Finite Group Databasebeta

← C113×#18357 #43286377

Subgroups — C113×#18357 #43286377

Order 28928.

934 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3491C211yesmaximal, characteristic
2C113×#3218C212yesmaximal, complemented
3C113×#2628C211yesmaximal, characteristic, complemented
4C113×#1603C214yesmaximal, complemented
5C113×#1602C212yesmaximal, complemented
6C113×#1601C212yesmaximal
7C113×#1512C212yesmaximal, complemented
8C113×#1464C211yesmaximal, characteristic, complemented
9#552×C113—22no—
10#552×C113—22no—
11#551×C113—22no—
12#551×C113—22no—
13#543×C113C2211yescharacteristic
14#539×C113—21no—
15#539×C113C2212yes—
16#534×C113C2211yescharacteristic
17C2×C4⋊Q8×C113C2211yescharacteristic, complemented
18#529×C113—21no—
19#529×C113C2212yes—
20C2×#123×C113—21no—
21#518×C113—21no—
22C2×#117×C113C2211yescharacteristic
23#497×C113—22no—
24#491×C113—22no—
25#462×C113—22no—
26#461×C113—22no—
27#451×C113C2214yescomplemented
28#448×C113C2214yes—
29#432×C113C2212yescomplemented
30#400×C113—21no—
31#399×C113—21no—
32#395×C113C2212yescomplemented
33#393×C113C2212yes—
34#389×C113—21no—
35#382×C113C2211yescharacteristic, complemented
36#380×C113—21no—
37#328×C113C2214yescomplemented
38#327×C113C2214yes—
39#324×C113C2212yescomplemented
40#323×C113C2212yes—
41C22×Q8×C113C2312yes—
42C22×D4×C113—21no—
43C23×C4×C113D411yescharacteristic
44C2×Q16×C113—24no—
45C2×SD16×C113—24no—
46C4⋊Q8×C113—22no—
47C4⋊Q8×C113—22no—
48#126×C113—22no—
49#126×C113—22no—
50#126×C113—22no—
51#126×C113—22no—
52#125×C113—21no—
53#125×C113—22no—
54#125×C113—22no—
55#125×C113D412yes—
56#124×C113—21no—
57#124×C113D412yes—
58#123×C113—22no—
59#123×C113—22no—
60#123×C113—22no—
61#123×C113—22no—
62#123×C113—22no—
63#123×C113—22no—
64#123×C113—22no—
65C22⋊Q8×C113—22no—
66C22⋊Q8×C113—22no—
67C22⋊Q8×C113—22no—
68C22⋊Q8×C113—21no—
69C22⋊Q8×C113—22no—
70C22⋊Q8×C113C2312yes—
71#121×C113—21no—
72#121×C113C2312yes—
73#120×C113—22no—
74C4×Q8×C113—21no—
75C4×Q8×C113D412yes—
76C4×D4×C113—22no—
77C4×D4×C113—22no—
78C4×D4×C113—21no—
79C4×D4×C113—22no—
80C4×D4×C113—22no—
81C4×D4×C113D412yes—
82#117×C113—22no—
83#117×C113—22no—
84#117×C113—22no—
85#117×C113—22no—
86#117×C113—22no—
87C2×C4⋊C4×C113—21no—
88C2×C4⋊C4×C113—21no—
89C2×C4⋊C4×C113—21no—
90C2×C4⋊C4×C113—21no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—22no—
93C2×C4⋊C4×C113D411yescharacteristic
94C2×C4⋊C4×C113C2311yescharacteristic
95C2×C22⋊C4×C113—22no—
96C2×C22⋊C4×C113—21no—
97C2×C22⋊C4×C113—21no—
98C2×C22⋊C4×C113—21no—
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×C113—21no—
114C24×C113C2×D411yescharacteristic
115C2×Q8×C113—21no—
116C2×Q8×C113—24no—
117C2×Q8×C113—82no—
118C2×Q8×C113C2×D412yes—
119C2×D4×C113—22no—
120C2×D4×C113—22no—
121C2×D4×C113—21no—
122C2×D4×C113—42no—
123C2×D4×C113—42no—
124C2×D4×C113C2×D412yes—
125C22×C4×C113—21no—
126C22×C4×C113—22no—
127C22×C4×C113—21no—
128C22×C4×C113—21no—
129C22×C4×C113—22no—
130C22×C4×C113—21no—
131C22×C4×C113—21no—
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—22no—
146C4⋊C4×C113—22no—
147C4⋊C4×C113—22no—
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—22no—
176C22⋊C4×C113—82no—
177C42×C113—22no—
178C42×C113—21no—
179C42×C113—21no—
180C42×C113—22no—
181C42×C113C2×D412yes—
182C42×C113C2×D412yes—
