Finite Group Databasebeta

← C2×#13124492 #16730115

Subgroups — C2×#13124492 #16730115

Order 3328.

2678 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic52C211yesmaximal, characteristic, complemented
2C22×#88155C211yesmaximal, characteristic
3C2×#11719231C212yesmaximal
4#13124492C2116yesmaximal, direct product factor
5C2×#11718529C214yesmaximal, complemented
6C2×#11718548C214yesmaximal, complemented
7C2×#11718665C212yesmaximal, complemented
8C2×C13×#427C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C23×Dic26C2212yes—
11C23×C8×C13C2211yescharacteristic
12C2×C13×#117C2212yes—
13C22×#6099C2211yescharacteristic
14C22×Dic52—28no—
15C22×Dic52C2212yes—
16C22×Dic52C2212yes—
17C22×Dic52C2218yescomplemented
18C2×#88155—28no—
19C2×#88155C2218yes—
20C22×#6094C2212yes—
21C22×C8×D13C2212yes—
22#11719231—28no—
23#11719231C22116yes—
24C2×#88151C2218yes—
25C2×#88140—24no—
26C2×#88129—22no—
27C2×#88123—22no—
28C13×#427C2218yescomplemented
29C2×C13×#107C2212yes—
30C2×C13×#106C2212yes—
31#11718665C22116yescomplemented
32C2×#88050C2218yes—
33#11718548C22132yescomplemented
34#11718529C22132yescomplemented
35C23×C4×C13C2311yescharacteristic
36C22×C22⋊D13D412yes—
37C23×Dic13—22no—
38C2×#6127—24no—
39C2×#6127—24no—
40C2×#6127D414yes—
41C2×#6127C2314yes—
42C22×D52D411yescharacteristic
43C22×C4×D13C2312yes—
44C22×Dic26—28no—
45C22×Dic26—28no—
46C22×Dic26—22no—
47C22×Dic26—24no—
48C22×Dic26D411yescharacteristic
49C22×Dic26C2318yes—
50C22×Dic26C2314yes—
51C22×C8×C13D418yes—
52C22×C8×C13C2311yescharacteristic
53C22×C8×C13C2311yescharacteristic
54C22×C8×C13C2314yes—
55C13×#117—24no—
56C13×#117C2318yes—
57C2×C13×C4⋊C4C2314yes—
58C2×C13×C22⋊C4—22no—
59C2×C42×C13—22no—
60C2×#6103—28no—
61C2×C4⋊Dic13—28no—
62C2×#6099—24no—
63C2×#6099C2314yes—
64C22×#1055C2312yes—
65C2×Dic52—28no—
66C2×Dic52—28no—
67C2×Dic52—232no—
68C2×Dic52C2318yes—
69C2×Dic52C2318yes—
70#88155—232no—
71C2×#6094—28no—
72C2×#6094C2318yes—
73C2×C8×D13—28no—
74C2×C8×D13C2318yes—
75#88151—216no—
76#88151C23132yes—
77#88140—232no—
78#88129—216no—
79#88123—216no—
80C13×#107C2318yes—
81C13×#106C2318yes—
82#88050C23132yes—
83C2×#3059—131nomaximal, Sylow
84C24×C13C2×D411yescharacteristic
85C23×D13C2×D412yes—
86C22×C4×C13—24no—
87C22×C4×C13C2×D414yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D412yes—
90C22×C4×C13#4114yes—
91C22×C4×C13C2411yescharacteristic
92C22×C4×C13C2412yes—
93C2×C22⋊D13—28no—
94C2×C22⋊D13C2×D418yes—
95C22×Dic13—28no—
96C22×Dic13—24no—
97C22×Dic13—48no—
98C22×Dic13C2×D412yes—
99#6127—216no—
100#6127—28no—
101#6127—28no—
102C2×D52—24no—
103C2×D52C2×D414yes—
104C2×C4×D13—24no—
105C2×C4×D13—24no—
106C2×C4×D13C2×D414yes—
107C2×C4×D13C2414yes—
108C2×Dic26—24no—
109C2×Dic26—28no—
110C2×Dic26—216no—
111C2×Dic26—28no—
112C2×Dic26—216no—
113C2×Dic26—28no—
114C2×Dic26—24no—
115C2×Dic26—48no—
116C2×Dic26—416no—
117C2×Dic26C2×D414yes—
118C2×Dic26C2418yes—
119C2×C8×C13C2×D414yes—
120C2×C8×C13C2×D414yes—
121C2×C8×C13C2×D4116yes—
122C2×C8×C13C2412yes—
123C2×C8×C13C2412yes—
