Finite Group Databasebeta

← C113×#18923 #43286943

Subgroups — C113×#18923 #43286943

Order 28928.

1122 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3497C211yesmaximal, characteristic
2C113×#3227C211yesmaximal, characteristic, complemented
3C113×#3206C211yesmaximal, characteristic, complemented
4C2×#475×C113C211yesmaximal, characteristic, complemented
5C113×#1651C214yesmaximal, complemented
6C113×#1642C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10C2×2−1+4×C113—21no—
11#550×C113—21no—
12#550×C113C2212yes—
13D4×Q8×C113—21no—
14D4×Q8×C113C2212yes—
15#548×C113—22no—
16#548×C113—22no—
17#537×C113—22no—
18#537×C113—21no—
19#532×C113—22no—
20#532×C113C2211yescharacteristic
21#532×C113C2211yescharacteristic
22C2×C4⋊Q8×C113C2211yescharacteristic
23C2×C4×Q8×C113C2211yescharacteristic
24#498×C113C2212yes—
25#492×C113—21no—
26#487×C113—21no—
27#486×C113C2212yes—
28#481×C113—22no—
29#476×C113—22no—
30#475×C113—22no—
31#475×C113C2214yes—
32#461×C113C2214yes—
33#448×C113—22no—
34#431×C113C2211yescharacteristic
35#431×C113C2211yescharacteristic
36C2×#106×C113—21no—
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×SD16×C113—24no—
55C22×C8×C113—21no—
56C4⋊Q8×C113—22no—
57C4⋊Q8×C113—21no—
58C4⋊Q8×C113—21no—
59C4⋊Q8×C113—21no—
60C4⋊Q8×C113D411yescharacteristic
61C4⋊Q8×C113C2312yes—
62C4⋊Q8×C113C2311yescharacteristic
63#127×C113—22no—
64#127×C113D411yescharacteristic
65#127×C113C2311yescharacteristic
66#124×C113—24no—
67#124×C113—21no—
68#124×C113—21no—
69C22⋊Q8×C113—22no—
70C22⋊Q8×C113—24no—
71C22⋊Q8×C113—22no—
72C22⋊Q8×C113—24no—
73#121×C113—24no—
74#121×C113—22no—
75#121×C113—24no—
76#121×C113—24no—
77#121×C113—21no—
78#121×C113—21no—
79#121×C113—22no—
80#121×C113D412yes—
81#121×C113D412yes—
82C4×Q8×C113—21no—
83C4×Q8×C113—21no—
84C4×Q8×C113D412yes—
85C4×Q8×C113C2312yes—
86C4×D4×C113—24no—
87C4×D4×C113—22no—
88C4×D4×C113—22no—
89C4×D4×C113—21no—
90C4×D4×C113—21no—
91C4×D4×C113D412yes—
92C4×D4×C113C2312yes—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113—21no—
96C2×C4⋊C4×C113D411yescharacteristic
97C2×C42×C113—21no—
98C2×C42×C113C2311yescharacteristic
99#106×C113—24no—
100#106×C113—24no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113—21no—
103C4⋊C8×C113C2312yes—
104C4⋊C8×C113C2312yes—
105#103×C113—24no—
106#103×C113—24no—
107#102×C113—24no—
108C22⋊C8×C113—21no—
109C22⋊C8×C113—21no—
110C4×C8×C113—21no—
111C4×C8×C113C2312yes—
112#41×C113—416no—
113#41×C113—44no—
114#41×C113—48no—
115#41×C113—44no—
116#41×C113—42no—
117#41×C113—42no—
118#41×C113—42no—
119#41×C113—42no—
120C2×Q8×C113—24no—
121C2×Q8×C113—21no—
122C2×Q8×C113—21no—
123C2×Q8×C113—22no—
124C2×Q8×C113—21no—
125C2×Q8×C113—22no—
126C2×Q8×C113—44no—
127C2×Q8×C113—48no—
128C2×Q8×C113—44no—
129C2×Q8×C113—41no—
130C2×Q8×C113—82no—
131C2×Q8×C113SD1614yescomplemented
132C2×Q8×C113C2×D412yes—
133C2×D4×C113—24no—
134C2×D4×C113—22no—
135C2×D4×C113—22no—
136C2×D4×C113—24no—
137C2×D4×C113—21no—
138C2×D4×C113—21no—
139C2×D4×C113—21no—
140C2×D4×C113—21no—
141C2×D4×C113C2×D412yes—
142C2×D4×C113C2×D412yes—
143C22×C4×C113—21no—
144C22×C4×C113—24no—
145C22×C4×C113—24no—
146C22×C4×C113—21no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—41no—
150C22×C4×C113C2×D411yescharacteristic
151C22×C4×C113C2×D411yescharacteristic
152C22×C4×C113C2×D411yescharacteristic
153SD16×C113—84no—
154C2×C8×C113—22no—
155C2×C8×C113—22no—
156C2×C8×C113—22no—
157C2×C8×C113—42no—
158C4⋊C4×C113—24no—
159C4⋊C4×C113—22no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113—21no—
164C4⋊C4×C113—22no—
165C4⋊C4×C113—22no—
166C4⋊C4×C113—41no—
167C4⋊C4×C113—41no—
168C4⋊C4×C113C2×D412yes—
169C4⋊C4×C113C2×D412yes—
170C4⋊C4×C113C2×D412yes—
171C22⋊C4×C113—24no—
172C22⋊C4×C113—24no—
