Finite Group Databasebeta

← C4×#16811062 #27537416

Subgroups — C4×#16811062 #27537416

Order 13568.

674 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811062C211yesmaximal, characteristic
2C4×#13133236C211yesmaximal, characteristic
3C4×Q16×D53C211yesmaximal, characteristic, complemented
4#20276585C211yesmaximal, characteristic, complemented
5#20276583C211yesmaximal, characteristic, complemented
6#20276580C211yesmaximal, characteristic, complemented
7#20276576C211yesmaximal, characteristic, complemented
8C4×Dic424C211yesmaximal, characteristic, complemented
9C4×#13133163C211yesmaximal, characteristic, complemented
10C4×#13133161C211yesmaximal, characteristic, complemented
11#20276502C211yesmaximal, characteristic, complemented
12#20276433C211yesmaximal, characteristic, complemented
13#20276424C211yesmaximal, characteristic
14C4×#13133156C211yesmaximal, characteristic, complemented
15C4×SD32×C53C211yesmaximal, characteristic, complemented
16C2×#13133236C2211yescharacteristic
17C2×Q16×D53C2211yescharacteristic
18C4×#11719947—21no—
19C4×Q8×D53—21no—
20#16811062C418yesdirect product factor
21C2×Dic424C2211yescharacteristic
22C2×#13133163C2211yescharacteristic
23C2×#13133161C2211yescharacteristic
24C2×#13133156C2211yescharacteristic
25C2×#13133156C2211yescharacteristic
26C4×Dic212C2211yescharacteristic
27C4×Dic212C2211yescharacteristic
28Q16×Dic53C2211yescharacteristic
29#16810717C2211yescharacteristic
30#16810717C2211yescharacteristic
31C4×#11719925—21no—
32#16810715—21no—
33#16810714—21no—
34C4×#11719923—21no—
35D8×Dic53C2211yescharacteristic
36#16810660C2211yescharacteristic
37#107×D53C2211yescharacteristic
38#16810616—21no—
39#103×D53—21no—
40C4×C8×D53C2211yescharacteristic
41#16810450C2211yescharacteristic
42#16810449C2211yescharacteristic
43#16810448C2211yescharacteristic
44#16810428C2211yescharacteristic
45#16810428C2211yescharacteristic
46#16810427C2211yescharacteristic
47#16810426C2211yescharacteristic
48#16810426C2211yescharacteristic
49#16810424C2211yescharacteristic
50#16810398C2211yescharacteristic
51#16810398C2211yescharacteristic
52C4×#11719908C2211yescharacteristic
53C2×SD32×C53C2211yescharacteristic
54C4×Q16×C53C2211yescharacteristic
55C4×D8×C53C2211yescharacteristic
56C53×#367C2211yescharacteristic
57C53×#358C2211yescharacteristic
58C53×#357C2211yescharacteristic
59C4×C16×C53C2211yescharacteristic
60C2×#11719947—21no—
61C2×Q8×D53—21no—
62#13133236—22no—
63#13133236C2×C414yes—
64C2×Dic212C2311yescharacteristic
65C2×Dic212C2311yescharacteristic
66C2×#11719925—21no—
67Q16×D53—22no—
68Q16×D53C2×C414yescomplemented
69C2×#11719923—21no—
70C2×C8×D53D411yescharacteristic
71C2×C8×D53C2311yescharacteristic
72Q8×Dic53—21no—
73C4×Dic106—21no—
74C4×Dic106—21no—
75C4×Dic106—41no—
76#13133182—21no—
77#13133182—21no—
78#13133182—41no—
79D4×Dic53—21no—
80C4×C22⋊D53—41no—
81#13133177—41no—
82#13133175—21no—
83#13133173—41no—
84C4⋊C4×D53—21no—
85C4⋊C4×D53—41no—
86C2×C4×Dic53—41no—
87C42×D53—41no—
88C42×D53D411yescharacteristic
89Dic424C2×C414yescomplemented
90#13133163C2×C414yescomplemented
91#13133161C2×C414yescomplemented
92#13133156—22no—
