Finite Group Databasebeta

← C22×#63848 #11900564

Subgroups — C22×#63848 #11900564

Order 1152.

2977 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C22×#3722C211yesmaximal, characteristic
6C22×#3722C211yesmaximal, characteristic
7C22×Dic32C211yesmaximal, characteristic, complemented
8C2×#63848C2124yesmaximal, direct product factor
9C22×#898—31nomaximal
10C22×#898—31nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×#3752C22112yes—
19C2×C3×C4⋊Dic3C22112yescomplemented
20C2×C3×Dic3⋊C4C22112yescomplemented
21C2×Dic3⋊Dic3C22112yescomplemented
22C2×#3722C22112yes—
23C2×#3722C22112yes—
24C2×Dic32C22112yescomplemented
25#63848C22164yesdirect product factor
26C22×C3×C4⋊C4—31no—
27C22×C3×C4⋊C4—31no—
28C22×(C2×D3)⋊C4—31no—
29C22×(C2×D3)⋊C4—31no—
30C22×(C2×D3)⋊C4—31no—
31C22×(C2×D3)⋊C4—31no—
32C22×(C2×D3)⋊C4—31no—
33C22×(C2×D3)⋊C4—31no—
34C22×(C2×D3)⋊C4—61no—
35C22×C4⋊Dic3—31no—
36C22×C4⋊Dic3D311yescharacteristic, complemented
37C22×Dic3⋊C4—31no—
38C22×Dic3⋊C4D311yescharacteristic, complemented
39C22×C4×Dic3—31no—
40C22×C4×Dic3—31no—
41C2×#898—324no—
42C2×#898—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⋊Dic3C2316yes—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3—24no—
55C22×C3×Dic3—24no—
56C22×C3×Dic3C2316yes—
57C22×C3×Dic3C2316yes—
58C22×C3×Dic3C2316yes—
59C22×C3×Dic3C2316yes—
60#3752C23116yes—
61C3×C4⋊Dic3C23116yescomplemented
62C3×Dic3⋊C4C23116yescomplemented
63Dic3⋊Dic3C23116yescomplemented
64#3722C23116yes—
65#3722C23116yes—
66Dic32C23116yescomplemented
67C22×#126—91noSylow
68C24×D3—31no—
69C24×D3—31no—
70C24×D3—61no—
71C23×C3×C4—21no—
72C23×C3×C4—31no—
73C23×C3×C4—31no—
74C23×C3×C4—31no—
75C23×C3×C4—31no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C2×D311yescharacteristic
78C23×Dic3—31no—
79C23×Dic3—31no—
80C23×Dic3—61no—
81C23×Dic3C2×D311yescharacteristic
82C23×Dic3C2×D311yescharacteristic
83C23×Dic3C2×D311yescharacteristic
84C23×Dic3C2×D311yescharacteristic
85C2×C3×C4⋊C4—312no—
86C2×C3×C4⋊C4—312no—
87C2×(C2×D3)⋊C4—312no—
88C2×(C2×D3)⋊C4—312no—
89C2×(C2×D3)⋊C4—312no—
90C2×(C2×D3)⋊C4—312no—
91C2×(C2×D3)⋊C4—312no—
92C2×(C2×D3)⋊C4—312no—
93C2×(C2×D3)⋊C4—612no—
94C2×C4⋊Dic3—312no—
95C2×C4⋊Dic3C2×D3112yescomplemented
96C2×Dic3⋊C4—312no—
97C2×Dic3⋊C4C2×D3112yescomplemented
98C2×C4×Dic3—312no—
99C2×C4×Dic3—312no—
100#898—364no—
101#898—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⋊Dic3C2414yes—
115C2×C3×Dic3—212no—
116C2×C3×Dic3—212no—
117C2×C3×Dic3—212no—
118C2×C3×Dic3—212no—
119C2×C3×Dic3C2414yes—
120C2×C3×Dic3C2414yes—
121C2×C3×Dic3C2414yes—
122C2×C3×Dic3C2414yes—
123C2×#126—924no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4—31no—
126C22×C4⋊C4—91no—
127C22×C22⋊C4—91no—
128C22×C22⋊C4—91no—
129C22×C22⋊C4—91no—
130C22×C42—91no—
131C24×C3—21no—
132C24×C3C22×D311yescharacteristic
133C24×C3C22×D311yescharacteristic
134C23×D3—36no—
135C23×D3—36no—
136C23×D3—66no—
137C23×D3—68no—
138C23×D3—64no—
139C23×D3—64no—
140C23×D3—64no—
141C23×D3—64no—
142C23×D3—64no—
143C23×D3—64no—
144C23×D3—124no—
145C23×D3—124no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—26no—
