Finite Group Databasebeta

← C2×#20273343 #27352115

Subgroups — C2×#20273343 #27352115

Order 13568.

986 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811152C211yesmaximal, characteristic
2C2×#16810678C211yesmaximal, characteristic, complemented
3C2×#16810678C211yesmaximal, characteristic, complemented
4#20273343C218yesmaximal, direct product factor
5C2×#16810364C211yesmaximal, characteristic, complemented
6C2×#16810364C211yesmaximal, characteristic, complemented
7C2×#16810363C211yesmaximal, characteristic, complemented
8C2×C53×#329C211yesmaximal, characteristic, complemented
9#16811152—22no—
10#16811152—22no—
11#16811152C414yes—
12#16811152C2214yes—
13C2×#13133210—21no—
14C2×#13133209C2211yescharacteristic
15C2×#13133199—21no—
16C2×#13133193C411yescharacteristic
17C2×#13133188C411yescharacteristic
18C2×Q8×Dic53C411yescharacteristic
19C2×D4×Dic53C411yescharacteristic
20C2×#13133177—21no—
21C2×#13133173—21no—
22C2×C42×D53C2211yescharacteristic
23#16810678—22no—
24#16810678—22no—
25#16810678C2214yescomplemented
26#16810678C2214yescomplemented
27C2×#13133146—21no—
28C2×#13133146—21no—
29C2×#13133129—21no—
30C2×#13133129—21no—
31C2×#13133128C2211yescharacteristic
32C2×#13133128C2211yescharacteristic
33#16810364C2214yescomplemented
34#16810364C2214yescomplemented
35#16810363C2214yescomplemented
36C2×#124×C53C2211yescharacteristic
37C2×#97×C53C2211yescharacteristic
38C2×#97×C53C2211yescharacteristic
39C53×#329C2214yescomplemented
40C22×C22⋊D53—21no—
41C23×Dic53—21no—
42C22×C4×D53C2×C411yescharacteristic
43C22×C4×D53D411yescharacteristic
44C22×C4×D53D411yescharacteristic
45C22×#88322—21no—
46C22×#88322—21no—
47#13133210—24no—
48#13133210—24no—
49#13133209—21no—
50#13133209—21no—
51#13133209C2×C412yes—
52#13133209C2312yes—
53#13133199—24no—
54#13133199—24no—
55#13133193—22no—
56#13133193C2×C414yes—
57#13133188—22no—
58#13133188C2×C414yes—
59Q8×Dic53—22no—
60Q8×Dic53C2×C414yes—
61D4×Dic53—22no—
62D4×Dic53C2×C414yes—
63#13133177—24no—
64#13133177—24no—
65#13133173—24no—
66#13133173—24no—
67C2×C4⋊Dic53—21no—
68C2×C4⋊Dic53C2×C411yescharacteristic
69C2×C4⋊Dic53C2×C411yescharacteristic
70C2×#11719919—21no—
71C2×#11719919—21no—
72C2×#11719919—21no—
73C2×C22⋊Dic53—21no—
74C2×C22⋊Dic53—21no—
75C2×#11719921—21no—
76C2×C4×Dic53—21no—
77C2×C4×Dic53C2×C411yescharacteristic
78C2×C4×Dic53D411yescharacteristic
79C2×C4×Dic53D411yescharacteristic
80C42×D53C2×C412yes—
81C42×D53D412yes—
82C42×D53D412yes—
83C42×D53C2312yes—
84#13133146—24no—
85#13133146—24no—
86#13133129—24no—
87#13133129—24no—
88#13133128—21no—
89#13133128—21no—
90#13133128C2312yes—
91#13133128C2312yes—
92C22×Q8×C53C2×C411yescharacteristic
93C22×D4×C53C2×C411yescharacteristic
94C22×C8×C53—21no—
95C22×C8×C53—21no—
96#124×C53—21no—
97#124×C53—21no—
98#124×C53C2×C412yes—
99#124×C53C2312yes—
100C2×C22⋊C4×C53—21no—
101C2×C22⋊C4×C53—21no—
102C2×C42×C53C2311yescharacteristic
