Finite Group Databasebeta

← C2×#10591154 #11857368

Subgroups — C2×#10591154 #11857368

Order 1152.

2117 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic
2C22×#3711C212yesmaximal, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5#10591154C218yesmaximal, direct product factor
6C2×(C2×D3)⋊(C3⋊C8)C212yesmaximal, complemented
7C2×#5207—31nomaximal
8C2×#4726—31nomaximal
9C24×C3×D3C411yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3×Dic3C411yescharacteristic
12C22×C3×C4×D3—28no—
13C22×C3×C4×D3C414yes—
14C22×C3×C4×D3C411yescharacteristic
15C22×C3×C4×D3C411yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2214yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2212yescomplemented
20C22×C3×C3⋊C8C2212yescomplemented
21C2×#3711—28no—
22C2×#3711C2218yescomplemented
23#63657C2214yescomplemented
24C3×#830C2214yescomplemented
25(C2×D3)⋊(C3⋊C8)C2218yescomplemented
26C24×C3×C4—31no—
27C23×C4×D3D311yescharacteristic
28C22×#208—32no—
29C22×ΓL(1,𝔽25)—32no—
30C2×C3×C22⋊C8—31no—
31#5207—38no—
32C2×#830—31no—
33C2×#830—31no—
34C2×#830—32no—
35C2×#830—61no—
36C2×#830D311yescharacteristic, complemented
37C2×(C2×D3)⋊C8—32no—
38#4726—38no—
39C24×C32C2×C411yescharacteristic
40C23×C3×D3—24no—
41C23×C3×D3—24no—
42C23×C3×D3—24no—
43C23×C3×D3C2×C414yes—
44C23×C3×D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4—24no—
47C22×C32×C4C2×C411yescharacteristic
48C22×C32×C4C2×C412yes—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—24no—
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C414yes—
54C22×C3×Dic3C2×C411yescharacteristic
55C2×C3×C4×D3—24no—
56C2×C3×C4×D3—24no—
57C2×C3×C4×D3—24no—
58C2×C3×C4×D3—216no—
59C2×C3×C4×D3—216no—
60C2×C3×C4×D3C2×C414yes—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3C2×C414yes—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3D418yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×C4×D3C2312yes—
67C2×C3⋊(C3⋊C8)—24no—
68C2×C3⋊(C3⋊C8)C2314yescomplemented
69C2×C3×C3⋊C8—24no—
70C2×C3×C3⋊C8C2314yescomplemented
71#3711—216no—
72C2×#407—91noSylow
73C25×C3—31no—
74C24×D3Dic311yescharacteristic
75C23×C3×C4—21no—
76C23×C3×C4—31no—
77C23×C3×C4—31no—
78C23×C3×C4—31no—
79C23×C3×C4—34no—
80C23×C3×C4—31no—
81C23×C3×C4—31no—
82C23×C3×C4—34no—
83C23×C3×C4—68no—
84C23×C3×C4C2×D311yescharacteristic
85C23×C3×C4C2×D311yescharacteristic
86C23×Dic3Dic311yescharacteristic
87C22×C4×D3—28no—
88C22×C4×D3Dic311yescharacteristic
89C22×C4×D3Dic311yescharacteristic
90C22×C4×D3Dic314yes—
91C22×C4×D3C2×D314yes—
92C22×C4×D3C2×D311yescharacteristic
93C22×C4×D3C2×D311yescharacteristic
94C22×C3×C8—32no—
95C2×#208—38no—
96C2×#208—68no—
97C22×C3⋊C8—32no—
98C22×C3⋊C8—32no—
99C22×C3⋊C8—62no—
100C22×C3⋊C8C2×D312yescomplemented
101C2×ΓL(1,𝔽25)—38no—
102C2×ΓL(1,𝔽25)—68no—
103C3×C22⋊C8—34no—
104#830—34no—
105#830—34no—
106#830—38no—
107#830—64no—
108#830C2×D314yescomplemented
109(C2×D3)⋊C8—38no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32M1614yescomplemented
113C23×C32C22×C412yes—
114C23×C32C22×C411yescharacteristic
115C22×C3×D3—232no—
116C22×C3×D3—22no—
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—28no—
121C22×C3×D3—28no—
