Finite Group Databasebeta

← C113×#18367 #43286387

Subgroups — C113×#18367 #43286387

Order 28928.

928 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3493C211yesmaximal, characteristic
2C113×#3218C212yesmaximal, complemented
3C113×#2628C211yesmaximal, characteristic, complemented
4C113×#1606C214yesmaximal, complemented
5C113×#1605C212yesmaximal, complemented
6C113×#1604C212yesmaximal, 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#497×C113—22no—
24#491×C113—22no—
25#462×C113—22no—
26#461×C113—22no—
27#451×C113C2214yes—
28#448×C113C2214yes—
29#432×C113C2212yes—
30#400×C113—21no—
31#399×C113—21no—
32#395×C113C2212yes—
33#393×C113C2212yes—
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×C113C2312yes—
43C23×C4×C113D411yescharacteristic
44C2×Q16×C113—24no—
45C2×SD16×C113—24no—
46C4⋊Q8×C113—22no—
47C4⋊Q8×C113—22no—
48C4⋊Q8×C113—22no—
49#126×C113—22no—
50#126×C113—22no—
51#126×C113—22no—
52#126×C113—22no—
53#125×C113—21no—
54#125×C113—22no—
55#125×C113D412yes—
56#124×C113—21no—
57#124×C113—22no—
58#124×C113—22no—
59#124×C113D412yes—
60#123×C113—22no—
61#123×C113—22no—
62#123×C113—22no—
63C22⋊Q8×C113—21no—
64C22⋊Q8×C113—21no—
65C22⋊Q8×C113—21no—
66C22⋊Q8×C113—22no—
67C22⋊Q8×C113C2312yes—
68#121×C113—21no—
69#121×C113—21no—
70#121×C113—22no—
71#121×C113—22no—
72#121×C113—22no—
73#121×C113—21no—
74#121×C113C2312yes—
75#120×C113—22no—
76C4×Q8×C113—22no—
77C4×Q8×C113—21no—
78C4×Q8×C113D412yes—
79C4×D4×C113—22no—
80C4×D4×C113—22no—
81C4×D4×C113—22no—
82C4×D4×C113—21no—
83C4×D4×C113—22no—
84C4×D4×C113—22no—
85C4×D4×C113D412yes—
86#117×C113—22no—
87#117×C113—22no—
88#117×C113—21no—
89#117×C113—22no—
90#117×C113—22no—
91#117×C113—22no—
92C2×C4⋊C4×C113—22no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113—21no—
96C2×C4⋊C4×C113—22no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C4⋊C4×C113C2311yescharacteristic
99C2×C22⋊C4×C113—22no—
100C2×C22⋊C4×C113D411yescharacteristic
101C2×C22⋊C4×C113C2311yescharacteristic
102C2×C42×C113D411yescharacteristic
103C2×C42×C113C2311yescharacteristic
104C4⋊C8×C113—22no—
105#103×C113—24no—
106#103×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—24no—
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
142Q16×C113—84no—
143SD16×C113—84no—
144C2×C8×C113—24no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—22no—
147C4⋊C4×C113—21no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—21no—
151C4⋊C4×C113—22no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—22no—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—42no—
158C4⋊C4×C113—41no—
159C4⋊C4×C113—41no—
160C4⋊C4×C113—42no—
161C4⋊C4×C113—82no—
162C4⋊C4×C113C2×D412yes—
163C4⋊C4×C113C2×D412yes—
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—22no—
174C22⋊C4×C113—22no—
175C22⋊C4×C113—82no—
176C42×C113—22no—
177C42×C113—22no—
178C42×C113—21no—
179C42×C113—21no—
180C42×C113—22no—
181C42×C113C2×D412yes—
182C42×C113C2×D412yes—
183C23×C113—21no—
184C23×C113—22no—
185C23×C113—21no—
186C23×C113—21no—
187C23×C113—41no—
188C23×C113—41no—
