Finite Group Databasebeta

← C2×#13113742 #15832680

Subgroups — C2×#13113742 #15832680

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718685C211yesmaximal, characteristic
2C2×#11718492C211yesmaximal, characteristic
3C2×C4×#6107C211yesmaximal, characteristic
4#13113742C218yesmaximal, direct product factor
5C2×#11718072C211yesmaximal, characteristic
6C2×#11718048C211yesmaximal, characteristic
7C2×#11718046C211yesmaximal, characteristic
8C2×C13×Q8⋊C8C211yesmaximal, characteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C22×#6107C411yescharacteristic
11C2×C4×Dic26C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88075C411yescharacteristic
15C2×#88055—21no—
16C2×#88054—21no—
17C4×#6107C414yes—
18C4×#6107C2214yes—
19#11718685—22no—
20#11718685C2214yes—
21C2×#88050C411yescharacteristic
22C2×#88047C411yescharacteristic
23C2×C4⋊#1055—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×#88043—21no—
26C2×C4×#1055C2211yescharacteristic
27C2×C4×#1055C2211yescharacteristic
28#11718492—22no—
29#11718492C2214yes—
30C13×Q8⋊C8C2214yes—
31#11718072C2214yes—
32#11718048C2214yes—
33#11718046C2214yes—
34C22×Q8×C13C2×C411yescharacteristic
35C22×Dic26C2×C411yescharacteristic
36C22×C8×C13—21no—
37C22×C8×C13—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13C2×C412yes—
41C4×Q8×C13C2312yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4C2×C411yescharacteristic
44C2×C42×C13—21no—
45C2×C42×C13C2311yescharacteristic
46C2×#6107—24no—
47C2×#6107C2×C414yes—
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×#6101—21no—
50C2×C4×Dic13—21no—
51C22×#1055—21no—
52C22×#1055C2×C411yescharacteristic
53C22×#1055C2×C411yescharacteristic
54C22×#1055D411yescharacteristic
55C22×#1055D411yescharacteristic
56C4×Dic26—21no—
57C4×Dic26—21no—
58C4×Dic26C2×C412yes—
59C4×Dic26C2312yes—
60C13×C4⋊C8—21no—
61C13×C4⋊C8C2312yes—
62C4×C8×C13—21no—
63C4×C8×C13C2312yes—
64#88075C2×C414yes—
65#88055—24no—
66#88054—24no—
67#88050C2×C414yes—
68#88047C2×C414yes—
69C4⋊#1055—21no—
70C4⋊#1055—24no—
71C4⋊#1055C2312yes—
72#88043—24no—
73C4×#1055C2×C412yes—
74C4×#1055D412yes—
75C4×#1055C2312yes—
76C4×#1055C2312yes—
77C2×#1593—131nomaximal, Sylow
78C2×Q8×C13—21no—
79C2×Q8×C13—22no—
80C2×Q8×C13—22no—
81C2×Q8×C13C22×C412yes—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C22×Dic13—21no—
88C22×Dic13—21no—
89C2×Dic26—22no—
90C2×Dic26—22no—
91C2×Dic26—21no—
92C2×Dic26C22×C412yes—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—42no—
96C2×C8×C13—42no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4C22×C412yes—
101C42×C13—22no—
102C42×C13—22no—
103C42×C13C22×C411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13#4111yescharacteristic
106C42×C13C2411yescharacteristic
107#6107—28no—
108C4⋊Dic13—21no—
109C4⋊Dic13C22×C412yes—
110#6101—22no—
111#6101—22no—
112C4×Dic13—22no—
113C4×Dic13—22no—
114C2×#1055—22no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—42no—
119C2×#1055M1614yes—
120C2×#1055C22×C412yes—
121C2×#1055C22×C412yes—
122C2×#1055C2×D412yes—
123C2×#1055C2×D412yes—
124C2×#446—131no—
125C2×#446—131no—
126C2×C4×Q16—131no—
127#1593—138no—
128C2×#334—131no—
129C2×Q8⋊C8—131no—
130C2×Q8⋊C8D1311yescharacteristic
131C2×#322—131no—
132C23×C13C4×D411yescharacteristic
133Q8×C13—22no—
134Q8×C13—22no—
135Q8×C13—42no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C2×M1612yes—
145C2×C4×C13#13112yes—
146C2×C4×C13#13712yes—
147C2×C4×C13#13712yes—
148C2×C4×C13C23×C411yescharacteristic
149C2×C4×C13C22×D411yescharacteristic
150C2×C4×C13C2×#4111yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155Dic26—22no—
156Dic26—22no—
157Dic26—42no—
158C8×C13—42no—
159C8×C13—42no—
160#1055—22no—
161#1055—22no—
162#1055—22no—
163#1055—42no—
164#1055C2×M1614yes—
165C22×Q16—131no—
166C2×C4×Q8—131no—
167C2×C4×Q8C2×D1311yescharacteristic
168#446—134no—
169#446—134no—
170#446—262no—
171#446—262no—
172C4×Q16—134no—
173C4×Q16—134no—
174C2×#107—131no—
175C2×C4⋊C8—131no—
176C2×C4⋊C8—261no—
177C2×C4⋊C8—261no—
178C2×C4⋊C8C2×D1311yescharacteristic