93#13133156C2×C414yescomplemented
94C2×#11719908C2311yescharacteristic
95C2×#11719908C2311yescharacteristic
96#13133151C2311yescharacteristic
97#13133151C2311yescharacteristic
98#13133150—21no—
99#13133148—21no—
100#13133142—21no—
101#13133142—21no—
102#13133141—21no—
103#13133140—21no—
104#13133140—21no—
105#13133138—21no—
106C4×#88322D411yescharacteristic
107C8×Dic53D411yescharacteristic
108C8×Dic53C2311yescharacteristic
109C2×Q16×C53C2311yescharacteristic
110C2×D8×C53C2311yescharacteristic
111C4×Q8×C53—21no—
112C4×D4×C53—21no—
113SD32×C53C2×C414yescomplemented
114C2×C16×C53C2311yescharacteristic
115C2×C16×C53C2311yescharacteristic
116#107×C53C2311yescharacteristic
117#107×C53C2311yescharacteristic
118#103×C53—21no—
119#102×C53—21no—
120C4×C8×C53C2311yescharacteristic
121C2×Q8×C53—21no—
122C2×D4×C53—21no—
123C22×C4×C53—41no—
124C2×C22⋊D53—41no—
125C22×Dic53—41no—
126C22×Dic53—41no—
127Q8×D53—24no—
128Q8×D53—42no—
129#11719947—24no—
130#11719947—42no—
131C2×C4×D53—41no—
132C2×C4×D53—41no—
133C2×C4×D53D811yescharacteristic
134C2×C4×D53D811yescharacteristic
135C2×C4×D53C2×D411yescharacteristic
136C2×Dic106—21no—
137C2×Dic106—21no—
138C2×Dic106—41no—
139Q16×C53—21no—
140Q16×C53C22×C412yes—
141D8×C53—21no—
142D8×C53C22×C412yes—
143C2×C8×C53C2×D411yescharacteristic
144C2×C8×C53C2411yescharacteristic
145C4⋊C4×C53—21no—
146C4⋊C4×C53—21no—
147C4⋊C4×C53—41no—
148C22⋊C4×C53—41no—
149C42×C53—41no—
150C42×C53C2×D411yescharacteristic
151C22⋊Dic53—41no—
152#11719925—24no—
153#11719923—24no—
154#11719921—41no—
155C4⋊Dic53—21no—
156C4⋊Dic53—21no—
157C4⋊Dic53—41no—
158#11719919—41no—
159#11719919—41no—
160#11719919—41no—
161#11719919—41no—
162#11719919—41no—
163C4×Dic53—41no—
164C4×Dic53—41no—
165C4×Dic53—41no—
166C4×Dic53—41no—
167C4×Dic53—41no—
168C4×Dic53—41no—
169C4×Dic53D811yescharacteristic
170C4×Dic53D811yescharacteristic
171C4×Dic53C2×D411yescharacteristic
172C2×#88322C2×D411yescharacteristic
173C2×#88322C2×D411yescharacteristic
174Dic212—21no—
175Dic212—21no—
176Dic212C22×C412yes—
177Dic212C22×C412yes—
178C8×D53—22no—
179C8×D53C22×C412yes—
180C8×D53#4112yes—
181C16×C53—21no—
182C16×C53C22×C412yes—
183#11719908—21no—
184#11719908C22×C412yes—
185C23×C53—41no—
186C22×D53C2×D811yescharacteristic
187Q8×C53—22no—
188Q8×C53—41no—
189D4×C53—22no—
190D4×C53—41no—
191C2×C4×C53—41no—
192C2×C4×C53—41no—
193C2×C4×C53—41no—
194C2×C4×C53—82no—
195C2×C4×C53C2×D811yescharacteristic
196C2×C4×C53C2×D811yescharacteristic
197C2×C4×C53C22×D411yescharacteristic
198C22⋊D53—44no—
199C2×Dic53—41no—
200C2×Dic53—41no—
201C2×Dic53—44no—
202C2×Dic53—41no—
203C2×Dic53—41no—
204C2×Dic53—82no—
205C2×Dic53C2×D811yescharacteristic
206C2×Dic53C2×D811yescharacteristic
207C2×Dic53C2×D811yescharacteristic
208C4×D53—22no—
209C4×D53—41no—
210C4×D53—44no—
211C4×D53—82no—
212C4×D53C4×D412yes—
213C4×D53#13512yes—
214Dic106—22no—
215Dic106—22no—
216Dic106—41no—
217Dic106—41no—
218Dic106—44no—
219C8×C53—21no—
220C8×C53C23×C411yescharacteristic
221C8×C53C2×#4111yescharacteristic
222#88322—21no—
223#88322C4×D412yes—
224C4×#510—531nomaximal, Sylow
225C22×C53—42no—
226C22×C53—81no—
227C22×C53—81no—
