Finite Group Databasebeta

← C2×C22⋊C4×#1057 #16796905

Subgroups — C2×C22⋊C4×#1057 #16796905

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#1057C211yesmaximal, characteristic
2C22×C22⋊#1057C211yesmaximal, characteristic
3C22×C4×#1057C212yesmaximal, complemented
4C22⋊C4×#1057C218yesmaximal, direct product factor
5C2×#11718290C212yesmaximal, complemented
6C2×C22⋊C4×Dic13C211yesmaximal, characteristic
7C24×Dic13C2211yescharacteristic
8C23×#1057—28no—
9C23×#1057C418yescomplemented
10C23×#1057C2211yescharacteristic
11C23×#1057C2212yes—
12C23×#1057C2214yes—
13C23×#1057C2211yescharacteristic
14C22×C13×C22⋊C4C411yescharacteristic
15C22×C22⋊Dic13C411yescharacteristic
16C22×C4×Dic13C2212yes—
17C2×C22⋊#1057C418yescomplemented
18C2×C22⋊#1057C2214yes—
19C2×C4×#1057—28no—
20C2×C4×#1057C2218yescomplemented
21C2×#88071C412yes—
22C22⋊C4×Dic13C414yes—
23C22⋊C4×Dic13C2214yes—
24#11718290C2218yescomplemented
25C25×C13C2×C411yescharacteristic
26C23×C4×C13C2×C412yes—
27C23×Dic13—24no—
28C23×Dic13—24no—
29C23×Dic13C2×C412yes—
30C23×Dic13C2×C411yescharacteristic
31C23×Dic13C2×C414yes—
32C23×Dic13C2×C414yes—
33C23×Dic13C2×C412yes—
34C23×Dic13C2312yes—
35C23×Dic13C2311yescharacteristic
36C22×#1057—24no—
37C22×#1057—24no—
38C22×#1057—24no—
39C22×#1057—232no—
40C22×#1057—216no—
41C22×#1057C2×C418yes—
42C22×#1057C2×C414yes—
43C22×#1057C2×C414yes—
44C22×#1057C2×C4116yescomplemented
45C22×#1057D418yes—
46C22×#1057C2314yes—
47C22×#1057C2312yes—
48C22×#1057C2312yes—
49C2×C13×C22⋊C4C818yescomplemented
50C2×C13×C22⋊C4C2×C414yes—
51C2×C22⋊Dic13C818yescomplemented
52C2×C22⋊Dic13C2×C414yes—
53C2×C4×Dic13—24no—
54C2×C4×Dic13—24no—
55C2×C4×Dic13C2×C414yes—
56C2×C4×Dic13C2314yes—
57C22⋊#1057C2×C4116yescomplemented
58C4×#1057—216no—
59#88071C2×C418yes—
60C2×C8×C22⋊C4—131nomaximal, Sylow
61C24×C13—24no—
62C24×C13—24no—
63C24×C13C4214yes—
64C24×C13C2×C814yes—
65C24×C13C2×C814yes—
66C24×C13C22×C412yes—
67C24×C13C22×C411yescharacteristic
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13C2×C818yescomplemented
71C22×C4×C13C22×C414yes—
72C22×Dic13—24no—
73C22×Dic13—24no—
74C22×Dic13—24no—
75C22×Dic13—28no—
76C22×Dic13—28no—
77C22×Dic13—28no—
78C22×Dic13—216no—
79C22×Dic13—24no—
80C22×Dic13—24no—
81C22×Dic13C4214yes—
82C22×Dic13C4218yes—
83C22×Dic13C2×C818yescomplemented
84C22×Dic13C22×C412yes—
85C22×Dic13C22×C414yes—
86C22×Dic13C22×C414yes—
87C22×Dic13C22×C414yes—
88C22×Dic13C22×C411yescharacteristic
89C22×Dic13C22×C412yes—
90C22×Dic13C22×C412yes—
91C22×Dic13C2×D414yes—
92C22×Dic13#4114yes—
93C22×Dic13C2411yescharacteristic
94C2×#1057—28no—
95C2×#1057—216no—
96C2×#1057—24no—
97C2×#1057—24no—
98C2×#1057—24no—
99C2×#1057—232no—
100C2×#1057C22⋊C4116yesdirect product factor
101C2×#1057C22×C418yes—
102C2×#1057C22×C414yes—
103C2×#1057C22×C414yes—
104C2×#1057C2×D418yes—
105C13×C22⋊C4C2×C8116yescomplemented
106C22⋊Dic13C2×C8116yescomplemented
107C4×Dic13—28no—
108C4×Dic13—24no—
109C4×Dic13—24no—
110C24×C8—131no—
111C22×C22⋊C8—131no—
112C22×C4×C8—132no—
113C2×C4×C22⋊C4—131no—
114C8×C22⋊C4—138no—
115C2×#336—132no—
116C23×C13—24no—
117C23×C13—24no—
118C23×C13—28no—
119C23×C13—28no—
120C23×C13—216no—
121C23×C13—216no—