149C22×C3×C4—36no—
150C22×C3×C4—36no—
151C22×C3×C4—36no—
152C22×C3×C4—36no—
153C22×C3×C4—44no—
154C22×C3×C4—64no—
155C22×C3×C4—64no—
156C22×C3×C4—64no—
157C22×C3×C4—64no—
158C22×C3×C4C22×D316yes—
159C22×C3×C4C22×D316yes—
160C22×Dic3—24no—
161C22×Dic3—24no—
162C22×Dic3—24no—
163C22×Dic3—24no—
164C22×Dic3—36no—
165C22×Dic3—36no—
166C22×Dic3—66no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—124no—
170C22×Dic3C22×D316yes—
171C22×Dic3C22×D316yes—
172C22×Dic3C22×D316yes—
173C22×Dic3C22×D316yes—
174C3×C4⋊C4—316no—
175C3×C4⋊C4—316no—
176(C2×D3)⋊C4—316no—
177(C2×D3)⋊C4—316no—
178(C2×D3)⋊C4—316no—
179(C2×D3)⋊C4—316no—
180(C2×D3)⋊C4—316no—
181(C2×D3)⋊C4—316no—
182(C2×D3)⋊C4—616no—
183C4⋊Dic3—316no—
184C4⋊Dic3C22×D3116yescomplemented
185Dic3⋊C4—316no—
186Dic3⋊C4C22×D3116yescomplemented
187C4×Dic3—316no—
188C4×Dic3—316no—
189C22×C32#126116yescomplemented
190C22×C32C2×#4116yes—
191C22×C32C2×#4116yes—
192C22×C32C2×#4116yes—
193C22×C32C2511yescharacteristic
194C2×C3⋊D3—24no—
195C2×C3⋊D3—24no—
196C2×C3⋊D3—24no—
197C2×C3⋊D3—424no—
198C32×C4—24no—
199C3⋊Dic3—24no—
200C3×Dic3—24no—
201C3×Dic3—24no—
202C3×Dic3—24no—
203C3×Dic3—24no—
204C25—91no—
205C23×C4—31no—
206C23×C4—31no—
207C23×C4—31no—
208C23×C4—31no—
209C23×C4—91no—
210C23×C4D3211yescharacteristic
211#126—964no—
212C2×C4⋊C4—312no—
213C2×C4⋊C4—312no—
214C2×C4⋊C4—912no—
215C2×C22⋊C4—912no—
216C2×C22⋊C4—912no—
217C2×C22⋊C4—912no—
218C2×C42—912no—
219C23×C3—23no—
220C23×C3—24no—
221C23×C3—24no—
222C23×C3—24no—
223C23×C3#23514yes—
224C23×C3#23514yes—
225C23×C3#23714yes—
226C23×C3#23714yes—
227C23×C3#23914yes—
228C23×C3#23914yes—
229C23×C3C23×D313yes—
230C23×C3C23×D313yes—
231C22×D3—34no—
232C22×D3—34no—
233C22×D3—64no—
234C22×D3—624no—
235C22×D3—612no—
236C22×D3—612no—
237C22×D3—612no—
238C22×D3—612no—
239C22×D3—612no—
240C22×D3—612no—
241C22×D3—1212no—
242C22×D3—1212no—
243C22×D3—1232no—
244C22×D3—1216no—
245C22×D3—1216no—
246C2×C3×C4—212no—
247C2×C3×C4—212no—
248C2×C3×C4—24no—
249C2×C3×C4—34no—
250C2×C3×C4—34no—
251C2×C3×C4—34no—
252C2×C3×C4—34no—
253C2×C3×C4—412no—
254C2×C3×C4—612no—
255C2×C3×C4—612no—
256C2×C3×C4—612no—
257C2×C3×C4—612no—
258C2×C3×C4C23×D314yes—
259C2×C3×C4C23×D314yes—
260C2×Dic3—212no—
261C2×Dic3—212no—
262C2×Dic3—212no—
263C2×Dic3—212no—
264C2×Dic3—34no—
265C2×Dic3—34no—
266C2×Dic3—64no—
267C2×Dic3—612no—
268C2×Dic3—612no—
269C2×Dic3—1212no—
270C2×Dic3C23×D314yes—
271C2×Dic3C23×D314yes—
272C2×Dic3C23×D314yes—
273C2×Dic3C23×D314yes—
274C2×C32C2×#126112yescomplemented
275C2×C32C22×#4111yescharacteristic
276C2×C32C22×#4111yescharacteristic
277C2×C32C22×#4111yescharacteristic
278C3⋊D3—44no—
279C24—96no—
280C24—184no—
281C24—184no—
282C24—184no—
283C24C2×D3211yescharacteristic
284C22×C4—24no—
285C22×C4—36no—
286C22×C4—36no—
287C22×C4—36no—
288C22×C4—36no—
289C22×C4—64no—
290C22×C4—64no—
291C22×C4—64no—
292C22×C4—64no—
293C22×C4—96no—
294C22×C4—184no—
295C22×C4C2×D3216yes—
296C4⋊C4—316no—
297C4⋊C4—316no—
298C4⋊C4—916no—
299C22⋊C4—916no—
300C22⋊C4—916no—
301C22⋊C4—916no—
302C42—916no—
303C22×C3—26no—
304C22×C3—26no—
305C22×C3—26no—