124C13×C4⋊C4—24no—
125C13×C4⋊C4C2418yes—
126C13×C22⋊C4—28no—
127C42×C13—28no—
128#6103—232no—
129C4⋊Dic13—232no—
130#6099—28no—
131C2×#1055—24no—
132C2×#1055C2414yes—
133Dic52—216no—
134Dic52—216no—
135#6094—216no—
136C8×D13—216no—
137C23×Q16—131no—
138C22×#131—131no—
139C2×#536—132no—
140#3059—1316no—
141C2×#470—134no—
142C2×#467—134no—
143C2×#427D1311yescharacteristic, complemented
144C2×#419—132no—
145C23×C13—24no—
146C23×C13#12114yes—
147C23×C13C22×D412yes—
148C23×C13C22×D411yescharacteristic
149C22×D13—24no—
150C22×D13—28no—
151C22×D13C22×D414yes—
152C2×C4×C13—28no—
153C2×C4×C13—48no—
154C2×C4×C13#12114yes—
155C2×C4×C13#12118yes—
156C2×C4×C13C22×D412yes—
157C2×C4×C13C22×D411yescharacteristic
158C2×C4×C13C22×D412yes—
159C2×C4×C13C22×D414yes—
160C2×C4×C13C2×#4112yes—
161C2×C4×C13C2×#4114yes—
162C2×C4×C13C2511yescharacteristic
163C22⋊D13—216no—
164C2×Dic13—24no—
165C2×Dic13—28no—
166C2×Dic13—416no—
167C2×Dic13—48no—
168C2×Dic13C22×D414yes—
169D52—28no—
170C4×D13—28no—
171C4×D13—24no—
172C4×D13—24no—
173Dic26—28no—
174Dic26—28no—
175Dic26—28no—
176Dic26—416no—
177Dic26—48no—
178C8×C13C22×D414yes—
179C8×C13C22×D414yes—
180#1055—24no—
181C22×#41—131no—
182C23×Q8—132no—
183C22×Q16—132no—
184C22×Q16—132no—
185C22×Q16—138no—
186C22×Q16—268no—
187C2×#131—138no—
188C2×#131—268no—
189C22×M16—131no—
190C22×M16—132no—
191C23×C8—132no—
192C23×C8C2×D1311yescharacteristic
193#536—1316no—
194#536—268no—
195C2×C4⋊Q8—262no—
196C2×#124—262no—
197C2×#123—264no—
198C2×C22⋊Q8—138no—
199C2×#117C2×D1312yes—
200#470—1332no—
201#467—1332no—
202#427C2×D1318yescomplemented
203C2×#107C2×D1312yes—
204C2×#106C2×D1312yes—
205#419—1316no—
206C2×#103—138no—
207C22×C13—28no—
208C22×C13—24no—
209C22×C13C2×#12114yes—
210C22×C13C2×#12112yes—
211C22×C13#57814yes—
212C22×C13C23×D411yescharacteristic
213C2×D13—24no—
214C2×D13—28no—
215C2×D13—48no—
216C4×C13—48no—
217C4×C13C2×#12114yes—
218C4×C13C2×#12112yes—
219C4×C13C23×D411yescharacteristic
220C4×C13C22×#4111yescharacteristic
221Dic13—24no—
222Dic13—48no—
223C2×#41—134no—
224C2×#41—134no—
225C2×#41—264no—
226C2×#41—264no—
227C22×Q8—131no—
228C22×Q8—134no—
229C22×Q8—138no—
230C22×Q8—262no—
231C22×Q8—264no—
232C22×Q8—268no—
233C22×Q8—268no—
234C22×D4—132no—
235C22×D4—131no—
236C23×C4—132no—
237C23×C4—262no—
238C23×C4C22×D1311yescharacteristic
239C2×Q16—138no—
240C2×Q16—138no—
241C2×Q16—268no—
242C2×Q16—268no—
243C2×Q16—2632no—
244#131—2632no—
245C2×M16—134no—
246C2×M16—138no—
247C2×M16—264no—
248C2×M16—268no—
249C22×C8—132no—
250C22×C8—138no—
251C22×C8—268no—
252C22×C8D5218yes—
253C22×C8C22×D1311yescharacteristic
254C22×C8C22×D1311yescharacteristic
255C22×C8C22×D1314yes—
256C4⋊Q8—2616no—
257#124—2616no—
258#123—2632no—
259C22⋊Q8—1332no—
260C22⋊Q8—2616no—
261#117—24no—
262#117C22×D1318yes—
263C2×C4⋊C4—268no—
264C2×C4⋊C4C22×D1314yes—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—268no—
267C2×C42—22no—
268#107C22×D1318yes—
269#106C22×D1318yes—
270#103—1332no—
271C2×C13—24no—
272C2×C13#305914yescomplemented
