Finite Group Databasebeta

← C2×#13130945 #16799057

Subgroups — C2×#13130945 #16799057

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88103C211yesmaximal, characteristic
2C2×#11719079C212yesmaximal
3C22×#88100C211yesmaximal, characteristic
4#13130945C218yesmaximal, 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×#88103—24no—
15C2×#88103C2214yes—
16C2×#88100—24no—
17C2×#88100C2214yes—
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×#1057D412yes—
30C2×C4×#261—22no—
31C2×C4×#261—21no—
32C2×C4×#261Q814yes—
33C2×C4×#261C2312yes—
34C2×#6118—24no—
35C2×#6118—24no—
36C2×#6118—22no—
37C2×#6118C2314yes—
38C2×D13⋊C8—22no—
39C2×D13⋊C8—22no—
40C2×D13⋊C8D412yes—
41C2×D13⋊C8C2312yes—
42C22×C8×C13C2×C411yescharacteristic
43C2×C13×C4⋊C4C2×C412yes—
44C2×#6103—22no—
45C2×C4⋊Dic13C2×C412yes—
46C2×C4×Dic13—22no—
47C22×#1055C2×C411yescharacteristic
48C2×C8×D13C2×C412yes—
49C2×C8×D13D414yes—
50C2×C8×D13Q814yes—
51C2×C8×D13C2312yes—
52#88146—22no—
53#88146—22no—
54#88146C2×C414yes—
55#88146C2314yes—
56#88112—28no—
57C4⋊#1057—28no—
58#88103—28no—
59#88100—28no—
60C13×#107C2×C414yescomplemented
61#88058C2×C414yescomplemented
62#88048C2×C418yescomplemented
63C2×#1946—131nomaximal, Sylow
64C23×D13#4111yescharacteristic
65C22×#261—24no—
66C22×#261—22no—
67C22×#261—42no—
68C22×#261—42no—
69C22×C4×C13—22no—
70C22×C4×C13C22×C411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13C2×D411yescharacteristic
73C2×C4×D13C22×C411yescharacteristic
74C2×C4×D13C2×D412yes—
75C2×C4×D13C2×D411yescharacteristic
76C2×C4×D13C2×Q812yes—
77C2×C4×D13C2×Q812yes—
78C2×C4×D13#4112yes—
79C2×C4×D13#4111yescharacteristic
80C2×C4×D13C2411yescharacteristic
81C2×#1057—24no—
82C2×#1057—24no—
83C2×#1057—44no—
84C2×#1057C2×D414yes—
85C4×#261—24no—
86C4×#261—22no—
87C4×#261C2×Q814yes—
88#6118—24no—
89#6118—24no—
90#6118—44no—
91D13⋊C8—24no—
92D13⋊C8—22no—
93D13⋊C8—22no—
94C2×C8×C13C4⋊C414yes—
95C2×C8×C13C22×C412yes—
96C13×C4⋊C4—22no—
97C13×C4⋊C4C22×C414yes—
98#6103—24no—
99#6103—24no—
100C4⋊Dic13—22no—
101C4⋊Dic13C22×C414yes—
102C4×Dic13—24no—
103C4×Dic13—24no—
104C2×#1055C4⋊C414yes—
105C2×#1055C22×C412yes—
106C8×D13C4⋊C418yes—
107C8×D13C2×D414yes—
108C8×D13C2×Q814yes—
109C22×#108—131no—
110C2×#427—131no—
111C2×#424—132no—
112C22×#97—131no—
113#1946—138no—
114C2×#339—132no—
115C23×C13C4×D411yescharacteristic
116C22×D13—22no—
117C22×D13—22no—
118C22×D13C4×D411yescharacteristic
119C22×D13C22⋊Q812yes—
120C22×D13#12512yes—
121C22×D13C2×#4111yescharacteristic
122C2×#261—24no—
123C2×#261—42no—
124C2×#261—42no—
125C2×#261—48no—
126C2×C4×C13—24no—
127C2×C4×C13—44no—
128C2×C4×C13C2×C4⋊C412yes—
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13C4×Q812yes—
131C2×C4×C13C23×C411yescharacteristic
132C2×Dic13—24no—
133C2×Dic13—44no—
134C2×Dic13C4×D411yescharacteristic
135C2×Dic13#12112yes—
136C2×Dic13C4⋊Q812yes—
137C2×Dic13C22×D411yescharacteristic
138C4×D13C2×C4⋊C412yes—
139C4×D13C4×Q812yes—
140C4×D13#12112yes—
141C4×D13C22⋊Q812yes—
142C4×D13#12512yes—
143C4×D13C4⋊Q812yes—
144C4×D13C22×D411yescharacteristic
145C4×D13C22×Q811yescharacteristic
146C4×D13C22×Q811yescharacteristic
147C4×D13C2×#4111yescharacteristic
148#1057—24no—
149#1057—44no—
150C8×C13C2×C4⋊C414yes—
151#1055C2×C4⋊C414yes—
152C22×M16—132no—
153C23×C8—131no—
154C23×C8—131no—
155C2×#117—132no—
156C22×C42—131no—
157C2×#108—134no—
158C2×#108—264no—
159#427—134no—
160#427—134no—
161C2×#107—131no—
162C2×#107#26111yescharacteristic, complemented
163C2×#106—132no—
164#424—138no—
165#424—264no—
166C2×C4⋊C8—262no—
167C2×C4⋊C8—262no—
168C2×#97—134no—
169C2×#97—264no—
170#339—138no—
171C22×C13#38912yes—
172C22×C13#44412yes—
173C22×C13#44412yes—
174C22×C13C2×C4×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—24no—
180C2×D13—24no—
181C2×D13#38912yes—
182C2×D13C2×C22⋊Q811yescharacteristic
