Finite Group Databasebeta

← C2×#13125372 #16732549

Subgroups — C2×#13125372 #16732549

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719205C212yesmaximal
2#13125372C2116yesmaximal, direct product factor
3C2×#11718537C214yesmaximal, complemented
4C2×#11718535C212yesmaximal, complemented
5C2×#11718539C212yesmaximal, complemented
6C2×#11718625C212yesmaximal
7C2×#11718767C211yesmaximal, characteristic
8C2×#11718762C211yesmaximal, characteristic
9C22×C13×#107C211yesmaximal, characteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C2×#88180C2212yes—
13C2×#88180C2211yescharacteristic
14C2×#88178—24no—
15C22×#6099C2211yescharacteristic
16#11719205—28no—
17#11719205C22116yes—
18C2×#88144—22no—
19C2×#88144C2214yes—
20C2×#88142—22no—
21C2×#88142C2214yes—
22C2×C13×#107C2212yes—
23C2×C13×#107C2212yes—
24C2×C13×#107C2218yes—
25#11718767C2218yes—
26C2×#88058C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88057C2212yes—
29#11718762C2218yes—
30C2×#88055C2212yes—
31C2×C8×Dic13C2212yes—
32#11718625C22116yes—
33C2×#88048C2214yes—
34C2×#88047C2214yes—
35#11718539C22116yescomplemented
36#11718537C22132yescomplemented
37#11718535C22116yescomplemented
38C23×C4×C13—22no—
39C23×C4×C13C2311yescharacteristic
40C22×Dic26—24no—
41C22×C8×C13Q818yescomplemented
42C22×C8×C13C2311yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C22×C8×C13C2314yes—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4C2314yes—
48C2×C13×C4⋊C4C2318yes—
49C2×C22⋊Dic13—22no—
50C2×C22⋊Dic13D412yes—
51#88180—24no—
52#88180D414yes—
53#88180C2318yes—
54#88180C2314yes—
55C2×C4⋊Dic13—24no—
56C2×C4⋊Dic13D411yescharacteristic
57C2×C4⋊Dic13D411yescharacteristic
58C2×C4⋊Dic13C2312yes—
59C2×C4⋊Dic13C2312yes—
60#88178—232no—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13C2312yes—
65C2×#6099Q818yescomplemented
66C2×#6099C2314yes—
67C22×#1055C2312yes—
68#88144—216no—
69#88144—28no—
70#88144C23116yes—
71#88142—216no—
72#88142—28no—
73#88142C23116yes—
74C13×#107C2318yes—
75C13×#107C2318yes—
76#88058C2314yes—
77#88058C2314yes—
78#88057C2318yes—
79#88055C2318yes—
80C8×Dic13C2318yes—
81#88048C23116yes—
82#88047C23116yes—
83C2×#3164—131nomaximal, Sylow
84C24×C13C2×D411yescharacteristic
85C22×C4×C13—24no—
86C22×C4×C13—28no—
87C22×C4×C13—84no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×Q814yes—
91C22×C4×C13C2×Q814yes—
92C22×C4×C13C2411yescharacteristic
93C22×C4×C13C2412yes—
94C22×Dic13—22no—
95C22×Dic13—22no—
96C22×Dic13C2×D412yes—
97C22×Dic13C2×D412yes—
98C2×Dic26—216no—
99C2×Dic26—88no—
100C2×C8×C13C2×Q814yes—
101C2×C8×C13C2×Q814yes—
102C2×C8×C13C2×Q8116yescomplemented
103C2×C8×C13C2412yes—
104C2×C8×C13C2412yes—
105C13×C4⋊C4—28no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4C2418yes—
108C22⋊Dic13—28no—
109C22⋊Dic13C2×D418yes—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—216no—
113C4⋊Dic13C2×D414yes—
114C4⋊Dic13C2×D414yes—
