Finite Group Databasebeta

← C4×#63570 #11783879

Subgroups — C4×#63570 #11783879

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×C42×Dic3C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal
5#10589162C212yesmaximal, complemented
6C4×#825—31nomaximal
7C4×#805—31nomaximal
8C2×#3828C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C4×#638—22no—
11#64135C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C412yescomplemented
13#64081—21no—
14C42×C3⋊D3—21no—
15C4×#634C412yescomplemented
16C2×C3×C4×Dic3—22no—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×#208C2212yes—
19C3×#803—21no—
20C3×C4×C3⋊C8—21no—
21#63570C418yesdirect product factor
22C4×#235—31no—
23C4×#235—31no—
24C4×#235—61no—
25C3×C4×M16—31no—
26C3×C43—31no—
27C2×#825—32no—
28C42×Dic3D311yescharacteristic, complemented
29C2×#805—32no—
30C4×#208D311yescharacteristic, complemented
31#4555—32no—
32#4523—32no—
33C22×C32×C4D412yes—
34C22×C32×C4C2311yescharacteristic
35C2×#638—21no—
36#3828—22no—
37#3828C2×C414yes—
38C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—22no—
41C2×#634C2×C411yescharacteristic
42C22×C3×Dic3—22no—
43C32×C42C2×C412yes—
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46#3757—21no—
47#3752—22no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49#3750—22no—
50C4×C3⋊Dic3—22no—
51C4×C3⋊Dic3—21no—
52C3×C4×Dic3—28no—
53C3×C4×Dic3—22no—
54C3×C4×Dic3C2×C414yescomplemented
55C3×#208—22no—
56C3×#208C2×C414yescomplemented
57C2×C3×C3⋊C8—22no—
58C4×#104—91noSylow
59C2×#235—31no—
60C2×#235—31no—
61C2×#235—61no—
62C2×C3×M16—32no—
63C2×C3×C42—21no—
64C2×C3×C42—32no—
65C2×C3×C42—62no—
66C2×C3×C42C2×D311yescharacteristic
67C2×C3×C42C2×D311yescharacteristic
68C4×#67—64no—
69C4×#67—62no—
70C4×#67—62no—
71#926—31no—
72#926—31no—
73#926—61no—
74C2×C4×Dic3—22no—
75C2×C4×Dic3C2×D312yes—
76C2×#208C2×D312yes—
77C4×D12—32no—
78C4×D12—32no—
79C4×D12—62no—
80#872—62no—
81#872—61no—
82#872—61no—
83C42×D3—62no—
84C42×D3—61no—
85C42×D3—61no—
86C4×Dic6—32no—
87C4×Dic6—32no—
88C4×Dic6—62no—
89C3×#97—61no—
90C3×C4×C8—61no—
91#825—38no—
92#805—38no—
93#803—21no—
94C4×C3⋊C8—21no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—21no—
97C2×C32×C4—24no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4C22⋊C412yes—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C22×C412yes—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104#638—24no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—22no—
107C4⋊(C3⋊D3)—21no—
108C4⋊(C3⋊D3)C4212yescomplemented
109C4×C3⋊D3—24no—
110C4×C3⋊D3—44no—
111#634—21no—
112#634C4212yescomplemented
113C2×C3×Dic3—28no—
114C2×C3×Dic3—24no—
115C3×C3⋊C8—24no—
116C4×#41—91no—
117C2×#104—92no—
118C4×M16—31no—
119C43—31no—
120#339—92no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4—62no—
124C22×C3×C4D1212yes—
125C22×C3×C4#6712yes—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C2×#67—62no—
129C2×#67—61no—
130C2×#67—61no—
131C22×Dic3—22no—
132#235—34no—
