Finite Group Databasebeta

← C2×#13130944 #16799056

Subgroups — C2×#13130944 #16799056

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88104C211yesmaximal, characteristic
2C2×#11719079C212yesmaximal
3C22×C8×#261C211yesmaximal, characteristic
4#13130944C218yesmaximal, direct product factor
5C2×#11718247C212yesmaximal
6C2×#11718541C211yesmaximal, characteristic
7C22×C4×#261C2211yescharacteristic
8C22×#6118C2212yes—
9C22×D13⋊C8C2211yescharacteristic
10C22×C8×D13C2211yescharacteristic
11C2×#88146C2212yes—
12C2×#88112—22no—
13C2×C4⋊#1057—22no—
14C2×#88104—24no—
15C2×#88104C2214yes—
16C2×C8×#261—24no—
17C2×C8×#261C2214yes—
18#11719079—24no—
19#11719079C2218yes—
20C2×C13×#107C411yescharacteristic, complemented
21C2×#88058C411yescharacteristic, complemented
22C2×#88048C412yescomplemented
23#11718541C414yescomplemented
24#11718541C2214yes—
25#11718247C2218yes—
26C23×#261—21no—
27C22×C4×D13C2311yescharacteristic
28C22×#1057—22no—
29C22×#1057D411yescharacteristic
30C22×#1057D411yescharacteristic
31C2×C4×#261—22no—
32C2×C4×#261—21no—
33C2×C4×#261Q814yes—
34C2×C4×#261C2312yes—
35C2×#6118—24no—
36C2×#6118—24no—
37C2×#6118—22no—
38C2×#6118C2314yes—
39C2×D13⋊C8—22no—
40C2×D13⋊C8—22no—
41C2×D13⋊C8D412yes—
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×D13D414yes—
51C2×C8×D13Q814yes—
52C2×C8×D13C2312yes—
53#88146—22no—
54#88146—22no—
55#88146C2×C414yes—
56#88146C2314yes—
57#88112—28no—
58C4⋊#1057—28no—
59#88104—28no—
60C8×#261—28no—
61C13×#107C2×C414yescomplemented
62#88058C2×C414yescomplemented
63#88048C2×C418yescomplemented
64C2×#1945—131nomaximal, Sylow
65C23×D13#4111yescharacteristic
66C22×#261—24no—
67C22×#261—24no—
68C22×#261—24no—
69C22×#261—22no—
70C22×C4×C13—22no—
71C22×C4×C13C22×C411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13C2×D411yescharacteristic
74C2×C4×D13C22×C411yescharacteristic
75C2×C4×D13C2×D412yes—
76C2×C4×D13C2×D411yescharacteristic
77C2×C4×D13C2×Q812yes—
78C2×C4×D13C2×Q812yes—
79C2×C4×D13#4112yes—
80C2×C4×D13#4111yescharacteristic
81C2×C4×D13C2411yescharacteristic
82C2×#1057—22no—
83C2×#1057—22no—
84C2×#1057—24no—
85C2×#1057—44no—
86C2×#1057C2×D412yes—
87C2×#1057C2×D412yes—
88C4×#261—24no—
89C4×#261—22no—
90C4×#261C2×Q814yes—
91#6118—24no—
92#6118—24no—
93#6118—44no—
94D13⋊C8—24no—
95D13⋊C8—22no—
96D13⋊C8—22no—
97C2×C8×C13C4⋊C414yes—
98C2×C8×C13C22×C412yes—
99C13×C4⋊C4—22no—
100C13×C4⋊C4C22×C414yes—
101#6103—24no—
102#6103—24no—
103C4⋊Dic13—22no—
104C4⋊Dic13C22×C414yes—
105C4×Dic13—24no—
106C4×Dic13—24no—
107C2×#1055C4⋊C414yes—
108C2×#1055C22×C412yes—
109C8×D13C4⋊C418yes—
110C8×D13C2×D414yes—
111C8×D13C2×Q814yes—
112C22×#108—131no—
113C2×#427—131no—
114C2×#424—132no—
115C22×C4×C8—131no—
116#1945—138no—
