Finite Group Databasebeta

← C2×#13120074 #16034873

Subgroups — C2×#13120074 #16034873

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120074C2116yesmaximal, direct product factor
2C2×#11718321C212yesmaximal
3C2×#11718647C211yesmaximal, characteristic
4C2×#11718308C212yesmaximal
5C2×#11718633C212yesmaximal
6C2×#11718637C211yesmaximal, characteristic
7C2×#11718311C212yesmaximal
8C2×#11718311C212yesmaximal
9C2×#11718310C212yesmaximal
10C2×C13×#400C211yesmaximal, characteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C13×#400C2218yes—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33#11718647C2218yes—
34#11718637C2218yes—
35#11718633C22116yes—
36#11718321C22116yes—
37#11718311C22116yes—
38#11718311C22116yes—
39#11718310C22116yes—
40#11718308C22116yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C2×C13×C4⋊C4—42no—
51C2×C13×C4⋊C4—42no—
52C2×C13×C4⋊C4C2314yes—
53C2×C13×C4⋊C4C2314yes—
54C2×C4⋊Dic13—42no—
55C2×C4⋊Dic13—42no—
56C2×C4⋊Dic13C2314yes—
57C2×C4⋊Dic13C2314yes—
58C2×#6101—28no—
59C2×#6101—28no—
60C2×#6101—28no—
61C2×#6101—28no—
62C2×#6101—44no—
63C2×#6101C2318yes—
64C2×#6101C2318yes—
65C2×#6101C2318yes—
66C2×#6101C2318yes—
67C2×#6101C2318yes—
68C2×C4×Dic13—28no—
69C2×C4×Dic13—28no—
70C2×C4×Dic13Q818yes—
71C2×C4×Dic13C2318yes—
72C2×C4×Dic13C2318yes—
73C2×C4×Dic13C2314yes—
74C13×#95C2318yes—
75C13×#95C2318yes—
76C13×#95C2314yes—
77#88071C2318yes—
78#88071C2318yes—
79#88071C2318yes—
80#88071C2314yes—
81#88071C2318yes—
82#88071C2318yes—
83C2×#2571—131nomaximal, Sylow
84C24×C13C2411yescharacteristic
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—24no—
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—24no—
91C22×C4×C13—24no—
92C22×C4×C13—24no—
93C22×C4×C13—24no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—24no—
97C22×C4×C13C2×Q814yes—
98C22×C4×C13C2414yes—
99C22×C4×C13C2412yes—
100C22×C4×C13C2414yes—
101C22×C4×C13C2412yes—
102C22×C4×C13C2412yes—
103C22×Dic13—24no—
104C22×Dic13—24no—
105C22×Dic13—24no—
106C22×Dic13—24no—
107C22×Dic13—24no—
108C22×Dic13—24no—
109C22×Dic13—24no—
110C22×Dic13—24no—
111C22×Dic13—24no—
112C22×Dic13C2×Q818yes—
113C22×Dic13#4118yes—
114C22×Dic13#4118yes—
115C22×Dic13C2414yes—
116C22×Dic13C2414yes—
117C22×Dic13C2414yes—
118C22×Dic13C2414yes—
119C13×C4⋊C4—44no—
120C13×C4⋊C4—44no—
121C4⋊Dic13—44no—
122C4⋊Dic13—44no—
123#6101—216no—
124#6101—216no—
125#6101—216no—
126#6101—216no—
127#6101—48no—
128C4×Dic13—216no—
129C4×Dic13—216no—
130C4×Dic13C2×Q8116yes—
131#2571—1316no—
132C2×#400—132no—
133C2×#400—131no—
134C2×#400D1311yescharacteristic
135C2×#389—132no—
136C2×#389—132no—
137C2×#384—131no—
138C2×#382—132no—
139C2×#382—132no—
140C2×C4×C4⋊C4—132no—
141C23×C13C22×Q812yes—
142C23×C13C2×#4114yes—
143C23×C13C2×#4114yes—
144C23×C13H(5,𝔽2)12yes—
145C23×C132−1+412yes—
146C23×C13C2511yescharacteristic
147C2×C4×C13—28no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—24no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—24no—
155C2×C4×C13—24no—
156C2×C4×C13—24no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—24no—
160C2×C4×C13—48no—
161C2×C4×C13—48no—
162C2×C4×C13—44no—
163C2×C4×C13—44no—
164C2×C4×C13C22×Q814yes—
165C2×Dic13—24no—
166C2×Dic13—24no—
167C2×Dic13—24no—
168C2×Dic13—24no—
169C2×Dic13—24no—
170C2×Dic13—24no—
171C2×Dic13—24no—
172C2×Dic13—24no—
173C2×Dic13—24no—
174C2×Dic13—48no—
175C2×Dic13—48no—
176C2×Dic13—48no—
177C2×Dic13#125132yes—
178C2×Dic13C22×Q818yes—
179C2×Dic13C2×#4118yes—
180C2×Dic13C2×#4118yes—
181C22×C4⋊C4—132no—
182C22×C4⋊C4—132no—
183C22×C4⋊C4—132no—
184C22×C4⋊C4—132no—
185C22×C4⋊C4—132no—
186C22×C4⋊C4—131no—
187C22×C4⋊C4—131no—
188C22×C4⋊C4C2×D1311yescharacteristic
189C22×C4⋊C4C2×D1311yescharacteristic
190C22×C42—131no—
191C22×C42—132no—
192C22×C42—132no—
193#400—138no—
194#400—1316no—
195#400C2×D1318yes—
196#389—1316no—
197#389—1316no—
198#384—138no—
199#382—1316no—
200#382—1316no—
201C4×C4⋊C4—1316no—
202C2×#95—132no—
