Finite Group Databasebeta

← C113×#18372 #43286392

Subgroups — C113×#18372 #43286392

Order 28928.

904 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3493C211yesmaximal, characteristic
2C113×#3239C212yesmaximal, complemented
3C113×#2628C211yesmaximal, characteristic, complemented
4C113×#1618C214yesmaximal, complemented
5C113×#1617C212yesmaximal, complemented
6C113×#1616C212yesmaximal, complemented
7C113×#1512C212yesmaximal, complemented
8C113×#1464C211yesmaximal, characteristic, complemented
9#556×C113—22no—
10#555×C113—22no—
11#553×C113—22no—
12#552×C113—22no—
13#544×C113C2211yescharacteristic
14#538×C113—21no—
15#538×C113C2212yes—
16#537×C113C2211yescharacteristic
17C2×C4⋊Q8×C113C2211yescharacteristic
18#529×C113—21no—
19#529×C113C2212yes—
20#525×C113—21no—
21#520×C113—21no—
22C2×#117×C113C2211yescharacteristic
23#501×C113—22no—
24#489×C113—22no—
25#484×C113C2214yes—
26#481×C113C2214yes—
27#475×C113—22no—
28#474×C113—22no—
29#432×C113C2212yes—
30#400×C113C2212yes—
31#399×C113C2212yes—
32#395×C113—21no—
33#393×C113—21no—
34#389×C113—21no—
35#382×C113C2211yescharacteristic
36#380×C113—21no—
37#328×C113C2214yes—
38#327×C113C2214yes—
39#324×C113C2212yes—
40#323×C113C2212yes—
41C2×#41×C113—21no—
42C22×Q8×C113—21no—
43C23×C4×C113D411yescharacteristic
44C4⋊Q8×C113—22no—
45C4⋊Q8×C113—22no—
46C4⋊Q8×C113—22no—
47#126×C113—22no—
48#126×C113—22no—
49#126×C113—22no—
50#126×C113—22no—
51#125×C113—21no—
52#125×C113—22no—
53#125×C113D412yes—
54#124×C113—21no—
55#124×C113—22no—
56#124×C113—22no—
57#124×C113D412yes—
58#123×C113—22no—
59#123×C113—22no—
60#123×C113—22no—
61C22⋊Q8×C113—21no—
62C22⋊Q8×C113—21no—
63C22⋊Q8×C113—21no—
64C22⋊Q8×C113—22no—
65C22⋊Q8×C113C2312yes—
66#121×C113—21no—
67#121×C113—21no—
68#121×C113—22no—
69#121×C113—22no—
70#121×C113—22no—
71#121×C113—21no—
72#121×C113C2312yes—
73#120×C113—22no—
74C4×Q8×C113—22no—
75C4×Q8×C113—21no—
76C4×Q8×C113D412yes—
77C4×D4×C113—22no—
78C4×D4×C113—22no—
79C4×D4×C113—22no—
80C4×D4×C113—21no—
81C4×D4×C113—22no—
82C4×D4×C113—22no—
83C4×D4×C113D412yes—
84#117×C113—22no—
85#117×C113—22no—
86#117×C113—21no—
87#117×C113—22no—
88#117×C113—22no—
89#117×C113—22no—
90C2×C4⋊C4×C113—22no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113—22no—
94C2×C4⋊C4×C113D411yescharacteristic
95C2×C4⋊C4×C113C2312yes—
96C2×C4⋊C4×C113C2311yescharacteristic
97C2×C22⋊C4×C113—22no—
98C2×C22⋊C4×C113D411yescharacteristic
99C2×C22⋊C4×C113C2311yescharacteristic
100C2×C42×C113D411yescharacteristic
101C2×C42×C113C2311yescharacteristic
102#107×C113—24no—
103#106×C113—24no—
104C4⋊C8×C113—22no—
105#103×C113—24no—
106#102×C113—24no—
107C22⋊C8×C113C2314yes—
108#97×C113—22no—
109#95×C113—22no—
110#95×C113—21no—
111#95×C113—22no—
112#95×C113C2312yes—
113C24×C113C2×D411yescharacteristic
114#41×C113—42no—
115#41×C113—42no—
116C2×Q8×C113—21no—
117C2×Q8×C113—21no—
118C2×Q8×C113—42no—
119C2×Q8×C113—82no—
120C2×Q8×C113C2×D412yes—
121C2×D4×C113—21no—
122C2×D4×C113—22no—
123C2×D4×C113—22no—
124C2×D4×C113—22no—
125C2×D4×C113—21no—
126C2×D4×C113C2×D412yes—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—22no—
134C22×C4×C113—22no—
135C22×C4×C113—41no—
136C22×C4×C113C2×D411yescharacteristic
137C22×C4×C113C2×D411yescharacteristic
138C22×C4×C113C2×D411yescharacteristic
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2411yescharacteristic
142C2×C8×C113—24no—
143C4⋊C4×C113—21no—
144C4⋊C4×C113—22no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—22no—
147C4⋊C4×C113—21no—
148C4⋊C4×C113—21no—
149C4⋊C4×C113—22no—
150C4⋊C4×C113—22no—
