Finite Group Databasebeta

← C22×#63904 #11899901

Subgroups — C22×#63904 #11899901

Order 1152.

5393 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic
3C23×#624C211yesmaximal, characteristic, complemented
4C22×#3752C211yesmaximal, characteristic, complemented
5C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C22×Dic32C211yesmaximal, characteristic, complemented
8C2×#63904C2124yesmaximal, direct product factor
9C22×C4×#67—31nomaximal
10C22×#893—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×#626C4116yescomplemented
21C22×#626C22112yes—
22C22×#624—28no—
23C22×#624C22112yescomplemented
24C2×#3752C22112yescomplemented
25C2×C3×Dic3⋊C4C22112yescomplemented
26C2×(C2×D3)⋊Dic3C22112yescomplemented
27C2×Dic32C22112yescomplemented
28#63904C22164yesdirect product factor
29C24×C3×C4—31no—
30C23×#67—31no—
31C23×D12—31no—
32C23×C4×D3—31no—
33C23×C4×D3—31no—
34C23×C4×D3D311yescharacteristic, complemented
35C22×C3×C4⋊C4—31no—
36C22×#217—31no—
37C2×C4×#67—324no—
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4—31no—
40C22×(C2×D3)⋊C4—31no—
41C22×(C2×D3)⋊C4—61no—
42C22×Dic3⋊C4D311yescharacteristic, complemented
43C22×C4×Dic3—31no—
44C22×C4×Dic3—31no—
45C2×#893—324no—
46C24×C32C2311yescharacteristic
47C23×C3⋊D3—24no—
48C23×C3⋊D3—24no—
49C23×C3⋊D3C2×C418yescomplemented
50C23×C3⋊D3C2316yes—
51C23×C3×D3—24no—
52C23×C3×D3—24no—
53C23×C3×D3C2×C418yescomplemented
54C23×C3×D3C2316yes—
55C22×C32×C4—24no—
56C22×C32×C4C2316yes—
57C22×C3⋊Dic3—24no—
58C22×C3⋊Dic3C2316yes—
59C22×C3×Dic3—24no—
60C22×C3×Dic3C2×C418yescomplemented
61C22×C3×Dic3D418yescomplemented
62C22×C3×Dic3C2316yes—
63C22×C3×Dic3C2316yes—
64C22×C3×Dic3C2316yes—
65C2×C3×C4×D3—248no—
66C2×C3×C4×D3C23116yescomplemented
67C2×#626C2×C4196yescomplemented
68C2×#626C23116yes—
69C2×#624—248no—
70C2×#624C23116yescomplemented
71#3752C23116yescomplemented
72C3×Dic3⋊C4C23116yescomplemented
73(C2×D3)⋊Dic3C23116yescomplemented
74Dic32C23116yescomplemented
75C22×C4×D4—91noSylow
76C25×C3—31no—
77C24×D3—31no—
78C24×D3—31no—
79C24×D3—61no—
80C24×D3C2×D311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—31no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4—312no—
86C23×C3×C4—68no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C22×#67—316no—
90C22×#67—312no—
91C23×Dic3—31no—
92C23×Dic3—31no—
93C23×Dic3—61no—
94C23×Dic3C2×D311yescharacteristic
95C23×Dic3C2×D311yescharacteristic
96C23×Dic3C2×D311yescharacteristic
97C22×D12—316no—
98C22×D12—312no—
99C22×C4×D3—28no—
100C22×C4×D3—312no—
101C22×C4×D3—312no—
102C22×C4×D3—68no—
103C22×C4×D3—68no—
104C22×C4×D3C2×D3112yescomplemented
105C2×C3×C4⋊C4—312no—
106C2×#217—312no—
107C4×#67—364no—
108C2×(C2×D3)⋊C4—312no—
109C2×(C2×D3)⋊C4—312no—
110C2×(C2×D3)⋊C4—312no—
111C2×(C2×D3)⋊C4—612no—
112C2×Dic3⋊C4C2×D3112yescomplemented
113C2×C4×Dic3—312no—
114C2×C4×Dic3—312no—
115#893—364no—
116C23×C32C22×C414yes—
117C23×C32C2×D414yes—
118C23×C32#4114yes—
119C23×C32C2413yes—
120C22×C3⋊D3—232no—
121C22×C3⋊D3—212no—
122C22×C3⋊D3—212no—
123C22×C3⋊D3C22×C4124yescomplemented
