Finite Group Databasebeta

← C2×#13130073 #16792805

Subgroups — C2×#13130073 #16792805

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊(C22⋊C8)C212yesmaximal, complemented
2#13130073C218yesmaximal, direct product factor
3C2×#11718285C212yesmaximal, complemented
4C2×#11718287C212yesmaximal, complemented
5C22×C4×D52C211yesmaximal, characteristic
6C23×D52C411yescharacteristic
7C23×C4×D13C411yescharacteristic
8C23×C4×D13C2211yescharacteristic
9C22×D13⋊C8—22no—
10C22×C42×C13C411yescharacteristic
11C22×#6103C411yescharacteristic
12C22×#6103C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C2×C4×D52—22no—
15C2×C4×D52—22no—
16C2×C4×D52—24no—
17C2×C4×D52C414yes—
18C2×C4×D52C2214yes—
19C2×C22⋊#1057C2214yes—
20D13⋊(C22⋊C8)—24no—
21D13⋊(C22⋊C8)C2218yescomplemented
22C2×#88111—22no—
23#11718287C2218yescomplemented
24#11718285C2218yescomplemented
25C24×D13C2×C411yescharacteristic
26C24×D13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C23×Dic13C2311yescharacteristic
32C22×D52—22no—
33C22×D52—22no—
34C22×D52—24no—
35C22×D52C818yescomplemented
36C22×D52C2×C414yes—
37C22×C4×D13—21no—
38C22×C4×D13—22no—
39C22×C4×D13—21no—
40C22×C4×D13—44no—
41C22×C4×D13—44no—
42C22×C4×D13C2×C414yes—
43C22×C4×D13C2×C412yes—
44C22×C4×D13D412yes—
45C22×C4×D13D412yes—
46C22×C4×D13D414yes—
47C22×C4×D13C2312yes—
48C22×#1057—24no—
49C2×D13⋊C8—28no—
50C2×D13⋊C8—48no—
51C2×C42×C13—21no—
52C2×C42×C13—22no—
53C2×C42×C13—21no—
54C2×C42×C13C2×C414yes—
55C2×#6103—22no—
56C2×#6103—22no—
57C2×#6103—22no—
58C2×#6103—22no—
59C2×#6103C2×C412yes—
60C2×#6103C2×C414yes—
61C2×#6103C2312yes—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13C2×C412yes—
65C2×C4⋊Dic13C2312yes—
66C4×D52—28no—
67C4×D52—28no—
68C4×D52—28no—
69C4×D52—28no—
70C22⋊#1057—24no—
71C22⋊#1057C2318yes—
72#88111—28no—
73C2×#1459—131nomaximal, Sylow
74C24×C13C22×C411yescharacteristic
75C23×D13—21no—
76C23×D13—21no—
77C23×D13—22no—
78C23×D13—42no—
79C23×D13—42no—
80C23×D13—42no—
81C23×D13—42no—
82C23×D13C22⋊C412yes—
83C23×D13C22⋊C412yes—
84C23×D13C2×C814yes—
85C23×D13C2×C814yescomplemented
86C23×D13M1614yes—
87C23×D13C22×C412yes—
88C23×D13C22×C412yes—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—24no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—42no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C412yes—
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C2×C814yescomplemented
100C22×C4×C13C22×C412yes—
101C22×C4×C13C22×C412yes—
102C22×C4×C13C22×C412yes—
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—42no—
106C22×Dic13—42no—
107C22×Dic13C22×C412yes—
108C22×Dic13C22×C411yescharacteristic
109C22×Dic13C2×D412yes—
110C22×Dic13C2×D412yes—
111C22×Dic13C2411yescharacteristic
112C2×D52—216no—
113C2×D52—216no—
114C2×D52—28no—
115C2×D52—28no—
116C2×D52C2×C8116yescomplemented
117C2×C4×D13—28no—
118C2×C4×D13—24no—
119C2×C4×D13—24no—
120C2×C4×D13—44no—
121C2×C4×D13—48no—
122C2×C4×D13—44no—
123C2×C4×D13—44no—
124C2×C4×D13—44no—
125C2×C4×D13—48no—
126C2×C4×D13—44no—
127C2×C4×D13—48no—
128C2×C4×D13C22⋊C414yes—
129C2×C4×D13C22⋊C414yes—
130C2×C4×D13C2×D414yes—
131C2×C4×D13C2×D414yes—
132C2×#1057—28no—
133C2×#1057—48no—
134D13⋊C8—416no—
135C42×C13—24no—
136C42×C13—24no—
137#6103—28no—
138#6103—24no—
139#6103—24no—
140C4⋊Dic13—24no—
141C4⋊Dic13—24no—
142C22×C4×D4—131no—
143C22×C22⋊C8—132no—
144#1459—138no—
145C2×#324—132no—
146C2×#323—132no—
147C23×C13—22no—
148C23×C13—22no—
149C23×C13C2×C22⋊C411yescharacteristic
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13C22×C812yes—