133#235—34no—
134#235—64no—
135#235—64no—
136#235—62no—
137#235—62no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—61no—
141C2×C4×D3—62no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—64no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×Dic6—31no—
148C2×Dic6—31no—
149C2×Dic6—61no—
150C3×M16—34no—
151C3×M16—62no—
152C2×C3×C8—62no—
153C3×C42—22no—
154C3×C42—21no—
155C3×C42—21no—
156C3×C42—34no—
157C3×C42—68no—
158C3×C42—62no—
159C3×C42C4×D312yes—
160C3×C42C4×D312yes—
161C3×C42D1211yescharacteristic
162C3×C42D1211yescharacteristic
163C3×C42#6711yescharacteristic
164C3×C42#6711yescharacteristic
165#217—62no—
166#217—61no—
167#217—61no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171C4⋊Dic3—32no—
172C4⋊Dic3—32no—
173C4⋊Dic3—62no—
174Dic3⋊C4—64no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177C4×Dic3—28no—
178C4×Dic3—22no—
179C4×Dic3—64no—
180C4×Dic3—62no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3C4×D314yescomplemented
186#208—22no—
187#208C4×D314yescomplemented
188C2×C3⋊C8—22no—
189C22×C32—22no—
190C22×C32C2×C22⋊C411yescharacteristic
191C22×C32C4×D412yes—
192C2×C3⋊D3—22no—
193C2×C3⋊D3—42no—
194C32×C4—22no—
195C32×C4#10414yescomplemented
196C32×C4C2×C4211yescharacteristic
197C32×C4#11711yescharacteristic
198C32×C4C4×D412yes—
199C3⋊Dic3—22no—
200C3⋊Dic3—42no—
201C3×Dic3—28no—
202C2×#41—91no—
203C2×M16—32no—
204C4×Q8—92no—
205C4×D4—92no—
206C4×D4—182no—
207#117—91no—
208#117—181no—
209C2×C42—32no—
210C2×C42—62no—
211C2×C42—181no—
212C2×C42D3211yescharacteristic
213#104—98no—
214#97—61no—
215C4×C8—61no—
216C23×C3—21no—
217C23×C3C2×D1211yescharacteristic
218C23×C3C2×#6711yescharacteristic
219C22×D3—62no—
220C22×D3—61no—
221C22×D3—61no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—44no—
231C2×C3×C4—68no—
232C2×C3×C4—64no—
233C2×C3×C4(C2×D3)⋊C412yes—
234C2×C3×C4(C2×D3)⋊C412yes—
235C2×C3×C4(C2×D3)⋊C412yes—
236C2×C3×C4(C2×D3)⋊C412yes—
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4C2×C4×D312yes—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×C4×D311yescharacteristic
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4#23512yes—
243C2×C3×C4#23512yes—
244C2×C3×C4C2×#6711yescharacteristic
245#67—68no—
246#67—64no—
247#67—64no—
248C2×Dic3—28no—
249C2×Dic3—24no—
250C2×Dic3—62no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—64no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256D12—32no—
257D12—32no—
258D12—62no—
259D12—62no—
260D12—61no—
261D12—61no—
262C4×D3—68no—
263C4×D3—64no—
264C4×D3—64no—
265C4×D3—128no—
266C4×D3—124no—
267C4×D3—124no—
268Dic6—32no—
269Dic6—32no—
270Dic6—62no—
271Dic6—62no—
272Dic6—61no—
273Dic6—61no—
274C3×C8—64no—
275C3⋊C8—24no—
276C2×C32—22no—
277C2×C32C4×C22⋊C411yescharacteristic
278C2×C32C2×#10412yes—
279C3⋊D3—42no—
280#41—94no—
281#41—182no—
282C2×Q8—91no—
283C2×D4—91no—
284C2×D4—181no—
285C22×C4—62no—
286C22×C4—181no—
287C22×C4—182no—
288C22×C4#62612yes—
