Finite Group Databasebeta

← C113×#18627 #43286647

Subgroups — C113×#18627 #43286647

Order 28928.

992 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3511C211yesmaximal, characteristic
2C113×#3227C211yesmaximal, characteristic, complemented
3C2×#494×C113C211yesmaximal, characteristic, complemented
4C113×#3079C211yesmaximal, characteristic, complemented
5C113×#1634C214yesmaximal, complemented
6C113×#1632C214yesmaximal, complemented
7C113×#1548C211yesmaximal, characteristic, complemented
8C113×#1492C211yesmaximal, characteristic, complemented
9C113×#1476C211yesmaximal, characteristic, complemented
10C22×Q16×C113—22no—
11#556×C113—21no—
12#555×C113C2212yes—
13#554×C113C2212yes—
14#553×C113—22no—
15#548×C113—22no—
16#547×C113—21no—
17#542×C113—22no—
18#537×C113—21no—
19#533×C113—21no—
20#532×C113—21no—
21#532×C113C2211yescharacteristic
22C2×C4⋊Q8×C113C2211yescharacteristic
23C2×C4⋊Q8×C113C2211yescharacteristic
24#520×C113—21no—
25C4×#41×C113C2211yescharacteristic
26#498×C113—21no—
27#494×C113—22no—
28#494×C113C2214yes—
29#486×C113—21no—
30#481×C113—22no—
31#477×C113C2212yes—
32#476×C113C2212yes—
33#476×C113C2214yes—
34#475×C113—21no—
35#474×C113—21no—
36#431×C113C2211yescharacteristic
37#428×C113—21no—
38#423×C113C2211yescharacteristic
39#417×C113—21no—
40C2×C4×C8×C113C2211yescharacteristic
41#333×C113C2214yes—
42Q8⋊C8×C113C2212yes—
43D4⋊C8×C113C2214yes—
44D4⋊C8×C113C2212yes—
45C2×#41×C113—22no—
46C2×#41×C113—21no—
47C2×#41×C113D411yescharacteristic
48C22×Q8×C113—21no—
49C22×Q8×C113D412yes—
50C2×Q16×C113—28no—
51C2×Q16×C113—48no—
52C2×M16×C113—21no—
53C22×C8×C113—21no—
54C4⋊Q8×C113—21no—
55C4⋊Q8×C113—21no—
56C4⋊Q8×C113—21no—
57C4⋊Q8×C113—21no—
58C4⋊Q8×C113—21no—
59C4⋊Q8×C113D412yes—
60C4⋊Q8×C113D411yescharacteristic
61C4⋊Q8×C113C2312yes—
62C4⋊Q8×C113C2312yes—
63#127×C113D411yescharacteristic
64#126×C113—24no—
65#125×C113—22no—
66#124×C113—22no—
67#124×C113—24no—
68#124×C113—21no—
69#123×C113—24no—
70C22⋊Q8×C113—22no—
71C22⋊Q8×C113—22no—
72C22⋊Q8×C113—22no—
73C22⋊Q8×C113—24no—
74#121×C113—22no—
75#121×C113—24no—
76#121×C113—22no—
77#121×C113—22no—
78#121×C113—21no—
79#121×C113D412yes—
80C4×Q8×C113—22no—
81C4×Q8×C113—22no—
82C4×Q8×C113D411yescharacteristic
83C4×Q8×C113C2311yescharacteristic
84C4×D4×C113—22no—
85C4×D4×C113—24no—
86C4×D4×C113—22no—
87C4×D4×C113—21no—
88C4×D4×C113—21no—
89C4×D4×C113—21no—
90C4×D4×C113D411yescharacteristic
91C4×D4×C113C2311yescharacteristic
92C4×D4×C113C2312yes—
93#117×C113—22no—
94#117×C113—22no—
95#117×C113—21no—
96#117×C113D411yescharacteristic
97C2×C4⋊C4×C113—21no—
98C2×C4⋊C4×C113—21no—
99C2×C4⋊C4×C113—22no—
100C2×C4⋊C4×C113—21no—
101C2×C4⋊C4×C113—21no—
102C2×C42×C113—21no—
103C2×C42×C113C2311yescharacteristic
104#107×C113—22no—
105#106×C113—22no—
106#106×C113—24no—
107C4⋊C8×C113—21no—
108C4⋊C8×C113C2312yes—
109C4⋊C8×C113C2312yes—
110#103×C113—22no—
111#102×C113—22no—
112#102×C113—24no—
