Finite Group Databasebeta

← C2×#13123554 #16726800

Subgroups — C2×#13123554 #16726800

Order 3328.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88202C212yesmaximal, complemented
2#13123554C2116yesmaximal, direct product factor
3C2×#11718672C218yesmaximal, complemented
4C2×#11718585C211yesmaximal, characteristic, complemented
5C2×#11718895C212yesmaximal, complemented
6C22×#88043C211yesmaximal, characteristic, complemented
7C2×C13×#532C211yesmaximal, characteristic
8C22×C13×#41C2212yes—
9C13×#532C418yes—
10C13×#532C2218yes—
11C2×C13×C4⋊Q8C411yescharacteristic
12C2×C13×#127C411yescharacteristic
13C2×C13×#124C412yes—
14C2×C13×#121C414yes—
15C2×C4×D4×C13C2214yes—
16C22×C42×C13C2211yescharacteristic
17C2×#88202—216no—
18C2×#88202C22116yescomplemented
19C22×#6099C2212yes—
20C22×#6099C2214yes—
21C23×#1055C2214yes—
22C23×#1055C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24#11718895C22116yescomplemented
25C2×C22⋊#1055C2218yes—
26#11718672C22164yescomplemented
27#11718585C2218yescomplemented
28C2×C4⋊#1055C2214yes—
29C2×#88043C2214yes—
30C2×#88043C2218yescomplemented
31C2×C13×#41—28no—
32C2×C13×#41—28no—
33C2×C13×#41C2×C418yes—
34C2×C13×#41C2318yes—
35C22×Q8×C13C2×C412yes—
36C22×D4×C13C2×C414yes—
37C22×D4×C13C2×C412yes—
38C22×D4×C13C2×C414yes—
39C23×C4×C13C2×C412yes—
40C23×C4×C13C2314yes—
41C23×C4×C13C2311yescharacteristic
42C13×C4⋊Q8C2×C418yes—
43C13×#127C2×C418yes—
44C13×#124C2×C4116yes—
45C13×#121C2×C4132yes—
46C4×D4×C13C2×C4116yes—
47C4×D4×C13C23116yes—
48C2×C13×C4⋊C4C2×C414yes—
49C2×C13×C22⋊C4C2×C418yes—
50C2×C42×C13C2×C411yescharacteristic
51C2×C42×C13C2×C411yescharacteristic
52C2×C42×C13C2×C414yes—
53C2×C42×C13C2312yes—
54C2×C42×C13C2314yes—
55#88202—264no—
56C2×#6099—28no—
57C2×#6099—216no—
58C2×#6099C23116yes—
59C2×#6099C2318yes—
60C22×#1055—24no—
61C22×#1055—216no—
62C22×#1055D418yescomplemented
63C22×#1055C23116yes—
64C22×#1055C2314yes—
65C22×#1055C2312yes—
66C22×#1055C2314yes—
67C22×#1055C2312yes—
68C22×#1055C2314yes—
69C22⋊#1055C23132yes—
70C4⋊#1055C23116yes—
71#88043C23116yes—
72C2×#2932—131nomaximal, Sylow
73C24×C13C22×C414yes—
74C24×C13C22×C411yescharacteristic
75C13×#41—232no—
76C13×#41—216no—
77C13×#41—216no—
78C2×Q8×C13—28no—
79C2×Q8×C13C22×C418yes—
80C2×D4×C13—216no—
81C2×D4×C13—28no—
82C2×D4×C13—48no—
83C2×D4×C13C22×C4116yes—
84C2×D4×C13C22×C418yes—
85C2×D4×C13C22×C4116yes—
86C22×C4×C13—28no—
87C22×C4×C13—28no—
88C22×C4×C13—44no—
89C22×C4×C13C22×C412yes—
90C22×C4×C13C22×C412yes—
91C22×C4×C13C22×C414yes—
92C22×C4×C13C22×C418yes—
93C22×C4×C13C22×C418yes—
94C22×C4×C13C22×C411yescharacteristic
95C22×C4×C13C22×C412yes—
96C22×C4×C13C2×D414yes—
97C22×C4×C13#4114yes—
98C22×C4×C13C2418yes—
99C22×C4×C13C2412yes—
100C22×C4×C13C2411yescharacteristic
101C13×C4⋊C4C22×C4116yes—
102C13×C22⋊C4C22×C4132yes—
103C42×C13C22×C414yes—
104C42×C13C22×C414yes—
105C42×C13C22×C414yes—
106C42×C13C2414yes—
107#6099—216no—
108#6099—232no—
