Finite Group Databasebeta

← C2×#13130258 #16793943

Subgroups — C2×#13130258 #16793943

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719054C211yesmaximal, characteristic
2C2×#11719061C211yesmaximal, characteristic
3#13130258C218yesmaximal, direct product factor
4C2×#11718298C212yesmaximal
5C2×#11718241C212yesmaximal
6C2×#11719283C211yesmaximal, characteristic
7C2×C4×Q8×C13C411yescharacteristic, complemented
8C2×#88200C2211yescharacteristic
9C2×#88198C411yescharacteristic, complemented
10#11719283—22no—
11#11719283—22no—
12#11719283C414yescomplemented
13#11719283C2214yes—
14C2×#88151C2211yescharacteristic
15C2×#88150—21no—
16C2×#88143—21no—
17C2×#88142C411yescharacteristic, complemented
18C2×#88126—21no—
19C2×C42×D13C2211yescharacteristic
20C2×C4×Dic26—21no—
21C2×C4×Dic26C411yescharacteristic, complemented
22C2×(C2×#261)⋊C4—21no—
23C2×(C2×#261)⋊C4—21no—
24C2×(C2×#261)⋊C4C2212yes—
25C2×#88111C2212yes—
26C2×#88110—21no—
27C2×C4⋊#1057—21no—
28#11719061—22no—
29#11719061C2214yes—
30#11719054—22no—
31#11719054C2214yes—
32#11718298C2218yes—
33#11718241C2218yes—
34C23×#261—22no—
35C22×Q8×C13C2×C411yescharacteristic
36C22×C4×D13D411yescharacteristic
37C22×C4×D13D411yescharacteristic
38C22×C4×D13C2311yescharacteristic
39C22×Dic26—21no—
40C22×Dic26C2×C411yescharacteristic
41C22×#1057—22no—
42C4×Q8×C13—22no—
43C4×Q8×C13C2×C414yescomplemented
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4C2×C411yescharacteristic
46C2×C42×C13—21no—
47C2×C42×C13C2×C411yescharacteristic
48#88200—21no—
49#88200—21no—
50#88200C2×C412yes—
51#88200C2312yes—
52#88198—22no—
53#88198C2×C414yescomplemented
54C2×#6103—21no—
55C2×#6103—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13C2×C411yescharacteristic
58C2×#6101—21no—
59C2×#6101—21no—
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13C2×C411yescharacteristic
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67#88151—21no—
68#88151—21no—
69#88151C2×C412yes—
70#88151C2312yes—
71#88150—24no—
72#88150—24no—
73#88143—24no—
74#88143—24no—
75#88142—22no—
76#88142C2×C414yescomplemented
77#88126—24no—
78#88126—24no—
79C42×D13C2×C412yes—
80C42×D13D412yes—
81C42×D13D412yes—
82C42×D13C2312yes—
83C4×Dic26—22no—
84C4×Dic26—24no—
85C4×Dic26—24no—
86C4×Dic26C2×C414yescomplemented
87(C2×#261)⋊C4—22no—
88(C2×#261)⋊C4—24no—
89(C2×#261)⋊C4—24no—
90(C2×#261)⋊C4C2314yes—
91#88111—22no—
92#88111C2314yes—
93#88110—24no—
94C4⋊#1057—24no—
95C2×#1515—131nomaximal, Sylow
96C23×D13C2×D411yescharacteristic
97C22×#261—24no—
98C22×#261—44no—
99C22×#261—44no—
100C22×#261—44no—
101C2×Q8×C13—21no—
102C2×Q8×C13—42no—
103C2×Q8×C13C22×C412yes—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22×C411yescharacteristic
109C22×Dic13—21no—
110C22×Dic13—21no—
111C22×Dic13C22⋊C411yescharacteristic
112C22×Dic13C22⋊C411yescharacteristic
113C22×Dic13C2×D411yescharacteristic
114C2×C4×D13—24no—
115C2×C4×D13—42no—
116C2×C4×D13—42no—
117C2×C4×D13C22⋊C412yes—
118C2×C4×D13C22⋊C412yes—
119C2×C4×D13C22×C411yescharacteristic
120C2×C4×D13C2×D412yes—
121C2×C4×D13C2×D411yescharacteristic
122C2×C4×D13C2×D412yes—
123C2×C4×D13C2×D411yescharacteristic
124C2×C4×D13C2411yescharacteristic
125C2×Dic26—21no—
126C2×Dic26—24no—
127C2×Dic26—44no—
128C2×Dic26—42no—
129C2×Dic26C22×C412yes—
130C2×#1057—24no—
131C2×#1057—44no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4C22×C412yes—