113C22⋊C8×C113—21no—
114C4×C8×C113—21no—
115C4×C8×C113—21no—
116C4×C8×C113C2312yes—
117#41×C113—22no—
118#41×C113—22no—
119#41×C113—42no—
120#41×C113—42no—
121#41×C113—84no—
122C2×Q8×C113—21no—
123C2×Q8×C113—22no—
124C2×Q8×C113—22no—
125C2×Q8×C113—44no—
126C2×Q8×C113—44no—
127C2×Q8×C113—41no—
128C2×Q8×C113C2×D411yescharacteristic
129C2×Q8×C113C2×D414yes—
130C2×D4×C113—21no—
131C2×D4×C113—22no—
132C2×D4×C113—24no—
133C2×D4×C113—21no—
134C2×D4×C113—21no—
135C2×D4×C113C2×D412yes—
136C2×D4×C113C2×D411yescharacteristic
137C22×C4×C113—24no—
138C22×C4×C113—22no—
139C22×C4×C113—21no—
140C22×C4×C113—21no—
141C22×C4×C113—21no—
142C22×C4×C113—22no—
143C22×C4×C113—41no—
144C22×C4×C113C2×D411yescharacteristic
145C22×C4×C113C2×D411yescharacteristic
146C22×C4×C113C2×D411yescharacteristic
147Q16×C113—416no—
148M16×C113—42no—
149C2×C8×C113—24no—
150C2×C8×C113—22no—
151C2×C8×C113—22no—
152C2×C8×C113—22no—
153C4⋊C4×C113—24no—
154C4⋊C4×C113—24no—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—21no—
159C4⋊C4×C113—22no—
160C4⋊C4×C113—22no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113—22no—
164C4⋊C4×C113—41no—
165C4⋊C4×C113—41no—
166C4⋊C4×C113C2×D411yescharacteristic
167C4⋊C4×C113C2×D412yes—
168C4⋊C4×C113C2×D411yescharacteristic
169C22⋊C4×C113—24no—
170C22⋊C4×C113—24no—
171C22⋊C4×C113—24no—
172C22⋊C4×C113—21no—
173C22⋊C4×C113—21no—
174C22⋊C4×C113—22no—
175C22⋊C4×C113—21no—
176C22⋊C4×C113—22no—
177C42×C113—24no—
178C42×C113—21no—
179C42×C113—21no—
180C42×C113—21no—
181C42×C113C2×D411yescharacteristic
182C42×C113C2×D411yescharacteristic
183C42×C113C2×D411yescharacteristic
184C42×C113C2411yescharacteristic
185C23×C113—21no—
186C23×C113—22no—
187C23×C113#12011yescharacteristic
188Q8×C113—21no—
189Q8×C113—21no—
190Q8×C113—44no—
191Q8×C113—44no—
192Q8×C113—42no—
193Q8×C113—44no—
194Q8×C113—82no—
195D4×C113—21no—
196D4×C113—21no—
197D4×C113—24no—
198D4×C113—42no—
199D4×C113—44no—
200D4×C113—42no—
201D4×C113—42no—
202D4×C113—84no—
203C2×C4×C113—22no—
204C2×C4×C113—22no—
205C2×C4×C113—21no—
206C2×C4×C113—21no—
207C2×C4×C113—22no—
208C2×C4×C113—21no—
209C2×C4×C113—24no—
210C2×C4×C113—42no—
211C2×C4×C113—42no—
212C2×C4×C113—42no—
213C2×C4×C113—42no—
214C2×C4×C113—42no—
215C2×C4×C113—42no—
216C2×C4×C113—82no—
217C2×C4×C113—84no—
218C2×C4×C113—82no—
219C2×C4×C113#12011yescharacteristic
220C2×C4×C113#12011yescharacteristic
221C2×C4×C113#12011yescharacteristic
222C2×C4×C113#13512yes—
223C2×C4×C113#13712yes—
224C2×C4×C113C22×D411yescharacteristic
225C2×C4×C113C22×D411yescharacteristic
226C2×C4×C113C22×D411yescharacteristic
227C8×C113—24no—
228C8×C113—42no—
229C8×C113—42no—
230C22×C113—21no—
231C22×C113—21no—
232C22×C113—41no—
233C22×C113—42no—
234C22×C113—41no—
235C22×C113—42no—
236C22×C113—41no—
237C22×C113—42no—
238C22×C113#45212yes—
239C22×C113C2×#12011yescharacteristic
240C4×C113—21no—
241C4×C113—21no—
242C4×C113—41no—
243C4×C113—42no—