203C2×#95—132no—
204C2×#95—131no—
205C2×#95—132no—
206C2×#95—132no—
207C2×#95—132no—
208C2×#95C2×D1312yes—
209C2×#95C2×D1311yescharacteristic
210C2×#95C2×D1312yes—
211C22×C13C2×#12518yes—
212C22×C13#54414yes—
213C22×C13#55514yes—
214C22×C13#55618yes—
215C22×C13#55914yes—
216C22×C13C23×Q811yescharacteristic
217C22×C13C22×#4112yes—
218C22×C13C22×#4112yes—
219C22×C13C2×H(5,𝔽2)11yescharacteristic
220C22×C13C2×2−1+411yescharacteristic
221C4×C13—24no—
222C4×C13—44no—
223C4×C13—44no—
224C4×C13—42no—
225C4×C13—42no—
226Dic13—44no—
227Dic13—44no—
228Dic13—44no—
229Dic13C2×#125116yes—
230C23×C4—132no—
231C23×C4—132no—
232C23×C4—132no—
233C23×C4—132no—
234C23×C4C22×D1311yescharacteristic
235C23×C4C22×D1311yescharacteristic
236C23×C4C22×D1312yes—
237C23×C4C22×D1312yes—
238C23×C4C22×D1311yescharacteristic
239C2×C4⋊C4—42no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—138no—
242C2×C4⋊C4—138no—
243C2×C4⋊C4—138no—
244C2×C4⋊C4—138no—
245C2×C4⋊C4—138no—
246C2×C4⋊C4—134no—
247C2×C4⋊C4—134no—
248C2×C4⋊C4—268no—
249C2×C4⋊C4—268no—
250C2×C4⋊C4—268no—
251C2×C4⋊C4—268no—
252C2×C4⋊C4—524no—
253C2×C4⋊C4—522no—
254C2×C4⋊C4—522no—
255C2×C4⋊C4C22×D1314yes—
256C2×C4⋊C4C22×D1314yes—
257C2×C42—138no—
258C2×C42—134no—
259C2×C42—138no—
260C2×C42—138no—
261C2×C42—268no—
262C2×C42—268no—
263#95—138no—
264#95—134no—
265#95—138no—
266#95—138no—
267#95—138no—
268#95—138no—
269#95C22×D1318yes—
270#95C22×D1314yes—
271#95C22×D1318yes—
272C2×C13#257118yescomplemented
273C2×C13C22×#12512yes—
274C2×C13C2×#54411yescharacteristic
275C2×C13C2×#55511yescharacteristic
276C2×C13C2×#55612yes—
277C2×C13C2×#55911yescharacteristic
278C24C23×D1311yescharacteristic
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—138no—
292C22×C4—138no—
293C22×C4—138no—
294C22×C4—134no—
295C22×C4—134no—
296C22×C4—134no—
297C22×C4—134no—
298C22×C4—264no—
299C22×C4—264no—
300C22×C4—264no—
301C22×C4—264no—
302C22×C4—264no—
303C22×C4—264no—
304C22×C4—264no—
305C22×C4—264no—
306C22×C4—264no—
307C22×C4Q8×D1314yes—
308C22×C4C23×D1314yes—
309C22×C4C23×D1312yes—
310C22×C4C23×D1314yes—
311C22×C4C23×D1312yes—
312C22×C4C23×D1312yes—
313C4⋊C4—44no—
314C4⋊C4—44no—
315C4⋊C4—2616no—
316C4⋊C4—2616no—
317C4⋊C4—2616no—
318C4⋊C4—2616no—
319C4⋊C4—528no—
320C4⋊C4—524no—
321C4⋊C4—524no—
322C42—1316no—
323C42—2616no—
324C42—2616no—
325C13C2×#257111yescharacteristic, complemented, Sylow
326C23#8825112yes—
327C23C2×Q8×D1312yes—
328C23#41×D1314yes—
329C23#41×D1314yes—
330C23#8825712yes—
331C23C24×D1311yescharacteristic
332C2×C4—28no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—138no—
350C2×C4—138no—
351C2×C4—138no—
352C2×C4—1332no—
353C2×C4—264no—
354C2×C4—264no—
355C2×C4—264no—
356C2×C4—264no—
357C2×C4—264no—
358C2×C4—264no—
359C2×C4—264no—
360C2×C4—264no—
361C2×C4—264no—
362C2×C4—528no—
363C2×C4—528no—
364C2×C4—528no—
365C2×C4C2×Q8×D1314yes—
366C22#1171932814yes—
367C22#1171936914yes—
368C22#1171937514yes—
369C22D13×#12518yes—
370C22#1171940718yes—
371C22C2×#8825111yescharacteristic
372C22C22×Q8×D1311yescharacteristic
373C22C2×#41×D1312yes—
374C22C2×#41×D1312yes—
375C22C2×#8825711yescharacteristic
376C4—24no—
377C4—44no—
378C4—44no—
379C4—42no—
380C4—42no—
381C4—1316no—
382C4—524no—
383C4—524no—
384C4—524no—
385C2#1312007418yesdirect product factor
386C2C2×D13×#12512yes—
387C2C2×#1171932811yescharacteristic
388C2C2×#1171937511yescharacteristic
389C2C2×#1171940712yes—
390C2C2×#1171936911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#400C2
socle, prime radicalC24×C13C24
hypercenterC2×#400D13
hypocenterC13C2×#2571
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #13120074C2direct (N × H)
272. C2×C13#2571semidirect
325. C13C2×#2571semidirect
385. C2#13120074direct (N × H)

Maximal subgroups

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

subgroupindex
#131200742
C2×#117183212
C2×#117186472
C2×#117183082
C2×#117186332
C2×#117186372
C2×#117183112
C2×#117183102
C2×C13×#4002
C2×#257113