Finite Group Databasebeta

← #11857365

Subgroups — #11857365

Order 1152.

2697 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63818C212yesmaximal, complemented
3C3×#5207C212yesmaximal, complemented
4#10591159C214yesmaximal, complemented
5#10591152C214yesmaximal, complemented
6#10591074C212yesmaximal, complemented
7D3×#407—32nomaximal
8C24×C3⋊D3C411yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C411yescharacteristic
11C22×C4×C3⋊D3—28no—
12C22×C4×C3⋊D3C411yescharacteristic
13C22×C4×C3⋊D3C412yes—
14C22×C4×C3⋊D3C411yescharacteristic
15C22×C4×C3⋊D3C412yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2212yes—
18C22×C4×C3⋊D3C2212yes—
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#208C2214yescomplemented
21C2×#3712C2214yescomplemented
22#63818—28no—
23C2×#3710C2214yescomplemented
24C3×#830C2218yescomplemented
25#63557C2218yescomplemented
26C23×C4×D3—32no—
27C23×C4×D3—61no—
28C2×D3×M16—34no—
29C3×#407—32no—
30#5207D312yescomplemented
31#5126—34no—
32#4726—38no—
33D3×C22⋊C8—38no—
34C24×C32C2×C411yescharacteristic
35C23×C3⋊D3—24no—
36C23×C3⋊D3—28no—
37C23×C3⋊D3C2×C411yescharacteristic
38C23×C3⋊D3C2×C412yes—
39C23×C3⋊D3C2×C411yescharacteristic
40C23×C3⋊D3C2×C412yes—
41C22×C32×C4—24no—
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4C2×C412yes—
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C412yes—
49C22×C3⋊Dic3C2×C412yes—
50C22×C3⋊Dic3C2×C411yescharacteristic
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—28no—
55C2×C4×C3⋊D3—28no—
56C2×C4×C3⋊D3—28no—
57C2×C4×C3⋊D3—28no—
58C2×C4×C3⋊D3C2×C412yes—
59C2×C4×C3⋊D3C2×C412yes—
60C2×C4×C3⋊D3C2×C412yes—
61C2×C4×C3⋊D3C2×C412yes—
62C2×C4×C3⋊D3C2×C412yes—
63C2×C4×C3⋊D3C2×C411yescharacteristic
64C2×C4×C3⋊D3C2×C411yescharacteristic
65C2×C4×C3⋊D3D418yes—
66C2×C4×C3⋊D3C2312yes—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C3×#208—28no—
70C2×C3×C3⋊C8C2318yescomplemented
71#3712—28no—
72#3710—28no—
73C2×#407—91noSylow
74C24×D3—32no—
75C24×D3—61no—
76C23×C3×C4—21no—
77C23×C3×C4C2×D312yes—
78C23×Dic3—32no—
79C23×Dic3—61no—
80C22×C4×D3—32no—
81C22×C4×D3—34no—
82C22×C4×D3—34no—
83C22×C4×D3—32no—
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—34no—
87C22×C4×D3—34no—
88C22×C4×D3—61no—
89C22×C4×D3—62no—
90C22×C4×D3—62no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C22×C4×D3—62no—
94C22×C4×D3—61no—
95C22×C4×D3—62no—
96C22×C4×D3—616no—
97C22×C4×D3—616no—
98C2×C3×M16—34no—
99C2×#208C2×D314yescomplemented
100D3×M16—616no—
101C2×ΓL(1,𝔽25)—38no—
102C2×D3×C8—38no—
103C3×C22⋊C8—38no—
104#830C2×D318yescomplemented
105(C2×D3)⋊C8—316no—
106C23×C32—22no—
107C23×C32—24no—
108C23×C32C22×C411yescharacteristic
109C23×C32C22×C412yes—
110C22×C3⋊D3—232no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3—24no—
113C22×C3⋊D3—24no—
114C22×C3⋊D3—24no—
115C22×C3⋊D3—24no—
