Finite Group Databasebeta

← C2×#13130478 #16795425

Subgroups — C2×#13130478 #16795425

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719080C211yesmaximal, characteristic, complemented
2C2×#11719076C211yesmaximal, characteristic
3#13130478C218yesmaximal, direct product factor
4C2×#11718254C211yesmaximal, characteristic, complemented
5C2×#11718244C211yesmaximal, characteristic, complemented
6C2×#11718243C211yesmaximal, characteristic
7C2×#11718251C211yesmaximal, characteristic, complemented
8C2×#11718513C211yesmaximal, characteristic
9C22×#6118—21no—
10C22×#6095C411yescharacteristic
11C2×#88147C2211yescharacteristic
12C2×#88141C2211yescharacteristic
13C2×#88111—21no—
14C2×#88110—21no—
15C2×C4⋊#1057—21no—
16C2×C4⋊#1057C2211yescharacteristic
17C2×C4⋊#1057C2211yescharacteristic
18C2×C4×#1057C2211yescharacteristic
19C2×C4×#1057C2211yescharacteristic
20#11719080—22no—
21#11719080C2214yescomplemented
22#11719076—22no—
23#11719076C2214yes—
24C2×C13×#106C411yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C2×#88050C411yescharacteristic
27C2×#88049C411yescharacteristic
28#11718513C414yes—
29#11718513C2214yes—
30#11718254C2214yescomplemented
31#11718251C2214yescomplemented
32#11718244C2214yescomplemented
33#11718243C2214yes—
34C22×D52C2×C411yescharacteristic
35C22×C4×D13—21no—
36C22×Dic26C2×C411yescharacteristic
37C22×#1057—21no—
38C22×#1057—21no—
39C22×#1057—21no—
40C22×#1057D411yescharacteristic
41C22×#1057D411yescharacteristic
42C2×#6118—24no—
43C2×#6118—44no—
44C22×C8×C13C2×C411yescharacteristic
45C2×C13×C4⋊C4C2×C411yescharacteristic
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×#6103—21no—
48C2×#6101—21no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13C2311yescharacteristic
51C22×#1055C2×C411yescharacteristic
52C2×#6095—24no—
53C2×#6095C2×C414yes—
54#88147—21no—
55#88147—21no—
56#88147C2×C412yes—
57#88147C2312yes—
58#88141—21no—
59#88141—21no—
60#88141C2×C412yes—
61#88141C2312yes—
62#88111—24no—
63#88110—24no—
64C4⋊#1057—24no—
65C4⋊#1057—21no—
66C4⋊#1057—21no—
67C4⋊#1057C2312yes—
68C4⋊#1057C2312yes—
69C4×#1057—21no—
70C4×#1057D412yes—
71C4×#1057C2312yes—
72C4×#1057C2312yes—
73C13×#106C2×C414yes—
74C8×Dic13C2×C412yes—
75C8×Dic13C2312yes—
76#88050C2×C414yes—
77#88049C2×C414yes—
78C2×#1592—131nomaximal, Sylow
79C23×D13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13C22×C411yescharacteristic
83C22×Dic13—21no—
84C22×Dic13C2×D411yescharacteristic
85C22×Dic13#4111yescharacteristic
86C2×D52—22no—
87C2×D52—22no—
88C2×D52—21no—
89C2×D52C22×C412yes—
90C2×C4×D13—22no—
91C2×C4×D13—22no—
92C2×C4×D13—42no—
93C2×C4×D13—42no—
94C2×Dic26—22no—
95C2×Dic26—22no—
96C2×Dic26—21no—
97C2×Dic26C22×C412yes—
98C2×#1057—22no—
99C2×#1057—22no—
100C2×#1057—22no—
101C2×#1057—22no—
102C2×#1057—22no—
103C2×#1057—42no—
104C2×#1057—42no—
105C2×#1057—42no—
106C2×#1057C2×D412yes—
107C2×#1057C2×D412yes—
108#6118—48no—
109C2×C8×C13M1614yescomplemented
110C2×C8×C13C22×C412yes—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4C22×C412yes—