109C2×#1055—28no—
110C2×#1055—24no—
111C2×#1055—28no—
112C2×#1055—232no—
113C2×#1055C2×D418yes—
114C2×#1055C2×D4116yescomplemented
115C2×#1055C2414yes—
116C2×#1055C2418yes—
117C2×#1055C2414yes—
118C22×#131—132no—
119C2×#532D1311yescharacteristic
120#2932—1316no—
121C2×#435—138no—
122C2×#423—131no—
123C2×#408—132no—
124C22×#97—131no—
125C23×C13—24no—
126C23×C13—28no—
127C23×C13—216no—
128C23×C13C4×D414yes—
129C23×C13C23×C418yes—
130C23×C13C23×C412yes—
131C23×C13C23×C411yescharacteristic
132Q8×C13—216no—
133D4×C13—232no—
134D4×C13—216no—
135D4×C13—416no—
136C2×C4×C13—28no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—216no—
140C2×C4×C13—28no—
141C2×C4×C13—28no—
142C2×C4×C13—48no—
143C2×C4×C13C4×D414yes—
144C2×C4×C13C4×D418yes—
145C2×C4×C13C23×C414yes—
146C2×C4×C13C23×C414yes—
147C2×C4×C13C23×C418yes—
148C2×C4×C13C23×C411yescharacteristic
149C2×C4×C13C23×C412yes—
150C2×C4×C13C22×D412yes—
151C2×C4×C13C22×D414yes—
152C2×C4×C13C2×#4112yes—
153C2×C4×C13C2×#4114yes—
154C2×C4×C13C2511yescharacteristic
155#1055—28no—
156#1055—24no—
157#1055C22×D418yes—
158C22×#41C2×D1312yes—
159C2×#131—1316no—
160C2×#131—2616no—
161C22×M16—132no—
162C22×M16—134no—
163C23×C8—131no—
164C23×C8—131no—
165C23×C8—134no—
166#532Dic1318yes—
167#532C2×D1318yes—
168C2×C4⋊Q8Dic1311yescharacteristic
169C2×#127Dic1311yescharacteristic
170C2×#124Dic1312yes—
171C2×#121Dic1314yes—
172C2×C4×D4C2×D1314yes—
173C22×C42C2×D1311yescharacteristic
174#435—1364no—
175#423—138no—
176C2×C4⋊C8—134no—
177#408—1316no—
178C2×C22⋊C8—138no—
179C2×#97—134no—
180C2×#97—138no—
181C22×C13—28no—
182C22×C13—24no—
183C22×C13—28no—
184C22×C13—216no—
185C22×C13—416no—
186C22×C13C2×C4×D414yes—
187C22×C13C2×C4×D412yes—
188C22×C13#56814yes—
189C22×C13C24×C411yescharacteristic
190C4×C13—28no—
191C4×C13—24no—
192C4×C13—24no—
193C4×C13C2×C4×D412yes—
194C4×C13C2×C4×D414yes—
195C4×C13C23×D411yescharacteristic
196C4×C13C22×#4111yescharacteristic
197C2×#41—28no—
198C2×#41—28no—
199C2×#41C2×Dic1318yes—
200C2×#41C22×D1318yes—
201C22×Q8C2×Dic1312yes—
202C22×D4C2×Dic1314yes—
203C22×D4C2×Dic1312yes—
204C22×D4C2×Dic1314yes—
205C23×C4C2×Dic1312yes—
206C23×C4C22×D1314yes—
207C23×C4C22×D1311yescharacteristic
208#131—2664no—
209C2×M16—138no—
210C2×M16—1316no—
211C2×M16—2616no—
212C2×M16—268no—
213C22×C8—138no—
214C22×C8—134no—
215C22×C8—132no—
216C22×C8—1316no—
217C22×C8—134no—
218C22×C8—134no—
219C22×C8—132no—
220C22×C8—2616no—
221C22×C8—264no—
222C4⋊Q8C2×Dic1318yes—
223#127C2×Dic1318yes—
224#124C2×Dic13116yes—
225#121C2×Dic13132yes—
226C4×D4C2×Dic13116yes—
227C4×D4C22×D13116yes—
228C2×C4⋊C4C2×Dic1314yes—
229C2×C22⋊C4C2×Dic1318yes—
230C2×C42C2×Dic1311yescharacteristic
231C2×C42C2×Dic1311yescharacteristic
232C2×C42C2×Dic1314yes—
233C2×C42C22×D1314yes—
234C2×C42C22×D1312yes—
235C4⋊C8—1316no—
236C22⋊C8—1332no—
237#97—1316no—
238C2×C13—24no—
239C2×C13—48no—
240C2×C13#293214yescomplemented
241C2×C13C22×C4×D411yescharacteristic
