Finite Group Databasebeta

← C2×#13129181 #16770604

Subgroups — C2×#13129181 #16770604

Order 3328.

7086 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129181C2132yesmaximal, direct product factor
2C2×#11719440C214yesmaximal, complemented
3C2×#11719439C211yesmaximal, characteristic, complemented
4C2×#11719284C212yesmaximal, complemented
5C2×#11719286C214yesmaximal, complemented
6C2×#11719431C214yesmaximal, complemented
7C2×#11719434C214yesmaximal, complemented
8C2×#11719287C214yesmaximal, complemented
9C2×#11719429C214yesmaximal, complemented
10C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
11C2×#11719285C212yesmaximal, complemented
12C2×Q82×C13C211yesmaximal, characteristic, complemented
13C22×#6131C2214yes—
14C22×Q8×D13C2212yes—
15Q82×C13C22116yescomplemented
16C2×C13×C4⋊Q8C2214yes—
17C2×C13×C4⋊Q8C2214yes—
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C13C2214yes—
20C2×C4×Q8×C13C2212yes—
21C2×#88201C2214yes—
22C2×#88201C2212yes—
23C2×#88200C2218yes—
24C2×#88200C2214yes—
25C2×#88200C2212yes—
26C2×#88198C2212yes—
27C2×#88198C2214yes—
28#11719440C22164yescomplemented
29#11719439C22116yescomplemented
30#11719434C22164yescomplemented
31#11719431C22164yescomplemented
32#11719429C22164yescomplemented
33D13×C4⋊Q8C22116yescomplemented
34#11719287C22164yescomplemented
35#11719286C22164yescomplemented
36#11719285C22132yescomplemented
37#11719284C22132yescomplemented
38C2×#88152C2214yes—
39C2×#88150C2218yes—
40C2×#88150C2218yes—
41C2×#88149C2214yes—
42C2×#88149C2212yes—
43C2×#88148C2218yes—
44C2×#88148C2218yes—
45C2×#88148C2214yes—
46C2×#88146C2214yes—
47C2×C4⋊C4×D13C2214yes—
48C2×C4⋊C4×D13C2214yes—
49C2×#88144C2212yes—
50C2×#88143C2218yes—
51C2×#88142C2214yes—
52C2×#88130C2218yes—
53C2×#88129C2214yes—
54C2×C4×D52C2214yes—
55C2×C4×D52C2214yes—
56C2×C4×D52C2212yes—
57C2×#88126C2214yes—
58C2×#88126C2214yes—
59C2×C42×D13C2211yescharacteristic
60C2×#88124C2214yes—
61C2×#88123C2211yescharacteristic
62C22×Q8×C13C2312yes—
63C22×Q8×C13C2314yes—
64C22×Q8×C13C2312yes—
65C2×#6131—416no—
66C2×#6131C23132yes—
67C2×Q8×D13—48no—
68C2×Q8×D13C23116yes—
69C22×D52C2312yes—
70C22×D52C2314yes—
71C22×D52C2314yes—
72C22×C4×D13C2312yes—
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2314yes—
75C22×C4×D13C2314yes—
76C22×C4×D13C2318yes—
77C22×Dic26C2312yes—
78C22×Dic26C2314yes—
79C13×C4⋊Q8C2318yes—
80C13×C4⋊Q8C23132yes—
81C13×C4⋊Q8C23132yes—
82C4×Q8×C13C23116yes—
83C4×Q8×C13C23132yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C4⋊C4C2318yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2314yes—
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2314yes—
90C2×C42×C13C2314yes—
91#88201C23132yes—
92#88201C23116yes—
93#88200C23164yes—
94#88200C23132yes—
95#88200C23116yes—
96#88198C23116yes—
97#88198C23132yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100C2×#6103C2314yes—
101C2×#6103C2318yes—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×#6103C2318yes—
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2312yes—
107C2×C4⋊Dic13C2314yes—
108C2×#6101C2318yes—
109C2×#6101C2318yes—
110C2×#6101C2314yes—
111C2×#6101C2314yes—
112C2×#6101C2318yes—
113C2×C4×Dic13C2312yes—
114C2×C4×Dic13C2311yescharacteristic
115C2×C4×Dic13C2314yes—
116#88152C23132yes—
117#88150C23164yes—
118#88150C23164yes—
119#88149C23116yes—
120#88149C23132yes—
