Finite Group Databasebeta

← C2×#13114362 #15845551

Subgroups — C2×#13114362 #15845551

Order 3328.

618 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×#11718739C211yesmaximal, characteristic
2C2×#11718682C211yesmaximal, characteristic
3C2×#11718685C211yesmaximal, characteristic
4#13114362C218yesmaximal, direct product factor
5C2×#11718072C211yesmaximal, characteristic
6C2×#11718138C211yesmaximal, characteristic
7C2×#11718073C211yesmaximal, characteristic
8C2×C13×#477C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C13×#477—22no—
13C13×#477C2214yes—
14C2×C13×#107—21no—
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17C2×#88075—21no—
18#11718739—22no—
19#11718739C2214yes—
20#11718685—22no—
21#11718685C2214yes—
22#11718682—22no—
23#11718682C2214yes—
24C2×#88047—21no—
25C2×#88047—21no—
26C2×#88047—21no—
27C2×C4⋊#1055—21no—
28C2×C4⋊#1055C2211yescharacteristic
29C2×C4⋊#1055C2211yescharacteristic
30C2×#88043—21no—
31C2×C4×#1055C2211yescharacteristic
32#11718138C2214yes—
33#11718073C2214yes—
34#11718072C2214yes—
35C22×Q8×C13—21no—
36C22×Q8×C13D411yescharacteristic
37C22×Dic26—21no—
38C22×C8×C13—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8C2312yes—
43C4×Q8×C13—21no—
44C4×Q8×C13—21no—
45C4×Q8×C13D412yes—
46C4×Q8×C13C2312yes—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C42×C13—21no—
52C2×C42×C13C2311yescharacteristic
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C22×#1055—21no—
56C22×#1055—21no—
57C22×#1055D411yescharacteristic
58C22×#1055D411yescharacteristic
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123C2312yes—
63C13×#107—24no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8C2312yes—
66C13×#103—24no—
67#88075—24no—
68#88047—24no—
69#88047—24no—
70#88047—24no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73C4⋊#1055—24no—
74C4⋊#1055C2312yes—
75C4⋊#1055C2312yes—
76#88043—24no—
77C4×#1055D412yes—
78C4×#1055C2312yes—
79C2×#1696—131nomaximal, Sylow
80C2×Q8×C13—21no—
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—22no—
84C2×Q8×C13—41no—
85C2×Q8×C13—82no—
86C2×Q8×C13C2×D412yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4111yescharacteristic
93C22×Dic13—41no—
94C2×Dic26—22no—
95C2×Dic26—41no—
96C2×Dic26—82no—
97C2×C8×C13—22no—
98C2×C8×C13—42no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4C2×D412yes—
107C42×C13—22no—
108C42×C13—22no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13C2411yescharacteristic
113C4⋊Dic13—22no—
114C4⋊Dic13—22no—
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117C2×#1055—22no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—42no—
121C2×#1055—42no—
122C2×#1055Q1614yes—
123C2×#1055C2×D412yes—
124C2×#1055C2×D412yes—
125C2×#500—131no—
126C2×#477—131no—
127C2×#477D1311yescharacteristic
128C2×#446—131no—
129#1696—138no—
130C2×#334—131no—
131C2×#333—131no—
132C2×#333—131no—
133C23×C13#12111yescharacteristic
134Q8×C13—22no—
135Q8×C13—22no—
136Q8×C13—42no—
137Q8×C13—82no—
138Q8×C13—82no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—82no—
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13C2×Q1612yes—
150C2×C4×C13#13712yes—
151C2×C4×C13#13712yes—
152C2×C4×C13#13712yes—
153C2×C4×C13C22×D411yescharacteristic
154C2×C4×C13C22×D411yescharacteristic
155C2×C4×C13C2×#4111yescharacteristic
156C2×Dic13—42no—
157C2×Dic13—82no—
158Dic26—82no—
159Dic26—82no—
160C8×C13—42no—
161#1055—22no—
162#1055—42no—
163#1055—42no—
164#1055C2×Q1614yes—
165C2×C4⋊Q8—131no—
166C2×C4⋊Q8C2×D1311yescharacteristic
167C2×C4×Q8C2×D1311yescharacteristic
168#500—134no—
169#500—262no—
170#477—22no—
171#477—134no—
172#477—262no—
173#477C2×D1314yes—
174#446—134no—
175#446—262no—
176C2×#107—21no—
177C2×#107—261no—
178C2×#107—261no—
179C2×#107—261no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8—131no—
