Finite Group Databasebeta

← C22×#63858 #11900566

Subgroups — C22×#63858 #11900566

Order 1152.

2849 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C22×Dic32C211yesmaximal, characteristic, complemented
8C2×#63858C2124yesmaximal, direct product factor
9C22×#898—31nomaximal
10C22×#879—31nomaximal
11C24×C3×D3C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×#3750C22112yescomplemented
19C2×C3×(C2×D3)⋊C4C22112yes—
20C2×C3×C4⋊Dic3C22112yescomplemented
21C2×Dic3⋊Dic3C22112yescomplemented
22C2×(C2×D3)⋊Dic3C22112yes—
23C2×(C2×D3)⋊Dic3C22112yes—
24C2×Dic32C22112yescomplemented
25#63858C22164yesdirect product factor
26C22×C3×C4⋊C4—31no—
27C22×C3×C22⋊C4—31no—
28C22×#217—31no—
29C22×#217—31no—
30C22×(C2×D3)⋊C4—31no—
31C22×(C2×D3)⋊C4—31no—
32C22×(C2×D3)⋊C4D311yescharacteristic
33C22×C4⋊Dic3—31no—
34C22×C4⋊Dic3D311yescharacteristic, complemented
35C22×Dic3⋊C4—31no—
36C22×Dic3⋊C4—31no—
37C22×Dic3⋊C4—31no—
38C22×Dic3⋊C4—61no—
39C22×C4×Dic3—31no—
40C22×C4×Dic3—31no—
41C2×#898—324no—
42C2×#879—324no—
43C24×C32C2311yescharacteristic
44C23×C3×D3—24no—
45C23×C3×D3—24no—
46C23×C3×D3—24no—
47C23×C3×D3C2316yes—
48C22×C32×C4—24no—
49C22×C32×C4C2316yes—
50C22×C3⋊Dic3—24no—
51C22×C3⋊Dic3—24no—
52C22×C3⋊Dic3C2316yes—
53C22×C3⋊Dic3C2316yes—
54C22×C3×Dic3—24no—
55C22×C3×Dic3—24no—
56C22×C3×Dic3—24no—
57C22×C3×Dic3C2316yes—
58C22×C3×Dic3C2316yes—
59C22×C3×Dic3C2316yes—
60#3750C23116yescomplemented
61C3×(C2×D3)⋊C4C23116yes—
62C3×C4⋊Dic3C23116yescomplemented
63Dic3⋊Dic3C23116yescomplemented
64(C2×D3)⋊Dic3C23116yes—
65(C2×D3)⋊Dic3C23116yes—
66Dic32C23116yescomplemented
67C22×#126—91noSylow
68C25×C3—31no—
69C24×D3C2×D311yescharacteristic
70C23×C3×C4—21no—
71C23×C3×C4—31no—
72C23×C3×C4—31no—
73C23×C3×C4—31no—
74C23×C3×C4C2×D311yescharacteristic
75C23×C3×C4C2×D311yescharacteristic
76C23×Dic3—31no—
77C23×Dic3—31no—
78C23×Dic3—31no—
79C23×Dic3—31no—
80C23×Dic3—61no—
81C23×Dic3—61no—
82C23×Dic3C2×D311yescharacteristic
83C23×Dic3C2×D311yescharacteristic
84C23×Dic3C2×D311yescharacteristic
85C2×C3×C4⋊C4—312no—
86C2×C3×C22⋊C4—312no—
87C2×#217—312no—
88C2×#217—312no—
89C2×(C2×D3)⋊C4—312no—
90C2×(C2×D3)⋊C4—312no—
91C2×(C2×D3)⋊C4C2×D3112yes—
92C2×C4⋊Dic3—312no—
93C2×C4⋊Dic3C2×D3112yescomplemented
94C2×Dic3⋊C4—312no—
95C2×Dic3⋊C4—312no—
96C2×Dic3⋊C4—312no—
97C2×Dic3⋊C4—612no—
98C2×C4×Dic3—312no—
99C2×C4×Dic3—312no—
100#898—364no—
101#879—364no—
102C23×C32#4114yes—
103C23×C32#4114yes—
104C23×C32#4114yes—
105C23×C32C2413yes—
106C22×C3×D3—212no—
107C22×C3×D3—212no—
108C22×C3×D3—212no—
109C22×C3×D3—416no—
110C22×C3×D3C2414yes—
111C2×C32×C4—212no—
112C2×C32×C4C2414yes—
113C2×C3⋊Dic3—212no—
114C2×C3⋊Dic3—212no—
115C2×C3⋊Dic3C2414yes—
116C2×C3⋊Dic3C2414yes—
117C2×C3×Dic3—212no—
118C2×C3×Dic3—212no—
119C2×C3×Dic3—212no—
120C2×C3×Dic3C2414yes—
121C2×C3×Dic3C2414yes—
122C2×C3×Dic3C2414yes—
123C2×#126—924no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4—91no—
126C22×C4⋊C4—91no—
127C22×C22⋊C4—31no—
128C22×C22⋊C4—91no—
129C22×C22⋊C4—91no—
130C22×C42—91no—
131C24×C3—21no—
132C24×C3—36no—
