Finite Group Databasebeta

← C2×#20290618 #28319177

Subgroups — C2×#20290618 #28319177

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D53⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×#16811565C211yesmaximal, characteristic
3#20290618C218yesmaximal, direct product factor
4C2×#16811496C214yesmaximal, complemented
5C22×C4⋊C4×D53C211yesmaximal, characteristic
6C22×D53⋊C8C2212yes—
7C22×C4⋊#6157C2212yes—
8C22×C22⋊#6157—21no—
9C2×#13133274—21no—
10D53⋊(C22⋊C8)—22no—
11D53⋊(C22⋊C8)C2214yes—
12C2×C22⋊#88324—21no—
13#16811565—22no—
14#16811565C2214yes—
15C2×(C2×#6157)⋊C4—21no—
16#16811496C22116yescomplemented
17C23×C4×D53—21no—
18C23×C4×D53C2211yescharacteristic
19C22×C4⋊Dic53C411yescharacteristic, complemented
20C22×#11719919—21no—
21C2×C4⋊C4×D53—21no—
22C2×C4⋊C4×D53—22no—
23C2×C4⋊C4×D53—22no—
24C2×C4⋊C4×D53—21no—
25C2×C4⋊C4×D53C412yescomplemented
26C2×C4⋊C4×D53C414yescomplemented
27C2×C4⋊C4×D53C2212yes—
28C2×C4⋊C4×D53C2214yes—
29C22×C4⋊C4×C53C411yescharacteristic, complemented
30C23×#6157—22no—
31C2×D53⋊C8—22no—
32C2×D53⋊C8—28no—
33C2×D53⋊C8C2314yes—
34C22×#88324—22no—
35C2×C4⋊#6157—28no—
36C2×C4⋊#6157—22no—
37C2×C4⋊#6157C2314yes—
38C2×C22⋊#6157—24no—
39C2×C22⋊#6157—44no—
40#13133274—24no—
41C22⋊#88324—24no—
42(C2×#6157)⋊C4—24no—
43C24×D53D411yescharacteristic
44C23×Dic53—21no—
45C23×Dic53D411yescharacteristic
46C22×C4×D53—28no—
47C22×C4×D53—24no—
48C22×C4×D53—22no—
49C22×C4×D53—22no—
50C22×C4×D53—24no—
51C22×C4×D53—44no—
52C22×C4×D53—44no—
53C22×C4×D53C2×C411yescharacteristic
54C22×C4×D53C2×C412yes—
55C22×C4×D53D411yescharacteristic
56C22×C4×D53D412yes—
57C22×C4×D53D412yes—
58C22×C4×D53D411yescharacteristic
59C22×C4×D53C2312yes—
60C22×C4×D53C2311yescharacteristic
61C2×C4⋊Dic53—21no—
62C2×C4⋊Dic53—22no—
63C2×C4⋊Dic53C2×C412yes—
64C2×C4⋊Dic53C2×C414yescomplemented
65C2×#11719919—22no—
66C2×#11719919—24no—
67C2×#11719919—22no—
68C2×#11719919—24no—
69C4⋊C4×D53—24no—
70C4⋊C4×D53—24no—
71C4⋊C4×D53—24no—
72C4⋊C4×D53—22no—
73C4⋊C4×D53—24no—
74C4⋊C4×D53—24no—
75C4⋊C4×D53—22no—
76C4⋊C4×D53C2×C414yes—
77C4⋊C4×D53C2×C418yescomplemented
78C4⋊C4×D53C2314yes—
79C23×C4×C53—21no—
80C23×C4×C53C2×C411yescharacteristic
81C2×C4⋊C4×C53—21no—
82C2×C4⋊C4×C53—22no—
83C2×C4⋊C4×C53C2×C412yes—
84C2×C4⋊C4×C53C2×C414yescomplemented
85C24×C53C22⋊C411yescharacteristic
86C23×D53—24no—
87C23×D53—24no—
88C23×D53C22⋊C411yescharacteristic
89C23×D53C22⋊C412yes—
90C23×D53D814yes—
91C23×D53SD1614yes—
92C23×D53C2×D412yes—
93C23×D53C2×D411yescharacteristic
94C22×#6157—24no—
95C22×#6157—44no—
96C22×#6157—44no—
97C22×#6157—44no—
98C22×C4×C53—24no—
99C22×C4×C53—22no—
100C22×C4×C53—24no—
101C22×C4×C53—44no—
102C22×C4×C53C22⋊C411yescharacteristic
103C22×C4×C53C22⋊C412yes—
104C22×C4×C53C22×C412yes—
105C22×C4×C53C22×C411yescharacteristic
106C22×Dic53—24no—
107C22×Dic53—22no—
108C22×Dic53—24no—
109C22×Dic53—44no—
110C22×Dic53C22⋊C411yescharacteristic
111C22×Dic53C22⋊C412yes—
112C22×Dic53C2×D412yes—
113C22×Dic53C2×D411yescharacteristic
