Finite Group Databasebeta

← #11801060

Subgroups — #11801060

Order 1152.

2857 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63849C212yesmaximal, complemented
3C3×#5212C212yesmaximal, complemented
4#10591714C212yesmaximal
5#10591705C212yesmaximal, complemented
6#10591325C212yesmaximal, complemented
7#10591260C212yesmaximal, complemented
8#10591219C212yesmaximal, complemented
9#73862—32nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C22×C4×C3⋊D3—28no—
14C22×C4×C3⋊D3C418yescomplemented
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#217C2214yes—
20C2×C3×C4⋊Dic3C2214yescomplemented
21C2×#3722C2214yes—
22C2×#3722C2214yes—
23C2×Dic32C2214yescomplemented
24#63849—28no—
25C3×C3⋊#95C2214yescomplemented
26#63579C2214yescomplemented
27C23×C4×D3—32no—
28C23×C4×D3—61no—
29C2×#892—34no—
30C3×#380—32no—
31#5212D312yescomplemented
32#4987—34no—
33#4955—34no—
34Dic3×C22⋊C4—34no—
35#4666—34no—
36#4664—34no—
37C24×C32C2311yescharacteristic
38C23×C3⋊D3—24no—
39C23×C3⋊D3—24no—
40C23×C3⋊D3—24no—
41C23×C3⋊D3C2×C414yes—
42C23×C3⋊D3C2311yescharacteristic
43C23×C3⋊D3C2311yescharacteristic
44C22×C32×C4—24no—
45C22×C32×C4C2×C414yes—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3C2×C414yes—
50C22×C3⋊Dic3C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—232no—
56C2×C4×C3⋊D3C2×C414yes—
57C2×C4×C3⋊D3C2×C414yes—
58C2×C4×C3⋊D3C2×C414yes—
59C2×C4×C3⋊D3C2×C414yes—
60C2×C4×C3⋊D3D418yes—
61C22×C3×Dic3C2318yes—
62C3×#217—28no—
63C3×C4⋊Dic3—28no—
64#3722—28no—
65#3722—28no—
66Dic32—28no—
67#2280—91noSylow
68C24×D3—32no—
69C24×D3—61no—
70C23×C3×C4—21no—
71C23×C3×C4C2×D312yes—
72C23×Dic3—32no—
73C23×Dic3—61no—
74C22×C4×D3—32no—
75C22×C4×D3—316no—
76C22×C4×D3—32no—
77C22×C4×D3—32no—
78C22×C4×D3—32no—
79C22×C4×D3—68no—
80C22×C4×D3—61no—
81C22×C4×D3—61no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C4×D3—616no—
85C22×C4×D3—616no—
86C2×C3×C4⋊C4—34no—
87C2×C3×C22⋊C4—34no—
88C2×#217C2×D314yes—
89C2×(C2×D3)⋊C4—38no—
90C2×(C2×D3)⋊C4—38no—
91C2×C4⋊Dic3C2×D314yescomplemented
92C2×C4×Dic3—38no—
93#892—616no—
94C3×#95—34no—
95C3⋊#95—38no—
96C3⋊#95C2×D314yescomplemented
97C23×C32—22no—
98C23×C32—22no—
99C23×C32C22×C412yes—
100C23×C32#4114yes—
101C23×C32C2411yescharacteristic
102C22×C3⋊D3—232no—
103C22×C3⋊D3—28no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—28no—
109C22×C3⋊D3—28no—
110C22×C3⋊D3C22×C412yes—
111C22×C3⋊D3C22×C412yes—
112C22×C3⋊D3C2×D414yes—
113C22×C3⋊D3#4114yes—
114C2×C32×C4—22no—
115C2×C32×C4—28no—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C2×D414yes—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—28no—
121C2×C3⋊Dic3C22×C412yes—
122C2×C3⋊Dic3C22×C412yes—
123C2×C3⋊Dic3C2×D414yes—
124C4×C3⋊D3—28no—
125C4×C3⋊D3—28no—
126C4×C3⋊D3—28no—
127C4×C3⋊D3C22⋊C4116yescomplemented
128C2×C3×Dic3—28no—
129C2×C3×Dic3—28no—
130C2×C3×Dic3—28no—
131C24×C4—91no—
132C2×#117—92no—
133#381—92no—
134#380—32no—
135#380—92no—
136#379—92no—
137C4×C22⋊C4—92no—
138C4×C22⋊C4—92no—
139C24×C3—21no—
140C24×C3C22×D312yes—
141C23×D3—32no—
142C23×D3—32no—
143C23×D3—38no—
144C23×D3—64no—
145C23×D3—61no—
146C23×D3—61no—
147C23×D3—68no—
148C23×D3—68no—
149C23×D3—68no—
150C23×D3—68no—
151C23×D3—68no—
152C23×D3—64no—
153C23×D3—64no—
154C22×C3×C4—28no—
155C22×C3×C4—28no—