114C13×C4⋊C4C22×C412yes—
115#6103—22no—
116#6103—22no—
117#6101—22no—
118#6101—22no—
119C4×Dic13—22no—
120C4×Dic13—22no—
121C4×Dic13C22×C411yescharacteristic
122C4×Dic13C2×D411yescharacteristic
123C4×Dic13#4111yescharacteristic
124C4×Dic13C2411yescharacteristic
125C2×#1055—22no—
126C2×#1055C22×C412yes—
127#6095—28no—
128C2×#446—131no—
129C2×C4×SD16—131no—
130C2×#436—131no—
131#1592—138no—
132C2×#335—131no—
133C2×Q8⋊C8—131no—
134C2×D4⋊C8—131no—
135C2×#322—131no—
136C23×C13C4×D411yescharacteristic
137C22×D13—22no—
138C22×D13—42no—
139C22×D13—42no—
140C22×D13—42no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C2×M1612yes—
147C2×C4×C13#13112yes—
148C2×C4×C13C23×C411yescharacteristic
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—42no—
152C2×Dic13C4×D411yescharacteristic
153C2×Dic13C4×D411yescharacteristic
154C2×Dic13AGL(1,ℤ/8)12yes—
155C2×Dic13#13712yes—
156C2×Dic13C22×D411yescharacteristic
157C2×Dic13C2×#4111yescharacteristic
158D52—22no—
159D52—22no—
160D52—42no—
161C4×D13—42no—
162C4×D13—42no—
163C4×D13—44no—
164Dic26—22no—
165Dic26—22no—
166Dic26—42no—
167#1057—22no—
168#1057—22no—
169#1057—42no—
170#1057—42no—
171#1057—42no—
172C8×C13C2×M1614yescomplemented
173#1055—22no—
174C22×SD16—131no—
175C22×M16—261no—
176C2×C4×Q8—131no—
177C2×C4×D4—131no—
178#446—134no—
179#446—262no—
180C4×SD16—134no—
181C4×SD16—134no—
182#436—134no—
183#436—262no—
184C2×#106#26111yescharacteristic
185C2×C4⋊C8—131no—
186C2×C4⋊C8—131no—
187C2×C4⋊C8—261no—
188C2×#103—131no—
189C2×#102—131no—
190C2×C22⋊C8—261no—
191C2×#97—261no—
192C2×C4×C8—131no—
193C2×C4×C8—131no—
194C2×C4×C8—131no—
195#335—134no—
196Q8⋊C8—134no—
197D4⋊C8—134no—
198#322—134no—
199C22×C13#43612yes—
200C22×C13#44012yes—
201C22×C13#44412yes—
202C22×C13C2×C4×D411yescharacteristic
203C2×D13—42no—
204C2×D13—42no—
205C2×D13—42no—
206C2×D13—84no—
207C4×C13—42no—
208C4×C13—42no—
209C4×C13#43612yes—
210C4×C13C22×M1611yescharacteristic
211C4×C13C2×#13111yescharacteristic
212Dic13—21no—
213Dic13—21no—
214Dic13—42no—
215Dic13#44012yes—
216Dic13C2×AGL(1,ℤ/8)11yescharacteristic
217Dic13C2×#13711yescharacteristic
218C22×Q8—131no—
219C22×D4—131no—
220C23×C4—261no—
221C2×SD16—134no—
222C2×SD16—264no—
223C2×M16—264no—
224C2×M16—524no—
225C22×C8—131no—
226C22×C8—131no—
227C22×C8—131no—
228C22×C8—261no—
229C22×C8—261no—
230C22×C8—261no—
231C22×C8C2×#26111yescharacteristic
232C4×Q8—132no—
233C4×Q8—132no—
234C4×Q8—261no—
235C4×Q8—261no—
236C4×D4—132no—
237C4×D4—132no—
238C4×D4—261no—
239C4×D4—261no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4C2×#26111yescharacteristic
242C2×C4⋊C4C2×#26111yescharacteristic
243C2×C22⋊C4—261no—
244C2×C42—131no—
245C2×C42—261no—
246#106C2×#26114yes—
247C4⋊C8—132no—
248C4⋊C8—132no—
249C4⋊C8—261no—
250C4⋊C8—261no—
251C4⋊C8—264no—
252#103—134no—
253#102—134no—
254C22⋊C8—264no—
255#97—264no—
256C4×C8—132no—
257C4×C8—132no—
258C4×C8—132no—
259C4×C8—132no—
260C4×C8—132no—
261C4×C8—261no—