228C22×C53C22×D811yescharacteristic
229C2×D53—21no—
230C2×D53—21no—
231C2×D53C4×D812yes—
232C4×C53—21no—
233C4×C53—42no—
234C4×C53—81no—
235C4×C53—81no—
236C4×C53#51012yescomplemented
237C4×C53C2×C4×D411yescharacteristic
238C4×C53C2×#13511yescharacteristic
239Dic53—21no—
240Dic53—21no—
241Dic53—42no—
242Dic53—42no—
243Dic53—81no—
244Dic53—81no—
245Dic53C4×D812yes—
246C2×#510—531no—
247C4×#135—531no—
248C2×C4×Q16—531no—
249#2176—531no—
250#2176—531no—
251#2175—531no—
252#2175—531no—
253C4×Q32—531no—
254C4×Q32—531no—
255C4×SD32—531no—
256C4×SD32D5311yescharacteristic, complemented
257#2159—531no—
258#2141—531no—
259#2139—531no—
260C4×M32—531no—
261C2×C53—82no—
262C2×C53C2×C4×D811yescharacteristic
263C2×C53C2×#51011yescharacteristic
264C2×C53#341411yescharacteristic
265D53—22no—
266C2×#135—531no—
267C22×Q16—531no—
268C4×#41—1061no—
269C2×C4×Q8—1061no—
270#510—538no—
271C2×Q32—531no—
272C2×Q32—531no—
273C2×SD32—531no—
274C2×SD32C2×D5311yescharacteristic
275C2×M32—531no—
276C2×M32—531no—
277C4×Q16—531no—
278C4×Q16—531no—
279C4×Q16—531no—
280C4×Q16—531no—
281C4×Q16—531no—
282C4×Q16—1061no—
283C4×Q16—1061no—
284C4×Q16C2×D5311yescharacteristic
285C4×SD16—1061no—
286C4×SD16—1061no—
287C4×D8—531no—
288C4×D8C2×D5311yescharacteristic
289#427—531no—
290C2×#107—531no—
291#416—1061no—
292C2×#103—1061no—
293C2×C4×C8—531no—
294#367—531no—
295#367C2×D5311yescharacteristic
296#366—531no—
297#366—531no—
298#358—531no—
299#358—531no—
300#358—531no—
301#358—531no—
302#358—531no—
303#358C2×D5311yescharacteristic
304#357—531no—
305#357C2×D5311yescharacteristic
306#346—531no—
307#346—531no—
308C4×C16—531no—
309C4×C16C2×D5311yescharacteristic
310C53C4×#51011yescharacteristic, complemented, Sylow
311C2×#41—1061no—
312C22×Q8—1061no—
313#135—534no—
314#135—1062no—
315C2×Q16—534no—
316C2×Q16—531no—
317C2×Q16—531no—
318C2×Q16—1062no—
319C2×Q16—1061no—
320C2×Q16C22×D5311yescharacteristic
321C2×SD16—1061no—
322C2×D8C22×D5311yescharacteristic
323C22×C8—531no—
324C22×C8—531no—
325C4×Q8—21no—
326C4×Q8—1061no—
327C4×Q8—1061no—
328C4×Q8—1061no—
329C4×Q8—1061no—
330C4×Q8—1061no—
331C4×Q8—2121no—
332C4×Q8—2121no—
333C4×D4—21no—
334C4×D4—1061no—
335C4×D4—2121no—
336C4×D4—2121no—
337#117—1061no—
338#117—2121no—
339C2×C4⋊C4—1061no—
340C2×C4⋊C4—2121no—
341C2×C42—531no—
342C2×C42—2121no—
343C2×C42—2121no—
344Q32—534no—
345Q32—534no—
346SD32—534no—
347SD32C4×D5314yescomplemented
348M32—534no—
349M32—1062no—
350C2×C16—531no—
351C2×C16—531no—
352C2×C16C22×D5311yescharacteristic
353C2×C16C22×D5311yescharacteristic
354#107—531no—
355#107—531no—
356#107—1061no—
357#107C22×D5311yescharacteristic
358#107C22×D5311yescharacteristic
359#106—1061no—
360#103—21no—
361#103—1061no—
362#103—1061no—
363#103—1061no—
364#103—1061no—
365#103—1061no—
366#102—21no—
367#102—1061no—
368C4×C8—531no—
369C4×C8—531no—
370C4×C8—531no—
371C4×C8C22×D5311yescharacteristic
372#41—1064no—
373#41—2122no—
374C2×Q8—21no—
375C2×Q8—1064no—
376C2×Q8—1061no—
377C2×Q8—1061no—
378C2×Q8—2121no—
379C2×Q8—2122no—
380C2×D4—21no—
381C2×D4—2121no—
382C22×C4—41no—
383C22×C4—531no—
384C22×C4—531no—
385C22×C4—531no—
386C22×C4—2121no—
387C22×C4—2121no—