242C2×C13C2×#56812yes—
243C24C22×Dic1314yes—
244C24C22×Dic1311yescharacteristic
245#41—232no—
246#41—216no—
247#41—216no—
248C2×Q8—28no—
249C2×Q8C22×Dic1318yes—
250C2×D4—216no—
251C2×D4—28no—
252C2×D4—48no—
253C2×D4C22×Dic13116yes—
254C2×D4C22×Dic1318yes—
255C2×D4C22×Dic13116yes—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—44no—
259C22×C4D4×D1314yes—
260C22×C4#612914yes—
261C22×C4C22×Dic1312yes—
262C22×C4C22×Dic1312yes—
263C22×C4C22×Dic1314yes—
264C22×C4C22×Dic1318yes—
265C22×C4C22×Dic1318yes—
266C22×C4C22×Dic1311yescharacteristic
267C22×C4C22×Dic1312yes—
268C22×C4C23×D1318yes—
269C22×C4C23×D1312yes—
270C22×C4C23×D1311yescharacteristic
271M16—2632no—
272M16—2616no—
273C2×C8—138no—
274C2×C8—1316no—
275C2×C8—134no—
276C2×C8—134no—
277C2×C8—138no—
278C2×C8—2632no—
279C2×C8—268no—
280C2×C8—264no—
281C2×C8—268no—
282C4⋊C4C22×Dic13116yes—
283C22⋊C4C22×Dic13132yes—
284C42C22×Dic1314yes—
285C42C22×Dic1314yes—
286C42C22×Dic1314yes—
287C42C23×D1314yes—
288C13C2×#293211yescharacteristic, complemented, Sylow
289C23—24no—
290C23—28no—
291C23—216no—
292C23D4×Dic1314yes—
293C23C23×Dic1318yes—
294C23C23×Dic1312yes—
295C23C23×Dic1311yescharacteristic
296Q8—216no—
297D4—232no—
298D4—216no—
299D4—416no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—216no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—48no—
307C2×C4D4×Dic1314yes—
308C2×C4D4×Dic1318yes—
309C2×C4C2×D4×D1312yes—
310C2×C4C2×D4×D1314yes—
311C2×C4C2×#612912yes—
312C2×C4C2×#612914yes—
313C2×C4C23×Dic1314yes—
314C2×C4C23×Dic1314yes—
315C2×C4C23×Dic1318yes—
316C2×C4C23×Dic1311yescharacteristic
317C2×C4C23×Dic1312yes—
318C2×C4C24×D1311yescharacteristic
319C8—138no—
320C8—268no—
321C8—264no—
322C22—24no—
323C22—28no—
324C22—28no—
325C22—216no—
326C22—416no—
327C22C2×D4×Dic1314yes—
328C22C2×D4×Dic1312yes—
329C22#1171952414yes—
330C22C24×Dic1311yescharacteristic
331C4—28no—
332C4—24no—
333C4—24no—
334C4C2×D4×Dic1312yes—
335C4C2×D4×Dic1314yes—
336C4C22×D4×D1311yescharacteristic
337C4C22×#612911yescharacteristic
338C2—24no—
339C2—48no—
340C2#1312355414yesdirect product factor
341C2C22×D4×Dic1311yescharacteristic
342C2C2×#1171952412yes—
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#532C2
socleC23×C13C23×C4
cosocleC2×C4×C13C25
hypercenterC2×#532D13
hypocenterC13C2×#2932
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C22×#88202C2semidirect
2. #13123554C2direct (N × H)
3. C2×#11718672C2semidirect
4. C2×#11718585C2semidirect
5. C2×#11718895C2semidirect
6. C22×#88043C2semidirect
18. C2×#88202C22semidirect
24. #11718895C22semidirect
26. #11718672C22semidirect
27. #11718585C22semidirect
30. C2×#88043C22semidirect
62. C22×#1055D4semidirect
114. C2×#1055C2×D4semidirect
240. C2×C13#2932semidirect
288. C13C2×#2932semidirect
340. C2#13123554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882022
#131235542
C2×#117186722
C2×#117185852
C2×#117188952
C22×#880432
C2×C13×#5322
C2×#293213