114C2×C4×D53—24no—
115C2×C4×D53—24no—
116C2×C4×D53—24no—
117C2×C4×D53—28no—
118C2×C4×D53—28no—
119C2×C4×D53—28no—
120C2×C4×D53—28no—
121C2×C4×D53—24no—
122C2×C4×D53—28no—
123C2×C4×D53—24no—
124C2×C4×D53—48no—
125C2×C4×D53—416no—
126C2×C4×D53—48no—
127C2×C4×D53—44no—
128C2×C4×D53—48no—
129C2×C4×D53—44no—
130C2×C4×D53C22⋊C412yes—
131C2×C4×D53C22⋊C412yes—
132C2×C4×D53C22⋊C412yes—
133C2×C4×D53C22×C412yes—
134C2×C4×D53C22×C411yescharacteristic
135C2×C4×D53C2×D412yes—
136C2×C4×D53C2×D412yes—
137C2×C4×D53C2×D411yescharacteristic
138C2×C4×D53C2×D411yescharacteristic
139C2×C4×D53#4118yes—
140C2×C4×D53C2411yescharacteristic
141C22⋊#6157—48no—
142C2×#88324—24no—
143C2×#88324—44no—
144C4⋊#6157—28no—
145C4⋊#6157—44no—
146D53⋊C8—28no—
147D53⋊C8—44no—
148C4⋊C4×C53—22no—
149C4⋊C4×C53—24no—
150C4⋊C4×C53C22×C414yes—
151C4⋊Dic53—22no—
152C4⋊Dic53—24no—
153C4⋊Dic53C22×C414yes—
154#11719919—24no—
155#11719919—28no—
156#11719919—24no—
157C23×C53—22no—
158C23×C53—22no—
159C23×C53#10214yes—
160C23×C53C2×C22⋊C412yes—
161C23×C53C2×C22⋊C411yescharacteristic
162C22×D53—22no—
163C22×D53—22no—
164C22×D53—24no—
165C22×D53—24no—
166C22×D53—24no—
167C22×D53—24no—
168C22×D53—216no—
169C22×D53—216no—
170C22×D53#10214yes—
171C22×D53#10218yes—
172C22×D53C2×C22⋊C412yes—
173C22×D53C2×C22⋊C411yescharacteristic
174C22×D53#12314yes—
175C22×D53C2×D814yes—
176C22×D53C2×D812yes—
177C22×D53C2×SD1614yes—
178C22×D53C2×SD1612yes—
179C22×D53#13714yes—
180C22×D53C22×D411yescharacteristic
181C2×#6157—44no—
182C2×#6157—44no—
183C2×#6157—44no—
184C2×#6157—88no—
185C2×C4×C53—22no—
186C2×C4×C53—24no—
187C2×C4×C53—24no—
188C2×C4×C53—24no—
189C2×C4×C53—48no—
190C2×C4×C53—44no—
191C2×C4×C53C2×C22⋊C412yes—
192C2×C4×C53C2×C22⋊C411yescharacteristic
193C2×C4×C53#11714yes—
194C2×C4×C53C23×C411yescharacteristic
195C2×Dic53—22no—
196C2×Dic53—24no—
197C2×Dic53—24no—
198C2×Dic53—24no—
199C2×Dic53—48no—
200C2×Dic53—44no—
201C2×Dic53C2×C22⋊C412yes—
202C2×Dic53C2×C22⋊C411yescharacteristic
203C2×Dic53#12314yes—
204C2×Dic53C22×D411yescharacteristic
205C4×D53—24no—
206C4×D53—24no—
207C4×D53—24no—
208C4×D53—24no—
209C4×D53—24no—
210C4×D53—24no—
211C4×D53—44no—
212C4×D53—44no—
213C4×D53—416no—
214C4×D53—48no—
215C4×D53#11714yes—
216C4×D53#12314yes—
217C4×D53#12314yes—
218C4×D53C2×#4114yes—
219#88324—44no—
220C2×#1823—531nomaximal, Sylow
221C22×C53—28no—
222C22×C53—22no—
223C22×C53—22no—
224C22×C53#38112yes—
225C22×C53C2×#10214yes—
226C22×C53C2×#10212yes—
227C22×C53#41912yes—
228C22×C53C22×C22⋊C411yescharacteristic
229C2×D53—28no—
230C2×D53—22no—
231C2×D53—22no—
232C2×D53—28no—
233C2×D53—28no—
234C2×D53—216no—
235C2×D53#38112yes—
236C2×D53C2×#10214yes—
237C2×D53C2×#10212yes—
238C2×D53#41912yes—
239C2×D53#48018yes—
240C2×D53#48318yes—
241C2×D53C2×#12312yes—
242C2×D53C22×D811yescharacteristic
243C2×D53C22×SD1611yescharacteristic
244C2×D53C2×#13712yes—
245#6157—84no—
246C4×C53—22no—
247C4×C53—44no—
248C4×C53#38112yes—
249C4×C53C2×#11712yes—
250Dic53—22no—
251Dic53—44no—