182C2×C4⋊C8—261no—
183C2×C4⋊C8C2×D1311yescharacteristic
184C2×#103—21no—
185C2×#103—261no—
186C2×#97—261no—
187C2×C4×C8—131no—
188#334—134no—
189#333—134no—
190#333—134no—
191C22×C13#46212yes—
192C22×C13#47012yes—
193C22×C13#47212yes—
194C22×C13C2×#12111yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—42no—
198C4×C13—42no—
199C4×C13—82no—
200C4×C13#46212yes—
201C4×C13#47012yes—
202C4×C13C22×Q1611yescharacteristic
203C4×C13C2×#13711yescharacteristic
204C4×C13C2×#13711yescharacteristic
205C4×C13C2×#13711yescharacteristic
206Dic13—82no—
207C22×Q8—21no—
208C22×Q8—261no—
209C22×Q8C22⋊D1311yescharacteristic
210C22×C8—21no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—261no—
214C22×C8—261no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—132no—
219C4⋊Q8—261no—
220C4⋊Q8—261no—
221C4⋊Q8—261no—
222C4⋊Q8C22×D1312yes—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8C22⋊D1312yes—
226C4×Q8C22×D1312yes—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4C22⋊D1311yescharacteristic
233C2×C42—21no—
234C2×C42C22×D1311yescharacteristic
235#107—24no—
236#107—264no—
237#107—264no—
238#107—264no—
239C4⋊C8—21no—
240C4⋊C8—132no—
241C4⋊C8—132no—
242C4⋊C8—264no—
243C4⋊C8—261no—
244C4⋊C8—261no—
245C4⋊C8C22×D1312yes—
246#103—24no—
247#103—264no—
248#97—264no—
249C4×C8—132no—
250C4×C8—132no—
251C2×C13#169614yescomplemented
252C2×C13C2×#46211yescharacteristic
253C2×C13C2×#47011yescharacteristic
254C2×C13C2×#47211yescharacteristic
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×Q8—82no—
261C2×Q8—262no—
262C2×Q8—521no—
263C2×Q8—1042no—
264C2×Q8C2×C22⋊D1312yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—521no—
269C22×C4D4×D1311yescharacteristic
270C22×C4#612911yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272C2×C8—22no—
273C2×C8—42no—
274C2×C8—134no—
275C2×C8—132no—
276C2×C8—132no—
277C2×C8—262no—
278C2×C8—262no—
279C2×C8—262no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4C2×C22⋊D1312yes—
294C42—22no—
295C42—22no—
296C42D4×D1311yescharacteristic
297C42#612911yescharacteristic
298C42C2×C22⋊D1311yescharacteristic
299C42C23×D1311yescharacteristic
300C13C2×#169611yescharacteristic, complemented, Sylow
301C23#8819311yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—42no—
305Q8—82no—
306Q8—82no—
307Q8—1042no—
308Q8—1042no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—82no—
316C2×C4—522no—
317C2×C4—1042no—
318C2×C4Q16×D1312yes—
319C2×C4#8817212yes—
320C2×C4#8819311yescharacteristic
321C2×C4#8819311yescharacteristic
322C2×C4#8819311yescharacteristic
323C2×C4#8819612yes—
324C2×C4#8820512yes—
325C2×C4C2×D4×D1311yescharacteristic
326C2×C4C2×#612911yescharacteristic
327C2×C4C22×C22⋊D1311yescharacteristic
328C8—42no—
329C8—134no—
330C8—262no—
331C8—522no—
332C8—522no—
333C22#1171871312yes—
334C22#1171884312yes—
335C22#1171886012yes—
336C22C2×#8819311yescharacteristic
337C4—21no—
338C4—21no—
339C4—42no—
340C4—42no—
341C4—82no—
342C4—1042no—
343C4#1171871312yes—
344C4#1171884312yes—
345C4C2×Q16×D1311yescharacteristic
346C4C2×#8817211yescharacteristic
347C4C2×#8819611yescharacteristic
348C4C2×#8820511yescharacteristic
349C2#1311436214yesdirect product factor
350C2C2×#1171884311yescharacteristic
351C2C2×#1171871311yescharacteristic
352C2C2×#1171886011yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#477C2
socle, prime radicalC23×C13#121
hypercenterC2×#477D13
hypocenterC13C2×#1696
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
4. #13114362C2direct (N × H)
251. C2×C13#1696semidirect
300. C13C2×#1696semidirect
349. C2#13114362direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117186822
C2×#117186852
#131143622
C2×#117180722
C2×#117181382
C2×#117180732
C2×C13×#4772
C2×#169613