151C4⋊C4×C113—22no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—22no—
155C4⋊C4×C113—24no—
156C4⋊C4×C113—42no—
157C4⋊C4×C113—41no—
158C4⋊C4×C113—41no—
159C4⋊C4×C113—82no—
160C4⋊C4×C113C2×D412yes—
161C4⋊C4×C113C2×D412yes—
162C22⋊C4×C113—22no—
163C22⋊C4×C113—22no—
164C22⋊C4×C113—22no—
165C22⋊C4×C113—22no—
166C22⋊C4×C113—22no—
167C22⋊C4×C113—22no—
168C22⋊C4×C113—22no—
169C22⋊C4×C113—22no—
170C22⋊C4×C113—22no—
171C22⋊C4×C113—22no—
172C22⋊C4×C113—22no—
173C22⋊C4×C113—82no—
174C42×C113—22no—
175C42×C113—22no—
176C42×C113—21no—
177C42×C113—21no—
178C42×C113—22no—
179C42×C113C2×D412yes—
180C42×C113C2×D412yes—
181C23×C113—21no—
182C23×C113—22no—
183C23×C113—21no—
184C23×C113—21no—
185C23×C113—41no—
186C23×C113—41no—
187C23×C113C22×D411yescharacteristic
188Q8×C113—42no—
189Q8×C113—42no—
190Q8×C113—84no—
191Q8×C113—81no—
192D4×C113—42no—
193D4×C113—42no—
194D4×C113—42no—
195D4×C113—42no—
196D4×C113—82no—
197D4×C113—81no—
198D4×C113—82no—
199C2×C4×C113—21no—
200C2×C4×C113—21no—
201C2×C4×C113—21no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—22no—
205C2×C4×C113—21no—
206C2×C4×C113—22no—
207C2×C4×C113—22no—
208C2×C4×C113—41no—
209C2×C4×C113—41no—
210C2×C4×C113—42no—
211C2×C4×C113—42no—
212C2×C4×C113—44no—
213C2×C4×C113—41no—
214C2×C4×C113—41no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—42no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—82no—
222C2×C4×C113—82no—
223C2×C4×C113#12011yescharacteristic
224C2×C4×C113#12011yescharacteristic
225C2×C4×C113#12012yes—
226C2×C4×C113#13712yes—
227C2×C4×C113C22×D412yes—
228C8×C113—44no—
229C22×C113—21no—
230C22×C113—21no—
231C22×C113—42no—
232C22×C113—41no—
233C22×C113—42no—
234C22×C113—42no—
235C22×C113—41no—
236C22×C113—42no—
237C22×C113—41no—
238C22×C113—81no—
239C22×C113C2×#12011yescharacteristic
240C22×C113C2×#13711yescharacteristic
241C22×C113#57511yescharacteristic
242C4×C113—22no—
243C4×C113—21no—
244C4×C113—21no—
245C4×C113—22no—
246C4×C113—22no—
247C4×C113—42no—
248C4×C113—41no—
249C4×C113—42no—
250C4×C113—41no—
251C4×C113—42no—
252C4×C113—82no—
253C4×C113—82no—
254#18372C11311yesmaximal, characteristic, direct product factor, Sylow
255C2×C113—21no—
256C2×C113—21no—
257C2×C113—82no—
258C2×C113—81no—
259C2×C113#300711yescharacteristic
260C2×C113#302111yescharacteristic
261C2×C113#302811yescharacteristic
262#3493C2×C11311yescharacteristic
263#3239C2×C11312yescomplemented
264#2628C2×C11311yescharacteristic, complemented
265#1618C2×C11314yescomplemented
266#1617C2×C11312yescomplemented
267#1616C2×C11312yescomplemented
268#1512C2×C11312yescomplemented
269#1464C2×C11311yescharacteristic, complemented
270C113#1837211yescharacteristic, direct product factor, Sylow
271#556—22no—
272#555—22no—
273#553—22no—
274#552—22no—
275#544C22×C11311yescharacteristic
276#538—21no—
277#538C22×C11312yes—
278#537C22×C11311yescharacteristic
279C2×C4⋊Q8C22×C11311yescharacteristic
280#529—21no—
281#529C22×C11312yes—
282#525—21no—
283#520—21no—
284C2×#117C22×C11311yescharacteristic
285#501—22no—
286#489—22no—
287#484C22×C11314yes—
288#481C22×C11314yes—
289#475—22no—
290#474—22no—
291#432C22×C11312yes—
292#400C22×C11312yes—
293#399C22×C11312yes—
294#395—21no—
295#393—21no—
296#389—21no—
297#382C22×C11311yescharacteristic
298#380—21no—
299#328C22×C11314yes—
300#327C22×C11314yes—
301#324C22×C11312yes—
302#323C22×C11312yes—
303C2×#41—21no—
304C22×Q8—21no—
305C23×C4D4×C11311yescharacteristic
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#126—22no—
310#126—22no—
311#126—22no—
312#126—22no—
313#125—21no—