122C22×C3×D3—28no—
123C22×C3×D3C22⋊C414yes—
124C22×C3×D3M1614yescomplemented
125C22×C3×D3C22×C412yes—
126C22×C3×D3C22×C412yes—
127C2×C32×C4—22no—
128C2×C32×C4—24no—
129C2×C32×C4—24no—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D414yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—28no—
136C2×C3×Dic3C22⋊C414yes—
137C2×C3×Dic3C22×C412yes—
138C2×C3×Dic3C22×C412yes—
139C3×C4×D3—28no—
140C3×C4×D3—24no—
141C3×C4×D3—24no—
142C3×C4×D3—28no—
143C3×C4×D3C22⋊C418yes—
144C3×C4×D3C2×D418yes—
145C3⋊(C3⋊C8)—24no—
146C3×C3⋊C8—24no—
147C24×C4—31no—
148C22×M16—92no—
149#407—98no—
150C2×C22⋊C8—31no—
151C2×C22⋊C8—92no—
152C2×C22⋊C8—91no—
153C24×C3—21no—
154C24×C3—31no—
155C24×C3—31no—
156C24×C3—34no—
157C24×C3—64no—
158C24×C3—64no—
159C24×C3—64no—
160C24×C3C4×D311yescharacteristic
161C24×C3C2×Dic311yescharacteristic
162C23×D3—24no—
163C23×D3—24no—
164C23×D3—24no—
165C23×D3C2×Dic314yes—
166C23×D3C2×Dic311yescharacteristic
167C23×D3C2×Dic311yescharacteristic
168C22×C3×C4—24no—
169C22×C3×C4—24no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—38no—
177C22×C3×C4—32no—
178C22×C3×C4—34no—
179C22×C3×C4—31no—
180C22×C3×C4—34no—
181C22×C3×C4—34no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—44no—
185C22×C3×C4—64no—
186C22×C3×C4—616no—
187C22×C3×C4—616no—
188C22×C3×C4—64no—
189C22×C3×C4—64no—
190C22×C3×C4—64no—
191C22×C3×C4C4×D311yescharacteristic
192C22×C3×C4C4×D312yes—
193C22×C3×C4C2×Dic311yescharacteristic
194C22×C3×C4C2×Dic312yes—
195C22×C3×C4C22×D312yes—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×Dic3—24no—
200C22×Dic3C2×Dic311yescharacteristic
201C22×Dic3C2×Dic314yes—
202C22×Dic3C2×Dic311yescharacteristic
203C2×C4×D3—24no—
204C2×C4×D3—24no—
205C2×C4×D3—24no—
206C2×C4×D3—216no—
207C2×C4×D3—216no—
208C2×C4×D3C2×Dic314yes—
209C2×C4×D3C2×Dic312yes—
210C2×C4×D3C2×Dic314yes—
211C2×C4×D3C2×Dic312yes—
212C2×C4×D3#6718yes—
213C2×C4×D3C22×D312yes—
214C2×C4×D3C22×D312yes—
215C2×C3×C8—34no—
216C2×C3×C8—64no—
217#208—616no—
218C2×C3⋊C8—24no—
219C2×C3⋊C8—34no—
220C2×C3⋊C8—34no—
221C2×C3⋊C8—64no—
222C2×C3⋊C8—64no—
223C2×C3⋊C8—64no—
224C2×C3⋊C8—124no—
225C2×C3⋊C8C22×D314yescomplemented
226ΓL(1,𝔽25)—616no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—28no—
230C22×C32C2×C22⋊C412yes—
231C22×C32C2×M1612yes—
232C22×C32C2×M1612yes—
233C22×C32C2×M1614yescomplemented
234C22×C32C23×C411yescharacteristic
235C2×C3×D3—232no—
236C2×C3×D3—22no—
237C2×C3×D3—22no—
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3—28no—
241C2×C3×D3—28no—
242C2×C3×D3C2×C22⋊C414yes—
243C2×C3×D3C2×M1614yescomplemented
244C32×C4—22no—
245C32×C4C2×C22⋊C412yes—
246C32×C4C22×D412yes—
247C3×Dic3—22no—
248C3×Dic3C2×C22⋊C414yes—
249C25—31no—
250C23×C4—31no—
251C23×C4—31no—
252C23×C4—31no—
253C23×C4—34no—
254C23×C4—31no—
255C23×C4—34no—
256C23×C4—31no—
257C23×C4—68no—
258C23×C4D3211yescharacteristic
259C2×M16—98no—
260C2×M16—188no—
261C22×C8—32no—
262C22×C8—92no—
263C22⋊C8—34no—
264C22⋊C8—98no—
265C22⋊C8—94no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—24no—
271C23×C3—21no—
272C23×C3—22no—
273C23×C3—34no—
274C23×C3—34no—
275C23×C3—32no—
276C23×C3—32no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—68no—