103#97×C53—21no—
104#97×C53—21no—
105#97×C53C2312yes—
106#97×C53C2312yes—
107C24×C53—21no—
108C23×D53C22⋊C411yescharacteristic
109C2×Q8×C53—21no—
110C2×Q8×C53—42no—
111C2×Q8×C53C22×C412yes—
112C2×D4×C53—21no—
113C2×D4×C53—42no—
114C2×D4×C53C22×C412yes—
115C22×C4×C53—21no—
116C22×C4×C53C22×C411yescharacteristic
117C22×C4×C53C2×D411yescharacteristic
118C22×C4×C53C2×D411yescharacteristic
119C2×C22⋊D53—24no—
120C2×C22⋊D53—44no—
121C22×Dic53—21no—
122C22×Dic53—21no—
123C22×Dic53—24no—
124C22×Dic53—44no—
125C22×Dic53C22⋊C411yescharacteristic
126C22×Dic53C22⋊C411yescharacteristic
127C22×Dic53C22⋊C411yescharacteristic
128C2×C4×D53—42no—
129C2×C4×D53—42no—
130C2×C4×D53—42no—
131C2×C4×D53C22⋊C412yes—
132C2×C4×D53C22⋊C412yes—
133C2×C4×D53C22⋊C412yes—
134C2×C4×D53C22×C412yes—
135C2×C4×D53C2×D412yes—
136C2×C4×D53C2×D412yes—
137C2×C8×C53—22no—
138C2×C8×C53—22no—
139C2×C8×C53—42no—
140C2×C8×C53—42no—
141C22⋊C4×C53—22no—
142C22⋊C4×C53—22no—
143C22⋊C4×C53—22no—
144C22⋊C4×C53—22no—
145C42×C53C22×C411yescharacteristic
146C42×C53C2×D411yescharacteristic
147C42×C53C2×D411yescharacteristic
148C42×C53C2411yescharacteristic
149C22⋊Dic53—24no—
150C22⋊Dic53—24no—
151#11719921—24no—
152C4⋊Dic53—21no—
153C4⋊Dic53—21no—
154C4⋊Dic53—24no—
155C4⋊Dic53C22×C412yes—
156C4⋊Dic53C22×C412yes—
157#11719919—22no—
158#11719919—22no—
159#11719919—22no—
160#11719919—22no—
161#11719919—24no—
162C4×Dic53—24no—
163C4×Dic53C22⋊C412yes—
164C4×Dic53C22⋊C412yes—
165C4×Dic53C22⋊C412yes—
166C4×Dic53C22×C412yes—
167C4×Dic53C2×D412yes—
168C4×Dic53C2×D412yes—
169C2×#88322—22no—
170C2×#88322—22no—
171C2×#88322—42no—
172C2×#88322—42no—
173C23×C53—22no—
174C23×C53—42no—
175C23×C53—42no—
176C23×C53—42no—
177C23×C53C2×C22⋊C411yescharacteristic
178C22×D53—22no—
179C22×D53—22no—
180C22×D53—22no—
181C22×D53C2×C22⋊C412yes—
182Q8×C53—42no—
183Q8×C53—42no—
184D4×C53—42no—
185D4×C53—42no—
186C2×C4×C53—22no—
187C2×C4×C53—22no—
188C2×C4×C53—22no—
189C2×C4×C53—22no—
190C2×C4×C53—42no—
191C2×C4×C53C2×C22⋊C411yescharacteristic
192C2×C4×C53C2×C22⋊C411yescharacteristic
193C2×C4×C53C2×C22⋊C411yescharacteristic
194C2×C4×C53C23×C411yescharacteristic
195C2×C4×C53C22×D411yescharacteristic
196C2×C4×C53C22×D411yescharacteristic
197C22⋊D53—48no—
198C2×Dic53—22no—
199C2×Dic53—22no—
200C2×Dic53—22no—
201C2×Dic53—22no—
202C2×Dic53—22no—
203C2×Dic53—48no—
204C2×Dic53—42no—
205C2×Dic53—42no—
206C2×Dic53C2×C22⋊C412yes—
207C2×Dic53C2×C22⋊C412yes—
208C2×Dic53C2×C22⋊C412yes—
209C4×D53—42no—
210C4×D53—42no—
211C4×D53—42no—
212C4×D53—42no—
213C4×D53—42no—
214C4×D53—42no—
215C8×C53—42no—
216C8×C53—42no—
217#88322—42no—
218#88322—42no—
219C2×#1535—531nomaximal, Sylow
220C22×C53—42no—
221C22×C53—42no—
222C22×C53—42no—
223C22×C53—84no—
224C22×C53#41312yes—
225C22×C53#42112yes—
226C22×C53#42112yes—
227C22×C53C22×C22⋊C411yescharacteristic
228C2×D53—22no—
229C2×D53—22no—
230C2×D53—22no—
231C2×D53—44no—
232C4×C53—21no—
