Finite Group Databasebeta

← C2×#13130461 #16795296

Subgroups — C2×#13130461 #16795296

Order 3328.

674 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×#11719158C211yesmaximal, characteristic
2C2×Q8×#1057C211yesmaximal, characteristic
3#13130461C218yesmaximal, direct product factor
4C2×#11718255C211yesmaximal, characteristic
5C2×Q8⋊#1057C211yesmaximal, characteristic
6C2×Q8⋊#1057C211yesmaximal, characteristic
7C2×#1057⋊C8C211yesmaximal, characteristic
8C2×Q16×Dic13C211yesmaximal, characteristic
9C22×C13×Q16C411yescharacteristic
10C2×Q8×Dic13C2211yescharacteristic
11C2×Q8×Dic13C2211yescharacteristic
12#11719158—22no—
13#11719158C2214yes—
14Q8×#1057—22no—
15Q8×#1057C2214yes—
16C2×#88112—21no—
17C2×#88110—21no—
18C2×C4⋊#1057—21no—
19C2×C4⋊#1057C2211yescharacteristic
20C2×C4⋊#1057C2211yescharacteristic
21C2×C4×#1057—21no—
22C2×C4×#1057C2211yescharacteristic
23C2×C4×#1057C2211yescharacteristic
24C2×#88075C411yescharacteristic
25C2×#88075C411yescharacteristic
26Q16×Dic13C414yes—
27Q16×Dic13C2214yes—
28C2×#88058C411yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30Q8⋊#1057C2214yes—
31Q8⋊#1057C2214yes—
32#11718255C2214yes—
33#1057⋊C8C2214yes—
34C22×Q8×C13C2×C411yescharacteristic
35C22×Q8×C13C2×C411yescharacteristic
36C22×#1057—21no—
37C22×#1057—21no—
38C22×#1057—21no—
39C22×#1057D411yescharacteristic
40C22×#1057D411yescharacteristic
41C2×C13×Q16—24no—
42C2×C13×Q16C2×C414yes—
43C22×C8×C13C2×C411yescharacteristic
44Q8×Dic13—21no—
45Q8×Dic13—21no—
46Q8×Dic13—21no—
47Q8×Dic13—21no—
48Q8×Dic13C2×C412yes—
49Q8×Dic13C2×C412yes—
50Q8×Dic13C2312yes—
51Q8×Dic13C2312yes—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13C2×C411yescharacteristic
55C2×C4⋊Dic13C2×C411yescharacteristic
56C2×C4×Dic13—21no—
57C2×C4×Dic13—21no—
58C2×C4×Dic13C2311yescharacteristic
59C22×#1055C2×C411yescharacteristic
60#88112—24no—
61#88110—24no—
62C4⋊#1057—24no—
63C4⋊#1057—21no—
64C4⋊#1057—21no—
65C4⋊#1057C2312yes—
66C4⋊#1057C2312yes—
67C4×#1057—24no—
68C4×#1057—21no—
69C4×#1057D412yes—
70C4×#1057C2312yes—
71C4×#1057C2312yes—
72#88075C2×C414yes—
73#88075C2×C414yes—
74#88058C2×C414yes—
75C8×Dic13C2×C412yes—
76C8×Dic13C2312yes—
77C2×#1587—131nomaximal, Sylow
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13M1614yes—
84C2×Q8×C13C22×C412yes—
85C2×Q8×C13C22×C412yes—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13C22×C411yescharacteristic
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13#4111yescharacteristic
93C2×#1057—24no—
94C2×#1057—22no—
95C2×#1057—22no—
96C2×#1057—22no—
97C2×#1057—22no—
98C2×#1057—22no—
99C2×#1057—42no—
100C2×#1057—42no—
101C2×#1057C2×D412yes—
102C2×#1057C2×D412yes—
103C13×Q16—28no—
104C2×C8×C13—22no—
105C2×C8×C13C22×C412yes—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13C22×C412yes—
113C4⋊Dic13C22×C412yes—
114C4×Dic13—22no—
115C4×Dic13—22no—
116C4×Dic13—22no—
117C4×Dic13—22no—
118C4×Dic13C22×C411yescharacteristic
119C4×Dic13C2×D411yescharacteristic
120C4×Dic13#4111yescharacteristic
121C4×Dic13C2411yescharacteristic
122C2×#1055—22no—
123C2×#1055C22×C412yes—
124C2×#446—131no—
125C2×C8×Q8—131no—
126C2×C4×Q16—131no—
127#1587—138no—
128C2×#334—131no—
129C2×Q8⋊C8—131no—
130C2×Q8⋊C8—131no—
131C2×#322—131no—
132C23×C13C4×D411yescharacteristic
133Q8×C13—22no—
134Q8×C13—24no—
135Q8×C13—22no—
136Q8×C13—22no—
137Q8×C13—42no—
138Q8×C13C2×M1614yes—
139C2×C4×C13—22no—
140C2×C4×C13—24no—
141C2×C4×C13—22no—
142C2×C4×C13—42no—
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C2×M1612yes—
145C2×C4×C13#13112yes—
146C2×C4×C13C23×C411yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13C4×D411yescharacteristic
153C2×Dic13C4×D411yescharacteristic
154C2×Dic13#13712yes—
155C2×Dic13#13712yes—
156C2×Dic13C22×D411yescharacteristic
157C2×Dic13C2×#4111yescharacteristic
158#1057—24no—
159#1057—22no—
160#1057—22no—
161#1057—42no—
162#1057—42no—
