Finite Group Databasebeta

← C4×#63365 #11783747

Subgroups — C4×#63365 #11783747

Order 1152.

618 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×#611C211yesmaximal, characteristic
2C4×C9×C22⋊C4C211yesmaximal, characteristic, complemented
3C4×#3676C211yesmaximal, characteristic, complemented
4C2×#63365C212yesmaximal
5#10588204C212yesmaximal, complemented
6C4×#806—31nomaximal
7C23×C4×C9C2211yescharacteristic
8C22×#611C2211yescharacteristic
9C22×C4×D9C411yescharacteristic, complemented
10C2×C9×C22⋊C4C2212yes—
11C2×C42×C9—21no—
12C2×#3676C2211yescharacteristic
13C2×#3676C2212yes—
14C4×#611—21no—
15C4×#611—21no—
16C4×#611—21no—
17C4×#611—21no—
18C2×(C2×D9)⋊C4C411yescharacteristic, complemented
19C2×Dic9⋊C4C411yescharacteristic, complemented
20C2×C4×Dic9—21no—
21C2×C4×Dic9C411yescharacteristic, complemented
22C9×#95—21no—
23C9⋊#95—21no—
24#63365C418yesdirect product factor
25C2×C4×#67—31no—
26C3×C4×C22⋊C4D311yescharacteristic
27C4×#217—31no—
28C2×#806—32no—
29#4527—32no—
30C24×C9C2311yescharacteristic
31C23×D9C2×C411yescharacteristic
32C22×C4×C9—22no—
33C22×C4×C9—42no—
34C22×C4×C9C2×C411yescharacteristic
35C22×C4×C9C2×C411yescharacteristic
36C22×C4×C9D411yescharacteristic
37C22×C4×C9D411yescharacteristic
38C22×C4×C9D411yescharacteristic
39C22×C4×C9D411yescharacteristic
40C2×#611—21no—
41C2×#611—21no—
42C2×#611—22no—
43C2×#611C2×C414yes—
44C22×Dic9—22no—
45C22×Dic9C2×C411yescharacteristic
46C22×Dic9C2×C411yescharacteristic
47C22×Dic9C2×C411yescharacteristic
48C2×C4×D9—21no—
49C2×C4×D9—21no—
50C2×C4×D9—42no—
51C9×C22⋊C4—22no—
52C9×C22⋊C4C2×C414yescomplemented
53C42×C9—42no—
54#3676—21no—
55#3676—21no—
56#3676—22no—
57#3676C2×C414yescomplemented
58(C2×D9)⋊C4—21no—
59(C2×D9)⋊C4—21no—
60Dic9⋊C4—21no—
61Dic9⋊C4—21no—
62C4×Dic9—21no—
63C4×Dic9—21no—
64C4×Dic9—42no—
65C4×#99—91noSylow
66C23×C3×C4C2×D311yescharacteristic
67C22×#67—31no—
68C22×C4×D3—31no—
69C2×C3×C22⋊C4C2×D312yes—
70C2×C3×C42—21no—
71C2×#217—32no—
72C2×#217—31no—
73C4×#67—61no—
74C4×#67—61no—
75C4×#67—61no—
76C4×#67—61no—
77C2×(C2×D3)⋊C4—31no—
78C2×Dic3⋊C4—31no—
79C2×C4×Dic3—31no—
80C2×C4×Dic3—61no—
81C3×#95—21no—
82C3⋊#95—61no—
83#806—38no—
84C23×C9—41no—
85C23×C9—41no—
86C23×C9C22×C411yescharacteristic
87C23×C9C22×C412yes—
88C23×C9C2×D411yescharacteristic
89C23×C9C2×D411yescharacteristic
90C23×C9#4112yes—
91C22×D9—21no—
92C22×D9—21no—
93C22×D9—41no—
94C22×D9—41no—
95C22×D9C4212yescomplemented
96C2×C4×C9—22no—
97C2×C4×C9—22no—
98C2×C4×C9—22no—
99C2×C4×C9—24no—
100C2×C4×C9—41no—
101C2×C4×C9—41no—
102C2×C4×C9—41no—
103C2×C4×C9—42no—
104C2×C4×C9—42no—
105C2×C4×C9C22⋊C411yescharacteristic
106C2×C4×C9C22⋊C411yescharacteristic
107C2×C4×C9C22⋊C411yescharacteristic
108C2×C4×C9C22⋊C411yescharacteristic
109#611—24no—
110#611—24no—
111C2×Dic9—21no—
112C2×Dic9—21no—
113C2×Dic9—21no—