133C24×C3—64no—
134C24×C3—64no—
135C24×C3—64no—
136C24×C3C22×D311yescharacteristic
137C24×C3C22×D311yescharacteristic
138C23×D3—24no—
139C23×D3—24no—
140C23×D3—24no—
141C23×D3C22×D316yes—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—26no—
145C22×C3×C4—36no—
146C22×C3×C4—36no—
147C22×C3×C4—36no—
148C22×C3×C4—44no—
149C22×C3×C4—64no—
150C22×C3×C4—64no—
151C22×C3×C4—64no—
152C22×C3×C4C22×D316yes—
153C22×C3×C4C22×D316yes—
154C22×Dic3—24no—
155C22×Dic3—24no—
156C22×Dic3—24no—
157C22×Dic3—36no—
158C22×Dic3—36no—
159C22×Dic3—36no—
160C22×Dic3—36no—
161C22×Dic3—66no—
162C22×Dic3—66no—
163C22×Dic3—68no—
164C22×Dic3—64no—
165C22×Dic3—64no—
166C22×Dic3—64no—
167C22×Dic3—64no—
168C22×Dic3—124no—
169C22×Dic3C22×D316yes—
170C22×Dic3C22×D316yes—
171C22×Dic3C22×D316yes—
172C3×C4⋊C4—316no—
173C3×C22⋊C4—316no—
174#217—316no—
175#217—316no—
176(C2×D3)⋊C4—316no—
177(C2×D3)⋊C4—316no—
178(C2×D3)⋊C4C22×D3116yes—
179C4⋊Dic3—316no—
180C4⋊Dic3C22×D3116yescomplemented
181Dic3⋊C4—316no—
182Dic3⋊C4—316no—
183Dic3⋊C4—316no—
184Dic3⋊C4—616no—
185C4×Dic3—316no—
186C4×Dic3—316no—
187C22×C32#126116yescomplemented
188C22×C32C2×#4116yes—
189C22×C32C2×#4116yes—
190C22×C32C2×#4116yes—
191C22×C32C2511yescharacteristic
192C2×C3×D3—24no—
193C2×C3×D3—24no—
194C2×C3×D3—24no—
195C2×C3×D3—424no—
196C32×C4—24no—
197C3⋊Dic3—24no—
198C3⋊Dic3—24no—
199C3×Dic3—24no—
200C3×Dic3—24no—
201C3×Dic3—24no—
202C25—31no—
203C23×C4—31no—
204C23×C4—31no—
205C23×C4—31no—
206C23×C4—91no—
207C23×C4—91no—
208C23×C4D3211yescharacteristic
209#126—964no—
210C2×C4⋊C4—312no—
211C2×C4⋊C4—912no—
212C2×C4⋊C4—912no—
213C2×C22⋊C4—312no—
214C2×C22⋊C4—912no—
215C2×C22⋊C4—912no—
216C2×C42—912no—
217C23×C3—23no—
218C23×C3—24no—
219C23×C3—24no—
220C23×C3—24no—
221C23×C3—34no—
222C23×C3—612no—
223C23×C3—612no—
224C23×C3—612no—
225C23×C3—1216no—
226C23×C3#23514yes—
227C23×C3#23514yes—
228C23×C3#23714yes—
229C23×C3#23714yes—
230C23×C3#23714yes—
231C23×C3#23914yes—
232C23×C3C23×D313yes—
233C23×C3C23×D313yes—
234C22×D3—212no—
235C22×D3—212no—
236C22×D3—212no—
237C22×D3—416no—
238C22×D3C23×D314yes—
239C2×C3×C4—212no—
240C2×C3×C4—212no—
241C2×C3×C4—24no—
242C2×C3×C4—34no—
243C2×C3×C4—34no—
244C2×C3×C4—34no—
245C2×C3×C4—412no—
246C2×C3×C4—612no—
247C2×C3×C4—612no—
248C2×C3×C4—612no—
249C2×C3×C4C23×D314yes—
250C2×C3×C4C23×D314yes—
251C2×Dic3—212no—
252C2×Dic3—212no—
253C2×Dic3—212no—
254C2×Dic3—34no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—624no—
261C2×Dic3—612no—
262C2×Dic3—612no—
263C2×Dic3—612no—
264C2×Dic3—612no—
265C2×Dic3—1212no—
266C2×Dic3C23×D314yes—
267C2×Dic3C23×D314yes—
268C2×Dic3C23×D314yes—
269C2×C32C2×#126112yescomplemented
270C2×C32C22×#4111yescharacteristic
271C2×C32C22×#4111yescharacteristic
272C2×C32C22×#4111yescharacteristic
273C3×D3—44no—
274C24—36no—
275C24—64no—
276C24—64no—
277C24—64no—
278C24C2×D3211yescharacteristic
279C22×C4—24no—
280C22×C4—36no—
281C22×C4—36no—
282C22×C4—36no—
283C22×C4—64no—
284C22×C4—64no—
285C22×C4—64no—
286C22×C4—96no—
287C22×C4—96no—
288C22×C4—184no—
289C22×C4—184no—