289C22×C4C2×D3211yescharacteristic
290M16—34no—
291M16—62no—
292C2×C8—62no—
293C4⋊C4—92no—
294C4⋊C4—182no—
295C22⋊C4—181no—
296C22⋊C4—182no—
297C42—34no—
298C42—68no—
299C42—62no—
300C42—182no—
301C42—181no—
302C42#62412yes—
303C42#62611yescharacteristic
304C42#62611yescharacteristic
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—42no—
310C22×C3C4×D1212yes—
311C22×C3C2×(C2×D3)⋊C411yescharacteristic
312C22×C3C2×(C2×D3)⋊C411yescharacteristic
313C22×C3C4×#6712yes—
314C2×D3—64no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—124no—
318C2×D3—122no—
319C2×D3—122no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—24no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—22no—
326C3×C4—42no—
327C3×C4—68no—
328C3×C4#80514yescomplemented
329C3×C4#82514yescomplemented
330C3×C4C42×D311yescharacteristic
331C3×C4C42×D311yescharacteristic
332C3×C4#87211yescharacteristic
333C3×C4#87211yescharacteristic
334C3×C4C4×D1212yes—
335C3×C4C4×#6712yes—
336Dic3—28no—
337Dic3—64no—
338Dic3—62no—
339Dic3—62no—
340Dic3—124no—
341Dic3—122no—
342Dic3—122no—
343C32C4×#10411yescharacteristic, complemented, Sylow
344C23—181no—
345C23C2×#62611yescharacteristic
346Q8—92no—
347Q8—181no—
348D4—92no—
349D4—184no—
350D4—181no—
351C2×C4—24no—
352C2×C4—68no—
353C2×C4—64no—
354C2×C4—181no—
355C2×C4—184no—
356C2×C4—182no—
357C2×C4—364no—
358C2×C4#372212yes—
359C2×C4#372212yes—
360C2×C4#379812yes—
361C2×C4C4×D3212yes—
362C2×C4C2×#62411yescharacteristic
363C2×C4C2×#62611yescharacteristic
364C8—64no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—21no—
368C2×C3—22no—
369C2×C3—42no—
370C2×C3C2×#80512yes—
371C2×C3C4×(C2×D3)⋊C411yescharacteristic
372C2×C3C4×(C2×D3)⋊C411yescharacteristic
373C2×C3C2×#82512yes—
374D3—124no—
375D3—122no—
376D3—122no—
377C22—22no—
378C22—182no—
379C22—362no—
380C22C4×#62612yes—
381C22C2×#372211yescharacteristic
382C4—22no—
383C4—68no—
384C4—182no—
385C4—362no—
386C4#6357014yesdirect product factor
387C4#6387411yescharacteristic
388C4C4×#62411yescharacteristic
389C4C4×#62612yes—
390C3—21no—
391C3C4×#80511yescharacteristic, complemented
392C3C4×#82511yescharacteristic, complemented
393C2—22no—
394C2—362no—
395C2C2×#6357012yes—
396C2C4×#372211yescharacteristic
subgroupG/H
centerC42#626
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C42×Dic3C2semidirect
3. C3×C4×#208C2semidirect
5. #10589162C2semidirect
12. C4×C4⋊(C3⋊D3)C4semidirect
15. C4×#634C4semidirect
21. #63570C4direct (N × H)
28. C42×Dic3D3semidirect
30. C4×#208D3semidirect
54. C3×C4×Dic3C2×C4semidirect
56. C3×#208C2×C4semidirect
108. C4⋊(C3⋊D3)C42semidirect
112. #634C42semidirect
185. C4×Dic3C4×D3semidirect
187. #208C4×D3semidirect
195. C32×C4#104semidirect
328. C3×C4#805semidirect
329. C3×C4#825semidirect
343. C32C4×#104semidirect
386. C4#63570direct (N × H)
391. C3C4×#805semidirect
392. C3C4×#825semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×C42×Dic32
C3×C4×#2082
C2×#635702
#105891622
C4×#8253
C4×#8053