117C2×#339—132no—
118C23×C13C4×D411yescharacteristic
119C22×D13—22no—
120C22×D13—22no—
121C22×D13C4×D411yescharacteristic
122C22×D13C22⋊Q812yes—
123C22×D13#12512yes—
124C22×D13C2×#4111yescharacteristic
125C2×#261—24no—
126C2×#261—24no—
127C2×#261—216no—
128C2×#261—24no—
129C2×C4×C13—24no—
130C2×C4×C13—44no—
131C2×C4×C13C2×C4⋊C412yes—
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13C4×Q812yes—
134C2×C4×C13C23×C411yescharacteristic
135C2×Dic13—24no—
136C2×Dic13—44no—
137C2×Dic13C4×D411yescharacteristic
138C2×Dic13#12112yes—
139C2×Dic13C4⋊Q812yes—
140C2×Dic13C22×D411yescharacteristic
141C4×D13C2×C4⋊C412yes—
142C4×D13C4×Q812yes—
143C4×D13#12112yes—
144C4×D13C22⋊Q812yes—
145C4×D13#12512yes—
146C4×D13C4⋊Q812yes—
147C4×D13C22×D411yescharacteristic
148C4×D13C22×Q811yescharacteristic
149C4×D13C22×Q811yescharacteristic
150C4×D13C2×#4111yescharacteristic
151#1057—22no—
152#1057—22no—
153#1057—44no—
154C8×C13C2×C4⋊C414yes—
155#1055C2×C4⋊C414yes—
156C22×M16—132no—
157C23×C8—131no—
158C23×C8—131no—
159C2×#117—132no—
160C22×C42—131no—
161C2×#108—134no—
162C2×#108—264no—
163#427—134no—
164#427—134no—
165C2×#107—131no—
166C2×#107#26111yescharacteristic, complemented
167C2×#106—132no—
168#424—138no—
169#424—264no—
170C2×C4⋊C8—262no—
171C2×C4⋊C8—262no—
172C2×C4×C8—134no—
173C2×C4×C8—264no—
174#339—138no—
175C22×C13#38912yes—
176C22×C13#44312yes—
177C22×C13#44312yes—
178C22×C13C2×C4×D411yescharacteristic
179C2×D13—21no—
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—24no—
184C2×D13—24no—
185C2×D13#38912yes—
186C2×D13C2×C22⋊Q811yescharacteristic
187C2×D13C2×#12511yescharacteristic
188#261—28no—
189C4×C13—44no—
190C4×C13#38912yes—
191C4×C13C22×C4⋊C411yescharacteristic
192C4×C13C2×C4×Q811yescharacteristic
193Dic13—44no—
194Dic13#38912yes—
195Dic13C2×#12111yescharacteristic
196Dic13C2×C4⋊Q811yescharacteristic
197C23×C4—131no—
198C23×C4—261no—
199C2×M16—134no—
200C2×M16—262no—
201C2×M16—264no—
202C2×M16—264no—
203C22×C8—131no—
204C22×C8—134no—
205C22×C8—134no—
206C22×C8—132no—
207C22×C8—132no—
208C22×C8—132no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—132no—
212C22×C8—262no—
213C22×C8—262no—
214C22×C8—262no—
215C22×C8C2×#26111yescharacteristic
216#117—134no—
217#117—134no—
218#117—262no—
219#117—262no—
220C2×C4⋊C4—132no—
221C2×C4⋊C4C2×#26112yes—
222C2×C22⋊C4—262no—
223C2×C42—132no—
224C2×C42—134no—
225C2×C42—262no—
226C2×C42—262no—
227C2×C42—261no—
228#108—268no—
229#107—134no—
230#107C2×#26114yescomplemented
231#106—138no—
232C4⋊C8—268no—
233C4⋊C8—268no—
234C4×C8—268no—
235C2×C13#194514yescomplemented
236C2×C13C2×#38911yescharacteristic
237C2×C13C2×#44311yescharacteristic
238C2×C13C2×#44311yescharacteristic
239D13—21no—
240D13—21no—