314#125—22no—
315#125D4×C11312yes—
316#124—21no—
317#124—22no—
318#124—22no—
319#124D4×C11312yes—
320#123—22no—
321#123—22no—
322#123—22no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—22no—
327C22⋊Q8C23×C11312yes—
328#121—21no—
329#121—21no—
330#121—22no—
331#121—22no—
332#121—22no—
333#121—21no—
334#121C23×C11312yes—
335#120—22no—
336C4×Q8—22no—
337C4×Q8—21no—
338C4×Q8D4×C11312yes—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—21no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4D4×C11312yes—
346#117—22no—
347#117—22no—
348#117—21no—
349#117—22no—
350#117—22no—
351#117—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C11311yescharacteristic
357C2×C4⋊C4C23×C11312yes—
358C2×C4⋊C4C23×C11311yescharacteristic
359C2×C22⋊C4—22no—
360C2×C22⋊C4D4×C11311yescharacteristic
361C2×C22⋊C4C23×C11311yescharacteristic
362C2×C42D4×C11311yescharacteristic
363C2×C42C23×C11311yescharacteristic
364#107—24no—
365#106—24no—
366C4⋊C8—22no—
367#103—24no—
368#102—24no—
369C22⋊C8C23×C11314yes—
370#97—22no—
371#95—22no—
372#95—21no—
373#95—22no—
374#95C23×C11312yes—
375C24C2×D4×C11311yescharacteristic
376#41—42no—
377#41—42no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8—82no—
382C2×Q8C2×D4×C11312yes—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4C2×D4×C11312yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—41no—
398C22×C4C2×D4×C11311yescharacteristic
399C22×C4C2×D4×C11311yescharacteristic
400C22×C4C2×D4×C11311yescharacteristic
401C22×C4C2×D4×C11311yescharacteristic
402C22×C4C2×D4×C11311yescharacteristic
403C22×C4C24×C11311yescharacteristic
404C2×C8—24no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—42no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—82no—
422C4⋊C4C2×D4×C11312yes—
423C4⋊C4C2×D4×C11312yes—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—82no—
436C42—22no—
437C42—22no—
438C42—21no—
439C42—21no—
440C42—22no—
441C42C2×D4×C11312yes—
442C42C2×D4×C11312yes—
443C23—21no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23C22×D4×C11311yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—84no—
453Q8—81no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—81no—
460D4—82no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4#120×C11311yescharacteristic
486C2×C4#120×C11311yescharacteristic
487C2×C4#120×C11312yes—
488C2×C4#137×C11312yes—
489C2×C4C22×D4×C11312yes—
490C8—44no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—81no—
501C22C2×#120×C11311yescharacteristic
502C22C2×#137×C11311yescharacteristic
503C22#575×C11311yescharacteristic
504C4—22no—
505C4—21no—
506C4—21no—
507C4—22no—
508C4—22no—
509C4—42no—
510C4—41no—
511C4—42no—
512C4—41no—
513C4—42no—
514C4—82no—
515C4—82no—
516C2—21no—
517C2—21no—
518C2—81no—
519C2—82no—
520C2C113×#300711yescharacteristic
521C2C113×#302111yescharacteristic
522C2C113×#302811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3493C2
LCSG ▷ C22×C4 ▷ 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×#3239C2semidirect
3. C113×#2628C2semidirect
4. C113×#1618C2semidirect
5. C113×#1617C2semidirect
6. C113×#1616C2semidirect
7. C113×#1512C2semidirect
8. C113×#1464C2semidirect
254. #18372C113direct (N × H)
263. #3239C2×C113semidirect
264. #2628C2×C113semidirect
265. #1618C2×C113semidirect
266. #1617C2×C113semidirect
267. #1616C2×C113semidirect
268. #1512C2×C113semidirect
269. #1464C2×C113semidirect
270. C113#18372direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#34932
C113×#32392
C113×#26282
C113×#16182
C113×#16172
C113×#16162
C113×#15122
C113×#14642
#18372113