152C23×C13C2×M1612yes—
153C23×C13C23×C411yescharacteristic
154C22×D13—24no—
155C22×D13—24no—
156C22×D13—22no—
157C22×D13—22no—
158C22×D13—24no—
159C22×D13—24no—
160C22×D13—42no—
161C22×D13—42no—
162C22×D13—42no—
163C22×D13—48no—
164C22×D13—48no—
165C22×D13—42no—
166C22×D13—42no—
167C22×D13—42no—
168C22×D13—48no—
169C22×D13—42no—
170C22×D13—42no—
171C22×D13—42no—
172C22×D13—48no—
173C22×D13—42no—
174C22×D13C22⋊C818yes—
175C22×D13C22⋊C818yes—
176C22×D13C2×C22⋊C414yes—
177C22×D13C22×C814yes—
178C22×D13C22×C814yescomplemented
179C22×D13C2×M1614yes—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—24no—
183C2×C4×C13—24no—
184C2×C4×C13—22no—
185C2×C4×C13—24no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13#9914yes—
192C2×C4×C13C2×C22⋊C412yes—
193C2×C4×C13C2×C22⋊C412yes—
194C2×C4×C13C22×C814yescomplemented
195C2×Dic13—24no—
196C2×Dic13—22no—
197C2×Dic13—41no—
198C2×Dic13—42no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203C2×Dic13C2×C22⋊C412yes—
204C2×Dic13C22×D412yes—
205D52—232no—
206C4×D13—28no—
207C4×D13—28no—
208C4×D13—44no—
209C4×D13—44no—
210C4×D13—48no—
211C4×D13—48no—
212#1057—48no—
213C23×D4—131no—
214C24×C4—131no—
215C24×C4—131no—
216C23×C8—262no—
217C2×C4×D4—134no—
218C2×C4×D4—134no—
219C2×C4×D4—262no—
220C2×C4×D4—264no—
221C2×C4×D4—262no—
222C22×C4⋊C4—131no—
223C22×C22⋊C4—131no—
224C22×C22⋊C4—131no—
225C22×C42#26111yescharacteristic
226C2×C22⋊C8—134no—
227C2×C22⋊C8—138no—
228C2×C22⋊C8—262no—
229C2×C22⋊C8—264no—
230#324—138no—
231#323—138no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—24no—
237C22×C13—24no—
238C22×C13C2×C22⋊C812yes—
239C22×C13C2×C22⋊C812yes—
240C22×C13C2×#9912yes—
241C22×C13#41312yes—
242C22×C13C22×C22⋊C411yescharacteristic
243C22×C13C23×C811yescharacteristic
244C22×C13C22×M1611yescharacteristic
245C2×D13—24no—
246C2×D13—24no—
247C2×D13—216no—
248C2×D13—24no—
249C2×D13—48no—
250C2×D13—44no—
251C2×D13—44no—
252C2×D13—44no—
253C2×D13—48no—
254C2×D13—42no—
255C2×D13—42no—
256C2×D13—48no—
257C2×D13—44no—
258C2×D13C2×C22⋊C818yes—
259C4×C13—24no—
260C4×C13—22no—
261C4×C13—42no—
262C4×C13C2×#9914yes—
263Dic13—22no—
264Dic13—22no—
265Dic13—42no—
266C25—131no—
267C25—131no—
268C22×D4—138no—
269C22×D4—134no—
270C22×D4—262no—
271C22×D4—262no—
272C22×D4—264no—
273C23×C4—131no—
274C23×C4—132no—
275C23×C4—132no—
276C23×C4—134no—
277C23×C4—132no—
278C23×C4—132no—
279C23×C4—131no—
280C23×C4—134no—
281C23×C4—262no—
282C23×C4—261no—
283C23×C4—261no—
284C23×C4—524no—
285C23×C4—524no—
286C23×C4C2×#26111yescharacteristic
287C23×C4C2×#26111yescharacteristic
288C23×C4C2×#26111yescharacteristic
289C22×C8—268no—
290C22×C8—264no—
291C22×C8—528no—
292C4×D4—268no—
293C4×D4—268no—
294C4×D4—268no—
295C4×D4—268no—
296C2×C4⋊C4—132no—
297C2×C4⋊C4—132no—
298C2×C4⋊C4—262no—
299C2×C4⋊C4—262no—
300C2×C22⋊C4—132no—
301C2×C22⋊C4—132no—
302C2×C22⋊C4—134no—
303C2×C22⋊C4—262no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C22⋊C4—262no—
307C2×C42—21no—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42C2×#26114yes—
311C22⋊C8—138no—
312C22⋊C8—268no—
313C22⋊C8—264no—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—22no—
317C2×C13#145914yescomplemented
318C2×C13C22×C22⋊C811yescharacteristic
319C2×C13C22×#9911yescharacteristic
320C2×C13C2×#41311yescharacteristic
321D13—28no—
322D13—44no—
323C24—132no—
324C24—134no—
325C24—134no—
326C24—132no—
327C24—132no—
328C24—134no—
329C24—132no—
330C24—262no—
331C24—261no—
332C24—261no—
333C24—522no—
334C24—522no—
335C24—522no—
336C24—522no—
337C24C22×#26111yescharacteristic