122C23×C13C4×C8116yescomplemented
123C23×C13C2×C4214yes—
124C23×C13C2×C4212yes—
125C23×C13C4×D414yes—
126C23×C13C22×C814yes—
127C23×C13C22×C814yes—
128C23×C13C22×C812yes—
129C23×C13C22×C812yes—
130C23×C13#13114yes—
131C23×C13C23×C411yescharacteristic
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—216no—
135C2×C4×C13C22×C818yescomplemented
136C2×Dic13—24no—
137C2×Dic13—24no—
138C2×Dic13—24no—
139C2×Dic13—28no—
140C2×Dic13—216no—
141C2×Dic13—24no—
142C2×Dic13—24no—
143C2×Dic13—28no—
144C2×Dic13—216no—
145C2×Dic13C2×C4214yes—
146C2×Dic13C2×C4212yes—
147C2×Dic13C2×C22⋊C414yes—
148C2×Dic13#11714yes—
149C2×Dic13C4×D418yes—
150C2×Dic13C4×D414yes—
151C2×Dic13C22×C818yescomplemented
152C2×Dic13C23×C411yescharacteristic
153C2×Dic13C23×C411yescharacteristic
154C2×Dic13C22×D412yes—
155C2×Dic13C2×#4112yes—
156#1057—24no—
157#1057—28no—
158#1057C2×C22⋊C418yesdirect product factor
159C24×C4—131no—
160C23×C8—131no—
161C23×C8—132no—
162C23×C8—131no—
163C23×C8—138no—
164C23×C8—134no—
165C23×C8—268no—
166C22×C22⋊C4—131no—
167C22×C22⋊C4#26111yescharacteristic
168C22×C42—132no—
169C2×C22⋊C8—138no—
170C2×C22⋊C8—134no—
171C2×C4×C8—138no—
172C2×C4×C8—268no—
173C4×C22⋊C4—134no—
174C4×C22⋊C4—134no—
175C2×#95—132no—
176#336—138no—
177C22×C13—24no—
178C22×C13—28no—
179C22×C13—28no—
180C22×C13—232no—
181C22×C13—24no—
182C22×C13C4×C22⋊C414yes—
183C22×C13C2×C4×C814yes—
184C22×C13C2×C4×C818yescomplemented
185C22×C13#40514yes—
186C22×C13C8×D418yes—
187C22×C13C8×D418yes—
188C22×C13C22×C4211yescharacteristic
189C22×C13C2×C4×D412yes—
190C22×C13C23×C811yescharacteristic
191C22×C13C23×C811yescharacteristic
192C22×C13C2×#13112yes—
193C4×C13—28no—
194Dic13—28no—
195Dic13—24no—
196Dic13C4×C22⋊C414yes—
197Dic13C22×C22⋊C411yescharacteristic
198Dic13C2×#11711yescharacteristic
199Dic13C2×C4×D412yes—
200C25C2×#26111yescharacteristic
201C23×C4—131no—
202C23×C4—134no—
203C23×C4—134no—
204C23×C4—132no—
205C23×C4—132no—
206C23×C4—132no—
207C23×C4—131no—
208C23×C4—264no—
209C23×C4—264no—
210C23×C4C2×#26112yes—
211C22×C8—132no—
212C22×C8—134no—
213C22×C8—138no—
214C22×C8—132no—
215C22×C8—134no—
216C22×C8—1316no—
217C22×C8—134no—
218C22×C8—138no—
219C22×C8—2616no—
220C22×C8—2632no—
221C22×C8—264no—
222C22×C8—264no—
223C22×C8—264no—
224C2×C22⋊C4—138no—
225C2×C22⋊C4—134no—
226C2×C22⋊C4#105718yesdirect product factor
227C2×C22⋊C4C2×#26114yes—
228C2×C42—134no—
229C2×C42—134no—
230C2×C42—264no—
231C2×C42—264no—
232C22⋊C8—1316no—
233C4×C8—2616no—
234#95—138no—
235C2×C13—28no—
236C2×C13C8×C22⋊C418yescomplemented
237C2×C13C2×C4×C22⋊C411yescharacteristic
238C2×C13C22×C4×C811yescharacteristic
239C2×C13C2×#40511yescharacteristic
240C2×C13C2×C8×D412yes—
241C2×C13C2×C8×D412yes—
242C24—24no—
243C24—24no—
244C24D13⋊C814yes—
245C24C4×#26114yes—
246C24C2×#105714yes—
247C24C22×#26112yes—
248C24C22×#26111yescharacteristic
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—132no—
252C22×C4—132no—
253C22×C4—134no—
254C22×C4—134no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—138no—
258C22×C4—134no—
259C22×C4—134no—
260C22×C4—138no—
261C22×C4—134no—
262C22×C4—132no—
263C22×C4—134no—
264C22×C4—268no—
265C22×C4—264no—
266C22×C4—2616no—