124C22×C3⋊D3C2414yes—
125C22×C3×D3—232no—
126C22×C3×D3—212no—
127C22×C3×D3—212no—
128C22×C3×D3C22×C4124yescomplemented
129C22×C3×D3C2414yes—
130C2×C32×C4—212no—
131C2×C32×C4C2414yes—
132C2×C3⋊Dic3—212no—
133C2×C3⋊Dic3C2414yes—
134C2×C3×Dic3—212no—
135C2×C3×Dic3C22×C4124yescomplemented
136C2×C3×Dic3C2×D4124yescomplemented
137C2×C3×Dic3C2414yes—
138C2×C3×Dic3C2414yes—
139C2×C3×Dic3C2414yes—
140C3×C4×D3—232no—
141#626C22×C4164yescomplemented
142#624—232no—
143C23×D4—91no—
144C24×C4—31no—
145C24×C4—91no—
146C2×C4×D4—924no—
147C22×C4⋊C4—31no—
148C22×C22⋊C4—91no—
149C22×C22⋊C4—91no—
150C22×C42—91no—
151C24×C3—21no—
152C24×C3—38no—
153C24×C3—36no—
154C24×C3—64no—
155C24×C3—64no—
156C24×C3C22×D311yescharacteristic
157C24×C3C22×D311yescharacteristic
158C23×D3—24no—
159C23×D3—24no—
160C23×D3—38no—
161C23×D3—38no—
162C23×D3—36no—
163C23×D3—36no—
164C23×D3—68no—
165C23×D3—66no—
166C23×D3—64no—
167C23×D3—64no—
168C23×D3—64no—
169C23×D3—64no—
170C23×D3—124no—
171C23×D3—124no—
172C23×D3C4×D318yescomplemented
173C23×D3C22×D316yes—
174C22×C3×C4—24no—
175C22×C3×C4—24no—
176C22×C3×C4—26no—
177C22×C3×C4—38no—
178C22×C3×C4—38no—
179C22×C3×C4—36no—
180C22×C3×C4—36no—
181C22×C3×C4—36no—
182C22×C3×C4—316no—
183C22×C3×C4—44no—
184C22×C3×C4—648no—
185C22×C3×C4—64no—
186C22×C3×C4C22×D316yes—
187C22×C3×C4C22×D316yes—
188C2×#67—396no—
189C2×#67—316no—
190C22×Dic3—24no—
191C22×Dic3—36no—
192C22×Dic3—36no—
193C22×Dic3—66no—
194C22×Dic3—64no—
195C22×Dic3—64no—
196C22×Dic3—124no—
197C22×Dic3C4×D318yescomplemented
198C22×Dic3#6718yescomplemented
199C22×Dic3C22×D316yes—
200C22×Dic3C22×D316yes—
201C22×Dic3C22×D316yes—
202C2×D12—396no—
203C2×D12—316no—
204C2×C4×D3—248no—
205C2×C4×D3—316no—
206C2×C4×D3—316no—
207C2×C4×D3—648no—
208C2×C4×D3—648no—
209C2×C4×D3C22×D3116yescomplemented
210C3×C4⋊C4—316no—
211#217—316no—
212(C2×D3)⋊C4—316no—
213(C2×D3)⋊C4—316no—
214(C2×D3)⋊C4—316no—
215(C2×D3)⋊C4—616no—
216Dic3⋊C4C22×D3116yescomplemented
217C4×Dic3—316no—
218C4×Dic3—316no—
219C22×C32C4×D4116yescomplemented
220C22×C32C23×C416yes—
221C22×C32C22×D416yes—
222C22×C32C2×#4116yes—
223C22×C32C2511yescharacteristic
224C2×C3⋊D3—248no—
225C2×C3⋊D3—24no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3C23×C418yescomplemented
228C2×C3×D3—248no—
229C2×C3×D3—24no—
230C2×C3×D3—24no—
231C2×C3×D3C23×C418yescomplemented
232C32×C4—24no—
233C3⋊Dic3—24no—
234C3×Dic3—24no—
235C3×Dic3C23×C418yescomplemented
236C3×Dic3C22×D418yescomplemented
237C25—31no—
238C25—91no—
239C22×D4—912no—
240C22×D4—916no—
241C23×C4—31no—
242C23×C4—31no—
243C23×C4—31no—
244C23×C4—312no—
245C23×C4—68no—
246C23×C4—912no—
247C23×C4—91no—
248C23×C4—188no—
249C23×C4D3211yescharacteristic
250C4×D4—964no—
251C2×C4⋊C4—312no—
252C2×C22⋊C4—912no—
253C2×C22⋊C4—912no—
254C2×C42—912no—
255C23×C3—23no—
256C23×C3—24no—
257C23×C3—24no—
258C23×C3—24no—
259C23×C3—324no—
260C23×C3—34no—
261C23×C3—632no—
262C23×C3—612no—
263C23×C3—612no—
264C23×C3C2×C4×D314yes—
265C23×C3C2×C4×D314yes—
266C23×C3#23514yes—
267C23×C3D3×D414yes—
268C23×C3#23914yes—