280C23×C3—68no—
281C23×C3—632no—
282C23×C3—62no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—68no—
286C23×C3—62no—
287C23×C3ΓL(1,𝔽25)14yescomplemented
288C23×C3#20814yescomplemented
289C23×C3C2×C4×D312yes—
290C23×C3C2×C4×D311yescharacteristic
291C23×C3C22×Dic312yes—
292C23×C3C22×Dic311yescharacteristic
293C22×D3—232no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—28no—
298C22×D3—22no—
299C22×D3—28no—
300C22×D3—28no—
301C22×D3#20814yescomplemented
302C22×D3#21714yes—
303C22×D3C22×Dic312yes—
304C22×D3C22×Dic312yes—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—24no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—34no—
316C2×C3×C4—32no—
317C2×C3×C4—38no—
318C2×C3×C4—38no—
319C2×C3×C4—32no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—42no—
323C2×C3×C4—68no—
324C2×C3×C4—68no—
325C2×C3×C4—68no—
326C2×C3×C4—62no—
327C2×C3×C4—64no—
328C2×C3×C4—64no—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4D3×D414yes—
332C2×C3×C4C22×Dic312yes—
333C2×C3×C4C22×Dic311yescharacteristic
334C2×C3×C4C2×#6714yes—
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—28no—
339C2×Dic3#21714yes—
340C2×Dic3C22×Dic312yes—
341C2×Dic3C22×Dic312yes—
342C4×D3—28no—
343C4×D3—24no—
344C4×D3—24no—
345C4×D3—28no—
346C4×D3#21718yes—
347C4×D3C2×#6718yes—
348C3×C8—64no—
349C3⋊C8—24no—
350C3⋊C8—64no—
351C3⋊C8—64no—
352C3⋊C8—124no—
353C2×C32—24no—
354C2×C32#40714yescomplemented
355C2×C32C22×C22⋊C411yescharacteristic
356C2×C32C22×M1611yescharacteristic
357C2×C32C22×M1611yescharacteristic
358C3×D3—24no—
359C3×D3—24no—
360C24—31no—
361C24—31no—
362C24—34no—
363C24—64no—
364C24—64no—
365C24—64no—
366C24D3×Dic311yescharacteristic
367C22×C4—24no—
368C22×C4—31no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—38no—
372C22×C4—34no—
373C22×C4—31no—
374C22×C4—32no—
375C22×C4—34no—
376C22×C4—34no—
377C22×C4—32no—
378C22×C4—64no—
379C22×C4—616no—
380C22×C4—616no—
381C22×C4—64no—
382C22×C4—64no—
383C22×C4—64no—
384C22×C4D3×Dic311yescharacteristic
385C22×C4D3×Dic312yes—
386C22×C4C2×D3212yes—
387C22×C4C2×D3211yescharacteristic
388M16—1816no—
389C2×C8—34no—
390C2×C8—64no—
391C2×C8—94no—
392C2×C8—184no—
393C22×C3—28no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—28no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—24no—
403C22×C3—22no—
404C22×C3—34no—
405C22×C3—34no—
406C22×C3—42no—
407C22×C3—48no—
408C22×C3—42no—
409C22×C3—632no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—68no—
415C22×C3—68no—
416C22×C3D3×C22⋊C412yes—
417C22×C3C2×ΓL(1,𝔽25)12yes—
418C22×C3C2×ΓL(1,𝔽25)14yescomplemented
419C22×C3D3×M1612yes—
420C22×C3C2×#20812yes—
421C22×C3C2×#20812yes—
422C22×C3C2×#20814yescomplemented
423C22×C3C2×#21712yes—
424C22×C3C22×C4×D311yescharacteristic
425C22×C3C23×Dic311yescharacteristic
426C2×D3—232no—
427C2×D3—28no—
428C2×D3—28no—
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3C2×#20814yescomplemented
434C2×D3C2×#21714yes—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—34no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4D3×C22⋊C412yes—
443C3×C4C2×#21712yes—
444C3×C4C2×D3×D412yes—
445C3×C4C22×#6712yes—
446Dic3—22no—
