Finite Group Databasebeta

← C2×#13130087 #16792849

Subgroups — C2×#13130087 #16792849

Order 3328.

1326 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719128C212yesmaximal, complemented
2#13130087C218yesmaximal, direct product factor
3C2×#11718285C212yesmaximal, complemented
4C2×#11718305C212yesmaximal
5C22×#88180C211yesmaximal, characteristic
6C24×C4×C13C411yescharacteristic
7C22×C22⋊Dic13C411yescharacteristic
8C22×C22⋊Dic13C2211yescharacteristic
9C2×#88180—22no—
10C2×#88180—22no—
11C2×#88180—24no—
12C2×#88180C414yes—
13C2×#88180C2214yes—
14C22×C4⋊Dic13C411yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4×Dic13C411yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C2×C22⋊#1057C2214yes—
19#11719128—24no—
20#11719128C2218yescomplemented
21C2×#88112—22no—
22C2×#88110—22no—
23#11718305C2218yes—
24#11718285C2218yescomplemented
25C25×C13C2×C411yescharacteristic
26C23×C4×C13—24no—
27C23×C4×C13—22no—
28C23×C4×C13—21no—
29C23×C4×C13—21no—
30C23×C4×C13—24no—
31C23×C4×C13C2×C414yes—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C23×Dic13C2×C411yescharacteristic
35C23×Dic13C2×C411yescharacteristic
36C23×Dic13C2×C411yescharacteristic
37C23×Dic13C2311yescharacteristic
38C22×#1057—24no—
39C2×C22⋊Dic13—22no—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—22no—
43C2×C22⋊Dic13C2×C412yes—
44C2×C22⋊Dic13C2×C414yes—
45C2×C22⋊Dic13C2312yes—
46#88180—28no—
47#88180—28no—
48#88180—28no—
49#88180—28no—
50C2×C4⋊Dic13—22no—
51C2×C4⋊Dic13—22no—
52C2×C4⋊Dic13—22no—
53C2×C4⋊Dic13—22no—
54C2×C4⋊Dic13C2×C414yes—
55C2×C4⋊Dic13C2×C412yes—
56C2×C4⋊Dic13C2312yes—
57C2×C4×Dic13—22no—
58C2×C4×Dic13—21no—
59C2×C4×Dic13—21no—
60C2×C4×Dic13C2×C414yes—
61C2×C4×Dic13C2×C412yes—
62C2×C4×Dic13D412yes—
63C2×C4×Dic13D412yes—
64C2×C4×Dic13D414yes—
65C2×C4×Dic13C2312yes—
66C22⋊#1057—24no—
67C22⋊#1057C2318yes—
68#88112—28no—
69#88110—28no—
70C2×#1464—131nomaximal, Sylow
71C24×C13—21no—
72C24×C13—21no—
73C24×C13—22no—
74C24×C13—42no—
75C24×C13—42no—
76C24×C13M1614yes—
77C24×C13C22×C411yescharacteristic
78C24×C13C22×C412yes—
79C22×C4×C13—216no—
80C22×C4×C13—28no—
81C22×C4×C13—28no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—28no—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—28no—
91C22×C4×C13C22⋊C412yes—
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13M1614yes—
95C22×C4×C13C22×C412yes—
96C22×C4×C13C22×C412yes—
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—42no—
102C22×Dic13—42no—
103C22×Dic13—42no—
104C22×Dic13—42no—
105C22×Dic13C22⋊C412yes—
106C22×Dic13C22⋊C412yes—
107C22×Dic13C22×C412yes—
108C22×Dic13C22×C412yes—
109C22×Dic13C22×C411yescharacteristic
110C22×Dic13C22×C412yes—
111C22×Dic13C2×D412yes—
112C22×Dic13C2×D412yes—
113C22×Dic13C2411yescharacteristic
114C2×#1057—28no—
115C2×#1057—48no—
116C22⋊Dic13—24no—
117C22⋊Dic13—28no—
118C22⋊Dic13—24no—
119C4⋊Dic13—24no—
120C4⋊Dic13—28no—
121C4⋊Dic13—24no—
122C4×Dic13—24no—
123C4×Dic13—24no—
124C4×Dic13C22⋊C414yes—