114C2×Dic9—21no—
115C2×Dic9—24no—
116C2×Dic9—42no—
117C2×Dic9—42no—
118C2×Dic9—41no—
119C2×Dic9—41no—
120C2×Dic9C4212yescomplemented
121C4×D9—42no—
122C4×D9—42no—
123C2×C4×D4—91no—
124C2×#99—92no—
125C4×C22⋊C4—91no—
126C4×C22⋊C4D911yescharacteristic, complemented
127#342—92no—
128C24×C3C22×D311yescharacteristic
129C23×D3—31no—
130C22×C3×C4—22no—
131C22×C3×C4—42no—
132C22×C3×C4C4×D311yescharacteristic
133C22×C3×C4C4×D311yescharacteristic
134C22×C3×C4D1211yescharacteristic
135C22×C3×C4D1211yescharacteristic
136C22×C3×C4#6711yescharacteristic
137C22×C3×C4#6711yescharacteristic
138C2×#67—34no—
139C2×#67—61no—
140C2×#67—62no—
141C2×#67—61no—
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—31no—
145C22×Dic3—62no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—122no—
149C3×C22⋊C4—22no—
150C3×C22⋊C4C4×D314yes—
151C3×C42—42no—
152#217—34no—
153#217—61no—
154#217—62no—
155#217—61no—
156(C2×D3)⋊C4—61no—
157(C2×D3)⋊C4—61no—
158Dic3⋊C4—61no—
159Dic3⋊C4—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—122no—
163C22×C9—21no—
164C22×C9—21no—
165C22×C9—21no—
166C22×C9—21no—
167C22×C9—21no—
168C22×C9—21no—
169C22×C9—42no—
170C22×C9—42no—
171C22×C9C2×C4211yescharacteristic
172C22×C9C2×C22⋊C411yescharacteristic
173C22×C9#11711yescharacteristic
174C22×C9C4×D412yes—
175C22×C9C4×D412yes—
176C2×D9—22no—
177C2×D9—42no—
178C2×D9—41no—
179C2×D9—41no—
180C2×D9—42no—
181C4×C9—21no—
182C4×C9—21no—
183C4×C9—21no—
184C4×C9—44no—
185C4×C9#9912yescomplemented
186Dic9—22no—
187Dic9—44no—
188Dic9—41no—
189Dic9—41no—
190C22×D4—91no—
191C23×C4—91no—
192C23×C4C2×D911yescharacteristic
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×D912yes—
202C2×C42—21no—
203C2×C42—91no—
204C2×C42—181no—
205#99—98no—
206#95—21no—
207#95—181no—
208C23×C3—41no—
209C23×C3—41no—
210C23×C3C2×C4×D311yescharacteristic
211C23×C3C2×C4×D312yes—
212C23×C3C2×D1211yescharacteristic
213C23×C3#23512yes—
214C23×C3C2×#6711yescharacteristic
215C22×D3—32no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—121no—
219C22×D3—121no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—24no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4(C2×D3)⋊C411yescharacteristic
231C2×C3×C4(C2×D3)⋊C411yescharacteristic
232C2×C3×C4(C2×D3)⋊C411yescharacteristic
233#67—64no—
234#67—64no—
235C2×Dic3—32no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—64no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245C4×D3—122no—
246C4×D3—122no—
247C2×C9—22no—
248C2×C9—22no—
249C2×C9—21no—
250C2×C9—21no—
251C2×C9C4×C22⋊C411yescharacteristic
252C2×C9C2×#9911yescharacteristic
253C2×C9#41011yescharacteristic
254D9—42no—
255C24—91no—
256C24C22×D911yescharacteristic
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×D911yescharacteristic
271C22×C4C4×D911yescharacteristic
272C22×C4D3611yescharacteristic