173C22⋊C4×C113—22no—
174C22⋊C4×C113—22no—
175C22⋊C4×C113—22no—
176C22⋊C4×C113—22no—
177C42×C113—22no—
178C42×C113—22no—
179C42×C113C2×D411yescharacteristic
180C42×C113C2×D411yescharacteristic
181C42×C113C2×D411yescharacteristic
182C42×C113C2411yescharacteristic
183C23×C113—22no—
184C23×C113—22no—
185C23×C113#12011yescharacteristic
186Q8×C113—22no—
187Q8×C113—24no—
188Q8×C113—48no—
189Q8×C113—41no—
190Q8×C113—41no—
191Q8×C113—42no—
192Q8×C113—44no—
193Q8×C113—82no—
194Q8×C113C2×SD1614yes—
195D4×C113—24no—
196D4×C113—42no—
197D4×C113—48no—
198D4×C113—44no—
199D4×C113—44no—
200D4×C113—41no—
201D4×C113—41no—
202D4×C113—42no—
203D4×C113—42no—
204D4×C113—81no—
205D4×C113—84no—
206C2×C4×C113—22no—
207C2×C4×C113—24no—
208C2×C4×C113—22no—
209C2×C4×C113—22no—
210C2×C4×C113—22no—
211C2×C4×C113—22no—
212C2×C4×C113—41no—
213C2×C4×C113—48no—
214C2×C4×C113—48no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—44no—
218C2×C4×C113—42no—
219C2×C4×C113—81no—
220C2×C4×C113—82no—
221C2×C4×C113#12011yescharacteristic
222C2×C4×C113#12011yescharacteristic
223C2×C4×C113#12011yescharacteristic
224C2×C4×C113C2×SD1612yes—
225C2×C4×C113AGL(1,ℤ/8)12yes—
226C2×C4×C113C22×D411yescharacteristic
227C2×C4×C113C22×D411yescharacteristic
228C2×C4×C113C22×D411yescharacteristic
229C8×C113—42no—
230C8×C113—42no—
231C8×C113—42no—
232C22×C113—21no—
233C22×C113—21no—
234C22×C113—42no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113—42no—
238C22×C113—42no—
239C22×C113—42no—
240C22×C113#45012yes—
241C22×C113C2×#12011yescharacteristic
242C4×C113—24no—
243C4×C113—21no—
244C4×C113—21no—
245C4×C113—21no—
246C4×C113—42no—
247C4×C113—42no—
248C4×C113—42no—
249C4×C113—82no—
250C4×C113#45012yes—
251C4×C113C22×SD1611yescharacteristic
252C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C113#57712yes—
254#18923C11311yesmaximal, characteristic, direct product factor, Sylow
255C2×C113—22no—
256C2×C113—82no—
257C2×C113—82no—
258C2×C113C2×#45011yescharacteristic
259C2×C113#301011yescharacteristic
260C2×C113#302211yescharacteristic
261#3497C2×C11311yescharacteristic
262#3227C2×C11311yescharacteristic, complemented
263#3206C2×C11311yescharacteristic, complemented
264C2×#475C2×C11311yescharacteristic, complemented
265#1651C2×C11314yescomplemented
266#1642C2×C11314yescomplemented
267#1540C2×C11311yescharacteristic, complemented
268#1480C2×C11311yescharacteristic, complemented
269#1479C2×C11311yescharacteristic, complemented
270C113#1892311yescharacteristic, direct product factor, Sylow
271C2×2−1+4—21no—
272#550—21no—
273#550C22×C11312yes—
274D4×Q8—21no—
275D4×Q8C22×C11312yes—
276#548—22no—
277#548—22no—
278#537—22no—
279#537—21no—
280#532—22no—
281#532C22×C11311yescharacteristic
282#532C22×C11311yescharacteristic
283C2×C4⋊Q8C22×C11311yescharacteristic
284C2×C4×Q8C22×C11311yescharacteristic
285#498C22×C11312yes—
286#492—21no—
287#487—21no—
288#486C22×C11312yes—
289#481—22no—
290#476—22no—
291#475—22no—
292#475C22×C11314yes—
293#461C22×C11314yes—
294#448—22no—
295#431C22×C11311yescharacteristic
296#431C22×C11311yescharacteristic
297C2×#106—21no—
298C2×C4⋊C8C22×C11311yescharacteristic
299C2×#103—21no—
300#332C22×C11312yes—
301#331C22×C11312yes—
302Q8⋊C8C22×C11314yes—
303D4⋊C8C22×C11314yes—
3042−1+4—44no—
3052−1+4—44no—
306C2×#41—24no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—21no—
310C2×#41—21no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—21no—
314C22×Q8D4×C11311yescharacteristic
315C2×SD16—24no—
316C22×C8—21no—
317C4⋊Q8—22no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8D4×C11311yescharacteristic
322C4⋊Q8C23×C11312yes—
323C4⋊Q8C23×C11311yescharacteristic
324#127—22no—
325#127D4×C11311yescharacteristic
326#127C23×C11311yescharacteristic