262C2×C13#159214yescomplemented
263C2×C13C2×#43611yescharacteristic
264C2×C13C2×#44011yescharacteristic
265C2×C13C2×#44411yescharacteristic
266D13—82no—
267C24—261no—
268C2×Q8—132no—
269C2×Q8—261no—
270C2×Q8—262no—
271C2×Q8—262no—
272C2×D4—132no—
273C2×D4—262no—
274C2×D4—261no—
275C2×D4—262no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—261no—
283C22×C4—522no—
284C22×C4—522no—
285C22×C4C22×#26111yescharacteristic
286SD16—268no—
287M16—528no—
288C2×C8—132no—
289C2×C8—132no—
290C2×C8—132no—
291C2×C8—262no—
292C2×C8—262no—
293C2×C8—262no—
294C2×C8—262no—
295C2×C8—262no—
296C2×C8—262no—
297C2×C8—522no—
298C2×C8—522no—
299C2×C8—522no—
300C2×C8#611814yescomplemented
301C2×C8C22×#26112yes—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—262no—
305C4⋊C4—262no—
306C4⋊C4C22×#26112yes—
307C4⋊C4C22×#26112yes—
308C22⋊C4—262no—
309C22⋊C4—262no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—262no—
315C42—262no—
316C13C2×#159211yescharacteristic, complemented, Sylow
317C23—262no—
318C23—522no—
319C23—522no—
320C23—522no—
321C23D4×#26111yescharacteristic
322Q8—262no—
323Q8—262no—
324Q8—522no—
325D4—262no—
326D4—262no—
327D4—522no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—132no—
333C2×C4—132no—
334C2×C4—131no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—262no—
339C2×C4—262no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—524no—
343C2×C4—522no—
344C2×C4C2×#611812yes—
345C2×C4D4×#26111yescharacteristic
346C2×C4#8824012yes—
347C2×C4C23×#26111yescharacteristic
348C8—262no—
349C8—262no—
350C8—262no—
351C8—522no—
352C8—522no—
353C8—522no—
354C8C2×#611814yescomplemented
355C22—522no—
356C22—522no—
357C22—522no—
358C22—1044no—
359C22#1171907612yes—
360C22#1171910612yes—
361C22#1171910812yes—
362C22C2×D4×#26111yescharacteristic
363C4—42no—
364C4—42no—
365C4—131no—
366C4—131no—
367C4—132no—
368C4—261no—
369C4—261no—
370C4—522no—
371C4#1171907612yes—
372C4C22×#611811yescharacteristic
373C4C2×#8824011yescharacteristic
374C2—1042no—
375C2#1313047814yesdirect product factor
376C2C2×#1171907611yescharacteristic
377C2C2×#1171910611yescharacteristic
378C2C2×#1171910811yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#106C4
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC4×Dic13C24
hypercenterC2×#106#261
hypocenterC13C2×#1592
LCSG ▷ C2×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
1. C2×#11719080C2semidirect
3. #13130478C2direct (N × H)
4. C2×#11718254C2semidirect
5. C2×#11718244C2semidirect
7. C2×#11718251C2semidirect
21. #11719080C22semidirect
30. #11718254C22semidirect
31. #11718251C22semidirect
32. #11718244C22semidirect
109. C2×C8×C13M16semidirect
172. C8×C13C2×M16semidirect
262. C2×C13#1592semidirect
300. C2×C8#6118semidirect
316. C13C2×#1592semidirect
354. C8C2×#6118semidirect
375. C2#13130478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190802
C2×#117190762
#131304782
C2×#117182542
C2×#117182442
C2×#117182432
C2×#117182512
C2×#117185132
C2×#159213