121#88148C23132yes—
122#88148C23164yes—
123#88148C23164yes—
124#88146C23132yes—
125C4⋊C4×D13C23132yes—
126C4⋊C4×D13C23132yes—
127#88144C23116yes—
128#88143C23164yes—
129#88142C23132yes—
130#88130C23164yes—
131#88129C23132yes—
132C4×D52C23132yes—
133C4×D52C23132yes—
134C4×D52C23116yes—
135#88126C23132yes—
136#88126C23132yes—
137C42×D13C2318yes—
138#88124C23132yes—
139#88123C2318yes—
140C2×#3544—131nomaximal, Sylow
141C23×D13C2414yes—
142C23×D13C2411yescharacteristic
143C2×Q8×C13—28no—
144C2×Q8×C13—44no—
145C2×Q8×C13—48no—
146C2×Q8×C13C2418yes—
147C2×Q8×C13C24116yes—
148C2×Q8×C13C2418yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2414yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C2412yes—
154C22×Dic13C2412yes—
155C22×Dic13C2414yes—
156C22×Dic13C2411yescharacteristic
157C22×Dic13C2414yes—
158#6131—464no—
159Q8×D13—432no—
160C2×D52—216no—
161C2×D52—28no—
162C2×D52—48no—
163C2×D52C2418yes—
164C2×D52C24116yes—
165C2×D52C24116yes—
166C2×C4×D13—24no—
167C2×C4×D13—216no—
168C2×C4×D13—28no—
169C2×C4×D13—216no—
170C2×C4×D13—416no—
171C2×C4×D13C2418yes—
172C2×C4×D13C2414yes—
173C2×C4×D13C24116yes—
174C2×C4×D13C24116yes—
175C2×C4×D13C24132yes—
176C2×Dic26—48no—
177C2×Dic26—44no—
178C2×Dic26C2418yes—
179C2×Dic26C24116yes—
180C13×C4⋊C4C24116yes—
181C13×C4⋊C4C24132yes—
182C13×C4⋊C4C2418yes—
183C13×C4⋊C4C24116yes—
184C42×C13C2414yes—
185C42×C13C24116yes—
186C42×C13C24116yes—
187#6103C24116yes—
188#6103C24116yes—
189#6103C24116yes—
190#6103C24132yes—
191#6103C24116yes—
192#6103C24116yes—
193#6103C24132yes—
194C4⋊Dic13C24116yes—
195C4⋊Dic13C2418yes—
196C4⋊Dic13C24116yes—
197#6101C24132yes—
198#6101C24132yes—
199#6101C24116yes—
200#6101C24116yes—
201#6101C24132yes—
202C4×Dic13C2418yes—
203C4×Dic13C2414yes—
204C4×Dic13C24116yes—
205#3544—1332no—
206C2×#563—134no—
207C2×Q82D1311yescharacteristic, complemented
208C2×#555—131no—
209C2×#554—132no—
210C2×#552—134no—
211C2×#547—134no—
212C2×#544—134no—
213C2×#542—134no—
214C2×#536—134no—
215C22×C4⋊Q8—131no—
216C2×#529—132no—
217C23×C13C2511yescharacteristic
218C22×D13—24no—
219C22×D13—28no—
220C22×D13—28no—
221C22×D13—28no—
222C22×D13H(5,𝔽2)14yes—
223C22×D13C2518yes—
224C22×D13C2512yes—
225Q8×C13—216no—
226Q8×C13—48no—
227Q8×C13—416no—
228C2×C4×C13—22no—
229C2×C4×C13—28no—
230C2×C4×C13—28no—
231C2×C4×C13—28no—
232C2×C4×C132−1+418yes—
233C2×C4×C13C2518yes—
234C2×C4×C13C2512yes—
235C2×C4×C13C2518yes—
236C2×C4×C13C2518yes—
237C2×C4×C13C2514yes—
238C2×Dic13—22no—
239C2×Dic13—28no—
240C2×Dic13—24no—
241C2×Dic13—28no—
242C2×Dic13C2514yes—
243C2×Dic13C2518yes—
244C2×Dic13C2512yes—
245C2×Dic13C2518yes—
246D52—232no—
247D52—216no—
248D52—416no—
249C4×D13—28no—
250C4×D13—232no—
251C4×D13—216no—
252C4×D13—232no—
253C4×D13—432no—
254Dic26—416no—
255Dic26—48no—
256C22×#41—134no—
257C23×Q8—132no—
258#563—1364no—
259Q82C2×D13116yescomplemented
260#555—1316no—
261#554—1332no—
262#552—1364no—
263#547—1364no—
264#544—1364no—
265#542—1364no—
266#536—1364no—
267C2×C4⋊Q8—132no—
268C2×C4⋊Q8—134no—
269C2×C4⋊Q8—1316no—
270C2×C4⋊Q8—134no—
271C2×C4⋊Q8—131no—
272C2×C4⋊Q8C2×D1311yescharacteristic
273C2×C4⋊Q8C2×D1314yes—
274C2×C4⋊Q8C2×D1314yes—
275#529—1332no—
276C2×#126—134no—
277C2×#126—138no—
278C2×#125—138no—
279C2×#125—132no—
280C2×#125—134no—
281C2×#124—132no—
282C2×#124—134no—
283C2×#124—134no—
284C2×#123—134no—