116C22×C3⋊D3—24no—
117C22×C3⋊D3—24no—
118C22×C3⋊D3—24no—
119C22×C3⋊D3C22⋊C414yes—
120C22×C3⋊D3M1618yescomplemented
121C22×C3⋊D3C22×C411yescharacteristic
122C22×C3⋊D3C22×C412yes—
123C22×C3⋊D3C22×C411yescharacteristic
124C2×C32×C4—22no—
125C2×C32×C4—24no—
126C2×C32×C4—24no—
127C2×C32×C4C22×C412yes—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D414yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—24no—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3C22⋊C414yes—
135C2×C3⋊Dic3C22×C412yes—
136C2×C3⋊Dic3C22×C411yescharacteristic
137C2×C3⋊Dic3C22×C411yescharacteristic
138C4×C3⋊D3—24no—
139C4×C3⋊D3—24no—
140C4×C3⋊D3—24no—
141C4×C3⋊D3—24no—
142C4×C3⋊D3—24no—
143C4×C3⋊D3—24no—
144C4×C3⋊D3C22⋊C414yes—
145C4×C3⋊D3C22⋊C414yes—
146C4×C3⋊D3C2×D414yes—
147C4×C3⋊D3C2×D414yes—
148C3×C3⋊C8—28no—
149C24×C4—91no—
150C22×M16—92no—
151#407—32no—
152#407—94no—
153#407—92no—
154C2×C22⋊C8—94no—
155C24×C3—21no—
156C24×C3C4×D312yes—
157C23×D3—32no—
158C23×D3—34no—
159C23×D3—34no—
160C23×D3—32no—
161C23×D3—61no—
162C23×D3—62no—
163C23×D3—62no—
164C23×D3—61no—
165C23×D3—68no—
166C23×D3—616no—
167C23×D3—68no—
168C23×D3—616no—
169C22×C3×C4—28no—
170C22×C3×C4—28no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4C4×D312yes—
176C22×C3×C4C4×D314yes—
177C22×C3×C4C22×D314yes—
178C22×C3×C4C22×D312yes—
179C22×Dic3—32no—
180C22×Dic3—34no—
181C22×Dic3—34no—
182C22×Dic3—32no—
183C22×Dic3—61no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—61no—
187C22×Dic3—68no—
188C22×Dic3—68no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—316no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—34no—
195C2×C4×D3—34no—
196C2×C4×D3—34no—
197C2×C4×D3—34no—
198C2×C4×D3—34no—
199C2×C4×D3—34no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—68no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—616no—
212C2×C4×D3—616no—
213C2×C4×D3—616no—
214C2×C4×D3—616no—
215C2×C4×D3—68no—
216C2×C4×D3—68no—
217C2×C4×D3—616no—
218C2×C4×D3—616no—
219C2×C4×D3—616no—
220C2×C4×D3—616no—
221C2×C4×D3—68no—
222C2×C4×D3—68no—
223C2×C4×D3—68no—
224C2×C4×D3—68no—
225C3×M16—68no—
226C2×C3×C8—38no—
227#208—28no—
228C2×C3⋊C8C22×D318yescomplemented
229ΓL(1,𝔽25)—616no—
230D3×C8—616no—
231C22×C32—28no—
232C22×C32—22no—
233C22×C32—22no—
234C22×C32—22no—
235C22×C32C2×C22⋊C412yes—
236C22×C32C2×M1614yescomplemented
237C22×C32C23×C411yescharacteristic
238C2×C3⋊D3—216no—
239C2×C3⋊D3—28no—
240C2×C3⋊D3—22no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—28no—
244C2×C3⋊D3—216no—
245C2×C3⋊D3C2×C22⋊C412yes—
246C2×C3⋊D3C2×C22⋊C412yes—
247C2×C3⋊D3C2×M1614yes—
248C2×C3⋊D3C2×M1614yescomplemented
249C32×C4—22no—
250C32×C4C2×C22⋊C412yes—
251C32×C4C22×D412yes—
252C3⋊Dic3—22no—
253C3⋊Dic3C2×C22⋊C412yes—
254C3⋊Dic3C2×C22⋊C412yes—
255C25—91no—
256C23×C4—91no—
257C23×C4—91no—
