Finite Group Databasebeta

← C4×#66968 #13077430

Subgroups — C4×#66968 #13077430

Order 1408.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66968C211yesmaximal, characteristic
2C4×Q8×D11C211yesmaximal, characteristic, complemented
3C4×#4341C211yesmaximal, characteristic
4C4×C11×SD16C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6C4×#4326C211yesmaximal, characteristic, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622415C211yesmaximal, characteristic, complemented
11#10622402C211yesmaximal, characteristic, complemented
12#10622384C211yesmaximal, characteristic
13#10622370C211yesmaximal, characteristic, complemented
14C4×Dic44C211yesmaximal, characteristic, complemented
15C4×#4313C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C4×C22⋊D11—21no—
26C2×C4×Dic11—21no—
27#66968C418yesdirect product factor
28C2×Dic44C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30C2×#4313C2211yescharacteristic
31#66945C2211yescharacteristic
32C4⋊C4×D11—21no—
33C4⋊C4×D11C2211yescharacteristic
34#66940—21no—
35#66940C2211yescharacteristic
36#66940C2211yescharacteristic
37(C22⋊D11)⋊C4—21no—
38#66930—21no—
39C42×D11—21no—
40C42×D11C2211yescharacteristic
41C4×Dic22—21no—
42C4×Dic22C2211yescharacteristic
43C4×Dic22C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C4×C8×C11C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54#66879C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C4×C11⋊C8C2211yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66Q8×D11—22no—
67Q8×D11C2×C414yescomplemented
68#4341—22no—
69#4341C2×C414yes—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11D411yescharacteristic
73C2×C4×D11D411yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C11×SD16C2×C414yescomplemented
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88#4326C2×C414yescomplemented
89#4324C2×C414yescomplemented
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11D411yescharacteristic
106C4×Dic11D411yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44C2×C414yescomplemented
111#4313—22no—
112#4313C2×C414yescomplemented
113C4×#137—111nomaximal, Sylow
114C23×C11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11C22×C412yes—
118D4×C11—21no—
119D4×C11C22×C412yes—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—24no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—24no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—42no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C4×D11—24no—
138C4×D11—22no—
139C4×D11—41no—
140C4×D11—42no—
141C4×D11C22×C412yes—
142C4×D11#4112yes—
143Dic22—21no—
144Dic22—21no—
145Dic22—24no—
146Dic22C22×C412yes—
147Dic22C22×C412yes—
148C8×C11—21no—
149C8×C11C22×C412yes—
150C11⋊C8—21no—
151C11⋊C8C22×C412yes—
152C2×#137—111no—
153C4×#41—111no—
154C2×C4×Q8—111no—
155#441—111no—
156#441—111no—
157#440—111no—
158#440—111no—
159C4×Q16—111no—
160C4×Q16—111no—
161C4×SD16—111no—
162C4×SD16D1111yescharacteristic, complemented
163#428—111no—
164#419—111no—
165#417—111no—
166C4×M16—111no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11C4×D412yes—
174C4×C11—22no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11#13712yescomplemented
179C4×C11C23×C411yescharacteristic
180C4×C11C2×#4111yescharacteristic
181Dic11—22no—
182Dic11—22no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11C4×D412yes—
188C2×#41—111no—
189C22×Q8—111no—
190#137—118no—
191C2×Q16—111no—
192C2×Q16—111no—
193C2×SD16—111no—
194C2×SD16C2×D1111yescharacteristic
195C2×M16—111no—
196C2×M16—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×Q8—221no—
203C4×Q8—221no—
204C4×Q8C2×D1111yescharacteristic
205C4×D4—111no—
206C4×D4—221no—
207C4×D4—221no—
208C4×D4C2×D1111yescharacteristic
209#117—111no—
210#117—221no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C42—111no—
214C2×C42—221no—
215C2×C42—221no—
216#107—111no—
217#107—111no—
218#106—111no—
219#106C2×D1111yescharacteristic
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#102—111no—
227#102C2×D1111yescharacteristic
228#97—111no—
229#97—111no—
230C4×C8—111no—
231C4×C8C2×D1111yescharacteristic
232C2×C11—42no—
233C2×C11C2×C4×D411yescharacteristic
234C2×C11C2×#13711yescharacteristic
235C2×C11#57511yescharacteristic
236D11—22no—
237#41—114no—
238#41—222no—
239C2×Q8—114no—
240C2×Q8—111no—
241C2×Q8—111no—
242C2×Q8—221no—
243C2×Q8—222no—
244C2×Q8C22×D1111yescharacteristic
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—21no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255Q16—114no—
256Q16—114no—
257SD16—114no—
258SD16C4×D1114yescomplemented
259M16—114no—
260M16—222no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8C22×D1111yescharacteristic
264C2×C8C22×D1111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—111no—
267C4⋊C4—111no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C42—21no—
280C42—111no—
281C42—111no—
282C42—111no—
283C42—221no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42C22×D1111yescharacteristic
290C11C4×#13711yescharacteristic, complemented, Sylow
291C23—21no—
292C23—111no—
293Q8—21no—
294Q8—112no—
295Q8—112no—
296Q8—224no—
297Q8—221no—
298Q8—221no—
299Q8C2×C4×D1112yes—
300D4—21no—
301D4—224no—
302D4C2×C4×D1112yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—111no—
308C2×C4—112no—
309C2×C4—112no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—222no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4D4×D1111yescharacteristic
323C2×C4D4×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C8—21no—
326C8—112no—
327C8—221no—
328C8C2×C4×D1112yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—112no—
333C22—221no—
334C22—221no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—112no—
341C4—221no—
342C4—221no—
343C4—222no—
344C4—222no—
345C4—441no—
346C4—441no—
347C4#6696812yesdirect product factor
348C4C22×C4×D1111yescharacteristic
349C4#41×D1111yescharacteristic
350C2—42no—
351C2—222no—
352C2C4×D4×D1111yescharacteristic
353C2C2×#6696811yescharacteristic
354C2#1062329911yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
cosocleC2×C4×C11C24
hypercenterC4×SD16D11
hypocenterC11C4×#137
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D11C2semidirect
4. C4×C11×SD16C2semidirect
5. #10622777C2semidirect
6. C4×#4326C2semidirect
7. C4×#4324C2semidirect
8. #10622474C2semidirect
9. #10622466C2semidirect
10. #10622415C2semidirect
11. #10622402C2semidirect
13. #10622370C2semidirect
14. C4×Dic44C2semidirect
15. C4×#4313C2semidirect
27. #66968C4direct (N × H)
67. Q8×D11C2×C4semidirect
78. C11×SD16C2×C4semidirect
88. #4326C2×C4semidirect
89. #4324C2×C4semidirect
110. Dic44C2×C4semidirect
112. #4313C2×C4semidirect
162. C4×SD16D11semidirect
178. C4×C11#137semidirect
258. SD16C4×D11semidirect
290. C11C4×#137semidirect
347. C4#66968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#669682
C4×Q8×D112
C4×#43412
C4×C11×SD162
#106227772
C4×#43262
C4×#43242
#106224742
#106224662
#106224152
#106224022
#106223842
#106223702
C4×Dic442
C4×#43132
C4×#13711