252Dic53#38112yes—
253Dic53C2×#12312yes—
254C23×C4⋊C4—531no—
255C22×C22⋊C8—531no—
256C2×#380—531no—
257#1823—538no—
258C2×#340—534no—
259C2×C53—24no—
260C2×C53#182314yescomplemented
261C2×C53C2×#38111yescharacteristic
262C2×C53C22×#10211yescharacteristic
263C2×C53C2×#41911yescharacteristic
264D53—24no—
265D53#182314yescomplemented
266D53C2×#48012yes—
267D53C2×#48312yes—
268C24×C4—531no—
269C24×C4—1061no—
270C23×C8—532no—
271C22×C4⋊C4—531no—
272C22×C4⋊C4—532no—
273C22×C4⋊C4—532no—
274C22×C4⋊C4—534no—
275C22×C4⋊C4—534no—
276C22×C4⋊C4—532no—
277C22×C4⋊C4—1061no—
278C22×C4⋊C4—1062no—
279C22×C4⋊C4—1062no—
280C22×C4⋊C4—1061no—
281C22×C4⋊C4—1061no—
282C22×C4⋊C4#615711yescharacteristic, complemented
283C22×C22⋊C4—1061no—
284C2×C22⋊C8—534no—
285C2×C22⋊C8—1061no—
286C2×C22⋊C8—1062no—
287C2×C22⋊C8—1061no—
288#380—534no—
289#380—1062no—
290C2×#95—1061no—
291#340—5316no—
292C53C2×#182311yescharacteristic, complemented, Sylow
293C25—531no—
294C23×C4—21no—
295C23×C4—531no—
296C23×C4—531no—
297C23×C4—531no—
298C23×C4—532no—
299C23×C4—531no—
300C23×C4—532no—
301C23×C4—532no—
302C23×C4—532no—
303C23×C4—531no—
304C23×C4—1068no—
305C23×C4—1064no—
306C23×C4—1064no—
307C23×C4—1062no—
308C23×C4—1062no—
309C23×C4—1061no—
310C23×C4—1062no—
311C23×C4—2124no—
312C23×C4—2124no—
313C23×C4C2×#615711yescharacteristic
314C22×C8—534no—
315C22×C8—1062no—
316C22×C8—1062no—
317C22×C8—1068no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—532no—
321C2×C4⋊C4—534no—
322C2×C4⋊C4—534no—
323C2×C4⋊C4—534no—
324C2×C4⋊C4—538no—
325C2×C4⋊C4—534no—
326C2×C4⋊C4—1062no—
327C2×C4⋊C4—1062no—
328C2×C4⋊C4—1064no—
329C2×C4⋊C4—1064no—
330C2×C4⋊C4—1064no—
331C2×C4⋊C4—1064no—
332C2×C4⋊C4—1064no—
333C2×C4⋊C4—1064no—
334C2×C4⋊C4—1064no—
335C2×C4⋊C4—1062no—
336C2×C4⋊C4—1062no—
337C2×C4⋊C4—1062no—
338C2×C4⋊C4—1061no—
339C2×C4⋊C4—1068no—
340C2×C4⋊C4—1062no—
341C2×C4⋊C4C2×#615712yes—
342C2×C4⋊C4C2×#615714yescomplemented
343C2×C22⋊C4—1064no—
344C2×C22⋊C4—2124no—
345C22⋊C8—1064no—
346C22⋊C8—1064no—
347#95—1064no—
348C24—531no—
349C24—534no—
350C24—534no—
351C24—532no—
352C24—532no—
353C24—531no—
354C24—1064no—
355C24—1064no—
356C24C22⋊#615711yescharacteristic
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—531no—
362C22×C4—531no—
363C22×C4—531no—
364C22×C4—538no—
365C22×C4—531no—
366C22×C4—531no—
367C22×C4—532no—
368C22×C4—532no—
369C22×C4—531no—
370C22×C4—532no—
371C22×C4—532no—
372C22×C4—532no—
373C22×C4—532no—
374C22×C4—532no—
375C22×C4—532no—
376C22×C4—1064no—
377C22×C4—1068no—
378C22×C4—1068no—
379C22×C4—1068no—
380C22×C4—1068no—
381C22×C4—1064no—
382C22×C4—1064no—
383C22×C4—1064no—
384C22×C4—1068no—
385C22×C4—1064no—
386C22×C4—1064no—
387C22×C4—1064no—
388C22×C4—1062no—
389C22×C4—1064no—
390C22×C4—2124no—
391C22×C4—2124no—
392C22×C4—21216no—
393C22×C4—2128no—
394C22×C4—2128no—
395C22×C4—2128no—
396C22×C4—2124no—
397C22×C4—2124no—
398C22×C4—2124no—
399C22×C4—2124no—
400C22×C4C22⋊#615712yes—
401C22×C4C22⋊#615711yescharacteristic