156C22×C3×C4—24no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—38no—
160C22×C3×C4C4×D318yes—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—38no—
165C22×Dic3—32no—
166C22×Dic3—64no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—68no—
170C22×Dic3—68no—
171C22×Dic3C22×D318yes—
172C2×C4×D3—38no—
173C2×C4×D3—316no—
174C2×C4×D3—38no—
175C2×C4×D3—38no—
176C2×C4×D3—38no—
177C2×C4×D3—64no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×C4×D3—64no—
181C2×C4×D3—68no—
182C2×C4×D3—664no—
183C2×C4×D3—68no—
184C2×C4×D3—68no—
185C2×C4×D3—664no—
186C2×C4×D3—68no—
187C2×C4×D3—68no—
188C2×C4×D3—68no—
189C2×C4×D3—68no—
190C3×C4⋊C4—68no—
191C3×C22⋊C4—68no—
192#217—28no—
193(C2×D3)⋊C4—616no—
194(C2×D3)⋊C4—616no—
195C4⋊Dic3—28no—
196C4×Dic3—616no—
197C22×C32—22no—
198C22×C32—22no—
199C22×C32—28no—
200C22×C32#11714yescomplemented
201C22×C32C23×C411yescharacteristic
202C22×C32C22×D412yes—
203C22×C32C2×#4112yes—
204C22×C32C2×#4112yes—
205C2×C3⋊D3—232no—
206C2×C3⋊D3—22no—
207C2×C3⋊D3—22no—
208C2×C3⋊D3—22no—
209C2×C3⋊D3—22no—
210C2×C3⋊D3—28no—
211C2×C3⋊D3—28no—
212C2×C3⋊D3C2×C22⋊C414yes—
213C2×C3⋊D3#11714yescomplemented
214C32×C4—22no—
215C32×C4C2×C22⋊C414yes—
216C3⋊Dic3—22no—
217C3⋊Dic3C2×C22⋊C414yes—
218C3×Dic3—48no—
219C25—91no—
220C23×C4—91no—
221C23×C4—91no—
222C23×C4—98no—
223C23×C4—91no—
224C23×C4—91no—
225C23×C4—91no—
226C23×C4—188no—
227C23×C4D3211yescharacteristic
228#117—188no—
229C2×C4⋊C4—34no—
230C2×C22⋊C4—34no—
231C2×C22⋊C4—94no—
232C2×C22⋊C4—94no—
233C2×C42—94no—
234#95—34no—
235#95—94no—
236C23×C3—24no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3—21no—
241C23×C3—24no—
242C23×C3—22no—
243C23×C3C2×C4×D314yes—
244C23×C3#23714yes—
245C23×C3#23914yes—
246C23×C3C23×D312yes—
247C22×D3—34no—
248C22×D3—34no—
249C22×D3—38no—
250C22×D3—38no—
251C22×D3—62no—
252C22×D3—62no—
253C22×D3—64no—
254C22×D3—64no—
255C22×D3—616no—
256C22×D3—616no—
257C22×D3—616no—
258C22×D3—64no—
259C22×D3—616no—
260C22×D3—664no—
261C22×D3—632no—
262C22×D3—632no—
263C22×D3—64no—
264C22×D3—64no—
265C22×D3—64no—
266C22×D3—616no—
267C22×D3—616no—
268C22×D3—64no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—64no—
274C2×C3×C4—24no—
275C2×C3×C4—216no—
276C2×C3×C4—24no—
277C2×C3×C4—216no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—24no—
281C2×C3×C4—68no—
282C2×C3×C4—68no—
283C2×C3×C4—68no—
284C2×C3×C4C2×C4×D314yes—
285C2×C3×C4C2×C4×D314yes—
286C2×C3×C4D3×D418yes—
287C2×Dic3—28no—
288C2×Dic3—28no—
289C2×Dic3—28no—
290C2×Dic3—34no—
291C2×Dic3—38no—
292C2×Dic3—34no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—64no—
296C2×Dic3—616no—
297C2×Dic3—616no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300C4×D3—332no—
301C4×D3—616no—
302C4×D3—616no—
303C4×D3—616no—
304C4×D3—616no—
305C4×D3—616no—
306C4×D3—616no—
307C4×D3—616no—
308C2×C32—24no—
309C2×C32C22×C22⋊C411yescharacteristic
310C2×C32C2×#11711yescharacteristic
311C2×C32C2×#11711yescharacteristic
312C2×C32#52514yes—
313C3⋊D3—24no—
314C3⋊D3—24no—
315C24—91no—
316C24—91no—
317C24—94no—
318C24—184no—
319C24—184no—
320C24—184no—
321C24C2×D3211yescharacteristic
322C22×C4—24no—
323C22×C4—38no—
324C22×C4—91no—
325C22×C4—94no—
326C22×C4—98no—
327C22×C4—91no—
328C22×C4—94no—
329C22×C4—94no—
330C22×C4—94no—
331C22×C4—94no—
