#1641C2×C11314yescomplemented
270#1540C2×C11311yescharacteristic, complemented
271#1480C2×C11311yescharacteristic, complemented
272#1479C2×C11311yescharacteristic, complemented
273C113#1892211yescharacteristic, direct product factor, Sylow
274C2×2−1+4—21no—
275C22×Q16—21no—
276#550—21no—
277#550C22×C11312yes—
278D4×Q8—21no—
279D4×Q8C22×C11312yes—
280#548—22no—
281#548—22no—
282#537—22no—
283#537—21no—
284#532—22no—
285#532C22×C11311yescharacteristic
286#532C22×C11311yescharacteristic
287C2×C4⋊Q8C22×C11311yescharacteristic
288C2×C4×Q8C22×C11311yescharacteristic
289#500—21no—
290#500C22×C11312yes—
291#486—21no—
292#486C22×C11312yes—
293#480—22no—
294#480—22no—
295#474—22no—
296#474C22×C11314yes—
297#462—22no—
298#462C22×C11314yes—
299#431C22×C11311yescharacteristic
300#431C22×C11311yescharacteristic
301C2×C4⋊C8C22×C11311yescharacteristic
302C2×#103—21no—
303#332C22×C11312yes—
304#331C22×C11312yes—
305Q8⋊C8C22×C11314yes—
306D4⋊C8C22×C11314yes—
3072−1+4—44no—
3082−1+4—44no—
309C2×#41—24no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—21no—
313C2×#41—21no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—21no—
317C22×Q8D4×C11311yescharacteristic
318C2×Q16—24no—
319C2×Q16—44no—
320C22×C8—21no—
321C4⋊Q8—22no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8D4×C11311yescharacteristic
326C4⋊Q8C23×C11312yes—
327C4⋊Q8C23×C11311yescharacteristic
328#127—22no—
329#127D4×C11311yescharacteristic
330#127C23×C11311yescharacteristic
331#124—24no—
332#124—21no—
333#124—21no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338#121—24no—
339#121—22no—
340#121—24no—
341#121—24no—
342#121—21no—
343#121—21no—
344#121—22no—
345#121D4×C11312yes—
346#121D4×C11312yes—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8D4×C11312yes—
350C4×Q8C23×C11312yes—
351C4×D4—24no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4D4×C11312yes—
357C4×D4C23×C11312yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4D4×C11311yescharacteristic
362C2×C42—21no—
363C2×C42C23×C11311yescharacteristic
364#107—24no—
365#107—24no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8C23×C11312yes—
369C4⋊C8C23×C11312yes—
370#103—24no—
371#102—24no—
372#102—24no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C4×C8—21no—
376C4×C8C23×C11312yes—
377#41—416no—
378#41—44no—
379#41—48no—
380#41—44no—
381#41—42no—
382#41—42no—
383#41—42no—
384#41—42no—
385C2×Q8—24no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—44no—
392C2×Q8—48no—
393C2×Q8—44no—
394C2×Q8—41no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8D8×C11314yes—
398C2×Q8C2×D4×C11312yes—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4C2×D4×C11312yes—
408C2×D4C2×D4×C11312yes—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4C2×D4×C11311yescharacteristic
417C22×C4C2×D4×C11311yescharacteristic
418C22×C4C2×D4×C11311yescharacteristic
419Q16—48no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—42no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4C2×D4×C11312yes—
435C4⋊C4C2×D4×C11312yes—
436C4⋊C4C2×D4×C11312yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C42—22no—
444C42—22no—
445C42C2×D4×C11311yescharacteristic
446C42C2×D4×C11311yescharacteristic
447C42C2×D4×C11311yescharacteristic
448C42C24×C11311yescharacteristic
449C23—22no—
450C23—22no—
451C23#120×C11311yescharacteristic
452Q8—22no—
453Q8—24no—
454Q8—48no—
455Q8—41no—
456Q8—41no—
457Q8—42no—
458Q8—42no—
459Q8—42no—
460Q8—82no—
461Q8C2×D8×C11314yes—
462D4—24no—
463D4—42no—
464D4—48no—
465D4—44no—
466D4—44no—
467D4—41no—
468D4—41no—
469D4—42no—
470D4—42no—
471D4—81no—
472D4—84no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—82no—
488C2×C4#120×C11311yescharacteristic
489C2×C4#120×C11311yescharacteristic
490C2×C4#120×C11311yescharacteristic
491C2×C4C2×D8×C11312yes—
492C2×C4AGL(1,ℤ/8)×C11312yes—
493C2×C4C22×D4×C11311yescharacteristic
494C2×C4C22×D4×C11311yescharacteristic
495C2×C4C22×D4×C11311yescharacteristic
496C8—42no—
497C8—42no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22#447×C11312yes—
508C22C2×#120×C11311yescharacteristic
509C4—24no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—82no—
517C4#447×C11312yes—
518C4C22×D8×C11311yescharacteristic
519C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
520C4#578×C11312yes—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×#447×C11311yescharacteristic
525C2C113×#301111yescharacteristic
526C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3497C2
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×#3226C2semidirect
3. C113×#3226C2semidirect
4. C2×#462×C113C2semidirect
5. C113×#1649C2semidirect
6. C113×#1641C2semidirect
7. C113×#1540C2semidirect
8. C113×#1480C2semidirect
9. C113×#1479C2semidirect
257. #18922C113direct (N × H)
265. #3226C2×C113semidirect
266. #3226C2×C113semidirect
267. C2×#462C2×C113semidirect
268. #1649C2×C113semidirect
269. #1641C2×C113semidirect
270. #1540C2×C113semidirect
271. #1480C2×C113semidirect
272. #1479C2×C113semidirect
273. C113#18922direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#34972
C113×#32262
C2×#462×C1132
C113×#16492
C113×#16412
C113×#15402
C113×#14802
C113×#14792
#18922113