Finite Group Databasebeta

← C2×#13130639 #16797167

Subgroups — C2×#13130639 #16797167

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88103C211yesmaximal, characteristic
2C2×#11719072C212yesmaximal
3C22×C8×#261C211yesmaximal, characteristic
4#13130639C218yesmaximal, direct product factor
5C2×#11718247C212yesmaximal
6C2×#11718521C211yesmaximal, characteristic
7C22×C4×#261C2211yescharacteristic
8C22×#6118C2212yes—
9C22×D13⋊C8C2211yescharacteristic
10C22×C8×D13C2211yescharacteristic
11C2×#88146C2212yes—
12C2×#88110—22no—
13C2×C4×#1057—22no—
14C2×#88103C418yescomplemented
15C2×#88103C2214yes—
16C2×C8×#261C418yescomplemented
17C2×C8×#261C2214yes—
18#11719072—24no—
19#11719072C2218yes—
20C2×C13×#106C411yescharacteristic, complemented
21C2×#88057C411yescharacteristic, complemented
22C2×#88047C412yescomplemented
23#11718521C414yescomplemented
24#11718521C2214yes—
25#11718247C2218yes—
26C23×#261—21no—
27C22×C4×D13C2311yescharacteristic
28C22×#1057—22no—
29C22×#1057D411yescharacteristic
30C22×#1057D411yescharacteristic
31C2×C4×#261—21no—
32C2×C4×#261—22no—
33C2×C4×#261C2×C414yes—
34C2×C4×#261C2312yes—
35C2×#6118—22no—
36C2×#6118—24no—
37C2×#6118C2×C418yes—
38C2×#6118C2314yes—
39C2×D13⋊C8C2×C414yes—
40C2×D13⋊C8D412yes—
41C2×D13⋊C8Q814yes—
42C2×D13⋊C8C2312yes—
43C22×C8×C13C2×C411yescharacteristic
44C2×C13×C4⋊C4C2×C412yes—
45C2×#6103—22no—
46C2×C4⋊Dic13C2×C412yes—
47C2×C4×Dic13—22no—
48C22×#1055C2×C411yescharacteristic
49C2×C8×D13C2×C412yes—
50C2×C8×D13C2×C414yes—
51C2×C8×D13C2×C414yes—
52C2×C8×D13C2312yes—
53#88146—22no—
54#88146—22no—
55#88146C2×C414yes—
56#88146C2314yes—
57#88110—28no—
58C4×#1057—28no—
59#88103C2×C4116yescomplemented
60C8×#261C2×C4116yescomplemented
61C13×#106C2×C414yescomplemented
62#88057C2×C414yescomplemented
63#88047C2×C418yescomplemented
64C2×#1772—131nomaximal, Sylow
65C23×D13#4111yescharacteristic
66C22×#261—28no—
67C22×#261—24no—
68C22×#261—22no—
69C22×C4×C13—22no—
70C22×C4×C13C22×C411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13C2×D411yescharacteristic
73C2×C4×D13C22×C411yescharacteristic
74C2×C4×D13C22×C412yes—
75C2×C4×D13C22×C412yes—
76C2×C4×D13C2×D411yescharacteristic
77C2×C4×D13C2×Q812yes—
78C2×C4×D13#4111yescharacteristic
79C2×C4×D13#4112yes—
80C2×C4×D13C2411yescharacteristic
81C2×#1057—28no—
82C2×#1057—24no—
83C2×#1057C4⋊C414yes—
84C2×#1057C4⋊C414yes—
85C2×#1057C2×D412yes—
86C2×#1057C2×D412yes—
87C4×#261—24no—
88C4×#261—22no—
89C4×#261C22×C414yes—
90#6118—28no—
91#6118—24no—
92#6118C22×C418yes—
93D13⋊C8C4⋊C418yes—
94D13⋊C8C22×C414yes—
95D13⋊C8C2×Q814yes—
96C2×C8×C13C4214yes—
97C2×C8×C13C22×C412yes—
98C13×C4⋊C4—22no—
99C13×C4⋊C4C22×C414yes—
100#6103—24no—
101#6103—24no—
102C4⋊Dic13—22no—
103C4⋊Dic13C22×C414yes—
104C4×Dic13—24no—