183C2×D13C2×#12511yescharacteristic
184#261—44no—
185C4×C13—44no—
186C4×C13#38912yes—
187C4×C13C22×C4⋊C411yescharacteristic
188C4×C13C2×C4×Q811yescharacteristic
189Dic13—44no—
190Dic13#38912yes—
191Dic13C2×#12111yescharacteristic
192Dic13C2×C4⋊Q811yescharacteristic
193C23×C4—131no—
194C23×C4—261no—
195C2×M16—134no—
196C2×M16—262no—
197C2×M16—264no—
198C2×M16—264no—
199C22×C8—131no—
200C22×C8—134no—
201C22×C8—134no—
202C22×C8—132no—
203C22×C8—132no—
204C22×C8—132no—
205C22×C8—132no—
206C22×C8—132no—
207C22×C8—262no—
208C22×C8—262no—
209C22×C8—262no—
210C22×C8C2×#26111yescharacteristic
211#117—134no—
212#117—134no—
213#117—262no—
214#117—262no—
215C2×C4⋊C4—132no—
216C2×C4⋊C4C2×#26112yes—
217C2×C22⋊C4—262no—
218C2×C42—132no—
219C2×C42—134no—
220C2×C42—262no—
221C2×C42—262no—
222C2×C42—261no—
223#108—268no—
224#107—134no—
225#107C2×#26114yescomplemented
226#106—138no—
227C4⋊C8—268no—
228C4⋊C8—268no—
229#97—268no—
230C2×C13#194614yescomplemented
231C2×C13C2×#38911yescharacteristic
232C2×C13C2×#44411yescharacteristic
233C2×C13C2×#44411yescharacteristic
234D13—21no—
235D13—21no—
236D13—22no—
237C24—131no—
238C22×C4—22no—
239C22×C4—131no—
240C22×C4—132no—
241C22×C4—132no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—132no—
245C22×C4—132no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—264no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4—522no—
252C22×C4—522no—
253C22×C4C22×#26111yescharacteristic
254M16—264no—
255M16—264no—
256M16—524no—
257C2×C8—134no—
258C2×C8—132no—
259C2×C8—134no—
260C2×C8—138no—
261C2×C8—134no—
262C2×C8—134no—
263C2×C8—262no—
264C2×C8—264no—
265C2×C8—262no—
266C2×C8—264no—
267C2×C8—264no—
268C2×C8—524no—
269C2×C8C4⋊#26114yes—
270C2×C8C22×#26112yes—
271C4⋊C4—22no—
272C4⋊C4—134no—
273C4⋊C4—262no—
274C4⋊C4C22×#26114yes—
275C22⋊C4—264no—
276C22⋊C4—264no—
277C42—134no—
278C42—264no—
279C42—264no—
280C42—262no—
281C42—264no—
282C13C2×#194611yescharacteristic, complemented, Sylow
283C23—132no—
284C23—132no—
285C23—131no—
286C23—131no—
287C23—262no—
288C23—262no—
289C23D4×#26111yescharacteristic
290C2×C4—24no—
291C2×C4—44no—
292C2×C4—132no—
293C2×C4—132no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—132no—
299C2×C4—132no—
300C2×C4—131no—
301C2×C4—132no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—132no—
306C2×C4—264no—
307C2×C4—264no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—528no—
311C2×C4—524no—
312C2×C4C2×C4⋊#26112yes—
313C2×C4D4×#26111yescharacteristic
314C2×C4Q8×#26112yes—
315C2×C4C23×#26111yescharacteristic
316C8—134no—
317C8—264no—
318C8—524no—
319C8C2×C4⋊#26114yes—
320C22—131no—
321C22—131no—
322C22—132no—
323C22—261no—
324C22—261no—
325C22—261no—
326C22—261no—
327C22—264no—
328C22—264no—
329C22#1171908312yes—
330C22#1171910412yes—
331C22#1171911212yes—
332C22C2×D4×#26111yescharacteristic
333C4—44no—
334C4—131no—
335C4—131no—
336C4—132no—
337C4—524no—
338C4—524no—
339C4#1171908312yes—
340C4C22×C4⋊#26111yescharacteristic
341C4C2×Q8×#26111yescharacteristic
342C2—261no—
343C2—261no—
344C2—262no—
345C2#1313094514yesdirect product factor
346C2C2×#1171908311yescharacteristic
347C2C2×#1171911211yescharacteristic
348C2C2×#1171910411yescharacteristic
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×#1946
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. #13130945C2direct (N × H)
20. C2×C13×#107C4semidirect
21. C2×#88058C4semidirect
22. C2×#88048C4semidirect
23. #11718541C4semidirect
60. C13×#107C2×C4semidirect
61. #88058C2×C4semidirect
62. #88048C2×C4semidirect
162. C2×#107#261semidirect
225. #107C2×#261semidirect
230. C2×C13#1946semidirect
282. C13C2×#1946semidirect
345. C2#13130945direct (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×#117190792
C22×#881002
#131309452
C2×#117182472
C2×#117185412
C2×#194613