306C22×C3—216no—
307C22×C3—21no—
308C22×C3#898116yescomplemented
309C22×C3#898116yescomplemented
310C22×C3C2×#23516yes—
311C22×C3C2×#23516yes—
312C22×C3C2×#23716yes—
313C22×C3C2×#23716yes—
314C22×C3C2×#23916yes—
315C22×C3C2×#23916yes—
316C22×C3C24×D311yescharacteristic
317C22×C3C24×D311yescharacteristic
318C2×D3—68no—
319C2×D3—64no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—64no—
324C2×D3—64no—
325C2×D3—124no—
326C2×D3—124no—
327C2×D3—1248no—
328C2×D3—1224no—
329C2×D3—1224no—
330C3×C4—24no—
331C3×C4—24no—
332C3×C4—44no—
333C3×C4—64no—
334C3×C4—64no—
335C3×C4—64no—
336C3×C4—64no—
337Dic3—24no—
338Dic3—24no—
339Dic3—24no—
340Dic3—24no—
341Dic3—64no—
342Dic3—64no—
343Dic3—124no—
344C32C22×#12611yescharacteristic, complemented, Sylow
345C23—94no—
346C23—1812no—
347C23—1812no—
348C23—1812no—
349C23—3616no—
350C23#379614yes—
351C23#379914yes—
352C23#380414yes—
353C23C22×D3213yes—
354C2×C4—212no—
355C2×C4—34no—
356C2×C4—34no—
357C2×C4—34no—
358C2×C4—34no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—94no—
364C2×C4—1812no—
365C2×C4C22×D3214yes—
366C2×C3—212no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3C2×#898112yescomplemented
371C2×C3C2×#898112yescomplemented
372C2×C3C22×#23511yescharacteristic
373C2×C3C22×#23511yescharacteristic
374C2×C3C22×#23711yescharacteristic
375C2×C3C22×#23711yescharacteristic
376C2×C3C22×#23911yescharacteristic
377C2×C3C22×#23911yescharacteristic
378D3—128no—
379D3—124no—
380D3—124no—
381C22—184no—
382C22—184no—
383C22—184no—
384C22—3624no—
385C22#63848116yesdirect product factor
386C22C2×#379616yes—
387C22C2×#379916yes—
388C22C2×#380416yes—
389C22C23×D3211yescharacteristic
390C4—24no—
391C4—64no—
392C4—64no—
393C4—64no—
394C4—64no—
395C4—184no—
396C3—21no—
397C3C22×#89811yescharacteristic, complemented
398C3C22×#89811yescharacteristic, complemented
399C2—364no—
400C2C2×#63848112yesdirect product factor
401C2C22×#379611yescharacteristic
402C2C22×#379911yescharacteristic
403C2C22×#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
2. C22×C3×C4⋊Dic3C2semidirect
3. C22×C3×Dic3⋊C4C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
7. C22×Dic32C2semidirect
8. C2×#63848C2direct (N × H)
19. C2×C3×C4⋊Dic3C22semidirect
20. C2×C3×Dic3⋊C4C22semidirect
21. C2×Dic3⋊Dic3C22semidirect
24. C2×Dic32C22semidirect
25. #63848C22direct (N × H)
36. C22×C4⋊Dic3D3semidirect
38. C22×Dic3⋊C4D3semidirect
61. C3×C4⋊Dic3C23semidirect
62. C3×Dic3⋊C4C23semidirect
63. Dic3⋊Dic3C23semidirect
66. Dic32C23semidirect
95. C2×C4⋊Dic3C2×D3semidirect
97. C2×Dic3⋊C4C2×D3semidirect
184. C4⋊Dic3C22×D3semidirect
186. Dic3⋊C4C22×D3semidirect
189. C22×C32#126semidirect
274. C2×C32C2×#126semidirect
308. C22×C3#898semidirect
309. C22×C3#898semidirect
344. C32C22×#126semidirect
370. C2×C3C2×#898semidirect
371. C2×C3C2×#898semidirect
385. C22#63848direct (N × H)
397. C3C22×#898semidirect
398. C3C22×#898semidirect
400. C2C2×#63848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37522
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C22×Dic3⋊Dic32
C22×#37222
C22×Dic322
C2×#638482
C22×#8983