105C4×Dic13—24no—
106C2×#1055C4214yes—
107C2×#1055C22×C412yes—
108C8×D13C4218yes—
109C8×D13C22×C414yes—
110C8×D13C22×C414yes—
111C22×#108—131no—
112C2×#427—131no—
113C2×#405—132no—
114C22×C4×C8—131no—
115#1772—138no—
116C2×#339—132no—
117C23×C13C4×D411yescharacteristic
118C22×D13—24no—
119C22×D13#11712yes—
120C22×D13C4×D411yescharacteristic
121C22×D13C4×Q812yes—
122C22×D13C2×#4111yescharacteristic
123C2×#261—28no—
124C2×#261—216no—
125C2×#261—24no—
126C2×C4×C13—24no—
127C2×C4×C13—44no—
128C2×C4×C13C2×C4212yes—
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13C4×Q812yes—
131C2×C4×C13C23×C411yescharacteristic
132C2×Dic13—24no—
133C2×Dic13—44no—
134C2×Dic13C2×C4⋊C412yes—
135C2×Dic13C4×D412yes—
136C2×Dic13C4×D411yescharacteristic
137C2×Dic13C22×D411yescharacteristic
138C4×D13C2×C4212yes—
139C4×D13C2×C4⋊C412yes—
140C4×D13#11712yes—
141C4×D13C4×D412yes—
142C4×D13C4×Q812yes—
143C4×D13C4×Q812yes—
144C4×D13C23×C411yescharacteristic
145C4×D13C23×C411yescharacteristic
146C4×D13C22×Q811yescharacteristic
147C4×D13C2×#4111yescharacteristic
148#1057—28no—
149#1057C2×C4⋊C414yes—
150#1057C2×C4⋊C414yes—
151C8×C13C2×C4214yes—
152#1055C2×C4214yes—
153C22×M16—132no—
154C23×C8—131no—
155C23×C8—131no—
156C2×#117—132no—
157C22×C42—131no—
158C2×#108—138no—
159C2×#108—134no—
160#427—134no—
161#427—134no—
162C2×#107—132no—
163C2×#106—131no—
164C2×#106#26111yescharacteristic, complemented
165#405—138no—
166#405—264no—
167C2×#97—262no—
168C2×C4×C8—138no—
169C2×C4×C8—134no—
170C2×C4×C8—262no—
171#339—138no—
172C22×C13C4×C4⋊C412yes—
173C22×C13#44314yes—
174C22×C13C2×C4×D411yescharacteristic
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—24no—
178C2×D13—24no—
179C2×D13C4×C4⋊C412yes—
180C2×D13C2×#11711yescharacteristic
181C2×D13C2×C4×Q811yescharacteristic
182#261—28no—
183C4×C13—44no—
184C4×C13C4×C4⋊C412yes—
185C4×C13C22×C4211yescharacteristic
186C4×C13C2×C4×Q811yescharacteristic
187Dic13—44no—
188Dic13C4×C4⋊C412yes—
189Dic13C22×C4⋊C411yescharacteristic
190Dic13C2×C4×D411yescharacteristic
191C23×C4—131no—
192C23×C4—261no—
193C2×M16—134no—
194C2×M16—138no—
195C2×M16—262no—
196C2×M16—264no—
197C22×C8—132no—
198C22×C8—134no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—132no—
202C22×C8—134no—
203C22×C8—131no—
204C22×C8—134no—
205C22×C8—134no—
206C22×C8—132no—
207C22×C8—132no—
208C22×C8—262no—
209C22×C8C2×#26111yescharacteristic
210#117—134no—
211#117—134no—
212#117—262no—
213#117—262no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4C2×#26112yes—
216C2×C22⋊C4—262no—
217C2×C42—132no—
218C2×C42—134no—
219C2×C42—262no—
220C2×C42—261no—
221C2×C42—262no—
222#108—1316no—
223#107—138no—
224#106—134no—
225#106C2×#26114yescomplemented
226#97—268no—
227C4×C8—1316no—
228C4×C8—268no—