115C4⋊Dic13C2414yes—
116C4⋊Dic13C2414yes—
117#6101—216no—
118#6101—216no—
119C4×Dic13—28no—
120C4×Dic13C2×D414yes—
121C4×Dic13C2414yes—
122#6099C2×Q8116yescomplemented
123C2×#1055C2×Q818yes—
124C2×#1055C2414yes—
125C2×#544—132no—
126#3164—1316no—
127C2×#501—134no—
128C2×#500—132no—
129C2×#499—132no—
130C2×#428—132no—
131C2×#427—131no—
132C22×#107D1311yescharacteristic
133C2×#405—131no—
134C23×C13—22no—
135C23×C13—22no—
136C23×C13C4⋊Q814yes—
137C23×C13C22×D412yes—
138C23×C13C22×D411yescharacteristic
139C2×C4×C13—28no—
140C2×C4×C13—48no—
141C2×C4×C13—88no—
142C2×C4×C13C4⋊Q818yes—
143C2×C4×C13C4⋊Q814yes—
144C2×C4×C13C22×D412yes—
145C2×C4×C13C22×D411yescharacteristic
146C2×C4×C13C22×Q812yes—
147C2×C4×C13C22×Q814yes—
148C2×C4×C13C22×Q812yes—
149C2×C4×C13C22×Q814yes—
150C2×C4×C13C2511yescharacteristic
151C2×Dic13—24no—
152C2×Dic13—24no—
153C2×Dic13—24no—
154C2×Dic13—24no—
155C2×Dic13—44no—
156C2×Dic13—44no—
157C2×Dic13C22×D414yes—
158C2×Dic13C22×D414yes—
159Dic26—816no—
160C8×C13C22×Q814yes—
161C8×C13C22×Q814yes—
162#1055C22×Q818yes—
163C22×M16—131no—
164C23×C8C2×D1311yescharacteristic
165#544—1316no—
166#544—268no—
167C2×C4⋊Q8—134no—
168C2×C4⋊Q8—262no—
169C2×#125—134no—
170C2×#125—262no—
171C2×C22⋊Q8—264no—
172C2×#117—131no—
173C2×#117—132no—
174C22×C4⋊C4C2×D1312yes—
175#501—1332no—
176#500—1316no—
177#499—1316no—
178#428—1316no—
179#427—138no—
180C2×#107—131no—
181C2×#107—131no—
182C2×#107—134no—
183C2×#107C2×D1312yes—
184C2×#107C2×D1312yes—
185C2×#107C2×D1318yes—
186C2×#106—132no—
187C2×#106—134no—
188#405—138no—
189C2×#97—132no—
190C2×C4×C8—132no—
191C22×C13—28no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13C2×C4⋊Q814yes—
195C22×C13C2×C4⋊Q812yes—
196C22×C13#57612yes—
197C22×C13#57812yes—
198C22×C13C23×D411yescharacteristic
199C4×C13—48no—
200C4×C13C2×C4⋊Q814yes—
201C4×C13C2×C4⋊Q812yes—
202C4×C13C23×Q811yescharacteristic
203C4×C13C23×Q811yescharacteristic
204Dic13—24no—
205Dic13—24no—
206Dic13—44no—
207Dic13—44no—
208C22×Q8—264no—
209C23×C4—22no—
210C23×C4C22×D1311yescharacteristic
211C2×M16—138no—
212C2×M16—134no—
213C22×C8—132no—
214C22×C8Dic2618yescomplemented
215C22×C8C22×D1311yescharacteristic
216C22×C8C22×D1311yescharacteristic
217C22×C8C22×D1314yes—
218C4⋊Q8—1316no—
219C4⋊Q8—268no—
220C4⋊Q8—2616no—
221#125—1316no—
222#125—268no—
223#125—2616no—
224C22⋊Q8—2632no—
225#117—134no—
226#117—134no—
227#117—138no—
228#117—264no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—132no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—264no—
236C2×C4⋊C4—264no—
237C2×C4⋊C4—264no—
238C2×C4⋊C4C22×D1314yes—
239C2×C4⋊C4C22×D1318yes—
240C2×C22⋊C4—132no—
241C2×C22⋊C4—262no—
242C2×C42—132no—
243C2×C42—262no—
244#107—134no—
245#107—134no—
246#107—1316no—
247#107C22×D1318yes—
248#107C22×D1318yes—
249#106—138no—
250#106—1316no—
251#97—138no—
252C4×C8—138no—
253C2×C13—24no—
254C2×C13#316414yescomplemented