189C23×C113C22×D411yescharacteristic
190Q8×C113—42no—
191Q8×C113—42no—
192Q8×C113—44no—
193Q8×C113—44no—
194Q8×C113—81no—
195D4×C113—42no—
196D4×C113—42no—
197D4×C113—42no—
198D4×C113—42no—
199D4×C113—82no—
200D4×C113—81no—
201D4×C113—82no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—21no—
205C2×C4×C113—21no—
206C2×C4×C113—21no—
207C2×C4×C113—22no—
208C2×C4×C113—21no—
209C2×C4×C113—22no—
210C2×C4×C113—22no—
211C2×C4×C113—41no—
212C2×C4×C113—41no—
213C2×C4×C113—42no—
214C2×C4×C113—42no—
215C2×C4×C113—44no—
216C2×C4×C113—41no—
217C2×C4×C113—41no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—42no—
224C2×C4×C113—82no—
225C2×C4×C113—82no—
226C2×C4×C113#12011yescharacteristic
227C2×C4×C113#12011yescharacteristic
228C2×C4×C113#12012yes—
229C2×C4×C113#13712yes—
230C2×C4×C113C22×D412yes—
231C8×C113—44no—
232C22×C113—21no—
233C22×C113—21no—
234C22×C113—42no—
235C22×C113—41no—
236C22×C113—42no—
237C22×C113—42no—
238C22×C113—41no—
239C22×C113—42no—
240C22×C113—41no—
241C22×C113—81no—
242C22×C113C2×#12011yescharacteristic
243C22×C113C2×#13711yescharacteristic
244C22×C113#57511yescharacteristic
245C4×C113—22no—
246C4×C113—21no—
247C4×C113—21no—
248C4×C113—22no—
249C4×C113—22no—
250C4×C113—42no—
251C4×C113—41no—
252C4×C113—42no—
253C4×C113—41no—
254C4×C113—42no—
255C4×C113—82no—
256C4×C113—82no—
257#18367C11311yesmaximal, characteristic, direct product factor, Sylow
258C2×C113—21no—
259C2×C113—21no—
260C2×C113—82no—
261C2×C113—81no—
262C2×C113#300711yescharacteristic
263C2×C113#302211yescharacteristic
264C2×C113#302711yescharacteristic
265#3493C2×C11311yescharacteristic
266#3218C2×C11312yescomplemented
267#2628C2×C11311yescharacteristic, complemented
268#1606C2×C11314yescomplemented
269#1605C2×C11312yescomplemented
270#1604C2×C11312yescomplemented
271#1512C2×C11312yescomplemented
272#1464C2×C11311yescharacteristic, complemented
273C113#1836711yescharacteristic, direct product factor, Sylow
274#556—22no—
275#555—22no—
276#553—22no—
277#552—22no—
278#544C22×C11311yescharacteristic
279#538—21no—
280#538C22×C11312yes—
281#537C22×C11311yescharacteristic
282C2×C4⋊Q8C22×C11311yescharacteristic
283#529—21no—
284#529C22×C11312yes—
285#525—21no—
286#520—21no—
287C2×#117C22×C11311yescharacteristic
288#497—22no—
289#491—22no—
290#462—22no—
291#461—22no—
292#451C22×C11314yes—
293#448C22×C11314yes—
294#432C22×C11312yes—
295#400—21no—
296#399—21no—
297#395C22×C11312yes—
298#393C22×C11312yes—
299#389—21no—
300#382C22×C11311yescharacteristic
301#380—21no—
302#328C22×C11314yes—
303#327C22×C11314yes—
304#324C22×C11312yes—
305#323C22×C11312yes—
306C2×#41—21no—
307C22×Q8C23×C11312yes—
308C23×C4D4×C11311yescharacteristic
309C2×Q16—24no—
310C2×SD16—24no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314#126—22no—
315#126—22no—
316#126—22no—
317#126—22no—
318#125—21no—
319#125—22no—
320#125D4×C11312yes—
321#124—21no—
322#124—22no—
323#124—22no—
324#124D4×C11312yes—
325#123—22no—
326#123—22no—
327#123—22no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8C23×C11312yes—
333#121—21no—