332C22×C4—184no—
333C22×C4—1832no—
334C22×C4—184no—
335C22×C4—184no—
336C22×C4—184no—
337C22×C4#62414yes—
338C22×C4C2×D3211yescharacteristic
339C22×C4C2×D3211yescharacteristic
340C4⋊C4—68no—
341C22⋊C4—68no—
342C22⋊C4—188no—
343C22⋊C4—188no—
344C42—188no—
345C22×C3—24no—
346C22×C3—216no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—24no—
350C22×C3—28no—
351C22×C3—28no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—24no—
357C22×C3#89218yescomplemented
358C22×C3C22×C4×D312yes—
359C22×C3C2×D3×D414yes—
360C22×C3C2×#23712yes—
361C22×C3C2×#23912yes—
362C22×C3D3×#4114yes—
363C2×D3—38no—
364C2×D3—38no—
365C2×D3—64no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—664no—
369C2×D3—664no—
370C2×D3—64no—
371C2×D3—64no—
372C2×D3—616no—
373C2×D3—616no—
374C2×D3—64no—
375C2×D3—64no—
376C2×D3—64no—
377C2×D3—64no—
378C2×D3—64no—
379C2×D3—68no—
380C2×D3—68no—
381C2×D3—68no—
382C2×D3—68no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—24no—
386C3×C4—128no—
387C3×C4D3×C22⋊C418yes—
388Dic3—38no—
389Dic3—48no—
390Dic3—64no—
391Dic3—64no—
392Dic3—64no—
393C32#228011yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—94no—
397C23—92no—
398C23—92no—
399C23—94no—
400C23—188no—
401C23—188no—
402C23—1832no—
403C23—182no—
404C23—182no—
405C23—182no—
406C23—182no—
407C23—188no—
408C23#379614yes—
409C23C2×#62412yes—
410C23C22×D3211yescharacteristic
411C2×C4—22no—
412C2×C4—28no—
413C2×C4—68no—
414C2×C4—68no—
415C2×C4—68no—
416C2×C4—92no—
417C2×C4—94no—
418C2×C4—916no—
419C2×C4—92no—
420C2×C4—188no—
421C2×C4—188no—
422C2×C4—188no—
423C2×C4—182no—
424C2×C4—188no—
425C2×C4C2×#62412yes—
426C2×C4C2×#62412yes—
427C2×C4#381114yes—
428C2×C3—28no—
429C2×C3—28no—
430C2×C3—21no—
431C2×C3—24no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3C2×D3×C22⋊C412yes—
435C2×C3C2×#89212yes—
436C2×C3D3×#11712yes—
437C2×C3#560614yes—
438C2×C3#562714yes—
439D3—68no—
440D3—68no—
441D3—68no—
442D3—68no—
443C22—28no—
444C22—22no—
445C22—22no—
446C22—94no—
447C22—94no—
448C22—1832no—
449C22—182no—
450C22—182no—
451C22—188no—
452C22—188no—
453C22—182no—
454C22—182no—
455C22#6384914yescomplemented
456C22C2×#379612yes—
457C22#6430612yes—
458C22C22×#62411yescharacteristic
459C22C2×#381112yes—
460C4—22no—
461C4—94no—
462C4—128no—
463C4—182no—
464C4#6397414yes—
465C3—21no—
466C3#7386212yescomplemented
467C2—24no—
468C2—184no—
469C2—184no—
470C2C2×#6384911yescharacteristic
471C2#1059492214yes—
472C2#1059496911yescharacteristic
473C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#2280
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63849C2semidirect
3. C3×#5212C2semidirect
5. #10591705C2semidirect
6. #10591325C2semidirect
7. #10591260C2semidirect
8. #10591219C2semidirect
14. C22×C4×C3⋊D3C4semidirect
20. C2×C3×C4⋊Dic3C22semidirect
23. C2×Dic32C22semidirect
25. C3×C3⋊#95C22semidirect
26. #63579C22semidirect
31. #5212D3semidirect
91. C2×C4⋊Dic3C2×D3semidirect
96. C3⋊#95C2×D3semidirect
127. C4×C3⋊D3C22⋊C4semidirect
200. C22×C32#117semidirect
213. C2×C3⋊D3#117semidirect
357. C22×C3#892semidirect
393. C32#2280semidirect
455. C22#63849semidirect
466. C3#73862semidirect

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×#638492
C3×#52122
#105917142
#105917052
#105913252
#105912602
#105912192
#738623