135C42×C13—24no—
136C42×C13C22⋊C412yes—
137C42×C13C22×C412yes—
138#6103—22no—
139#6103—22no—
140#6103—22no—
141#6103—22no—
142C4⋊Dic13—21no—
143C4⋊Dic13—22no—
144C4⋊Dic13—22no—
145C4⋊Dic13C22×C412yes—
146#6101—24no—
147#6101—22no—
148#6101—24no—
149#6101—24no—
150#6101—24no—
151#6101—22no—
152C4×Dic13—24no—
153C4×Dic13C22⋊C412yes—
154C4×Dic13C22⋊C412yes—
155C4×Dic13C22⋊C412yes—
156C4×Dic13C22×C412yes—
157C4×Dic13C2×D412yes—
158C4×Dic13C2×D412yes—
159C2×#533—131no—
160C2×#432—131no—
161C2×#383—131no—
162#1515—138no—
163C2×#328—132no—
164C2×#328—132no—
165C23×C13C2×C22⋊C411yescharacteristic
166C22×D13—22no—
167C22×D13—22no—
168C22×D13C2×C22⋊C411yescharacteristic
169C22×D13#13714yes—
170C22×D13C22×D411yescharacteristic
171C2×#261—44no—
172C2×#261—44no—
173C2×#261—44no—
174C2×#261—88no—
175Q8×C13—42no—
176Q8×C13—42no—
177C2×C4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13C2×C22⋊C412yes—
185C2×C4×C13C2×C22⋊C411yescharacteristic
186C2×C4×C13C2×C22⋊C412yes—
187C2×C4×C13C23×C411yescharacteristic
188C2×Dic13—22no—
189C2×Dic13—22no—
190C2×Dic13—22no—
191C2×Dic13—22no—
192C2×Dic13—22no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C2×Dic13C2×C22⋊C411yescharacteristic
196C2×Dic13C2×C22⋊C412yes—
197C2×Dic13C2×C22⋊C412yes—
198C2×Dic13C22×D411yescharacteristic
199C4×D13—24no—
200C4×D13—24no—
201C4×D13—42no—
202C4×D13—41no—
203C4×D13—41no—
204C4×D13—41no—
205C4×D13—42no—
206C4×D13—41no—
207Dic26—48no—
208Dic26—42no—
209Dic26—42no—
210#1057—44no—
211#533—134no—
212#533—134no—
213#533—262no—
214#533—262no—
215C2×C4⋊Q8—131no—
216C2×C4⋊Q8—131no—
217C2×#125—261no—
218C2×C22⋊Q8—131no—
219C2×C22⋊Q8—131no—
220C2×C22⋊Q8—261no—
221C2×C4×Q8—131no—
222C2×C4×Q8—261no—
223C2×C4×Q8#26111yescharacteristic, complemented
224C2×#117—261no—
225C22×C42—131no—
226#432—134no—
227#432—262no—
228C2×C4⋊C8—261no—
229C2×C22⋊C8—132no—
230C2×#97—261no—
231#383—134no—
232#383—262no—
233C2×#95—132no—
234C2×#95—261no—
235C2×#95—261no—
236#328—138no—
237#328—138no—
238C22×C13#41012yes—
239C22×C13#41912yes—
240C22×C13#42112yes—
241C22×C13C22×C22⋊C411yescharacteristic
242C2×D13—21no—
243C2×D13—21no—
244C2×D13—21no—
245C2×D13—21no—
246C2×D13—28no—
247C2×D13#41912yes—
248C2×D13C2×#13712yes—
249#261—84no—
250C4×C13—21no—
251C4×C13—21no—
252C4×C13—22no—
253C4×C13—22no—
254C4×C13—42no—
255C4×C13—42no—
256Dic13—21no—
257Dic13—21no—
258Dic13—22no—
259Dic13—22no—
260Dic13—42no—
261Dic13—42no—
262C22×Q8—131no—
263C22×Q8—261no—
264C22×Q8C2×#26111yescharacteristic
265C23×C4—131no—
266C23×C4—131no—
267C23×C4—131no—
268C23×C4—262no—
269C22×C8—262no—
270C4⋊Q8—134no—
271C4⋊Q8—134no—
272C4⋊Q8—262no—
273C4⋊Q8—262no—
274#125—264no—
275#125—264no—
276C22⋊Q8—132no—
277C22⋊Q8—132no—
278C22⋊Q8—132no—
279C22⋊Q8—132no—
280C22⋊Q8—261no—
281C22⋊Q8—261no—
282C22⋊Q8—264no—
283C22⋊Q8—264no—
284C22⋊Q8—261no—
285C22⋊Q8—261no—
286C4×Q8—22no—
287C4×Q8—134no—
288C4×Q8—264no—
289C4×Q8—264no—
290C4×Q8—262no—
291C4×Q8C2×#26114yescomplemented
292#117—264no—
293#117—264no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—131no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4C2×#26111yescharacteristic
303C2×C22⋊C4—261no—
304C2×C22⋊C4—261no—
305C2×C42—21no—
306C2×C42—131no—
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—132no—
310C2×C42—132no—
311C2×C42—132no—
312C2×C42—132no—
313C2×C42—261no—