334#121—21no—
335#121—22no—
336#121—22no—
337#121—22no—
338#121—21no—
339#121C23×C11312yes—
340#120—22no—
341C4×Q8—22no—
342C4×Q8—21no—
343C4×Q8D4×C11312yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C11312yes—
351#117—22no—
352#117—22no—
353#117—21no—
354#117—22no—
355#117—22no—
356#117—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4D4×C11311yescharacteristic
363C2×C4⋊C4C23×C11311yescharacteristic
364C2×C22⋊C4—22no—
365C2×C22⋊C4D4×C11311yescharacteristic
366C2×C22⋊C4C23×C11311yescharacteristic
367C2×C42D4×C11311yescharacteristic
368C2×C42C23×C11311yescharacteristic
369C4⋊C8—22no—
370#103—24no—
371#103—24no—
372C22⋊C8C23×C11314yes—
373#97—22no—
374#95—22no—
375#95—21no—
376#95—22no—
377#95C23×C11312yes—
378C24C2×D4×C11311yescharacteristic
379#41—42no—
380#41—42no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—24no—
384C2×Q8—82no—
385C2×Q8C2×D4×C11312yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4C2×D4×C11312yes—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4C2×D4×C11311yescharacteristic
402C22×C4C2×D4×C11311yescharacteristic
403C22×C4C2×D4×C11311yescharacteristic
404C22×C4C2×D4×C11311yescharacteristic
405C22×C4C2×D4×C11311yescharacteristic
406C22×C4C24×C11311yescharacteristic
407Q16—84no—
408SD16—84no—
409C2×C8—24no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—42no—
426C4⋊C4—82no—
427C4⋊C4C2×D4×C11312yes—
428C4⋊C4C2×D4×C11312yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—82no—
441C42—22no—
442C42—22no—
443C42—21no—
444C42—21no—
445C42—22no—
446C42C2×D4×C11312yes—
447C42C2×D4×C11312yes—
448C23—21no—
449C23—22no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23C22×D4×C11311yescharacteristic
455Q8—42no—
456Q8—42no—
457Q8—44no—
458Q8—44no—
459Q8—81no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4#120×C11311yescharacteristic
492C2×C4#120×C11311yescharacteristic
493C2×C4#120×C11312yes—
494C2×C4#137×C11312yes—
495C2×C4C22×D4×C11312yes—
496C8—44no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—42no—
503C22—41no—
504C22—42no—
505C22—41no—
506C22—81no—
507C22C2×#120×C11311yescharacteristic
508C22C2×#137×C11311yescharacteristic
509C22#575×C11311yescharacteristic
510C4—22no—
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—82no—
521C4—82no—
522C2—21no—
523C2—21no—
524C2—81no—
525C2—82no—
526C2C113×#300711yescharacteristic
527C2C113×#302211yescharacteristic
528C2C113×#302711yescharacteristic
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×#3218C2semidirect
3. C113×#2628C2semidirect
4. C113×#1606C2semidirect
5. C113×#1605C2semidirect
6. C113×#1604C2semidirect
7. C113×#1512C2semidirect
8. C113×#1464C2semidirect
257. #18367C113direct (N × H)
266. #3218C2×C113semidirect
267. #2628C2×C113semidirect
268. #1606C2×C113semidirect
269. #1605C2×C113semidirect
270. #1604C2×C113semidirect
271. #1512C2×C113semidirect
272. #1464C2×C113semidirect
273. C113#18367direct (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×#32182
C113×#26282
C113×#16062
C113×#16052
C113×#16042
C113×#15122
C113×#14642
#18367113