258C23×C4—91no—
259C23×C4—92no—
260C23×C4—92no—
261C23×C4—91no—
262C23×C4—92no—
263C23×C4—92no—
264C23×C4—91no—
265C23×C4—188no—
266C23×C4D3211yescharacteristic
267C2×M16—34no—
268C2×M16—94no—
269C2×M16—188no—
270C22×C8—94no—
271C22⋊C8—38no—
272C22⋊C8—98no—
273C23×C3—24no—
274C23×C3—28no—
275C23×C3—24no—
276C23×C3—28no—
277C23×C3—22no—
278C23×C3—21no—
279C23×C3C2×C4×D312yes—
280C23×C3C2×C4×D314yes—
281C22×D3—32no—
282C22×D3—38no—
283C22×D3—316no—
284C22×D3—32no—
285C22×D3—34no—
286C22×D3—64no—
287C22×D3—68no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—62no—
291C22×D3—68no—
292C22×D3—68no—
293C22×D3—68no—
294C22×D3—68no—
295C22×D3—68no—
296C22×D3—68no—
297C22×D3—68no—
298C22×D3—68no—
299C22×D3—64no—
300C22×D3—68no—
301C22×D3—68no—
302C22×D3—68no—
303C22×D3—68no—
304C22×D3—664no—
305C22×D3—664no—
306C22×D3—68no—
307C22×D3—64no—
308C22×D3—68no—
309C2×C3×C4—24no—
310C2×C3×C4—28no—
311C2×C3×C4—28no—
312C2×C3×C4—24no—
313C2×C3×C4—28no—
314C2×C3×C4—28no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—24no—
319C2×C3×C4C2×C4×D314yes—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4D3×D418yes—
322C2×C3×C4C23×D312yes—
323C2×Dic3—38no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—34no—
327C2×Dic3—64no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—68no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3—68no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C4×D3—38no—
338C4×D3—38no—
339C4×D3—38no—
340C4×D3—38no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—68no—
346C4×D3—68no—
347C4×D3—68no—
348C4×D3—68no—
349C4×D3—68no—
350C4×D3—68no—
351C4×D3—68no—
352C4×D3—68no—
353C4×D3—68no—
354C4×D3—68no—
355C4×D3—68no—
356C4×D3—68no—
357C3×C8—68no—
358C3⋊C8—28no—
359C2×C32—22no—
360C2×C32—24no—
361C2×C32C22×C22⋊C411yescharacteristic
362C2×C32C22×M1612yes—
363C3⋊D3—22no—
364C3⋊D3—24no—
365C3⋊D3#40714yescomplemented
366C24—92no—
367C24—91no—
368C24—92no—
369C24—91no—
370C24—184no—
371C24—188no—
372C24#62411yescharacteristic
373C22×C4—24no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—98no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—91no—
383C22×C4—92no—
384C22×C4—92no—
385C22×C4—92no—
386C22×C4—92no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—184no—
390C22×C4—188no—
391C22×C4—188no—
392C22×C4—188no—
393C22×C4—188no—
394C22×C4—184no—
395C22×C4—184no—
396C22×C4—184no—
397C22×C4#62411yescharacteristic
398C22×C4#62412yes—
399C22×C4C2×D3212yes—
400C22×C4C2×D3211yescharacteristic
401M16—68no—
402M16—188no—
403C2×C8—38no—
404C2×C8—188no—
405C22×C3—24no—
406C22×C3—216no—
407C22×C3—216no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—21no—
414C22×C3—24no—
415C22×C3—22no—
416C22×C3D3×C22⋊C414yes—
417C22×C3D3×M1618yescomplemented
418C22×C3C22×C4×D312yes—
419C2×D3—34no—
420C2×D3—38no—
421C2×D3—34no—
