Finite Group Databasebeta

← C22×#63879 #11899903

Subgroups — C22×#63879 #11899903

Order 1152.

5265 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C23×#625C211yesmaximal, characteristic
3C23×D3×Dic3C211yesmaximal, characteristic, complemented
4C22×#3750C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C22×Dic32C211yesmaximal, characteristic, complemented
8C2×#63879C2124yesmaximal, direct product factor
9C22×C4×#67—31nomaximal
10C22×#67⋊C4—31nomaximal
11C24×C3×D3C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3—28no—
19C22×C3×C4×D3C22112yescomplemented
20C22×#625C4116yescomplemented
21C22×#625C22112yes—
22C22×D3×Dic3—28no—
23C22×D3×Dic3C22112yescomplemented
24C2×#3750C22112yescomplemented
25C2×C3×(C2×D3)⋊C4C22112yescomplemented
26C2×(C2×D3)⋊Dic3C22112yescomplemented
27C2×Dic32C22112yescomplemented
28#63879C22164yesdirect product factor
29C24×C3×C4—31no—
30C23×#67—31no—
31C23×#67—31no—
32C24×Dic3—31no—
33C23×C4×D3—31no—
34C23×C4×D3D311yescharacteristic, complemented
35C22×C3×C22⋊C4—31no—
36C22×#217—31no—
37C2×C4×#67—324no—
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4D311yescharacteristic, complemented
40C22×Dic3⋊C4—31no—
41C22×Dic3⋊C4—31no—
42C22×Dic3⋊C4—61no—
43C22×C4×Dic3—31no—
44C22×C4×Dic3—31no—
45C2×#67⋊C4—324no—
46C24×C32C2311yescharacteristic
47C23×C3×D3—24no—
48C23×C3×D3—24no—
49C23×C3×D3—24no—
50C23×C3×D3—24no—
51C23×C3×D3C2×C418yescomplemented
52C23×C3×D3C2×C418yescomplemented
53C23×C3×D3C2316yes—
54C23×C3×D3C2316yes—
55C22×C32×C4—24no—
56C22×C32×C4C2316yes—
57C22×C3⋊Dic3—24no—
58C22×C3⋊Dic3C2×C418yescomplemented
59C22×C3⋊Dic3C2316yes—
60C22×C3⋊Dic3C2316yes—
61C22×C3×Dic3—24no—
62C22×C3×Dic3D418yescomplemented
63C22×C3×Dic3C2316yes—
64C22×C3×Dic3C2316yes—
65C2×C3×C4×D3—248no—
66C2×C3×C4×D3C23116yescomplemented
67C2×#625C2×C4196yescomplemented
68C2×#625C23116yes—
69C2×D3×Dic3—248no—
70C2×D3×Dic3C23116yescomplemented
71#3750C23116yescomplemented
72C3×(C2×D3)⋊C4C23116yescomplemented
73(C2×D3)⋊Dic3C23116yescomplemented
74Dic32C23116yescomplemented
75C22×C4×D4—91noSylow
76C25×C3—31no—
77C25×C3—31no—
78C24×D3C2×D311yescharacteristic
79C24×D3C2×D311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4—31no—
82C23×C3×C4—31no—
83C23×C3×C4—312no—
84C23×C3×C4—68no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C22×#67—316no—
88C22×#67—316no—
89C22×#67—312no—
90C22×#67—312no—
91C23×Dic3—31no—
92C23×Dic3—31no—
93C23×Dic3—31no—
94C23×Dic3—31no—
95C23×Dic3—312no—
96C23×Dic3—61no—
97C23×Dic3—61no—
98C23×Dic3—68no—
99C23×Dic3C2×D311yescharacteristic
100C23×Dic3C2×D311yescharacteristic
101C22×C4×D3—28no—
102C22×C4×D3—312no—
103C22×C4×D3—68no—
104C22×C4×D3C2×D3112yescomplemented
105C2×C3×C22⋊C4—312no—
106C2×#217—312no—
107C4×#67—364no—
108C2×(C2×D3)⋊C4—312no—
109C2×(C2×D3)⋊C4C2×D3112yescomplemented
110C2×Dic3⋊C4—312no—
111C2×Dic3⋊C4—312no—
112C2×Dic3⋊C4—612no—
113C2×C4×Dic3—312no—
114C2×C4×Dic3—312no—
115#67⋊C4—364no—
116C23×C32C22×C414yes—
117C23×C32C2×D414yes—
118C23×C32#4114yes—
119C23×C32C2413yes—
120C22×C3×D3—232no—