327#124—24no—
328#124—21no—
329#124—21no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334#121—24no—
335#121—22no—
336#121—24no—
337#121—24no—
338#121—21no—
339#121—21no—
340#121—22no—
341#121D4×C11312yes—
342#121D4×C11312yes—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8D4×C11312yes—
346C4×Q8C23×C11312yes—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4D4×C11312yes—
353C4×D4C23×C11312yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C11311yescharacteristic
358C2×C42—21no—
359C2×C42C23×C11311yescharacteristic
360#106—24no—
361#106—24no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8C23×C11312yes—
365C4⋊C8C23×C11312yes—
366#103—24no—
367#103—24no—
368#102—24no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C4×C8—21no—
372C4×C8C23×C11312yes—
373#41—416no—
374#41—44no—
375#41—48no—
376#41—44no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381C2×Q8—24no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—44no—
388C2×Q8—48no—
389C2×Q8—44no—
390C2×Q8—41no—
391C2×Q8—82no—
392C2×Q8SD16×C11314yescomplemented
393C2×Q8C2×D4×C11312yes—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—24no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4C2×D4×C11312yes—
403C2×D4C2×D4×C11312yes—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—41no—
411C22×C4C2×D4×C11311yescharacteristic
412C22×C4C2×D4×C11311yescharacteristic
413C22×C4C2×D4×C11311yescharacteristic
414SD16—84no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—42no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C2×D4×C11312yes—
430C4⋊C4C2×D4×C11312yes—
431C4⋊C4C2×D4×C11312yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C42—22no—
439C42—22no—
440C42C2×D4×C11311yescharacteristic
441C42C2×D4×C11311yescharacteristic
442C42C2×D4×C11311yescharacteristic
443C42C24×C11311yescharacteristic
444C23—22no—
445C23—22no—
446C23#120×C11311yescharacteristic
447Q8—22no—
448Q8—24no—
449Q8—48no—
450Q8—41no—
451Q8—41no—
452Q8—42no—
453Q8—44no—
454Q8—82no—
455Q8C2×SD16×C11314yes—
456D4—24no—
457D4—42no—
458D4—48no—
459D4—44no—
460D4—44no—
461D4—41no—
462D4—41no—
463D4—42no—
464D4—42no—
465D4—81no—
466D4—84no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4#120×C11311yescharacteristic
483C2×C4#120×C11311yescharacteristic
484C2×C4#120×C11311yescharacteristic
485C2×C4C2×SD16×C11312yes—
486C2×C4AGL(1,ℤ/8)×C11312yes—
487C2×C4C22×D4×C11311yescharacteristic
488C2×C4C22×D4×C11311yescharacteristic
489C2×C4C22×D4×C11311yescharacteristic
490C8—42no—
491C8—42no—
492C8—42no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22#450×C11312yes—
502C22C2×#120×C11311yescharacteristic
503C4—24no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4#450×C11312yes—
512C4C22×SD16×C11311yescharacteristic
513C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
514C4#577×C11312yes—
515C2—22no—
516C2—82no—
517C2—82no—
518C2C2×#450×C11311yescharacteristic
519C2C113×#301011yescharacteristic
520C2C113×#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×#3227C2semidirect
3. C113×#3206C2semidirect
4. C2×#475×C113C2semidirect
5. C113×#1651C2semidirect
6. C113×#1642C2semidirect
7. C113×#1540C2semidirect
8. C113×#1480C2semidirect
9. C113×#1479C2semidirect
131. C2×Q8×C113SD16semidirect
254. #18923C113direct (N × H)
262. #3227C2×C113semidirect
263. #3206C2×C113semidirect
264. C2×#475C2×C113semidirect
265. #1651C2×C113semidirect
266. #1642C2×C113semidirect
267. #1540C2×C113semidirect
268. #1480C2×C113semidirect
269. #1479C2×C113semidirect
270. C113#18923direct (N × H)
392. C2×Q8SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34972
C113×#32272
C113×#32062
C2×#475×C1132
C113×#16512
C113×#16422
C113×#15402
C113×#14802
C113×#14792
#18923113