402C22×C4C22×#615712yes—
403C22×C4C22×#615711yescharacteristic
404C2×C8—1064no—
405C2×C8—1068no—
406C2×C8—2124no—
407C2×C8—2124no—
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—534no—
411C4⋊C4—1064no—
412C4⋊C4—1064no—
413C4⋊C4—1068no—
414C4⋊C4—1068no—
415C4⋊C4—1064no—
416C4⋊C4—1062no—
417C4⋊C4—2124no—
418C4⋊C4C22×#615714yes—
419C22⋊C4—2128no—
420C23—22no—
421C23—22no—
422C23—534no—
423C23—532no—
424C23—532no—
425C23—534no—
426C23—531no—
427C23—531no—
428C23—538no—
429C23—534no—
430C23—534no—
431C23—534no—
432C23—532no—
433C23—1064no—
434C23—1064no—
435C23—1064no—
436C23—1064no—
437C23—10616no—
438C23—10616no—
439C23—1062no—
440C23—1062no—
441C23#1313327914yes—
442C23C2×C22⋊#615712yes—
443C23C2×C22⋊#615711yescharacteristic
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—534no—
451C2×C4—531no—
452C2×C4—531no—
453C2×C4—534no—
454C2×C4—534no—
455C2×C4—534no—
456C2×C4—534no—
457C2×C4—532no—
458C2×C4—1064no—
459C2×C4—1064no—
460C2×C4—1064no—
461C2×C4—1064no—
462C2×C4—1064no—
463C2×C4—1064no—
464C2×C4—1062no—
465C2×C4—1064no—
466C2×C4—1064no—
467C2×C4—1064no—
468C2×C4—4248no—
469C2×C4—2124no—
470C2×C4—2124no—
471C2×C4—2128no—
472C2×C4—21216no—
473C2×C4—2124no—
474C2×C4—2124no—
475C2×C4—2124no—
476C2×C4—2128no—
477C2×C4—2124no—
478C2×C4C2×C22⋊#615712yes—
479C2×C4C2×C22⋊#615711yescharacteristic
480C2×C4#1313329614yes—
481C2×C4C23×#615711yescharacteristic
482C8—2124no—
483C22—22no—
484C22—28no—
485C22—22no—
486C22—531no—
487C22—531no—
488C22—532no—
489C22—532no—
490C22—532no—
491C22—538no—
492C22—538no—
493C22—532no—
494C22—532no—
495C22—534no—
496C22—1068no—
497C22—1068no—
498C22—10616no—
499C22—1062no—
500C22—1068no—
501C22—1062no—
502C22#1681156612yes—
503C22C2×#1313327914yes—
504C22C2×#1313327912yes—
505C22#1681161612yes—
506C22C22×C22⋊#615711yescharacteristic
507C4—22no—
508C4—44no—
509C4—532no—
510C4—532no—
511C4—1062no—
512C4—4244no—
513C4—2124no—
514C4#1681156612yes—
515C4C2×#1313329612yes—
516C2—24no—
517C2—532no—
518C2—532no—
519C2—534no—
520C2—1064no—
521C2#2029061814yesdirect product factor
522C2C2×#1681156611yescharacteristic
523C2C22×#1313327911yescharacteristic
524C2C2×#1681161611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC22×C4⋊C4×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×D53D4
cosocleC2×C4×D53C24
hypercenterC22×C4⋊C4#6157
hypocenterC53C2×#1823
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20290618C2direct (N × H)
4. C2×#16811496C2semidirect
16. #16811496C22semidirect
19. C22×C4⋊Dic53C4semidirect
25. C2×C4⋊C4×D53C4semidirect
26. C2×C4⋊C4×D53C4semidirect
29. C22×C4⋊C4×C53C4semidirect
64. C2×C4⋊Dic53C2×C4semidirect
77. C4⋊C4×D53C2×C4semidirect
84. C2×C4⋊C4×C53C2×C4semidirect
260. C2×C53#1823semidirect
265. D53#1823semidirect
282. C22×C4⋊C4#6157semidirect
292. C53C2×#1823semidirect
342. C2×C4⋊C4C2×#6157semidirect
521. C2#20290618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D53⋊(C22⋊C8)2
C2×#168115652
#202906182
C2×#168114962
C22×C4⋊C4×D532
C2×#182353