233C4×C53—21no—
234C4×C53—21no—
235C4×C53—21no—
236C4×C53—21no—
237C4×C53—21no—
238C4×C53—42no—
239Dic53—22no—
240Dic53—22no—
241Dic53—22no—
242Dic53—42no—
243Dic53—42no—
244C2×#529—531no—
245C2×#432—531no—
246C2×#432—531no—
247#1535—538no—
248C2×#330—531no—
249C2×#330—531no—
250C2×#329—531no—
251C2×#329D5311yescharacteristic, complemented
252C2×C53—82no—
253C2×C53#153514yescomplemented
254C2×C53C2×#41311yescharacteristic
255C2×C53C2×#42111yescharacteristic
256C2×C53C2×#42111yescharacteristic
257D53—42no—
258#529—534no—
259#529—534no—
260#529—1062no—
261#529—1062no—
262C2×#126—1061no—
263C2×#125—531no—
264C2×#124C2×D5311yescharacteristic
265C2×#123—1061no—
266C2×C22⋊Q8—531no—
267C2×#121—531no—
268C2×C4×Q8—531no—
269C2×C4×D4—531no—
270C2×C4×D4—1061no—
271C2×#117—1061no—
272C22×C42—531no—
273#432—534no—
274#432—534no—
275#432—1062no—
276#432—1062no—
277C2×C4⋊C8—1061no—
278C2×C4⋊C8—1061no—
279C2×C22⋊C8—1061no—
280C2×C22⋊C8—1061no—
281C2×#97—531no—
282C2×#97—531no—
283C2×#97C2×D5311yescharacteristic
284C2×#97C2×D5311yescharacteristic
285#330—534no—
286#330—534no—
287#329—534no—
288#329C2×D5314yescomplemented
289C53C2×#153511yescharacteristic, complemented, Sylow
290C22×Q8C4×D5311yescharacteristic
291C22×D4—1061no—
292C22×D4C4×D5311yescharacteristic
293C23×C4—531no—
294C23×C4—531no—
295C23×C4—531no—
296C23×C4—1061no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—1061no—
300C22×C8—1061no—
301#126—1064no—
302#126—1064no—
303#125—532no—
304#125—532no—
305#125—1061no—
306#125—1061no—
307#124—21no—
308#124—21no—
309#124C4×D5312yes—
310#124C22×D5312yes—
311#123—1064no—
312#123—1064no—
313C22⋊Q8—534no—
314C22⋊Q8—1062no—
315#121—534no—
316#121—1062no—
317C4×Q8—534no—
318C4×Q8—1062no—
319C4×D4—534no—
320C4×D4—1062no—
321C4×D4—1064no—
322C4×D4—1064no—
323#117—1064no—
324#117—1064no—
325C2×C4⋊C4—531no—
326C2×C4⋊C4—531no—
327C2×C4⋊C4—1061no—
328C2×C4⋊C4—1061no—
329C2×C4⋊C4—1061no—
330C2×C4⋊C4—1061no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—1061no—
334C2×C22⋊C4—1061no—
335C2×C22⋊C4—1061no—
336C2×C42—531no—
337C2×C42—531no—
338C2×C42—531no—
339C2×C42—532no—
340C2×C42—532no—
341C2×C42—532no—
342C2×C42—532no—
343C2×C42—1061no—
344C2×C42C22×D5311yescharacteristic
345C4⋊C8—1064no—
346C4⋊C8—1064no—
347C22⋊C8—1064no—
348C22⋊C8—1064no—
349#97—21no—
350#97—21no—
351#97—532no—
352#97—532no—
353#97—1061no—
354#97—1061no—
355#97C22×D5312yes—
356#97C22×D5312yes—
357C24—21no—
358C24—531no—
359C2×Q8—21no—
360C2×Q8—42no—
361C2×Q8C2×C4×D5312yes—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—1064no—
365C2×D4—2124no—
366C2×D4C2×C4×D5312yes—
367C22×C4—21no—
368C22×C4—531no—
369C22×C4—531no—
370C22×C4—531no—
371C22×C4—532no—
372C22×C4—532no—
373C22×C4—532no—
374C22×C4—532no—
375C22×C4—532no—
376C22×C4—532no—
377C22×C4—1064no—
378C22×C4—1061no—
379C22×C4—1061no—
380C22×C4—2122no—
381C22×C4—2122no—
382C22×C4—2122no—
383C22×C4—2124no—