183C23×C113—21no—
184C23×C113—21no—
185C23×C113—22no—
186C23×C113—41no—
187C23×C113—41no—
188C23×C113—42no—
189C23×C113—81no—
190C23×C113—81no—
191C23×C113#13712yes—
192C23×C113C22×D411yescharacteristic
193Q8×C113—42no—
194Q8×C113—44no—
195Q8×C113—44no—
196Q8×C113—81no—
197D4×C113—42no—
198D4×C113—44no—
199D4×C113—42no—
200D4×C113—42no—
201D4×C113—81no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—21no—
205C2×C4×C113—21no—
206C2×C4×C113—22no—
207C2×C4×C113—22no—
208C2×C4×C113—22no—
209C2×C4×C113—21no—
210C2×C4×C113—21no—
211C2×C4×C113—21no—
212C2×C4×C113—41no—
213C2×C4×C113—41no—
214C2×C4×C113—42no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—41no—
218C2×C4×C113—41no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—42no—
224C2×C4×C113—42no—
225C2×C4×C113—82no—
226C2×C4×C113—81no—
227C2×C4×C113—82no—
228C2×C4×C113—81no—
229C2×C4×C113#12011yescharacteristic
230C2×C4×C113#12011yescharacteristic
231C2×C4×C113#12012yes—
232C2×C4×C113C22×D412yes—
233C8×C113—44no—
234C22×C113—21no—
235C22×C113—21no—
236C22×C113—22no—
237C22×C113—42no—
238C22×C113—41no—
239C22×C113—41no—
240C22×C113—42no—
241C22×C113—42no—
242C22×C113—42no—
243C22×C113—81no—
244C22×C113—162no—
245C22×C113C2×#12011yescharacteristic
246C22×C113C2×#13711yescharacteristic
247C22×C113#57511yescharacteristic
248C4×C113—21no—
249C4×C113—21no—
250C4×C113—22no—
251C4×C113—22no—
252C4×C113—41no—
253C4×C113—42no—
254C4×C113—41no—
255C4×C113—42no—
256C4×C113—41no—
257C4×C113—42no—
258C4×C113—82no—
259C4×C113—82no—
260#18357C11311yesmaximal, characteristic, direct product factor, Sylow
261C2×C113—21no—
262C2×C113—21no—
263C2×C113—42no—
264C2×C113—82no—
265C2×C113#300711yescharacteristic
266C2×C113#302211yescharacteristic
267C2×C113#302711yescharacteristic
268#3491C2×C11311yescharacteristic
269#3218C2×C11312yescomplemented
270#2628C2×C11311yescharacteristic, complemented
271#1603C2×C11314yescomplemented
272#1602C2×C11312yescomplemented
273#1601C2×C11312yes—
274#1512C2×C11312yescomplemented
275#1464C2×C11311yescharacteristic, complemented
276C113#1835711yescharacteristic, direct product factor, Sylow
277#552—22no—
278#552—22no—
279#551—22no—
280#551—22no—
281#543C22×C11311yescharacteristic
282#539—21no—
283#539C22×C11312yes—
284#534C22×C11311yescharacteristic
285C2×C4⋊Q8C22×C11311yescharacteristic, complemented
286#529—21no—
287#529C22×C11312yes—
288C2×#123—21no—
289#518—21no—
290C2×#117C22×C11311yescharacteristic
291#497—22no—
292#491—22no—
293#462—22no—
294#461—22no—
295#451C22×C11314yescomplemented
296#448C22×C11314yes—
297#432C22×C11312yescomplemented
298#400—21no—
299#399—21no—
300#395C22×C11312yescomplemented
301#393C22×C11312yes—
302#389—21no—
303#382C22×C11311yescharacteristic, complemented
304#380—21no—
305#328C22×C11314yescomplemented
306#327C22×C11314yes—
307#324C22×C11312yescomplemented
308#323C22×C11312yes—
309C22×Q8C23×C11312yes—
310C22×D4—21no—
311C23×C4D4×C11311yescharacteristic
312C2×Q16—24no—
313C2×SD16—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316#126—22no—
317#126—22no—
318#126—22no—
319#126—22no—
320#125—21no—
321#125—22no—
322#125—22no—
323#125D4×C11312yes—
324#124—21no—
325#124D4×C11312yes—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—22no—
332#123—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8—22no—