121C22×C3×D3—232no—
122C22×C3×D3—212no—
123C22×C3×D3—212no—
124C22×C3×D3—212no—
125C22×C3×D3—212no—
126C22×C3×D3C22×C4124yescomplemented
127C22×C3×D3C22×C4124yescomplemented
128C22×C3×D3C2414yes—
129C22×C3×D3C2414yes—
130C2×C32×C4—212no—
131C2×C32×C4C2414yes—
132C2×C3⋊Dic3—212no—
133C2×C3⋊Dic3C22×C4124yescomplemented
134C2×C3⋊Dic3C2414yes—
135C2×C3⋊Dic3C2414yes—
136C2×C3×Dic3—212no—
137C2×C3×Dic3C2×D4124yescomplemented
138C2×C3×Dic3C2414yes—
139C2×C3×Dic3C2414yes—
140C3×C4×D3—232no—
141#625C22×C4164yescomplemented
142D3×Dic3—232no—
143C23×D4—91no—
144C24×C4—31no—
145C24×C4—91no—
146C2×C4×D4—924no—
147C22×C4⋊C4—91no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—91no—
150C22×C42—91no—
151C24×C3—21no—
152C24×C3—38no—
153C24×C3—38no—
154C24×C3—36no—
155C24×C3—36no—
156C24×C3—64no—
157C24×C3—64no—
158C24×C3—64no—
159C24×C3—64no—
160C24×C3C22×D311yescharacteristic
161C24×C3C22×D311yescharacteristic
162C23×D3—24no—
163C23×D3—24no—
164C23×D3—24no—
165C23×D3—24no—
166C23×D3C4×D318yescomplemented
167C23×D3C4×D318yescomplemented
168C23×D3C22×D316yes—
169C23×D3C22×D316yes—
170C22×C3×C4—24no—
171C22×C3×C4—24no—
172C22×C3×C4—26no—
173C22×C3×C4—38no—
174C22×C3×C4—36no—
175C22×C3×C4—36no—
176C22×C3×C4—316no—
177C22×C3×C4—44no—
178C22×C3×C4—648no—
179C22×C3×C4—64no—
180C22×C3×C4C22×D316yes—
181C22×C3×C4C22×D316yes—
182C2×#67—396no—
183C2×#67—396no—
184C2×#67—316no—
185C2×#67—316no—
186C22×Dic3—24no—
187C22×Dic3—38no—
188C22×Dic3—38no—
189C22×Dic3—36no—
190C22×Dic3—36no—
191C22×Dic3—36no—
192C22×Dic3—36no—
193C22×Dic3—316no—
194C22×Dic3—66no—
195C22×Dic3—68no—
196C22×Dic3—66no—
197C22×Dic3—64no—
198C22×Dic3—64no—
199C22×Dic3—648no—
200C22×Dic3—124no—
201C22×Dic3#6718yescomplemented
202C22×Dic3C22×D316yes—
203C22×Dic3C22×D316yes—
204C2×C4×D3—248no—
205C2×C4×D3—316no—
206C2×C4×D3—648no—
207C2×C4×D3C22×D3116yescomplemented
208C3×C22⋊C4—316no—
209#217—316no—
210(C2×D3)⋊C4—316no—
211(C2×D3)⋊C4C22×D3116yescomplemented
212Dic3⋊C4—316no—
213Dic3⋊C4—316no—
214Dic3⋊C4—616no—
215C4×Dic3—316no—
216C4×Dic3—316no—
217C22×C32C4×D4116yescomplemented
218C22×C32C23×C416yes—
219C22×C32C22×D416yes—
220C22×C32C2×#4116yes—
221C22×C32C2511yescharacteristic
222C2×C3×D3—248no—
223C2×C3×D3—248no—
224C2×C3×D3—24no—
225C2×C3×D3—24no—
226C2×C3×D3—24no—
227C2×C3×D3—24no—
228C2×C3×D3C23×C418yescomplemented
229C2×C3×D3C23×C418yescomplemented
230C32×C4—24no—
231C3⋊Dic3—24no—
232C3⋊Dic3C23×C418yescomplemented
233C3×Dic3—24no—
234C3×Dic3C22×D418yescomplemented
235C25—31no—
236C25—31no—
237C22×D4—912no—
238C22×D4—916no—
239C23×C4—31no—
240C23×C4—31no—
241C23×C4—312no—
242C23×C4—68no—
243C23×C4—912no—
244C23×C4—91no—
245C23×C4—91no—
246C23×C4—188no—
247C23×C4D3211yescharacteristic
248C4×D4—964no—
249C2×C4⋊C4—912no—
250C2×C22⋊C4—312no—
251C2×C22⋊C4—912no—
252C2×C42—912no—
253C23×C3—23no—
254C23×C3—24no—
255C23×C3—24no—
256C23×C3—24no—
257C23×C3—324no—
258C23×C3—324no—
259C23×C3—34no—
260C23×C3—34no—
261C23×C3—632no—
262C23×C3—632no—
263C23×C3—612no—
264C23×C3—612no—
265C23×C3—612no—
266C23×C3—612no—