267C22×C4—268no—
268C22×C4—264no—
269C22×C4—268no—
270C22×C4—264no—
271C22×C4—264no—
272C22×C4—264no—
273C22×C4C2×#105718yescomplemented
274C22×C4C22×#26114yes—
275C2×C8—138no—
276C2×C8—134no—
277C2×C8—1316no—
278C2×C8—138no—
279C2×C8—134no—
280C2×C8—2632no—
281C2×C8—264no—
282C2×C8—268no—
283C2×C8—264no—
284C2×C8—2616no—
285C2×C8—264no—
286C22⋊C4—1316no—
287C22⋊C4C2×#1057116yesdirect product factor
288C42—264no—
289C42—264no—
290C42—268no—
291C13C2×C8×C22⋊C411yescharacteristic, complemented, Sylow
292C23—28no—
293C23—216no—
294C23—28no—
295C23—24no—
296C23—24no—
297C23—216no—
298C23C4×#1057116yescomplemented
299C23C2×D13⋊C814yes—
300C23C2×D13⋊C812yes—
301C23C2×C4×#26114yes—
302C23C2×C4×#26112yes—
303C23#8823814yes—
304C23D4×#26114yes—
305C23C22×#105714yes—
306C23C22×#105712yes—
307C23C23×#26111yescharacteristic
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—216no—
311C2×C4—134no—
312C2×C4—138no—
313C2×C4—134no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—132no—
317C2×C4—132no—
318C2×C4—132no—
319C2×C4—134no—
320C2×C4—138no—
321C2×C4—134no—
322C2×C4—264no—
323C2×C4—264no—
324C2×C4—268no—
325C2×C4—2616no—
326C2×C4—2616no—
327C2×C4—268no—
328C2×C4—264no—
329C2×C4—264no—
330C2×C4—264no—
331C2×C4C22×#105718yescomplemented
332C8—138no—
333C8—264no—
334C8—268no—
335C22—24no—
336C22—28no—
337C22—28no—
338C22—232no—
339C22—24no—
340C22#1171906214yes—
341C22#1171906318yes—
342C22C22⋊C4×#26114yes—
343C22C2×C4×#105714yes—
344C22C2×C4×#105718yescomplemented
345C22D4×#105718yes—
346C22C22×D13⋊C811yescharacteristic
347C22C22×C4×#26111yescharacteristic
348C22C2×#8823812yes—
349C22C2×D4×#26112yes—
350C22C23×#105711yescharacteristic
351C4—28no—
352C4—131no—
353C4—131no—
354C4—132no—
355C4—134no—
356C4—264no—
357C4—268no—
358C2—28no—
359C2C22⋊C4×#105718yesdirect product factor
360C2C2×C22⋊C4×#26111yescharacteristic
361C2C22×C4×#105711yescharacteristic
362C2C2×#1171906211yescharacteristic
363C2C2×D4×#105712yes—
364C2C2×#1171906312yes—
subgroupG/H
centerC24C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C2×C8×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×#1057C2semidirect
4. C22⋊C4×#1057C2direct (N × H)
5. C2×#11718290C2semidirect
9. C23×#1057C4semidirect
17. C2×C22⋊#1057C4semidirect
20. C2×C4×#1057C22semidirect
24. #11718290C22semidirect
44. C22×#1057C2×C4semidirect
49. C2×C13×C22⋊C4C8semidirect
51. C2×C22⋊Dic13C8semidirect
57. C22⋊#1057C2×C4semidirect
70. C22×C4×C13C2×C8semidirect
83. C22×Dic13C2×C8semidirect
100. C2×#1057C22⋊C4direct (N × H)
105. C13×C22⋊C4C2×C8semidirect
106. C22⋊Dic13C2×C8semidirect
122. C23×C13C4×C8semidirect
135. C2×C4×C13C22×C8semidirect
151. C2×Dic13C22×C8semidirect
158. #1057C2×C22⋊C4direct (N × H)
184. C22×C13C2×C4×C8semidirect
226. C2×C22⋊C4#1057direct (N × H)
236. C2×C13C8×C22⋊C4semidirect
273. C22×C4C2×#1057semidirect
287. C22⋊C4C2×#1057direct (N × H)
291. C13C2×C8×C22⋊C4semidirect
298. C23C4×#1057semidirect
331. C2×C4C22×#1057semidirect
344. C22C2×C4×#1057semidirect
359. C2C22⋊C4×#1057direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#10572
C22×C22⋊#10572
C22×C4×#10572
C22⋊C4×#10572
C2×#117182902
C2×C22⋊C4×Dic132
C2×C8×C22⋊C413