125C4×Dic13C22⋊C414yes—
126C4×Dic13C2×D414yes—
127C4×Dic13C2×D414yes—
128C22×#117—131no—
129C2×#432—132no—
130#1464—138no—
131C2×#324—132no—
132C2×#323—132no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—22no—
136C23×C13—22no—
137C23×C13—24no—
138C23×C13—24no—
139C23×C13—42no—
140C23×C13—42no—
141C23×C13—48no—
142C23×C13—48no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—42no—
147C23×C13C2×C22⋊C411yescharacteristic
148C23×C13C2×C22⋊C411yescharacteristic
149C23×C13C2×M1612yes—
150C23×C13C2×M1612yes—
151C23×C13C2×M1614yes—
152C23×C13C23×C411yescharacteristic
153C2×C4×C13—216no—
154C2×C4×C13—216no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—24no—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13—24no—
163C2×C4×C13—24no—
164C2×C4×C13C2×C22⋊C412yes—
165C2×C4×C13C2×C22⋊C412yes—
166C2×C4×C13C2×M1614yes—
167C2×Dic13—24no—
168C2×Dic13—24no—
169C2×Dic13—22no—
170C2×Dic13—22no—
171C2×Dic13—42no—
172C2×Dic13—41no—
173C2×Dic13—42no—
174C2×Dic13—42no—
175C2×Dic13—41no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13C2×C22⋊C412yes—
183C2×Dic13C2×C22⋊C414yes—
184C2×Dic13C22×D412yes—
185#1057—48no—
186C24×C4#26111yescharacteristic
187C2×#117—134no—
188C2×#117—134no—
189C2×#117—262no—
190C2×#117—262no—
191C2×#117—264no—
192C22×C4⋊C4—131no—
193C22×C4⋊C4—131no—
194C22×C22⋊C4—131no—
195C22×C22⋊C4—131no—
196C22×C42—131no—
197C22×C42—131no—
198#432—138no—
199#432—264no—
200C2×C4⋊C8—262no—
201C2×C22⋊C8—134no—
202C2×#97—262no—
203#324—138no—
204#323—138no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—24no—
210C22×C13—24no—
211C22×C13—24no—
212C22×C13—44no—
213C22×C13—44no—
214C22×C13—48no—
215C22×C13—42no—
216C22×C13—42no—
217C22×C13—48no—
218C22×C13#40712yes—
219C22×C13#40712yes—
220C22×C13#41012yes—
221C22×C13#41312yes—
222C22×C13C22×C22⋊C411yescharacteristic
223C22×C13C22×M1611yescharacteristic
224C22×C13C22×M1611yescharacteristic
225C4×C13—22no—
226C4×C13—22no—
227C4×C13—24no—
228Dic13—22no—
229Dic13—22no—
230Dic13—24no—
231Dic13—42no—
232Dic13—42no—
233C25C2×#26111yescharacteristic
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—131no—
240C23×C4—131no—
241C23×C4—131no—
242C23×C4—131no—
243C23×C4C2×#26114yes—
244C23×C4C2×#26111yescharacteristic
245C23×C4C2×#26111yescharacteristic
246C22×C8—264no—
247#117—268no—
248#117—268no—
249#117—268no—
250#117—268no—
251C2×C4⋊C4—132no—
252C2×C4⋊C4—134no—
253C2×C4⋊C4—132no—
254C2×C4⋊C4—262no—
255C2×C4⋊C4—262no—
256C2×C4⋊C4—262no—
257C2×C4⋊C4—262no—
258C2×C22⋊C4—132no—
259C2×C22⋊C4—134no—
260C2×C22⋊C4—132no—
261C2×C22⋊C4—262no—
262C2×C22⋊C4—262no—
263C2×C22⋊C4—262no—
264C2×C22⋊C4—262no—
265C2×C42—132no—
266C2×C42—132no—
267C2×C42—134no—
268C2×C42—132no—
269C2×C42—132no—
270C2×C42—134no—
271C2×C42—262no—
272C2×C42—261no—
273C2×C42—261no—
274C4⋊C8—268no—
275C22⋊C8—138no—
276C22⋊C8—264no—
277#97—268no—
278C2×C13—21no—
279C2×C13—21no—
280C2×C13—22no—
281C2×C13—44no—
282C2×C13#146414yescomplemented