290C22×C4C2×D3216yes—
291C4⋊C4—316no—
292C4⋊C4—916no—
293C4⋊C4—916no—
294C22⋊C4—316no—
295C22⋊C4—916no—
296C22⋊C4—916no—
297C42—916no—
298C22×C3—26no—
299C22×C3—26no—
300C22×C3—26no—
301C22×C3—216no—
302C22×C3—21no—
303C22×C3—64no—
304C22×C3—64no—
305C22×C3—64no—
306C22×C3—1224no—
307C22×C3#879116yescomplemented
308C22×C3#898116yescomplemented
309C22×C3C2×#23516yes—
310C22×C3C2×#23516yes—
311C22×C3C2×#23716yes—
312C22×C3C2×#23716yes—
313C22×C3C2×#23716yes—
314C22×C3C2×#23916yes—
315C22×C3C24×D311yescharacteristic
316C22×C3C24×D311yescharacteristic
317C2×D3—24no—
318C2×D3—24no—
319C2×D3—24no—
320C2×D3—424no—
321C3×C4—24no—
322C3×C4—24no—
323C3×C4—44no—
324C3×C4—64no—
325C3×C4—64no—
326C3×C4—64no—
327Dic3—24no—
328Dic3—24no—
329Dic3—24no—
330Dic3—68no—
331Dic3—64no—
332Dic3—64no—
333Dic3—64no—
334Dic3—64no—
335Dic3—124no—
336C32C22×#12611yescharacteristic, complemented, Sylow
337C23—34no—
338C23—612no—
339C23—612no—
340C23—612no—
341C23—1216no—
342C23#379514yes—
343C23#379614yes—
344C23#380414yes—
345C23C22×D3213yes—
346C2×C4—212no—
347C2×C4—34no—
348C2×C4—34no—
349C2×C4—34no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—94no—
354C2×C4—94no—
355C2×C4—1812no—
356C2×C4—1812no—
357C2×C4C22×D3214yes—
358C2×C3—212no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—124no—
363C2×C3C2×#879112yescomplemented
364C2×C3C2×#898112yescomplemented
365C2×C3C22×#23511yescharacteristic
366C2×C3C22×#23511yescharacteristic
367C2×C3C22×#23711yescharacteristic
368C2×C3C22×#23711yescharacteristic
369C2×C3C22×#23711yescharacteristic
370C2×C3C22×#23911yescharacteristic
371D3—44no—
372C22—64no—
373C22—64no—
374C22—64no—
375C22—1224no—
376C22#63858116yesdirect product factor
377C22C2×#379516yes—
378C22C2×#379616yes—
379C22C2×#380416yes—
380C22C23×D3211yescharacteristic
381C4—24no—
382C4—64no—
383C4—64no—
384C4—64no—
385C4—184no—
386C4—184no—
387C3—21no—
388C3C22×#87911yescharacteristic, complemented
389C3C22×#89811yescharacteristic, complemented
390C2—124no—
391C2C2×#63858112yesdirect product factor
392C2C22×#379511yescharacteristic
393C2C22×#379611yescharacteristic
394C2C22×#380411yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C22×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
7. C22×Dic32C2semidirect
8. C2×#63858C2direct (N × H)
18. C2×#3750C22semidirect
20. C2×C3×C4⋊Dic3C22semidirect
21. C2×Dic3⋊Dic3C22semidirect
24. C2×Dic32C22semidirect
25. #63858C22direct (N × H)
34. C22×C4⋊Dic3D3semidirect
60. #3750C23semidirect
62. C3×C4⋊Dic3C23semidirect
63. Dic3⋊Dic3C23semidirect
66. Dic32C23semidirect
93. C2×C4⋊Dic3C2×D3semidirect
180. C4⋊Dic3C22×D3semidirect
187. C22×C32#126semidirect
269. C2×C32C2×#126semidirect
307. C22×C3#879semidirect
308. C22×C3#898semidirect
336. C32C22×#126semidirect
363. C2×C3C2×#879semidirect
364. C2×C3C2×#898semidirect
376. C22#63858direct (N × H)
388. C3C22×#879semidirect
389. C3C22×#898semidirect
391. C2C2×#63858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×Dic3⋊Dic32
C22×(C2×D3)⋊Dic32
C22×Dic322
C2×#638582
C22×#8983
C22×#8793