255C2×C13C22×C4⋊Q811yescharacteristic
256C2×C13C2×#57611yescharacteristic
257C2×C13C2×#57811yescharacteristic
258C24D4×D1311yescharacteristic
259C2×Q8—2616no—
260C2×Q8—1048no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—84no—
264C22×C4—132no—
265C22×C4—132no—
266C22×C4—262no—
267C22×C4—262no—
268C22×C4C2×Dic2614yes—
269C22×C4D4×D1312yes—
270C22×C4D4×D1311yescharacteristic
271C22×C4Q8×D1314yes—
272C22×C4C23×D1312yes—
273C22×C4C23×D1311yescharacteristic
274M16—1316no—
275C2×C8—138no—
276C2×C8—134no—
277C2×C8C2×Dic2614yes—
278C2×C8C2×Dic2614yes—
279C2×C8C2×Dic26116yescomplemented
280C2×C8C23×D1312yes—
281C2×C8C23×D1312yes—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—134no—
285C4⋊C4—134no—
286C4⋊C4—134no—
287C4⋊C4—134no—
288C4⋊C4—2616no—
289C4⋊C4—2616no—
290C4⋊C4—2616no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4C23×D1318yes—
294C22⋊C4—138no—
295C22⋊C4—268no—
296C42—134no—
297C42—134no—
298C42—268no—
299C13C2×#316411yescharacteristic, complemented, Sylow
300C23—22no—
301C23—22no—
302C23#8814214yes—
303C23C2×D4×D1312yes—
304C23C2×D4×D1311yescharacteristic
305Q8—10416no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—88no—
309C2×C4—134no—
310C2×C4—134no—
311C2×C4—264no—
312C2×C4—264no—
313C2×C4—264no—
314C2×C4—264no—
315C2×C4—524no—
316C2×C4—524no—
317C2×C4#8814218yes—
318C2×C4#8814214yes—
319C2×C4C22×Dic2612yes—
320C2×C4C22×Dic2614yes—
321C2×C4C2×D4×D1311yescharacteristic
322C2×C4C2×D4×D1312yes—
323C2×C4C2×Q8×D1312yes—
324C2×C4C2×Q8×D1314yes—
325C2×C4C24×D1311yescharacteristic
326C8—138no—
327C8C22×Dic2614yes—
328C8C22×Dic2614yes—
329C22—22no—
330C22—22no—
331C22—28no—
332C22C2×#8814214yes—
333C22C2×#8814212yes—
334C22#1171946212yes—
335C22#1171947112yes—
336C22C22×D4×D1311yescharacteristic
337C4—48no—
338C4—264no—
339C4—264no—
340C4—524no—
341C4—524no—
342C4C2×#8814212yes—
343C4C2×#8814214yes—
344C4C23×Dic2611yescharacteristic
345C4C22×Q8×D1311yescharacteristic
346C2—24no—
347C2#1312537214yesdirect product factor
348C2C22×#8814211yescharacteristic
349C2C2×#1171946211yescharacteristic
350C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#107C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#107D13
hypocenterC13C2×#3164
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13125372C2direct (N × H)
3. C2×#11718537C2semidirect
4. C2×#11718535C2semidirect
5. C2×#11718539C2semidirect
35. #11718539C22semidirect
36. #11718537C22semidirect
37. #11718535C22semidirect
41. C22×C8×C13Q8semidirect
65. C2×#6099Q8semidirect
102. C2×C8×C13C2×Q8semidirect
122. #6099C2×Q8semidirect
214. C22×C8Dic26semidirect
254. C2×C13#3164semidirect
279. C2×C8C2×Dic26semidirect
299. C13C2×#3164semidirect
347. C2#13125372direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192052
#131253722
C2×#117185372
C2×#117185352
C2×#117185392
C2×#117186252
C2×#117187672
C2×#117187622
C22×C13×#1072
C2×#316413