Finite Group Databasebeta

← C4×#63581 #11783763

Subgroups — C4×#63581 #11783763

Order 1152.

1037 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C3×C4×#217C212yesmaximal, complemented
3C2×#63581C212yesmaximal
4#10589187C212yesmaximal, complemented
5C4×#806—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#638C2211yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic, complemented
9C2×#3757C2211yescharacteristic
10C4×#638—22no—
11C4×#638—22no—
12C2×#3752C411yescharacteristic, complemented
13C2×#3750C411yescharacteristic, complemented
14C2×C4×C3⋊Dic3C411yescharacteristic, complemented
15C2×C3×#217C2214yes—
16C2×C3×C4×Dic3—22no—
17C3×C3⋊#95—22no—
18#63581C418yesdirect product factor
19C2×C4×#67—32no—
20C2×C4×#67—61no—
21C3×C4×C22⋊C4—32no—
22C4×#217D312yescomplemented
23C2×#806—34no—
24#4527—34no—
25C24×C32C2311yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4—42no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D412yes—
31C22×C32×C4D412yes—
32C2×#638—22no—
33C2×#638—22no—
34C2×#638C2×C414yes—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—42no—
41C22×C3×Dic3—24no—
42#3757—22no—
43#3752—22no—
44#3750—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C3×#217—24no—
48C3×#217C2×C418yescomplemented
49C3×C4×Dic3—44no—
50C4×#99—91noSylow
51C23×C3×C4—21no—
52C23×C3×C4C2×D312yes—
53C22×#67—32no—
54C22×#67—61no—
55C22×C4×D3—32no—
56C22×C4×D3—61no—
57C2×C3×C22⋊C4—34no—
58C2×C3×C42—62no—
59C2×#217—32no—
60C2×#217—61no—
61C2×#217C2×D314yes—
62C4×#67—64no—
63C4×#67—64no—
64C4×#67—62no—
65C4×#67—62no—
66C4×#67—62no—
67C4×#67—62no—
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—61no—
70C2×Dic3⋊C4—32no—
71C2×Dic3⋊C4—61no—
72C2×C4×Dic3—22no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—61no—
75C3×#95—62no—
76C3⋊#95—22no—
77#806—316no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C22×C411yescharacteristic
81C23×C32C22×C412yes—
82C23×C32C2×D412yes—
83C23×C32#4112yes—
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3C4212yescomplemented
89C2×C32×C4—22no—
90C2×C32×C4—24no—
91C2×C32×C4—41no—
92C2×C32×C4—42no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C412yes—
95C2×C32×C4C22⋊C411yescharacteristic
96#638—28no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C4212yescomplemented
104C4×C3⋊D3—42no—
105C4×C3⋊D3—42no—
106C2×C3×Dic3—28no—
107C2×C3×Dic3—44no—
108C2×C3×Dic3—44no—
109C2×C4×D4—91no—
110C2×#99—92no—
111C4×C22⋊C4—32no—
112#342—92no—
113C24×C3—21no—
114C24×C3C22×D312yes—
115C23×D3—32no—
116C23×D3—61no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—44no—
122C22×C3×C4—44no—
123C22×C3×C4—64no—
124C22×C3×C4C4×D312yes—
125C22×C3×C4C4×D312yes—
126C22×C3×C4D1212yes—
127C22×C3×C4D1212yes—
128C22×C3×C4#6712yes—
129C22×C3×C4#6712yes—
130C2×#67—38no—
131C2×#67—64no—
132C2×#67—64no—
133C2×#67—64no—
134C2×#67—62no—
135C2×#67—64no—
136C2×#67—62no—
137C22×Dic3—24no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—124no—
149C2×C4×D3—124no—
150C3×C22⋊C4—38no—
151C3×C22⋊C4—64no—
152C3×C42—124no—
153#217—24no—
154#217—64no—
155#217—62no—
156#217—62no—
157#217C4×D318yescomplemented
158(C2×D3)⋊C4—64no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—62no—
161Dic3⋊C4—64no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164C4×Dic3—44no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—22no—
172C22×C32—22no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32C2×C4211yescharacteristic
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32#11711yescharacteristic
178C22×C32C4×D414yes—
179C2×C3⋊D3—22no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—41no—
182C2×C3⋊D3—41no—
183C2×C3⋊D3—42no—
184C32×C4—21no—
185C32×C4—22no—
186C32×C4#9912yescomplemented
187C3⋊Dic3—22no—
188C3⋊Dic3—41no—
189C3⋊Dic3—41no—
190C3×Dic3—48no—
191C22×D4—91no—
192C23×C4—91no—
193C23×C4D3211yescharacteristic
194C4×D4—182no—
195C4×D4—182no—
196C2×C4⋊C4—91no—
197C2×C22⋊C4—34no—
198C2×C22⋊C4—91no—
199C2×C22⋊C4—91no—
200C2×C42—62no—
201C2×C42—91no—
202#99—98no—
203#95—62no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—21no—
207C23×C3—22no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3C2×C4×D314yes—