273C2×C13C22×#12111yescharacteristic
274C2×C13C2×#57812yes—
275D13—44no—
276C24—132no—
277C24D4×D1311yescharacteristic
278#41—2616no—
279#41—268no—
280#41—268no—
281C2×Q8—134no—
282C2×Q8—138no—
283C2×Q8—264no—
284C2×Q8—264no—
285C2×Q8—268no—
286C2×Q8—268no—
287C2×Q8—2616no—
288C2×Q8—268no—
289C2×Q8—2616no—
290C2×Q8—528no—
291C2×Q8—5216no—
292C2×D4—138no—
293C2×D4—134no—
294C2×D4—268no—
295C2×D4—264no—
296C22×C4—24no—
297C22×C4—132no—
298C22×C4—134no—
299C22×C4—134no—
300C22×C4—264no—
301C22×C4—264no—
302C22×C4—268no—
303C22×C4—264no—
304C22×C4—528no—
305C22×C4C2×D5214yes—
306C22×C4D4×D1312yes—
307C22×C4D4×D1311yescharacteristic
308C22×C4#613114yes—
309C22×C4C23×D1312yes—
310C22×C4C23×D1311yescharacteristic
311Q16—2616no—
312Q16—2616no—
313M16—268no—
314M16—2616no—
315C2×C8—134no—
316C2×C8—264no—
317C2×C8—2616no—
318C2×C8C2×D5214yes—
319C2×C8C2×D5214yes—
320C2×C8C2×D52116yes—
321C2×C8C23×D1312yes—
322C2×C8C23×D1312yes—
323C4⋊C4—24no—
324C4⋊C4—2632no—
325C4⋊C4C23×D1318yes—
326C22⋊C4—28no—
327C22⋊C4—2632no—
328C42—28no—
329C13C2×#305911yescharacteristic, complemented, Sylow
330C23—24no—
331C23—134no—
332C23—264no—
333C23—268no—
334C23#8814914yes—
335C23C2×D4×D1312yes—
336C23C2×D4×D1311yescharacteristic
337Q8—268no—
338Q8—268no—
339Q8—268no—
340Q8—528no—
341Q8—5216no—
342D4—2616no—
343D4—268no—
344C2×C4—28no—
345C2×C4—48no—
346C2×C4—134no—
347C2×C4—264no—
348C2×C4—268no—
349C2×C4—264no—
350C2×C4—264no—
351C2×C4—268no—
352C2×C4—5216no—
353C2×C4—528no—
354C2×C4#8814914yes—
355C2×C4#8814918yes—
356C2×C4C22×D5212yes—
357C2×C4C22×D5214yes—
358C2×C4C2×D4×D1312yes—
359C2×C4C2×D4×D1311yescharacteristic
360C2×C4C2×#613112yes—
361C2×C4C2×#613114yes—
362C2×C4C24×D1311yescharacteristic
363C8—264no—
364C8C22×D5214yes—
365C8C22×D5214yes—
366C22—24no—
367C22—28no—
368C22—264no—
369C22—268no—
370C22—528no—
371C22C2×#8814914yes—
372C22C2×#8814912yes—
373C22#1171947614yes—
374C22C22×D4×D1311yescharacteristic
375C4—48no—
376C4—264no—
377C4—528no—
378C4C2×#8814912yes—
379C4C2×#8814914yes—
380C4C23×D5211yescharacteristic
381C4C22×#613111yescharacteristic
382C2—24no—
383C2—524no—
384C2#1312449214yesdirect product factor
385C2C22×#8814911yescharacteristic
386C2C2×#1171947612yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#427C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#427D13
hypocenterC13C2×#3059
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C23×Dic52C2semidirect
4. #13124492C2direct (N × H)
5. C2×#11718529C2semidirect
6. C2×#11718548C2semidirect
7. C2×#11718665C2semidirect
8. C2×C13×#427C2semidirect
17. C22×Dic52C22semidirect
28. C13×#427C22semidirect
31. #11718665C22semidirect
33. #11718548C22semidirect
34. #11718529C22semidirect
143. C2×#427D13semidirect
202. #427C2×D13semidirect
272. C2×C13#3059semidirect
329. C13C2×#3059semidirect
384. C2#13124492direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic522
C22×#881552
C2×#117192312
#131244922
C2×#117185292
C2×#117185482
C2×#117186652
C2×C13×#4272
C2×#305913