163C8×C13—22no—
164#1055—22no—
165C22×Q16#26111yescharacteristic
166C2×C4×Q8—131no—
167C2×C4×Q8—131no—
168#446—134no—
169#446—262no—
170C8×Q8—134no—
171C8×Q8—262no—
172C4×Q16—134no—
173C4×Q16—134no—
174C2×#107—131no—
175C2×C4⋊C8—131no—
176C2×C4⋊C8—131no—
177C2×C4⋊C8—261no—
178C2×C4⋊C8—261no—
179C2×#103—131no—
180C2×#103—131no—
181C2×#97—261no—
182C2×C4×C8—131no—
183C2×C4×C8—131no—
184C2×C4×C8—131no—
185C2×C4×C8—261no—
186#334—134no—
187Q8⋊C8—134no—
188Q8⋊C8—134no—
189#322—134no—
190C22×C13#43512yes—
191C22×C13#44112yes—
192C22×C13#44312yes—
193C22×C13C2×C4×D411yescharacteristic
194C4×C13—24no—
195C4×C13—42no—
196C4×C13#43512yes—
197C4×C13C22×M1611yescharacteristic
198C4×C13C2×#13111yescharacteristic
199Dic13—21no—
200Dic13—21no—
201Dic13—42no—
202Dic13—42no—
203Dic13#44112yes—
204Dic13C2×#13711yescharacteristic
205Dic13C2×#13711yescharacteristic
206C22×Q8C2×#26111yescharacteristic
207C22×Q8C2×#26111yescharacteristic
208C2×Q16—24no—
209C2×Q16C2×#26114yes—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—261no—
214C22×C8—261no—
215C22×C8—261no—
216C22×C8C2×#26111yescharacteristic
217C4×Q8—132no—
218C4×Q8—132no—
219C4×Q8—132no—
220C4×Q8—132no—
221C4×Q8—261no—
222C4×Q8—261no—
223C4×Q8—261no—
224C4×Q8—261no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C42—131no—
230C2×C42—261no—
231C2×C42—261no—
232#107—134no—
233C4⋊C8—132no—
234C4⋊C8—132no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—264no—
238C4⋊C8—264no—
239#103—134no—
240#103—134no—
241#97—264no—
242C4×C8—132no—
243C4×C8—132no—
244C4×C8—132no—
245C4×C8—132no—
246C4×C8—132no—
247C4×C8—261no—
248C4×C8—264no—
249C2×C13#158714yescomplemented
250C2×C13C2×#43511yescharacteristic
251C2×C13C2×#44111yescharacteristic
252C2×C13C2×#44311yescharacteristic
253C2×Q8—22no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8#612214yes—
259C2×Q8C22×#26112yes—
260C2×Q8C22×#26112yes—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4C22×#26111yescharacteristic
268Q16—28no—
269C2×C8—22no—
270C2×C8—132no—
271C2×C8—132no—
272C2×C8—132no—
273C2×C8—262no—
274C2×C8—262no—
275C2×C8—262no—
276C2×C8—264no—
277C2×C8—262no—
278C2×C8—262no—
279C2×C8—262no—
280C2×C8—522no—
281C2×C8—522no—
282C2×C8C22×#26112yes—
283C4⋊C4—132no—
284C4⋊C4—132no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C42—131no—
292C42—131no—
293C42—131no—
294C42—131no—
295C42—262no—
296C42—262no—
297C42—262no—
298C42—262no—
299C13C2×#158711yescharacteristic, complemented, Sylow
300C23D4×#26111yescharacteristic
301Q8—22no—
302Q8—24no—
303Q8—22no—
304Q8—22no—
305Q8—42no—
306Q8C2×#612214yes—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—42no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—262no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4#8823812yes—
323C2×C4D4×#26111yescharacteristic
324C2×C4C2×#612212yes—
325C2×C4C23×#26111yescharacteristic
326C8—22no—
327C8—262no—
328C8—262no—
329C8—264no—
330C8—262no—
331C8—522no—
332C8—522no—
333C22#1171911012yes—
334C22#1171911112yes—
335C22#1171914412yes—
336C22C2×D4×#26111yescharacteristic
337C4—24no—
338C4—42no—
339C4—131no—
340C4—131no—
341C4—132no—
342C4—261no—
343C4—261no—
344C4—522no—
345C4—522no—
346C4#1171914412yes—
347C4C2×#8823811yescharacteristic
348C4C22×#612211yescharacteristic
349C2#1313046114yesdirect product factor
350C2C2×#1171914411yescharacteristic
351C2C2×#1171911011yescharacteristic
352C2C2×#1171911111yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×Q16C4
socle, prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenterC22×Q16#261
hypocenterC13C2×#1587
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #13130461C2direct (N × H)
249. C2×C13#1587semidirect
299. C13C2×#1587semidirect
349. C2#13130461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191582
C2×Q8×#10572
#131304612
C2×#117182552
C2×Q8⋊#10572
C2×#1057⋊C82
C2×Q16×Dic132
C2×#158713