213C23×C3C2×C4×D312yes—
214C23×C3C2×D1212yes—
215C23×C3#23514yes—
216C23×C3C2×#6712yes—
217C22×D3—34no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—62no—
222C22×D3—62no—
223C22×D3—122no—
224C22×D3—122no—
225C22×D3—122no—
226C22×D3—122no—
227C2×C3×C4—24no—
228C2×C3×C4—24no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—44no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—44no—
239C2×C3×C4—42no—
240C2×C3×C4—68no—
241C2×C3×C4—124no—
242C2×C3×C4—124no—
243C2×C3×C4(C2×D3)⋊C412yes—
244C2×C3×C4(C2×D3)⋊C412yes—
245C2×C3×C4(C2×D3)⋊C412yes—
246C2×C3×C4(C2×D3)⋊C412yes—
247#67—616no—
248#67—68no—
249#67—68no—
250C2×Dic3—28no—
251C2×Dic3—34no—
252C2×Dic3—44no—
253C2×Dic3—44no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C4×D3—124no—
268C4×D3—124no—
269C4×D3—124no—
270C4×D3—124no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—24no—
274C2×C32C4×C22⋊C411yescharacteristic
275C2×C32C2×#9911yescharacteristic
276C2×C32#41011yescharacteristic
277C3⋊D3—42no—
278C24—91no—
279C24C2×D3211yescharacteristic
280C2×D4—94no—
281C2×D4—182no—
282C2×D4—182no—
283C22×C4—42no—
284C22×C4—64no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—181no—
289C22×C4—181no—
290C22×C4—362no—
291C22×C4#62411yescharacteristic
292C22×C4#62411yescharacteristic
293C22×C4#62612yes—
294C22×C4#62612yes—
295C4⋊C4—182no—
296C22⋊C4—38no—
297C22⋊C4—64no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—124no—
301C42—181no—
302C42—181no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—24no—
314C22×C3—21no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—44no—
318C22×C3—44no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3C42×D312yes—
322C22×C3#87212yes—
323C22×C3C4×D1214yes—
324C22×C3C2×(C2×D3)⋊C412yes—
325C22×C3C4×#6714yes—
326C2×D3—64no—
327C2×D3—64no—
328C2×D3—122no—
329C2×D3—124no—
330C2×D3—124no—
331C2×D3—124no—
332C2×D3—122no—
333C2×D3—122no—
334C2×D3—122no—
335C2×D3—124no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—42no—
342C3×C4—128no—
343C3×C4#80614yescomplemented
344Dic3—48no—
345Dic3—64no—
346Dic3—64no—
347Dic3—122no—
348Dic3—122no—
349Dic3—122no—
350Dic3—122no—
351C32C4×#9911yescharacteristic, complemented, Sylow
352C23—41no—
353C23—41no—
354C23—92no—
355C23—181no—
356C23—181no—
357C23—361no—
358C23—361no—
359C23#379812yes—
360C23C4×D3212yes—
361C23C2×#62411yescharacteristic
362C23C2×#62612yes—
363D4—188no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—68no—
369C2×C4—92no—
370C2×C4—124no—
371C2×C4—124no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—362no—
377C2×C4—362no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4#372211yescharacteristic
381C2×C4#372212yes—
382C2×C4#372211yescharacteristic
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—24no—
386C2×C3—24no—
387C2×C3—22no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—44no—
393C2×C3C4×(C2×D3)⋊C412yes—
394C2×C3C2×#80612yes—
395C2×C3#500612yes—
396D3—124no—
397D3—124no—
398C22—22no—
399C22—21no—
400C22—22no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—182no—
405C22—362no—
406C22—362no—
407C22—361no—
408C22—361no—
409C22#6387411yescharacteristic
410C22C4×#62411yescharacteristic
411C22C4×#62614yes—
412C22C2×#372211yescharacteristic
413C4—21no—
414C4—22no—
415C4—128no—
416C4—182no—
417C4—361no—
418C4—361no—
419C4#6358112yesdirect product factor
420C3—21no—
421C3C4×#80612yescomplemented
422C2—24no—
423C2—21no—
424C2—21no—
425C2—362no—
426C2#1059123211yescharacteristic
427C2C4×#372211yescharacteristic
428C2C2×#6358111yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#217C2semidirect
4. #10589187C2semidirect
8. C22×C4×C3⋊D3C4semidirect
12. C2×#3752C4semidirect
13. C2×#3750C4semidirect
14. C2×C4×C3⋊Dic3C4semidirect
18. #63581C4direct (N × H)
22. C4×#217D3semidirect
48. C3×#217C2×C4semidirect
88. C22×C3⋊D3C42semidirect
103. C2×C3⋊Dic3C42semidirect
157. #217C4×D3semidirect
186. C32×C4#99semidirect
343. C3×C4#806semidirect
351. C32C4×#99semidirect
419. C4#63581direct (N × H)
421. 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
C3×C4×#2172
C2×#635812
#105891872
C4×#8063