267C23×C3C2×C4×D314yes—
268C23×C3C2×C4×D314yes—
269C23×C3#23514yes—
270C23×C3D3×D414yes—
271C23×C3#23714yes—
272C23×C3C2×#6714yes—
273C23×C3C23×D313yes—
274C23×C3C23×D313yes—
275C22×D3—232no—
276C22×D3—232no—
277C22×D3—212no—
278C22×D3—212no—
279C22×D3—212no—
280C22×D3—212no—
281C22×D3C2×C4×D3124yescomplemented
282C22×D3C2×C4×D3124yescomplemented
283C22×D3C23×D314yes—
284C22×D3C23×D314yes—
285C2×C3×C4—212no—
286C2×C3×C4—212no—
287C2×C3×C4—24no—
288C2×C3×C4—324no—
289C2×C3×C4—34no—
290C2×C3×C4—34no—
291C2×C3×C4—412no—
292C2×C3×C4—632no—
293C2×C3×C4—612no—
294C2×C3×C4C23×D314yes—
295C2×C3×C4C23×D314yes—
296#67—364no—
297#67—364no—
298C2×Dic3—212no—
299C2×Dic3—324no—
300C2×Dic3—324no—
301C2×Dic3—34no—
302C2×Dic3—34no—
303C2×Dic3—34no—
304C2×Dic3—34no—
305C2×Dic3—624no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—612no—
309C2×Dic3—612no—
310C2×Dic3—632no—
311C2×Dic3—1212no—
312C2×Dic3C2×#67124yescomplemented
313C2×Dic3C23×D314yes—
314C2×Dic3C23×D314yes—
315C4×D3—232no—
316C4×D3—632no—
317C2×C32C2×C4×D4112yescomplemented
318C2×C32C24×C411yescharacteristic
319C2×C32C23×D411yescharacteristic
320C2×C32C22×#4111yescharacteristic
321C3×D3—28no—
322C3×D3—28no—
323C24—36no—
324C24—36no—
325C24—38no—
326C24—38no—
327C24—64no—
328C24—64no—
329C24—64no—
330C24—64no—
331C24C2×D3211yescharacteristic
332C2×D4—916no—
333C2×D4—996no—
334C22×C4—24no—
335C22×C4—36no—
336C22×C4—38no—
337C22×C4—36no—
338C22×C4—316no—
339C22×C4—648no—
340C22×C4—64no—
341C22×C4—916no—
342C22×C4—96no—
343C22×C4—98no—
344C22×C4—96no—
345C22×C4—1848no—
346C22×C4—184no—
347C22×C4C2×D3216yes—
348C4⋊C4—916no—
349C22⋊C4—316no—
350C22⋊C4—916no—
351C42—916no—
352C22×C3—26no—
353C22×C3—26no—
354C22×C3—26no—
355C22×C3—216no—
356C22×C3—21no—
357C22×C3—38no—
358C22×C3—38no—
359C22×C3—64no—
360C22×C3—64no—
361C22×C3—64no—
362C22×C3—64no—
363C22×C3—648no—
364C22×C3—648no—
365C22×C3#67⋊C4116yescomplemented
366C22×C3C4×#67116yescomplemented
367C22×C3C22×C4×D316yes—
368C22×C3C22×C4×D316yes—
369C22×C3C2×#23516yes—
370C22×C3C2×D3×D416yes—
371C22×C3C2×#23716yes—
372C22×C3C22×#6716yes—
373C22×C3C24×D311yescharacteristic
374C22×C3C24×D311yescharacteristic
375C2×D3—24no—
376C2×D3—24no—
377C2×D3—24no—
378C2×D3—24no—
379C2×D3—248no—
380C2×D3—248no—
381C2×D3C22×C4×D318yescomplemented
382C2×D3C22×C4×D318yescomplemented
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—38no—
386C3×C4—44no—
387C3×C4—64no—
388Dic3—24no—
389Dic3—38no—
390Dic3—38no—
391Dic3—68no—
392Dic3—64no—
393Dic3—64no—
394Dic3—124no—
395Dic3C22×#6718yescomplemented
396C32C22×C4×D411yescharacteristic, complemented, Sylow
397C23—324no—
398C23—324no—
399C23—34no—
400C23—34no—
401C23—612no—
402C23—612no—
403C23—612no—
404C23—612no—
405C23—632no—
406C23—632no—
407C23#379514yes—
408C23C4×D3214yes—
409C23D3×#6714yes—
410C23C22×D3213yes—
411D4—964no—
412C2×C4—212no—
413C2×C4—324no—
414C2×C4—34no—
415C2×C4—34no—
416C2×C4—632no—
417C2×C4—612no—
418C2×C4—924no—
419C2×C4—94no—
420C2×C4—94no—
421C2×C4—1832no—
422C2×C4—1812no—