338C2×D4—1316no—
339C2×D4—268no—
340C2×D4—268no—
341C2×D4—2616no—
342C2×D4—2616no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—132no—
351C22×C4—132no—
352C22×C4—131no—
353C22×C4—131no—
354C22×C4—134no—
355C22×C4—134no—
356C22×C4—134no—
357C22×C4—134no—
358C22×C4—132no—
359C22×C4—268no—
360C22×C4—261no—
361C22×C4—261no—
362C22×C4—264no—
363C22×C4—264no—
364C22×C4—528no—
365C22×C4—524no—
366C22×C4—524no—
367C22×C4—524no—
368C22×C4—524no—
369C22×C4—528no—
370C22×C4—528no—
371C22×C4—522no—
372C22×C4—524no—
373C22×C4—522no—
374C22×C4D13⋊C814yescomplemented
375C22×C4C22⋊#26111yescharacteristic
376C22×C4C22⋊#26112yes—
377C22×C4C22⋊#26111yescharacteristic
378C22×C4C22×#26112yes—
379C22×C4C22×#26112yes—
380C22×C4C22×#26112yes—
381C2×C8—268no—
382C2×C8—5216no—
383C2×C8—528no—
384C4⋊C4—264no—
385C4⋊C4—264no—
386C22⋊C4—264no—
387C22⋊C4—264no—
388C22⋊C4—268no—
389C42—24no—
390C42—24no—
391C13C2×#145911yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—134no—
395C23—138no—
396C23—134no—
397C23—134no—
398C23—138no—
399C23—134no—
400C23—264no—
401C23—264no—
402C23—262no—
403C23—262no—
404C23—264no—
405C23—264no—
406C23—522no—
407C23—522no—
408C23—528no—
409C23—528no—
410C23—522no—
411C23—522no—
412C23—522no—
413C23—528no—
414C23—522no—
415C23—522no—
416C23—528no—
417C23—522no—
418C23—522no—
419C23—522no—
420C23C2×D13⋊C812yes—
421C23D13⋊M1612yes—
422C23C2×C22⋊#26111yescharacteristic
423C23C2×C22⋊#26111yescharacteristic
424C23C23×#26111yescharacteristic
425D4—2632no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—132no—
438C2×C4—132no—
439C2×C4—264no—
440C2×C4—268no—
441C2×C4—268no—
442C2×C4—262no—
443C2×C4—524no—
444C2×C4—524no—
445C2×C4—528no—
446C2×C4—521no—
447C2×C4—522no—
448C2×C4—521no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—528no—
452C2×C4—522no—
453C2×C4#8810714yes—
454C2×C4C2×D13⋊C814yescomplemented
455C2×C4C2×C22⋊#26112yes—
456C2×C4C2×C22⋊#26112yes—
457C8—528no—
458C22—24no—
459C22—24no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—138no—
465C22—2616no—
466C22—264no—
467C22—264no—
468C22—264no—
469C22—524no—
470C22—524no—
471C22—528no—
472C22—524no—
473C22—524no—
474C22—528no—
475C22—528no—
476C22—522no—
477C22—522no—
478C22C2×#8810712yes—
479C22D13⋊(C22⋊C8)12yes—
480C22D13⋊(C22⋊C8)12yes—
481C22#1171913212yes—
482C22C22×D13⋊C811yescharacteristic
483C22C2×D13⋊M1611yescharacteristic
484C22C22×C22⋊#26111yescharacteristic
485C4—24no—
486C4—22no—
487C4—42no—
488C4—262no—
489C4—262no—
490C4—522no—
491C4C2×#8810714yes—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—268no—
496C2—524no—
497C2#1313007314yesdirect product factor
498C2C2×D13⋊(C22⋊C8)11yescharacteristic
499C2C22×#8810711yescharacteristic
500C2C2×#1171913211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D52C4
cosocleC22×Dic13C24
hypercenterC22×C42#261
hypocenterC13C2×#1459
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×D13⋊(C22⋊C8)C2semidirect
2. #13130073C2direct (N × H)
3. C2×#11718285C2semidirect
4. C2×#11718287C2semidirect
21. D13⋊(C22⋊C8)C22semidirect
23. #11718287C22semidirect
24. #11718285C22semidirect
35. C22×D52C8semidirect
85. C23×D13C2×C8semidirect
99. C22×C4×C13C2×C8semidirect
116. C2×D52C2×C8semidirect
178. C22×D13C22×C8semidirect
194. C2×C4×C13C22×C8semidirect
317. C2×C13#1459semidirect
374. C22×C4D13⋊C8semidirect
391. C13C2×#1459semidirect
454. C2×C4C2×D13⋊C8semidirect
497. C2#13130073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13⋊(C22⋊C8)2
#131300732
C2×#117182852
C2×#117182872
C22×C4×D522
C2×#145913