338C22⋊Q8C23×C11312yes—
339#121—21no—
340#121C23×C11312yes—
341#120—22no—
342C4×Q8—21no—
343C4×Q8D4×C11312yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4D4×C11312yes—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C11311yescharacteristic
362C2×C4⋊C4C23×C11311yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4D4×C11311yescharacteristic
369C2×C22⋊C4C23×C11311yescharacteristic
370C2×C42D4×C11311yescharacteristic
371C2×C42C23×C11311yescharacteristic
372C4⋊C8—22no—
373#103—24no—
374#103—24no—
375C22⋊C8C23×C11314yes—
376#97—22no—
377#95—22no—
378#95—21no—
379#95—22no—
380#95C23×C11312yes—
381C24—21no—
382C24C2×D4×C11311yescharacteristic
383C2×Q8—21no—
384C2×Q8—24no—
385C2×Q8—82no—
386C2×Q8C2×D4×C11312yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4C2×D4×C11312yes—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C11311yescharacteristic
405C22×C4C2×D4×C11311yescharacteristic
406C22×C4C2×D4×C11311yescharacteristic
407C22×C4C2×D4×C11311yescharacteristic
408C22×C4C2×D4×C11311yescharacteristic
409C22×C4C24×C11311yescharacteristic
410Q16—84no—
411SD16—84no—
412C2×C8—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—42no—
429C4⋊C4—82no—
430C4⋊C4C2×D4×C11312yes—
431C4⋊C4C2×D4×C11312yes—
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—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—82no—
445C42—22no—
446C42—21no—
447C42—21no—
448C42—22no—
449C42C2×D4×C11312yes—
450C42C2×D4×C11312yes—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—81no—
458C23—81no—
459C23#137×C11312yes—
460C23C22×D4×C11311yescharacteristic
461Q8—42no—
462Q8—44no—
463Q8—44no—
464Q8—81no—
465D4—42no—
466D4—44no—
467D4—42no—
468D4—42no—
469D4—81no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4#120×C11311yescharacteristic
498C2×C4#120×C11311yescharacteristic
499C2×C4#120×C11312yes—
500C2×C4C22×D4×C11312yes—
501C8—44no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—162no—
513C22C2×#120×C11311yescharacteristic
514C22C2×#137×C11311yescharacteristic
515C22#575×C11311yescharacteristic
516C4—21no—
517C4—21no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—82no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—82no—
532C2C113×#300711yescharacteristic
533C2C113×#302211yescharacteristic
534C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radical#534×C113C22
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×#1603C2semidirect
5. C113×#1602C2semidirect
7. C113×#1512C2semidirect
8. C113×#1464C2semidirect
17. C2×C4⋊Q8×C113C22semidirect
27. #451×C113C22semidirect
29. #432×C113C22semidirect
32. #395×C113C22semidirect
35. #382×C113C22semidirect
37. #328×C113C22semidirect
39. #324×C113C22semidirect
260. #18357C113direct (N × H)
269. #3218C2×C113semidirect
270. #2628C2×C113semidirect
271. #1603C2×C113semidirect
272. #1602C2×C113semidirect
274. #1512C2×C113semidirect
275. #1464C2×C113semidirect
276. C113#18357direct (N × H)
285. C2×C4⋊Q8C22×C113semidirect
295. #451C22×C113semidirect
297. #432C22×C113semidirect
300. #395C22×C113semidirect
303. #382C22×C113semidirect
305. #328C22×C113semidirect
307. #324C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34912
C113×#32182
C113×#26282
C113×#16032
C113×#16022
C113×#16012
C113×#15122
C113×#14642
#18357113