244C4×C113—41no—
245C4×C113—41no—
246C4×C113—44no—
247C4×C113—82no—
248C4×C113#45212yes—
249C4×C113#45312yes—
250C4×C113C2×#13511yescharacteristic
251C4×C113C2×#13711yescharacteristic
252C4×C113#57812yes—
253#18627C11311yesmaximal, characteristic, direct product factor, Sylow
254C2×C113—22no—
255C2×C113—81no—
256C2×C113—82no—
257C2×C113C2×#45211yescharacteristic
258C2×C113#301111yescharacteristic
259C2×C113C2×#45311yescharacteristic
260#3511C2×C11311yescharacteristic
261#3227C2×C11311yescharacteristic, complemented
262C2×#494C2×C11311yescharacteristic, complemented
263#3079C2×C11311yescharacteristic, complemented
264#1634C2×C11314yescomplemented
265#1632C2×C11314yescomplemented
266#1548C2×C11311yescharacteristic, complemented
267#1492C2×C11311yescharacteristic, complemented
268#1476C2×C11311yescharacteristic, complemented
269C113#1862711yescharacteristic, direct product factor, Sylow
270C22×Q16—22no—
271#556—21no—
272#555C22×C11312yes—
273#554C22×C11312yes—
274#553—22no—
275#548—22no—
276#547—21no—
277#542—22no—
278#537—21no—
279#533—21no—
280#532—21no—
281#532C22×C11311yescharacteristic
282C2×C4⋊Q8C22×C11311yescharacteristic
283C2×C4⋊Q8C22×C11311yescharacteristic
284#520—21no—
285C4×#41C22×C11311yescharacteristic
286#498—21no—
287#494—22no—
288#494C22×C11314yes—
289#486—21no—
290#481—22no—
291#477C22×C11312yes—
292#476C22×C11312yes—
293#476C22×C11314yes—
294#475—21no—
295#474—21no—
296#431C22×C11311yescharacteristic
297#428—21no—
298#423C22×C11311yescharacteristic
299#417—21no—
300C2×C4×C8C22×C11311yescharacteristic
301#333C22×C11314yes—
302Q8⋊C8C22×C11312yes—
303D4⋊C8C22×C11314yes—
304D4⋊C8C22×C11312yes—
305C2×#41—22no—
306C2×#41—21no—
307C2×#41D4×C11311yescharacteristic
308C22×Q8—21no—
309C22×Q8D4×C11312yes—
310C2×Q16—28no—
311C2×Q16—48no—
312C2×M16—21no—
313C22×C8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8D4×C11312yes—
320C4⋊Q8D4×C11311yescharacteristic
321C4⋊Q8C23×C11312yes—
322C4⋊Q8C23×C11312yes—
323#127D4×C11311yescharacteristic
324#126—24no—
325#125—22no—
326#124—22no—
327#124—24no—
328#124—21no—
329#123—24no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334#121—22no—
335#121—24no—
336#121—22no—
337#121—22no—
338#121—21no—
339#121D4×C11312yes—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8D4×C11311yescharacteristic
343C4×Q8C23×C11311yescharacteristic
344C4×D4—22no—
345C4×D4—24no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4D4×C11311yescharacteristic
351C4×D4C23×C11311yescharacteristic
352C4×D4C23×C11312yes—
353#117—22no—
354#117—22no—
355#117—21no—
356#117D4×C11311yescharacteristic
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C42—21no—
363C2×C42C23×C11311yescharacteristic
364#107—22no—
365#106—22no—
366#106—24no—
367C4⋊C8—21no—
368C4⋊C8C23×C11312yes—
369C4⋊C8C23×C11312yes—
370#103—22no—
371#102—22no—
372#102—24no—
373C22⋊C8—21no—
374C4×C8—21no—
375C4×C8—21no—
376C4×C8C23×C11312yes—