422C2×D3—38no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—616no—
428C2×D3—632no—
429C2×D3—64no—
430C2×D3—616no—
431C2×D3—632no—
432C2×D3—632no—
433C2×D3—616no—
434C2×D3—616no—
435C2×D3—632no—
436C2×D3—64no—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—64no—
441C3×C4—24no—
442C3×C4—24no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4D3×C22⋊C414yes—
446C3×C4C2×D3×D414yes—
447Dic3—34no—
448Dic3—34no—
449Dic3—62no—
450Dic3—62no—
451Dic3—64no—
452Dic3—64no—
453C32C2×#40711yescharacteristic, complemented, Sylow
454C23—24no—
455C23—22no—
456C23—91no—
457C23—91no—
458C23—92no—
459C23—98no—
460C23—94no—
461C23—184no—
462C23—184no—
463C23—184no—
464C23—184no—
465C23—184no—
466C23—184no—
467C23—1832no—
468C23—184no—
469C23—182no—
470C23C2×#62412yes—
471C23C2×#62411yescharacteristic
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—94no—
478C2×C4—94no—
479C2×C4—94no—
480C2×C4—94no—
481C2×C4—94no—
482C2×C4—92no—
483C2×C4—184no—
484C2×C4—184no—
485C2×C4—184no—
486C2×C4—184no—
487C2×C4—184no—
488C2×C4—184no—
489C2×C4—182no—
490C2×C4—184no—
491C2×C4—184no—
492C2×C4C2×#62412yes—
493C2×C4C2×#62411yescharacteristic
494C2×C4#381114yes—
495C2×C4C22×D3211yescharacteristic
496C8—68no—
497C2×C3—28no—
498C2×C3—24no—
499C2×C3—24no—
500C2×C3—28no—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3C2×D3×C22⋊C412yes—
504C2×C3C2×D3×M1614yes—
505D3—38no—
506D3—64no—
507D3—64no—
508D3—68no—
509D3—64no—
510D3—68no—
511C22—28no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—92no—
516C22—94no—
517C22—92no—
518C22—94no—
519C22—1816no—
520C22—188no—
521C22—1816no—
522C22—188no—
523C22—182no—
524C22—182no—
525C22—182no—
526C22#6381814yescomplemented
527C22#6397412yes—
528C22C22×#62411yescharacteristic
529C4—22no—
530C4—92no—
531C4—92no—
532C4—182no—
533C4#6397412yes—
534C4C2×#381112yes—
535C3—21no—
536C3D3×#40712yescomplemented
537C2—24no—
538C2—22no—
539C2—94no—
540C2—182no—
541C2—184no—
542C2C2×#6381812yes—
543C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC23×C32×C4C22
prime radicalC24×C3⋊D3C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C3×#5207C2semidirect
4. #10591159C2semidirect
5. #10591152C2semidirect
6. #10591074C2semidirect
20. C2×C3×#208C22semidirect
21. C2×#3712C22semidirect
23. C2×#3710C22semidirect
24. C3×#830C22semidirect
25. #63557C22semidirect
30. #5207D3semidirect
70. C2×C3×C3⋊C8C23semidirect
99. C2×#208C2×D3semidirect
104. #830C2×D3semidirect
120. C22×C3⋊D3M16semidirect
228. C2×C3⋊C8C22×D3semidirect
236. C22×C32C2×M16semidirect
248. C2×C3⋊D3C2×M16semidirect
365. C3⋊D3#407semidirect
417. C22×C3D3×M16semidirect
453. C32C2×#407semidirect
526. C22#63818semidirect
536. C3D3×#407semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×#638182
C3×#52072
#105911592
#105911522
#105910742
D3×#4073