314C2×C42C2×#26111yescharacteristic
315C4⋊C8—264no—
316C22⋊C8—134no—
317C22⋊C8—262no—
318#97—264no—
319#95—134no—
320#95—262no—
321#95—264no—
322#95—264no—
323C2×C13#151514yescomplemented
324C2×C13C2×#41011yescharacteristic
325C2×C13C2×#41911yescharacteristic
326C2×C13C2×#42111yescharacteristic
327D13—22no—
328D13—22no—
329C24—131no—
330C2×Q8—21no—
331C2×Q8—42no—
332C2×Q8—132no—
333C2×Q8—264no—
334C2×Q8—261no—
335C2×Q8—522no—
336C2×Q8—524no—
337C2×Q8C22×#26112yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—132no—
344C22×C4—132no—
345C22×C4—131no—
346C22×C4—132no—
347C22×C4—131no—
348C22×C4—132no—
349C22×C4—131no—
350C22×C4—131no—
351C22×C4—264no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—264no—
355C22×C4—522no—
356C22×C4—522no—
357C22×C4—524no—
358C22×C4—524no—
359C22×C4—524no—
360C22×C4C22⋊#26111yescharacteristic
361C22×C4C22⋊#26111yescharacteristic
362C22×C4C22×#26111yescharacteristic
363C2×C8—264no—
364C2×C8—524no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—132no—
368C4⋊C4—264no—
369C4⋊C4—264no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—262no—
373C4⋊C4—262no—
374C4⋊C4—264no—
375C4⋊C4—261no—
376C4⋊C4—264no—
377C4⋊C4C22×#26112yes—
378C22⋊C4—262no—
379C22⋊C4—262no—
380C22⋊C4—262no—
381C22⋊C4—262no—
382C42—24no—
383C42—132no—
384C42—132no—
385C42—132no—
386C42—132no—
387C42—132no—
388C42—132no—
389C42—264no—
390C42C22⋊#26112yes—
391C42C22×#26112yes—
392C13C2×#151511yescharacteristic, complemented, Sylow
393C23—131no—
394C23—131no—
395C23—134no—
396C23—262no—
397C23—262no—
398C23C2×C22⋊#26111yescharacteristic
399Q8—42no—
400Q8—42no—
401Q8—522no—
402Q8—522no—
403Q8—528no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—131no—
412C2×C4—131no—
413C2×C4—132no—
414C2×C4—132no—
415C2×C4—264no—
416C2×C4—264no—
417C2×C4—262no—
418C2×C4—262no—
419C2×C4—262no—
420C2×C4—262no—
421C2×C4—262no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—522no—
430C2×C4—524no—
431C2×C4—524no—
432C2×C4—524no—
433C2×C4—1048no—
434C2×C4C2×C22⋊#26112yes—
435C2×C4C2×C22⋊#26111yescharacteristic
436C2×C4C2×C22⋊#26112yes—
437C2×C4C23×#26111yescharacteristic
438C8—524no—
439C22—132no—
440C22—132no—
441C22—268no—
442C22—261no—
443C22—261no—
444C22—261no—
445C22—261no—
446C22#1171911612yes—
447C22#1171915312yes—
448C22#1171916612yes—
449C22C22×C22⋊#26111yescharacteristic
450C4—21no—
451C4—21no—
452C4—22no—
453C4—22no—
454C4—42no—
455C4—42no—
456C4—261no—
457C4—261no—
458C4—262no—
459C4—262no—
460C4—522no—
461C4—522no—
462C4—1044no—
463C2—262no—
464C2—262no—
465C2#1313025814yesdirect product factor
466C2C2×#1171911611yescharacteristic
467C2C2×#1171915311yescharacteristic
468C2C2×#1171916611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×C4×Q8#261
hypocenterC13C2×#1515
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13130258C2direct (N × H)
7. C2×C4×Q8×C13C4semidirect
9. C2×#88198C4semidirect
12. #11719283C4semidirect
17. C2×#88142C4semidirect
21. C2×C4×Dic26C4semidirect
43. C4×Q8×C13C2×C4semidirect
53. #88198C2×C4semidirect
76. #88142C2×C4semidirect
86. C4×Dic26C2×C4semidirect
223. C2×C4×Q8#261semidirect
291. C4×Q8C2×#261semidirect
323. C2×C13#1515semidirect
392. C13C2×#1515semidirect
465. C2#13130258direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190542
C2×#117190612
#131302582
C2×#117182982
C2×#117182412
C2×#117192832
C2×#151513