377#41—22no—
378#41—22no—
379#41—42no—
380#41—42no—
381#41—84no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—41no—
388C2×Q8C2×D4×C11311yescharacteristic
389C2×Q8C2×D4×C11314yes—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—24no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C2×D4×C11312yes—
396C2×D4C2×D4×C11311yescharacteristic
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C11311yescharacteristic
405C22×C4C2×D4×C11311yescharacteristic
406C22×C4C2×D4×C11311yescharacteristic
407Q16—416no—
408M16—42no—
409C2×C8—24no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4C2×D4×C11311yescharacteristic
427C4⋊C4C2×D4×C11312yes—
428C4⋊C4C2×D4×C11311yescharacteristic
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C22⋊C4—21no—
436C22⋊C4—22no—
437C42—24no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42C2×D4×C11311yescharacteristic
442C42C2×D4×C11311yescharacteristic
443C42C2×D4×C11311yescharacteristic
444C42C24×C11311yescharacteristic
445C23—21no—
446C23—22no—
447C23#120×C11311yescharacteristic
448Q8—21no—
449Q8—21no—
450Q8—44no—
451Q8—44no—
452Q8—42no—
453Q8—44no—
454Q8—82no—
455D4—21no—
456D4—21no—
457D4—24no—
458D4—42no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—84no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—82no—
477C2×C4—84no—
478C2×C4—82no—
479C2×C4#120×C11311yescharacteristic
480C2×C4#120×C11311yescharacteristic
481C2×C4#120×C11311yescharacteristic
482C2×C4#135×C11312yes—
483C2×C4#137×C11312yes—
484C2×C4C22×D4×C11311yescharacteristic
485C2×C4C22×D4×C11311yescharacteristic
486C2×C4C22×D4×C11311yescharacteristic
487C8—24no—
488C8—42no—
489C8—42no—
490C22—21no—
491C22—21no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—41no—
497C22—42no—
498C22#452×C11312yes—
499C22C2×#120×C11311yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—42no—
504C4—41no—
505C4—41no—
506C4—44no—
507C4—82no—
508C4#452×C11312yes—
509C4#453×C11312yes—
510C4C2×#135×C11311yescharacteristic
511C4C2×#137×C11311yescharacteristic
512C4#578×C11312yes—
513C2—22no—
514C2—81no—
515C2—82no—
516C2C2×#452×C11311yescharacteristic
517C2C113×#301111yescharacteristic
518C2C2×#453×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3511C2
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. C2×#494×C113C2semidirect
4. C113×#3079C2semidirect
5. C113×#1634C2semidirect
6. C113×#1632C2semidirect
7. C113×#1548C2semidirect
8. C113×#1492C2semidirect
9. C113×#1476C2semidirect
253. #18627C113direct (N × H)
261. #3227C2×C113semidirect
262. C2×#494C2×C113semidirect
263. #3079C2×C113semidirect
264. #1634C2×C113semidirect
265. #1632C2×C113semidirect
266. #1548C2×C113semidirect
267. #1492C2×C113semidirect
268. #1476C2×C113semidirect
269. C113#18627direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35112
C113×#32272
C2×#494×C1132
C113×#30792
C113×#16342
C113×#16322
C113×#15482
C113×#14922
C113×#14762
#18627113