Finite Group Databasebeta

← C4×#63633 #11783748

Subgroups — C4×#63633 #11783748

Order 1152.

1236 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3C4×#3757C211yesmaximal, characteristic, complemented
4C2×#63633C212yesmaximal
5#10589393C212yesmaximal, complemented
6C4×#806—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C2211yescharacteristic
9C22×C4×C3⋊D3C411yescharacteristic, complemented
10C2×C32×C22⋊C4C2212yes—
11C2×C32×C42—21no—
12C2×#3757C2211yescharacteristic
13C2×#3757C2212yes—
14C4×#638—21no—
15C4×#638—21no—
16C4×#638—21no—
17C4×#638—21no—
18C2×#3752C411yescharacteristic, complemented
19C2×#3750C411yescharacteristic, complemented
20C2×C4×C3⋊Dic3—21no—
21C2×C4×C3⋊Dic3C411yescharacteristic, complemented
22C32×#95—21no—
23#63658—21no—
24#63633C418yesdirect product factor
25C2×C4×#67—34no—
26C3×C4×C22⋊C4D314yescomplemented
27C4×#217—34no—
28C2×#806—38no—
29#4527—38no—
30C24×C32C2311yescharacteristic
31C23×C3⋊D3C2×C411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C2×#638—21no—
41C2×#638—21no—
42C2×#638—22no—
43C2×#638C2×C414yes—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—42no—
51C32×C22⋊C4—22no—
52C32×C22⋊C4C2×C414yescomplemented
53C32×C42—42no—
54#3757—21no—
55#3757—21no—
56#3757—22no—
57#3757C2×C414yescomplemented
58#3752—21no—
59#3752—21no—
60#3750—21no—
61#3750—21no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—42no—
65C4×#99—91noSylow
66C23×C3×C4C2×D314yes—
67C22×#67—34no—
68C22×C4×D3—34no—
69C2×C3×C22⋊C4C2×D318yes—
70C2×C3×C42—24no—
71C2×#217—38no—
72C2×#217—34no—
73C4×#67—64no—
74C4×#67—64no—
75C4×#67—64no—
76C4×#67—64no—
77C2×(C2×D3)⋊C4—34no—
78C2×Dic3⋊C4—34no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—64no—
81C3×#95—24no—
82C3⋊#95—64no—
83#806—332no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32C22×C411yescharacteristic
87C23×C32C22×C412yes—
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32#4112yes—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—41no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3C4212yescomplemented
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4—42no—
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109#638—24no—
110#638—24no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C4212yescomplemented
121C4×C3⋊D3—42no—
122C4×C3⋊D3—42no—
123C2×C4×D4—91no—
124C2×#99—92no—
125C4×C22⋊C4—91no—
126C4×C22⋊C4C3⋊D311yescharacteristic, complemented
127#342—92no—
128C24×C3C22×D314yes—
129C23×D3—34no—
130C22×C3×C4—28no—
131C22×C3×C4—48no—
132C22×C3×C4C4×D314yes—
133C22×C3×C4C4×D314yes—
134C22×C3×C4D1214yes—
135C22×C3×C4D1214yes—
136C22×C3×C4#6714yes—
137C22×C3×C4#6714yes—
138C2×#67—316no—
139C2×#67—64no—
140C2×#67—68no—
141C2×#67—64no—
142C22×Dic3—34no—
143C22×Dic3—34no—
144C22×Dic3—34no—
145C22×Dic3—68no—
146C2×C4×D3—64no—
147C2×C4×D3—64no—
148C2×C4×D3—128no—
149C3×C22⋊C4—28no—
150C3×C22⋊C4C4×D3116yescomplemented
151C3×C42—48no—
152#217—316no—
153#217—64no—
154#217—68no—
155#217—64no—
156(C2×D3)⋊C4—64no—
157(C2×D3)⋊C4—64no—
158Dic3⋊C4—64no—
159Dic3⋊C4—64no—
160C4×Dic3—64no—
161C4×Dic3—64no—
162C4×Dic3—128no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—21no—
169C22×C32—42no—
170C22×C32—42no—
171C22×C32C2×C4211yescharacteristic
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32#11711yescharacteristic
174C22×C32C4×D412yes—
175C22×C32C4×D412yes—
176C2×C3⋊D3—22no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—41no—
179C2×C3⋊D3—41no—
180C2×C3⋊D3—42no—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4—21no—
184C32×C4—44no—
185C32×C4#9912yescomplemented
186C3⋊Dic3—22no—
187C3⋊Dic3—44no—
188C3⋊Dic3—41no—
189C3⋊Dic3—41no—
190C22×D4—91no—
191C23×C4—91no—
192C23×C4C2×C3⋊D311yescharacteristic
193C4×D4—181no—
194C4×D4—181no—
195C4×D4—181no—
196C4×D4—181no—
197C2×C4⋊C4—91no—
198C2×C22⋊C4—92no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—91no—
201C2×C22⋊C4C2×C3⋊D312yes—
202C2×C42—21no—
203C2×C42—91no—
204C2×C42—181no—
205#99—98no—
206#95—21no—
207#95—181no—
208C23×C3—44no—
209C23×C3—44no—
210C23×C3C2×C4×D314yes—
211C23×C3C2×C4×D318yes—
212C23×C3C2×D1214yes—
213C23×C3#23518yes—
214C23×C3C2×#6714yes—
215C22×D3—38no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—124no—