229C2×C13#177214yescomplemented
230C2×C13C2×C4×C4⋊C411yescharacteristic
231C2×C13C2×#44312yes—
232D13—21no—
233D13—21no—
234D13—22no—
235C24—131no—
236C22×C4—22no—
237C22×C4—131no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—264no—
247C22×C4—262no—
248C22×C4—268no—
249C22×C4—262no—
250C22×C4C22×#26111yescharacteristic
251M16—138no—
252M16—268no—
253M16—264no—
254C2×C8—134no—
255C2×C8—132no—
256C2×C8—132no—
257C2×C8—138no—
258C2×C8—134no—
259C2×C8—134no—
260C2×C8—134no—
261C2×C8—134no—
262C2×C8—132no—
263C2×C8—134no—
264C2×C8—134no—
265C2×C8—138no—
266C2×C8—264no—
267C2×C8—268no—
268C2×C8C4×#26114yes—
269C2×C8C22×#26112yes—
270C4⋊C4—22no—
271C4⋊C4—134no—
272C4⋊C4—262no—
273C4⋊C4C22×#26114yes—
274C22⋊C4—264no—
275C22⋊C4—264no—
276C42—134no—
277C42—264no—
278C42—264no—
279C42—264no—
280C42—262no—
281C13C2×#177211yescharacteristic, complemented, Sylow
282C23—132no—
283C23—132no—
284C23—131no—
285C23—131no—
286C23—264no—
287C23D4×#26111yescharacteristic
288C2×C4—24no—
289C2×C4—44no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—132no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—132no—
304C2×C4—264no—
305C2×C4—268no—
306C2×C4—2616no—
307C2×C4—264no—
308C2×C4—524no—
309C2×C4C2×C4×#26112yes—
310C2×C4D4×#26111yescharacteristic
311C2×C4Q8×#26112yes—
312C2×C4C23×#26111yescharacteristic
313C8—134no—
314C8—134no—
315C8—134no—
316C8—268no—
317C8C2×C4×#26114yes—
318C22—131no—
319C22—131no—
320C22—132no—
321C22—262no—
322C22—262no—
323C22—264no—
324C22—264no—
325C22C4⋊C4×#26112yes—
326C22#1171910714yes—
327C22C2×D4×#26111yescharacteristic
328C4—44no—
329C4—131no—
330C4—131no—
331C4—132no—
332C4—268no—
333C4—524no—
334C4C4⋊C4×#26112yes—
335C4C22×C4×#26111yescharacteristic
336C4C2×Q8×#26111yescharacteristic
337C2—261no—
338C2—261no—
339C2—262no—
340C2#1313063914yesdirect product factor
341C2C2×C4⋊C4×#26111yescharacteristic
342C2C2×#1171910712yes—
subgroupG/H
centerC23D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C13×#106C4
socleC23×C13C4×D4
prime radicalC23×D13#41
cosocleC2×C4×D13C24
hypercenterC2×#106#261
hypocenterC13C2×#1772
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
4. #13130639C2direct (N × H)
14. C2×#88103C4semidirect
16. C2×C8×#261C4semidirect
20. C2×C13×#106C4semidirect
21. C2×#88057C4semidirect
22. C2×#88047C4semidirect
23. #11718521C4semidirect
59. #88103C2×C4semidirect
60. C8×#261C2×C4semidirect
61. C13×#106C2×C4semidirect
62. #88057C2×C4semidirect
63. #88047C2×C4semidirect
164. C2×#106#261semidirect
225. #106C2×#261semidirect
229. C2×C13#1772semidirect
281. C13C2×#1772semidirect
340. C2#13130639direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881032
C2×#117190722
C22×C8×#2612
#131306392
C2×#117182472
C2×#117185212
C2×#177213