388C22×C4—2121no—
389C22×C4—2121no—
390Q16—21no—
391Q16—532no—
392Q16—532no—
393Q16—1064no—
394Q16—1061no—
395Q16—1061no—
396Q16C2×C4×D5312yes—
397SD16—1064no—
398D8—21no—
399D8C2×C4×D5312yes—
400C2×C8—531no—
401C2×C8—532no—
402C2×C8—532no—
403C2×C8—531no—
404C2×C8—1062no—
405C2×C8D4×D5311yescharacteristic
406C2×C8C23×D5311yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—1061no—
411C4⋊C4—1061no—
412C4⋊C4—2121no—
413C4⋊C4—2121no—
414C4⋊C4—2121no—
415C4⋊C4—2121no—
416C4⋊C4—2121no—
417C4⋊C4—2121no—
418C22⋊C4—41no—
419C22⋊C4—2121no—
420C22⋊C4—2121no—
421C42—41no—
422C42—531no—
423C42—531no—
424C42—531no—
425C42—2121no—
426C42—2121no—
427C42—2121no—
428C42—2121no—
429C42—2121no—
430C42—2121no—
431C42D4×D5311yescharacteristic
432C16—21no—
433C16—532no—
434C16—1061no—
435C16C2×C4×D5312yes—
436C23—41no—
437C23—531no—
438Q8—22no—
439Q8—41no—
440Q8—1062no—
441Q8—1062no—
442Q8—2124no—
443Q8—2121no—
444Q8—2121no—
445D4—22no—
446D4—41no—
447D4—2124no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—531no—
453C2×C4—532no—
454C2×C4—532no—
455C2×C4—531no—
456C2×C4—531no—
457C2×C4—1062no—
458C2×C4—4242no—
459C2×C4—4242no—
460C2×C4—2121no—
461C2×C4—2124no—
462C2×C4—2124no—
463C2×C4—2121no—
464C2×C4—2121no—
465C2×C4—2121no—
466C2×C4—2121no—
467C2×C4D8×D5311yescharacteristic
468C2×C4D8×D5311yescharacteristic
469C2×C4C2×D4×D5311yescharacteristic
470C8—21no—
471C8—532no—
472C8—1061no—
473C8C22×C4×D5311yescharacteristic
474C8#41×D5311yescharacteristic
475C22—42no—
476C22—81no—
477C22—81no—
478C22—532no—
479C22—1061no—
480C22—1061no—
481C22C2×D8×D5311yescharacteristic
482C4—21no—
483C4—42no—
484C4—81no—
485C4—81no—
486C4—532no—
487C4—1061no—
488C4—1061no—
489C4—4241no—
490C4—4241no—
491C4—2122no—
492C4—2122no—
493C4#1681106212yesdirect product factor
494C4C4×D4×D5311yescharacteristic
495C4#135×D5311yescharacteristic
496C2—82no—
497C2—1062no—
498C2C4×D8×D5311yescharacteristic
499C2C2×#1681106211yescharacteristic
500C2#2028784811yescharacteristic
subgroupG/H
centerC2×C4D8×D53
commutatorC8×C53C23×C4
FrattiniC2×C8C23×D53
FittingC4×SD32×C53C2
socleC22×C53C22×D8
prime radicalC2×#13133236C22
cosocleC2×C8×C53C24
hypercenterC4×SD32D53
hypocenterC53C4×#510
LCSG ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C4×Q16×D53C2semidirect
4. #20276585C2semidirect
5. #20276583C2semidirect
6. #20276580C2semidirect
7. #20276576C2semidirect
8. C4×Dic424C2semidirect
9. C4×#13133163C2semidirect
10. C4×#13133161C2semidirect
11. #20276502C2semidirect
12. #20276433C2semidirect
14. C4×#13133156C2semidirect
15. C4×SD32×C53C2semidirect
20. #16811062C4direct (N × H)
68. Q16×D53C2×C4semidirect
89. Dic424C2×C4semidirect
90. #13133163C2×C4semidirect
91. #13133161C2×C4semidirect
93. #13133156C2×C4semidirect
113. SD32×C53C2×C4semidirect
236. C4×C53#510semidirect
256. C4×SD32D53semidirect
310. C53C4×#510semidirect
347. SD32C4×D53semidirect
493. C4#16811062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168110622
C4×#131332362
C4×Q16×D532
#202765852
#202765832
#202765802
#202765762
C4×Dic4242
C4×#131331632
C4×#131331612
#202765022
#202764332
#202764242
C4×#131331562
C4×SD32×C532
C4×#51053