423C2×C4C22×D3214yes—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—212no—
427C2×C3—21no—
428C2×C3—68no—
429C2×C3—68no—
430C2×C3C2×#67⋊C4112yescomplemented
431C2×C3C2×C4×#67112yescomplemented
432C2×C3C23×C4×D311yescharacteristic
433C2×C3C23×C4×D311yescharacteristic
434C2×C3C22×#23511yescharacteristic
435C2×C3C22×D3×D411yescharacteristic
436C2×C3C22×#23711yescharacteristic
437C2×C3C23×#6711yescharacteristic
438D3—28no—
439D3—28no—
440C22—38no—
441C22—38no—
442C22—64no—
443C22—64no—
444C22—648no—
445C22—648no—
446C22—64no—
447C22—64no—
448C22#63879116yesdirect product factor
449C22C2×#379516yes—
450C22C2×C4×D3216yes—
451C22C2×D3×#6716yes—
452C22C23×D3211yescharacteristic
453C4—24no—
454C4—38no—
455C4—64no—
456C4—98no—
457C4—184no—
458C3—21no—
459C3C22×#67⋊C411yescharacteristic, complemented
460C3C22×C4×#6711yescharacteristic, complemented
461C2—68no—
462C2—68no—
463C2C2×#63879112yesdirect product factor
464C2C22×#379511yescharacteristic
465C2C22×C4×D3211yescharacteristic
466C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC23×#625C2
cosocleC22×C32C25
hypercenterC23×C4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
3. C23×D3×Dic3C2semidirect
4. C22×#3750C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C22×Dic32C2semidirect
8. C2×#63879C2direct (N × H)
19. C22×C3×C4×D3C22semidirect
20. C22×#625C4semidirect
23. C22×D3×Dic3C22semidirect
24. C2×#3750C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×(C2×D3)⋊Dic3C22semidirect
27. C2×Dic32C22semidirect
28. #63879C22direct (N × H)
34. C23×C4×D3D3semidirect
39. C22×(C2×D3)⋊C4D3semidirect
51. C23×C3×D3C2×C4semidirect
52. C23×C3×D3C2×C4semidirect
58. C22×C3⋊Dic3C2×C4semidirect
62. C22×C3×Dic3D4semidirect
66. C2×C3×C4×D3C23semidirect
67. C2×#625C2×C4semidirect
70. C2×D3×Dic3C23semidirect
71. #3750C23semidirect
72. C3×(C2×D3)⋊C4C23semidirect
73. (C2×D3)⋊Dic3C23semidirect
74. Dic32C23semidirect
104. C22×C4×D3C2×D3semidirect
109. C2×(C2×D3)⋊C4C2×D3semidirect
126. C22×C3×D3C22×C4semidirect
127. C22×C3×D3C22×C4semidirect
133. C2×C3⋊Dic3C22×C4semidirect
137. C2×C3×Dic3C2×D4semidirect
141. #625C22×C4semidirect
166. C23×D3C4×D3semidirect
167. C23×D3C4×D3semidirect
201. C22×Dic3#67semidirect
207. C2×C4×D3C22×D3semidirect
211. (C2×D3)⋊C4C22×D3semidirect
217. C22×C32C4×D4semidirect
228. C2×C3×D3C23×C4semidirect
229. C2×C3×D3C23×C4semidirect
232. C3⋊Dic3C23×C4semidirect
234. C3×Dic3C22×D4semidirect
281. C22×D3C2×C4×D3semidirect
282. C22×D3C2×C4×D3semidirect
312. C2×Dic3C2×#67semidirect
317. C2×C32C2×C4×D4semidirect
365. C22×C3#67⋊C4semidirect
366. C22×C3C4×#67semidirect
381. C2×D3C22×C4×D3semidirect
382. C2×D3C22×C4×D3semidirect
395. Dic3C22×#67semidirect
396. C32C22×C4×D4semidirect
430. C2×C3C2×#67⋊C4semidirect
431. C2×C3C2×C4×#67semidirect
448. C22#63879direct (N × H)
459. C3C22×#67⋊C4semidirect
460. C3C22×C4×#67semidirect
463. C2C2×#63879direct (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
C23×#6252
C23×D3×Dic32
C22×#37502
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C22×Dic322
C2×#638792
C22×C4×#673
C22×#67⋊C43