269C23×C3C2×#6714yes—
270C23×C3C23×D313yes—
271C23×C3C23×D313yes—
272C22×D3—232no—
273C22×D3—212no—
274C22×D3—212no—
275C22×D3—324no—
276C22×D3—324no—
277C22×D3—34no—
278C22×D3—34no—
279C22×D3—624no—
280C22×D3—64no—
281C22×D3—632no—
282C22×D3—632no—
283C22×D3—612no—
284C22×D3—612no—
285C22×D3—612no—
286C22×D3—612no—
287C22×D3—1212no—
288C22×D3—1212no—
289C22×D3—1232no—
290C22×D3C2×C4×D3124yescomplemented
291C22×D3C23×D314yes—
292C2×C3×C4—212no—
293C2×C3×C4—212no—
294C2×C3×C4—24no—
295C2×C3×C4—324no—
296C2×C3×C4—324no—
297C2×C3×C4—34no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—412no—
301C2×C3×C4—632no—
302C2×C3×C4—612no—
303C2×C3×C4C23×D314yes—
304C2×C3×C4C23×D314yes—
305#67—364no—
306C2×Dic3—212no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—64no—
310C2×Dic3—612no—
311C2×Dic3—612no—
312C2×Dic3—1212no—
313C2×Dic3C2×C4×D3124yescomplemented
314C2×Dic3C2×#67124yescomplemented
315C2×Dic3C23×D314yes—
316C2×Dic3C23×D314yes—
317C2×Dic3C23×D314yes—
318D12—364no—
319C4×D3—232no—
320C4×D3—632no—
321C4×D3—632no—
322C2×C32C2×C4×D4112yescomplemented
323C2×C32C24×C411yescharacteristic
324C2×C32C23×D411yescharacteristic
325C2×C32C22×#4111yescharacteristic
326C3⋊D3—28no—
327C3×D3—28no—
328C24—36no—
329C24—38no—
330C24—64no—
331C24—64no—
332C24—96no—
333C24—98no—
334C24—184no—
335C24—184no—
336C24C2×D3211yescharacteristic
337C2×D4—916no—
338C2×D4—996no—
339C22×C4—24no—
340C22×C4—36no—
341C22×C4—36no—
342C22×C4—38no—
343C22×C4—38no—
344C22×C4—36no—
345C22×C4—316no—
346C22×C4—648no—
347C22×C4—64no—
348C22×C4—916no—
349C22×C4—96no—
350C22×C4—1848no—
351C22×C4—184no—
352C22×C4C2×D3216yes—
353C4⋊C4—316no—
354C22⋊C4—916no—
355C22⋊C4—916no—
356C42—916no—
357C22×C3—26no—
358C22×C3—26no—
359C22×C3—26no—
360C22×C3—21no—
361C22×C3—216no—
362C22×C3—38no—
363C22×C3—64no—
364C22×C3—64no—
365C22×C3—648no—
366C22×C3#893116yescomplemented
367C22×C3C4×#67116yescomplemented
368C22×C3C22×C4×D316yes—
369C22×C3C22×C4×D316yes—
370C22×C3C2×#23516yes—
371C22×C3C2×D3×D416yes—
372C22×C3C2×#23916yes—
373C22×C3C22×#6716yes—
374C22×C3C24×D311yescharacteristic
375C22×C3C24×D311yescharacteristic
376C2×D3—24no—
377C2×D3—24no—
378C2×D3—248no—
379C2×D3—38no—
380C2×D3—38no—
381C2×D3—68no—
382C2×D3—64no—
383C2×D3—64no—
384C2×D3—64no—
385C2×D3—64no—
386C2×D3—648no—
387C2×D3—648no—
388C2×D3—124no—
389C2×D3—124no—
390C2×D3—1248no—
391C2×D3C22×C4×D318yescomplemented
392C3×C4—24no—
393C3×C4—24no—
394C3×C4—38no—
395C3×C4—38no—
396C3×C4—44no—
397C3×C4—64no—
398Dic3—24no—
399Dic3—64no—
400Dic3—64no—
401Dic3—124no—
402Dic3C22×C4×D318yescomplemented
403Dic3C22×#6718yescomplemented
404C32C22×C4×D411yescharacteristic, complemented, Sylow
405C23—324no—
406C23—34no—
407C23—612no—
408C23—612no—
409C23—632no—
410C23—924no—
411C23—94no—
412C23—1812no—
413C23—1812no—
414C23—1832no—
415C23#379914yes—
416C23C4×D3214yes—
417C23D3×#6714yes—
418C23C22×D3213yes—
419D4—964no—
420C2×C4—212no—
421C2×C4—324no—
422C2×C4—324no—
423C2×C4—34no—
424C2×C4—34no—
425C2×C4—34no—
426C2×C4—632no—
427C2×C4—612no—
428C2×C4—94no—