241D13—22no—
242C24—131no—
243C22×C4—22no—
244C22×C4—131no—
245C22×C4—132no—
246C22×C4—132no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—264no—
254C22×C4—262no—
255C22×C4—264no—
256C22×C4—264no—
257C22×C4—262no—
258C22×C4C22×#26111yescharacteristic
259M16—264no—
260M16—264no—
261M16—524no—
262C2×C8—134no—
263C2×C8—132no—
264C2×C8—134no—
265C2×C8—138no—
266C2×C8—134no—
267C2×C8—132no—
268C2×C8—132no—
269C2×C8—262no—
270C2×C8—264no—
271C2×C8—262no—
272C2×C8—262no—
273C2×C8—262no—
274C2×C8—264no—
275C2×C8—524no—
276C2×C8C4⋊#26114yes—
277C2×C8C22×#26112yes—
278C4⋊C4—22no—
279C4⋊C4—134no—
280C4⋊C4—262no—
281C4⋊C4C22×#26114yes—
282C22⋊C4—264no—
283C22⋊C4—264no—
284C42—134no—
285C42—264no—
286C42—264no—
287C42—262no—
288C42—264no—
289C13C2×#194511yescharacteristic, complemented, Sylow
290C23—132no—
291C23—132no—
292C23—131no—
293C23—131no—
294C23—262no—
295C23—262no—
296C23D4×#26111yescharacteristic
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—132no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—132no—
307C2×C4—131no—
308C2×C4—132no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—132no—
313C2×C4—264no—
314C2×C4—264no—
315C2×C4—264no—
316C2×C4—2616no—
317C2×C4—264no—
318C2×C4—524no—
319C2×C4C2×C4⋊#26112yes—
320C2×C4D4×#26111yescharacteristic
321C2×C4Q8×#26112yes—
322C2×C4C23×#26111yescharacteristic
323C8—134no—
324C8—262no—
325C8—262no—
326C8—524no—
327C8C2×C4⋊#26114yes—
328C22—131no—
329C22—131no—
330C22—132no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22—261no—
335C22—264no—
336C22—264no—
337C22#1171908312yes—
338C22#1171910312yes—
339C22#1171911112yes—
340C22C2×D4×#26111yescharacteristic
341C4—44no—
342C4—131no—
343C4—131no—
344C4—132no—
345C4—268no—
346C4—524no—
347C4#1171908312yes—
348C4C22×C4⋊#26111yescharacteristic
349C4C2×Q8×#26111yescharacteristic
350C2—261no—
351C2—261no—
352C2—262no—
353C2#1313094414yesdirect product factor
354C2C2×#1171908311yescharacteristic
355C2C2×#1171910311yescharacteristic
356C2C2×#1171911111yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#107C4
socleC23×C13C4×D4
prime radicalC23×D13#41
cosocleC2×C4×D13C24
hypercenterC2×#107#261
hypocenterC13C2×#1945
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #13130944C2direct (N × H)
20. C2×C13×#107C4semidirect
21. C2×#88058C4semidirect
22. C2×#88048C4semidirect
23. #11718541C4semidirect
61. C13×#107C2×C4semidirect
62. #88058C2×C4semidirect
63. #88048C2×C4semidirect
166. C2×#107#261semidirect
230. #107C2×#261semidirect
235. C2×C13#1945semidirect
289. C13C2×#1945semidirect
353. C2#13130944direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881042
C2×#117190792
C22×C8×#2612
#131309442
C2×#117182472
C2×#117185412
C2×#194513