384C22×C4C2×C4×D5311yescharacteristic
385C22×C4D4×D5311yescharacteristic
386C22×C4D4×D5311yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—1062no—
392C2×C8—1062no—
393C2×C8—2122no—
394C2×C8—2122no—
395C4⋊C4—532no—
396C4⋊C4—532no—
397C4⋊C4—1064no—
398C4⋊C4—1064no—
399C4⋊C4—1061no—
400C4⋊C4—1061no—
401C4⋊C4—1062no—
402C4⋊C4—1062no—
403C4⋊C4—1062no—
404C4⋊C4—1062no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—1064no—
410C22⋊C4—1064no—
411C22⋊C4—1064no—
412C42—532no—
413C42—532no—
414C42—532no—
415C42—532no—
416C42—532no—
417C42—532no—
418C42—1064no—
419C42C2×C4×D5311yescharacteristic
420C42D4×D5311yescharacteristic
421C42D4×D5311yescharacteristic
422C42C23×D5311yescharacteristic
423C23—22no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—532no—
428C23—1062no—
429C23—1062no—
430C23—1062no—
431C23C22⋊C4×D5311yescharacteristic
432Q8—42no—
433Q8—42no—
434D4—42no—
435D4—42no—
436D4—2128no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—532no—
443C2×C4—532no—
444C2×C4—532no—
445C2×C4—1062no—
446C2×C4—1062no—
447C2×C4—1062no—
448C2×C4—1062no—
449C2×C4—1062no—
450C2×C4—2122no—
451C2×C4—2122no—
452C2×C4—2122no—
453C2×C4—2122no—
454C2×C4—2122no—
455C2×C4—2122no—
456C2×C4—2128no—
457C2×C4—2122no—
458C2×C4—2122no—
459C2×C4C22⋊C4×D5311yescharacteristic
460C2×C4C22⋊C4×D5311yescharacteristic
461C2×C4C22⋊C4×D5311yescharacteristic
462C2×C4C22×C4×D5311yescharacteristic
463C2×C4C2×D4×D5311yescharacteristic
464C2×C4C2×D4×D5311yescharacteristic
465C8—42no—
466C8—42no—
467C8—2122no—
468C8—2122no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—84no—
473C22—1062no—
474C22—1062no—
475C22—1062no—
476C22—2124no—
477C22#1681060412yes—
478C22#1681063812yes—
479C22#1681063812yes—
480C22C2×C22⋊C4×D5311yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—42no—
488C4—1062no—
489C4—1062no—
490C4—1062no—
491C4—2122no—
492C4—2122no—
493C2—82no—
494C2—2122no—
495C2#2027334314yesdirect product factor
496C2C2×#1681060411yescharacteristic
497C2C2×#1681063811yescharacteristic
498C2C2×#1681063811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC2×C53×#329C2
socleC23×C53C2×C22⋊C4
prime radicalC2×#13133188C4
cosocleC42×C53C24
hypercenterC2×#329D53
hypocenterC53C2×#1535
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. C2×#16810678C2semidirect
3. C2×#16810678C2semidirect
4. #20273343C2direct (N × H)
5. C2×#16810364C2semidirect
6. C2×#16810364C2semidirect
7. C2×#16810363C2semidirect
8. C2×C53×#329C2semidirect
25. #16810678C22semidirect
26. #16810678C22semidirect
33. #16810364C22semidirect
34. #16810364C22semidirect
35. #16810363C22semidirect
39. C53×#329C22semidirect
251. C2×#329D53semidirect
253. C2×C53#1535semidirect
288. #329C2×D53semidirect
289. C53C2×#1535semidirect
495. C2#20273343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111522
C2×#168106782
#202733432
C2×#168103642
C2×#168103632
C2×C53×#3292
C2×#153553