429C2×C4—1832no—
430C2×C4—1812no—
431C2×C4C22×D3214yes—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—212no—
436C2×C3—68no—
437C2×C3C2×#893112yescomplemented
438C2×C3C2×C4×#67112yescomplemented
439C2×C3C23×C4×D311yescharacteristic
440C2×C3C23×C4×D311yescharacteristic
441C2×C3C22×#23511yescharacteristic
442C2×C3C22×D3×D411yescharacteristic
443C2×C3C22×#23911yescharacteristic
444C2×C3C23×#6711yescharacteristic
445D3—28no—
446D3—68no—
447D3—68no—
448D3—128no—
449C22—38no—
450C22—64no—
451C22—64no—
452C22—648no—
453C22—98no—
454C22—184no—
455C22—184no—
456C22—1848no—
457C22#63904116yesdirect product factor
458C22C2×#379916yes—
459C22C2×C4×D3216yes—
460C22C2×D3×#6716yes—
461C22C23×D3211yescharacteristic
462C4—24no—
463C4—38no—
464C4—38no—
465C4—64no—
466C4—184no—
467C3—21no—
468C3C22×#89311yescharacteristic, complemented
469C3C22×C4×#6711yescharacteristic, complemented
470C2—68no—
471C2—188no—
472C2C2×#63904112yesdirect product factor
473C2C22×#379911yescharacteristic
474C2C22×C4×D3211yescharacteristic
475C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC23×#626C2
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×#624C2semidirect
4. C22×#3752C2semidirect
5. C22×C3×Dic3⋊C4C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C22×Dic32C2semidirect
8. C2×#63904C2direct (N × H)
19. C22×C3×C4×D3C22semidirect
20. C22×#626C4semidirect
23. C22×#624C22semidirect
24. C2×#3752C22semidirect
25. C2×C3×Dic3⋊C4C22semidirect
26. C2×(C2×D3)⋊Dic3C22semidirect
27. C2×Dic32C22semidirect
28. #63904C22direct (N × H)
34. C23×C4×D3D3semidirect
42. C22×Dic3⋊C4D3semidirect
49. C23×C3⋊D3C2×C4semidirect
53. C23×C3×D3C2×C4semidirect
60. C22×C3×Dic3C2×C4semidirect
61. C22×C3×Dic3D4semidirect
66. C2×C3×C4×D3C23semidirect
67. C2×#626C2×C4semidirect
70. C2×#624C23semidirect
71. #3752C23semidirect
72. C3×Dic3⋊C4C23semidirect
73. (C2×D3)⋊Dic3C23semidirect
74. Dic32C23semidirect
104. C22×C4×D3C2×D3semidirect
112. C2×Dic3⋊C4C2×D3semidirect
123. C22×C3⋊D3C22×C4semidirect
128. C22×C3×D3C22×C4semidirect
135. C2×C3×Dic3C22×C4semidirect
136. C2×C3×Dic3C2×D4semidirect
141. #626C22×C4semidirect
172. C23×D3C4×D3semidirect
197. C22×Dic3C4×D3semidirect
198. C22×Dic3#67semidirect
209. C2×C4×D3C22×D3semidirect
216. Dic3⋊C4C22×D3semidirect
219. C22×C32C4×D4semidirect
227. C2×C3⋊D3C23×C4semidirect
231. C2×C3×D3C23×C4semidirect
235. C3×Dic3C23×C4semidirect
236. C3×Dic3C22×D4semidirect
290. C22×D3C2×C4×D3semidirect
313. C2×Dic3C2×C4×D3semidirect
314. C2×Dic3C2×#67semidirect
322. C2×C32C2×C4×D4semidirect
366. C22×C3#893semidirect
367. C22×C3C4×#67semidirect
391. C2×D3C22×C4×D3semidirect
402. Dic3C22×C4×D3semidirect
403. Dic3C22×#67semidirect
404. C32C22×C4×D4semidirect
437. C2×C3C2×#893semidirect
438. C2×C3C2×C4×#67semidirect
457. C22#63904direct (N × H)
468. C3C22×#893semidirect
469. C3C22×C4×#67semidirect
472. C2C2×#63904direct (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×#6262
C23×#6242
C22×#37522
C22×C3×Dic3⋊C42
C22×(C2×D3)⋊Dic32
C22×Dic322
C2×#639042
C22×C4×#673
C22×#8933