179C2×#103—131no—
180C2×#103—131no—
181C2×#97—261no—
182C2×#97—261no—
183C2×C4×C8—131no—
184C2×C4×C8—131no—
185C2×C4×C8C2×D1311yescharacteristic
186#334—134no—
187Q8⋊C8—134no—
188Q8⋊C8C2×D1314yes—
189#322—134no—
190C22×C13#43612yes—
191C22×C13#44112yes—
192C22×C13#44412yes—
193C22×C13C2×C4×D411yescharacteristic
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—42no—
197C4×C13—42no—
198C4×C13#43612yes—
199C4×C13#44112yes—
200C4×C13C22×M1611yescharacteristic
201C4×C13C2×#13111yescharacteristic
202C4×C13C2×#13711yescharacteristic
203C4×C13C2×#13711yescharacteristic
204Dic13—42no—
205Dic13—42no—
206C22×Q8—131no—
207C22×Q8C4×D1311yescharacteristic
208C2×Q16—134no—
209C2×Q16—264no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—131no—
213C22×C8—131no—
214C22×C8—131no—
215C22×C8—131no—
216C22×C8—261no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—132no—
220C4×Q8—132no—
221C4×Q8—261no—
222C4×Q8—261no—
223C4×Q8C4×D1312yes—
224C4×Q8C22×D1312yes—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4C4×D1311yescharacteristic
229C2×C42—21no—
230C2×C42—261no—
231C2×C42C22×D1311yescharacteristic
232#107—134no—
233C4⋊C8—21no—
234C4⋊C8—132no—
235C4⋊C8—264no—
236C4⋊C8—264no—
237C4⋊C8—261no—
238C4⋊C8C22×D1312yes—
239#103—134no—
240#103—134no—
241#97—264no—
242#97—264no—
243C4×C8—21no—
244C4×C8—132no—
245C4×C8—132no—
246C4×C8—132no—
247C4×C8—132no—
248C4×C8C22×D1312yes—
249C2×C13#159314yescomplemented
250C2×C13C2×#43611yescharacteristic
251C2×C13C2×#44111yescharacteristic
252C2×C13C2×#44411yescharacteristic
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—132no—
257C2×Q8—261no—
258C2×Q8—262no—
259C2×Q8—262no—
260C2×Q8C2×C4×D1312yes—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4D4×D1311yescharacteristic
267C22×C4#612911yescharacteristic
268Q16—268no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—134no—
274C2×C8—132no—
275C2×C8—132no—
276C2×C8—132no—
277C2×C8—132no—
278C2×C8—262no—
279C2×C8—262no—
280C2×C8—262no—
281C2×C8—262no—
282C2×C8—522no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—132no—
287C4⋊C4—261no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4C2×C4×D1312yes—
291C42—22no—
292C42—22no—
293C42—262no—
294C42—262no—
295C42C2×C4×D1311yescharacteristic
296C42D4×D1311yescharacteristic
297C42#612911yescharacteristic
298C42C23×D1311yescharacteristic
299C13C2×#159311yescharacteristic, complemented, Sylow
300C23#8813511yescharacteristic
301Q8—22no—
302Q8—22no—
303Q8—42no—
304Q8—262no—
305Q8—262no—
306Q8—522no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—262no—
313C2×C4—262no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4#8813511yescharacteristic
317C2×C4#8813511yescharacteristic
318C2×C4#8813511yescharacteristic
319C2×C4#8815512yes—
320C2×C4M16×D1312yes—
321C2×C4#8816912yes—
322C2×C4#8817212yes—
323C2×C4C22×C4×D1311yescharacteristic
324C2×C4C2×D4×D1311yescharacteristic
325C2×C4C2×#612911yescharacteristic
326C8—42no—
327C8—42no—
328C8—134no—
329C8—262no—
330C8—262no—
331C8—262no—
332C8—522no—
333C22#1171839012yes—
334C22#1171845012yes—
335C22#1171848412yes—
336C22C2×#8813511yescharacteristic
337C4—21no—
338C4—21no—
339C4—42no—
340C4—42no—
341C4—522no—
342C4—522no—
343C4#1171839012yes—
344C4#1171845012yes—
345C4C2×#8815511yescharacteristic
346C4C2×M16×D1311yescharacteristic
347C4C2×#8816911yescharacteristic
348C4C2×#8817211yescharacteristic
349C2#1311374214yesdirect product factor
350C2C2×#1171839011yescharacteristic
351C2C2×#1171845011yescharacteristic
352C2C2×#1171848411yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×Q8⋊C8C2
socle, prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenterC2×Q8⋊C8D13
hypocenterC13C2×#1593
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13113742C2direct (N × H)
249. C2×C13#1593semidirect
299. C13C2×#1593semidirect
349. C2#13113742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186852
C2×#117184922
C2×C4×#61072
#131137422
C2×#117180722
C2×#117180482
C2×#117180462
C2×C13×Q8⋊C82
C2×#159313