273C22×C4D3611yescharacteristic
274C22×C4#61111yescharacteristic
275C22×C4#61111yescharacteristic
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×D914yescomplemented
286C42—42no—
287C42—181no—
288C42—181no—
289C42—362no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3C42×D311yescharacteristic
299C22×C3#87211yescharacteristic
300C22×C3C4×D1212yes—
301C22×C3C2×(C2×D3)⋊C411yescharacteristic
302C22×C3C4×#6712yes—
303C2×D3—62no—
304C2×D3—122no—
305C2×D3—121no—
306C2×D3—121no—
307C2×D3—122no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—44no—
312C3×C4#80612yes—
313Dic3—62no—
314Dic3—124no—
315Dic3—121no—
316Dic3—121no—
317C9C4×#9911yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23—92no—
321C23—181no—
322C23—181no—
323C23—361no—
324C23—361no—
325C23C2×C4×D911yescharacteristic
326C23C2×C4×D912yes—
327C23C2×D3611yescharacteristic
328C23#369712yes—
329C23C2×#61111yescharacteristic
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—181no—
345C2×C4—181no—
346C2×C4—184no—
347C2×C4—362no—
348C2×C4—362no—
349C2×C4—362no—
350C2×C4—362no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4(C2×D9)⋊C411yescharacteristic
354C2×C4(C2×D9)⋊C411yescharacteristic
355C2×C4(C2×D9)⋊C411yescharacteristic
356C2×C4(C2×D9)⋊C411yescharacteristic
357C2×C3—22no—
358C2×C3—22no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3C4×(C2×D3)⋊C411yescharacteristic
362C2×C3C2×#80611yescharacteristic
363C2×C3#500611yescharacteristic
364D3—122no—
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×D911yescharacteristic
379C22#6343411yescharacteristic
380C22C4×D3612yes—
381C22C2×(C2×D9)⋊C411yescharacteristic
382C22C4×#61112yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—182no—
388C4—364no—
389C4—361no—
390C4—361no—
391C4#6336512yesdirect product factor
392C3C4×#80611yescharacteristic
393C2—22no—
394C2—22no—
395C2—21no—
396C2—21no—
397C2—362no—
398C2C4×(C2×D9)⋊C411yescharacteristic
399C2C2×#6336511yescharacteristic
400C2#1058868611yescharacteristic
subgroupG/H
centerC2×C4(C2×D9)⋊C4
commutatorC22×C9C2×C42
FrattiniC24×C3C22×D3
FittingC4×C9×C22⋊C4C2
socleC22×C3C2×(C2×D3)⋊C4
prime radicalC22×#611C22
cosocleC24×C9C23
hypercenterC4×C22⋊C4D9
hypocenterC9C4×#99
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C9×C22⋊C4C2semidirect
3. C4×#3676C2semidirect
5. #10588204C2semidirect
9. C22×C4×D9C4semidirect
18. C2×(C2×D9)⋊C4C4semidirect
19. C2×Dic9⋊C4C4semidirect
21. C2×C4×Dic9C4semidirect
24. #63365C4direct (N × H)
52. C9×C22⋊C4C2×C4semidirect
57. #3676C2×C4semidirect
95. C22×D9C42semidirect
120. C2×Dic9C42semidirect
126. C4×C22⋊C4D9semidirect
185. C4×C9#99semidirect
285. C22⋊C4C4×D9semidirect
317. C9C4×#99semidirect
391. C4#63365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C4×C9×C22⋊C42
C4×#36762
C2×#633652
#105882042
C4×#8063