219C22×D3—124no—
220C2×C3×C4—28no—
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—216no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—48no—
228C2×C3×C4—48no—
229C2×C3×C4(C2×D3)⋊C414yes—
230C2×C3×C4(C2×D3)⋊C414yes—
231C2×C3×C4(C2×D3)⋊C414yes—
232C2×C3×C4(C2×D3)⋊C414yes—
233#67—616no—
234#67—616no—
235C2×Dic3—38no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—616no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—128no—
242C2×Dic3—128no—
243C2×Dic3—124no—
244C2×Dic3—124no—
245C4×D3—128no—
246C4×D3—128no—
247C2×C32—22no—
248C2×C32—22no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32C4×C22⋊C411yescharacteristic
252C2×C32C2×#9911yescharacteristic
253C2×C32#41011yescharacteristic
254C3⋊D3—42no—
255C24—91no—
256C24C22×C3⋊D311yescharacteristic
257C2×D4—94no—
258C2×D4—181no—
259C2×D4—182no—
260C2×D4—181no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—182no—
267C22×C4—181no—
268C22×C4—181no—
269C22×C4—362no—
270C22×C4C4×C3⋊D311yescharacteristic
271C22×C4C4×C3⋊D311yescharacteristic
272C22×C4C4⋊(C3⋊D3)11yescharacteristic
273C22×C4C4⋊(C3⋊D3)11yescharacteristic
274C22×C4#63811yescharacteristic
275C22×C4#63811yescharacteristic
276C4⋊C4—181no—
277C4⋊C4—181no—
278C22⋊C4—22no—
279C22⋊C4—94no—
280C22⋊C4—181no—
281C22⋊C4—182no—
282C22⋊C4—181no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C22⋊C4C4×C3⋊D314yescomplemented
286C42—42no—
287C42—181no—
288C42—181no—
289C42—362no—
290C22×C3—24no—
291C22×C3—24no—
292C22×C3—24no—
293C22×C3—24no—
294C22×C3—24no—
295C22×C3—24no—
296C22×C3—48no—
297C22×C3—48no—
298C22×C3C42×D314yes—
299C22×C3#87214yes—
300C22×C3C4×D1218yes—
301C22×C3C2×(C2×D3)⋊C414yes—
302C22×C3C4×#6718yes—
303C2×D3—68no—
304C2×D3—128no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—128no—
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—24no—
311C3×C4—416no—
312C3×C4#80618yescomplemented
313Dic3—68no—
314Dic3—1216no—
315Dic3—124no—
316Dic3—124no—
317C32C4×#9911yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23—92no—
321C23—181no—
322C23—181no—
323C23—361no—
324C23—361no—
325C23C2×C4×C3⋊D311yescharacteristic
326C23C2×C4×C3⋊D312yes—
327C23C2×C4⋊(C3⋊D3)11yescharacteristic
328C23#382812yes—
329C23C2×#63811yescharacteristic
330D4—184no—
331D4—184no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—92no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—184no—
345C2×C4—181no—
346C2×C4—181no—
347C2×C4—362no—
348C2×C4—362no—
349C2×C4—362no—
350C2×C4—362no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4#375211yescharacteristic
354C2×C4#375211yescharacteristic
355C2×C4#375211yescharacteristic
356C2×C4#375211yescharacteristic
357C2×C3—28no—
358C2×C3—28no—
359C2×C3—24no—
360C2×C3—24no—
361C2×C3C4×(C2×D3)⋊C414yes—
362C2×C3C2×#80614yes—
363C2×C3#500614yes—
364D3—128no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—182no—
374C22—362no—
375C22—362no—
376C22—361no—
377C22—361no—
378C22C42×C3⋊D311yescharacteristic
379C22#6408111yescharacteristic
380C22C4×C4⋊(C3⋊D3)12yes—
381C22C2×#375211yescharacteristic
382C22C4×#63812yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—182no—
388C4—364no—
389C4—361no—
390C4—361no—
391C4#6363312yesdirect product factor
392C3C4×#80614yescomplemented
393C2—22no—
394C2—22no—
395C2—21no—
396C2—21no—
397C2—362no—
398C2C4×#375211yescharacteristic
399C2C2×#6363311yescharacteristic
400C2#1059270511yescharacteristic
subgroupG/H
centerC2×C4#3752
commutatorC22×C32C2×C42
FrattiniC24C22×C3⋊D3
FittingC32×C4×C22⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C22⋊C4C2semidirect
3. C4×#3757C2semidirect
5. #10589393C2semidirect
9. C22×C4×C3⋊D3C4semidirect
18. C2×#3752C4semidirect
19. C2×#3750C4semidirect
21. C2×C4×C3⋊Dic3C4semidirect
24. #63633C4direct (N × H)
26. C3×C4×C22⋊C4D3semidirect
52. C32×C22⋊C4C2×C4semidirect
57. #3757C2×C4semidirect
95. C22×C3⋊D3C42semidirect
120. C2×C3⋊Dic3C42semidirect
126. C4×C22⋊C4C3⋊D3semidirect
150. C3×C22⋊C4C4×D3semidirect
185. C32×C4#99semidirect
285. C22⋊C4C4×C3⋊D3semidirect
312. C3×C4#806semidirect
317. C32C4×#99semidirect
391. C4#63633direct (N × H)
392. C3C4×#806semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C32×C4×C22⋊C42
C4×#37572
C2×#636332
#105893932
C4×#8063