283C2×C13C2×#40711yescharacteristic
284C2×C13C2×#41011yescharacteristic
285C2×C13C2×#41311yescharacteristic
286C24—22no—
287C24—21no—
288C24—21no—
289C24—42no—
290C24—42no—
291C24#612214yes—
292C24C22×#26111yescharacteristic
293C24C22×#26112yes—
294C22×C4—216no—
295C22×C4—28no—
296C22×C4—28no—
297C22×C4—28no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—28no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—132no—
307C22×C4—132no—
308C22×C4—132no—
309C22×C4—132no—
310C22×C4—131no—
311C22×C4—131no—
312C22×C4—132no—
313C22×C4—132no—
314C22×C4—132no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—522no—
320C22×C4—522no—
321C22×C4—522no—
322C22×C4—522no—
323C22×C4#612214yes—
324C22×C4C22⋊#26112yes—
325C22×C4C22⋊#26111yescharacteristic
326C22×C4C22⋊#26111yescharacteristic
327C22×C4C22×#26112yes—
328C22×C4C22×#26112yes—
329C2×C8—268no—
330C2×C8—528no—
331C4⋊C4—264no—
332C4⋊C4—264no—
333C4⋊C4—268no—
334C22⋊C4—264no—
335C22⋊C4—264no—
336C22⋊C4—268no—
337C42—134no—
338C42—134no—
339C42—134no—
340C42—134no—
341C42—264no—
342C42—264no—
343C13C2×#146411yescharacteristic, complemented, Sylow
344C23—22no—
345C23—22no—
346C23—24no—
347C23—24no—
348C23—22no—
349C23—22no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—48no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23C2×#612212yes—
359C23C2×#612212yes—
360C23C2×#612214yes—
361C23C2×C22⋊#26111yescharacteristic
362C23C2×C22⋊#26111yescharacteristic
363C23C23×#26111yescharacteristic
364C2×C4—216no—
365C2×C4—216no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—132no—
376C2×C4—132no—
377C2×C4—134no—
378C2×C4—264no—
379C2×C4—264no—
380C2×C4—262no—
381C2×C4—262no—
382C2×C4—521no—
383C2×C4—522no—
384C2×C4—521no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4C2×#612214yes—
394C2×C4C2×C22⋊#26112yes—
395C2×C4C2×C22⋊#26112yes—
396C8—528no—
397C22—24no—
398C22—24no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—48no—
406C22—44no—
407C22—48no—
408C22—42no—
409C22—42no—
410C22#1171911612yes—
411C22#1171913212yes—
412C22#1171916912yes—
413C22#1171916912yes—
414C22C22×#612211yescharacteristic
415C22C22×#612211yescharacteristic
416C22C22×C22⋊#26111yescharacteristic
417C4—24no—
418C4—22no—
419C4—22no—
420C4—262no—
421C4—262no—
422C4—264no—
423C4—522no—
424C4—522no—
425C2—22no—
426C2—21no—
427C2—21no—
428C2—44no—
429C2#1313008714yesdirect product factor
430C2C2×#1171916911yescharacteristic
431C2C2×#1171911611yescharacteristic
432C2C2×#1171913211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC24×C4#261
hypocenterC13C2×#1464
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11719128C2semidirect
2. #13130087C2direct (N × H)
3. C2×#11718285C2semidirect
20. #11719128C22semidirect
24. #11718285C22semidirect
282. C2×C13#1464semidirect
343. C13C2×#1464semidirect
429. C2#13130087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191282
#131300872
C2×#117182852
C2×#117183052
C22×#881802
C2×#146413