447Dic3C2×#21714yes—
448C32C2×#40711yescharacteristic, complemented, Sylow
449C23—22no—
450C23—22no—
451C23—32no—
452C23—32no—
453C23—34no—
454C23—34no—
455C23—68no—
456C23—68no—
457C23—632no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23—68no—
462C23—62no—
463C23#371114yescomplemented
464C23C2×D3×Dic312yes—
465C23C2×D3×Dic311yescharacteristic
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—32no—
470C2×C4—34no—
471C2×C4—38no—
472C2×C4—38no—
473C2×C4—32no—
474C2×C4—68no—
475C2×C4—68no—
476C2×C4—68no—
477C2×C4—62no—
478C2×C4—64no—
479C2×C4—64no—
480C2×C4C2×D3×Dic312yes—
481C2×C4C2×D3×Dic311yescharacteristic
482C2×C4D3×#6714yes—
483C2×C4C22×D3211yescharacteristic
484C8—64no—
485C8—184no—
486C2×C3—24no—
487C2×C3—24no—
488C2×C3—21no—
489C2×C3—24no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—44no—
493C2×C3—64no—
494C2×C3—64no—
495C2×C3#472614yescomplemented
496C2×C3#520714yescomplemented
497C2×C3C2×D3×C22⋊C411yescharacteristic
498C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
499C2×C3C2×D3×M1611yescharacteristic
500C2×C3C22×#20811yescharacteristic
501C2×C3C22×#20811yescharacteristic
502C2×C3C22×#21711yescharacteristic
503D3—24no—
504D3—24no—
505C22—22no—
506C22—28no—
507C22—22no—
508C22—34no—
509C22—34no—
510C22—632no—
511C22—62no—
512C22—68no—
513C22—68no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22D3×#20812yes—
518C22C2×#371112yes—
519C22C2×#371114yescomplemented
520C22D3×#21712yes—
521C22C22×D3×Dic311yescharacteristic
522C4—22no—
523C4—34no—
524C4—62no—
525C4D3×#21712yes—
526C4C2×D3×#6712yes—
527C3—21no—
528C3C2×#472611yescharacteristic, complemented
529C3C2×#520711yescharacteristic, complemented
530C2—24no—
531C2—64no—
532C2—64no—
533C2#1059115414yesdirect product factor
534C2C2×D3×#20811yescharacteristic
535C2C22×#371111yescharacteristic
536C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C3×D3C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3711C2semidirect
3. C2×#63657C2semidirect
4. C2×C3×#830C2semidirect
5. #10591154C2direct (N × H)
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
19. C22×C3⋊(C3⋊C8)C22semidirect
20. C22×C3×C3⋊C8C22semidirect
22. C2×#3711C22semidirect
23. #63657C22semidirect
24. C3×#830C22semidirect
25. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C2×#830D3semidirect
68. C2×C3⋊(C3⋊C8)C23semidirect
70. C2×C3×C3⋊C8C23semidirect
100. C22×C3⋊C8C2×D3semidirect
108. #830C2×D3semidirect
112. C23×C32M16semidirect
124. C22×C3×D3M16semidirect
225. C2×C3⋊C8C22×D3semidirect
233. C22×C32C2×M16semidirect
243. C2×C3×D3C2×M16semidirect
287. C23×C3ΓL(1,𝔽25)semidirect
288. C23×C3#208semidirect
301. C22×D3#208semidirect
354. C2×C32#407semidirect
418. C22×C3C2×ΓL(1,𝔽25)semidirect
422. C22×C3C2×#208semidirect
433. C2×D3C2×#208semidirect
448. C32C2×#407semidirect
463. C23#3711semidirect
495. C2×C3#4726semidirect
496. C2×C3#5207semidirect
519. C22C2×#3711semidirect
528. C3C2×#4726semidirect
529. C3C2×#5207semidirect
533. C2#10591154direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C22×#37112
C2×#636572
C2×C3×#8302
#105911542
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52073
C2×#47263