285C2×#123—138no—
286C2×#123—138no—
287C2×C22⋊Q8—132no—
288C2×C22⋊Q8—134no—
289C2×C22⋊Q8—138no—
290C2×C22⋊Q8—138no—
291C2×C22⋊Q8—138no—
292C2×#121—132no—
293C2×#121—134no—
294C2×C4×Q8C2×D1312yes—
295C2×C4×Q8C2×D1314yes—
296C2×C4×D4—134no—
297C2×C4×D4—132no—
298C2×C4×D4—134no—
299C2×#117—134no—
300C2×#117—134no—
301C2×#117—134no—
302C22×C4⋊C4—134no—
303C22×C4⋊C4—134no—
304C22×C42—131no—
305C22×C13C2×H(5,𝔽2)12yes—
306C22×C13C2×2−1+414yes—
307C22×C13C2611yescharacteristic
308C2×D13—24no—
309C2×D13—28no—
310C2×D13—28no—
311C2×D13—28no—
312C2×D13—28no—
313C2×D13—416no—
314C2×D13C2×H(5,𝔽2)14yes—
315C4×C13—22no—
316C4×C13—28no—
317C4×C13—28no—
318C4×C13—28no—
319C4×C13C2×2−1+418yes—
320Dic13—22no—
321Dic13—28no—
322Dic13—24no—
323Dic13—28no—
324C2×#41—1332no—
325C2×#41—5216no—
326C22×Q8—1316no—
327C22×Q8—132no—
328C22×Q8—134no—
329C22×Q8—528no—
330C22×Q8C22×D1312yes—
331C22×Q8C22×D1314yes—
332C22×Q8C22×D1312yes—
333C22×D4—132no—
334C22×D4—134no—
335C22×D4—134no—
336C23×C4—134no—
337C23×C4—132no—
338C23×C4—134no—
339C23×C4—131no—
340C23×C4—138no—
341C4⋊Q8—1316no—
342C4⋊Q8—1332no—
343C4⋊Q8—1332no—
344C4⋊Q8—138no—
345C4⋊Q8C22×D1318yes—
346C4⋊Q8C22×D13132yes—
347C4⋊Q8C22×D13132yes—
348#126—1332no—
349#126—1364no—
350#125—1316no—
351#125—1364no—
352#125—1332no—
353#124—1316no—
354#124—1332no—
355#124—1332no—
356#123—1332no—
357#123—1364no—
358#123—1364no—
359C22⋊Q8—1316no—
360C22⋊Q8—1332no—
361C22⋊Q8—1364no—
362C22⋊Q8—1364no—
363C22⋊Q8—1364no—
364#121—1316no—
365#121—1332no—
366C4×Q8C22×D13116yes—
367C4×Q8C22×D13132yes—
368C4×D4—1332no—
369C4×D4—1316no—
370C4×D4—1332no—
371#117—1332no—
372#117—1332no—
373#117—1332no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—138no—
376C2×C4⋊C4—138no—
377C2×C4⋊C4—132no—
378C2×C4⋊C4—138no—
379C2×C4⋊C4—134no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—1332no—
383C2×C4⋊C4—1332no—
384C2×C4⋊C4C22×D1312yes—
385C2×C4⋊C4C22×D1314yes—
386C2×C4⋊C4C22×D1314yes—
387C2×C4⋊C4C22×D1318yes—
388C2×C22⋊C4—134no—
389C2×C22⋊C4—134no—
390C2×C22⋊C4—138no—
391C2×C22⋊C4—134no—
392C2×C22⋊C4—138no—
393C2×C22⋊C4—134no—
394C2×C22⋊C4—134no—
395C2×C42—134no—
396C2×C42—132no—
397C2×C42—131no—
398C2×C42—138no—
399C2×C42C22×D1314yes—
400C2×C42C22×D1314yes—
401C2×C42C22×D1311yescharacteristic
402C2×C13#354414yescomplemented
403C2×C13C22×H(5,𝔽2)11yescharacteristic
404C2×C13C22×2−1+412yes—
405D13—24no—
406D13—48no—
407C24—131no—
408C24—134no—
409#41—5264no—
410C2×Q8—28no—
411C2×Q8—44no—
412C2×Q8—48no—
413C2×Q8—138no—
414C2×Q8—1316no—
415C2×Q8—528no—
416C2×Q8—524no—
417C2×Q8—5232no—
418C2×Q8C23×D1318yes—
419C2×Q8C23×D13116yes—
420C2×Q8C23×D1318yes—
421C2×D4—138no—
422C2×D4—1316no—
423C2×D4—1316no—
424C2×D4—2616no—
425C2×D4—268no—
426C2×D4—528no—
427C22×C4—134no—
428C22×C4—132no—
429C22×C4—131no—
430C22×C4—134no—
431C22×C4—138no—
432C22×C4—134no—
433C22×C4—1316no—
434C22×C4—1316no—
435C22×C4—1332no—
436C22×C4—264no—
437C22×C4—2616no—
438C22×C4—268no—
439C22×C4—2616no—
440C22×C4—5216no—
441C22×C4C23×D1311yescharacteristic
442C22×C4C23×D1314yes—
443C22×C4C23×D1314yes—
444C22×C4C23×D1314yes—
445C22×C4C23×D1312yes—
446C4⋊C4—1316no—
447C4⋊C4—1332no—
448C4⋊C4—1332no—
449C4⋊C4—138no—
450C4⋊C4—1332no—
451C4⋊C4—1316no—
452C4⋊C4—1316no—
453C4⋊C4—1316no—
454C4⋊C4C23×D1318yes—
455C4⋊C4C23×D13116yes—
456C4⋊C4C23×D13116yes—
457C4⋊C4C23×D13132yes—
458C22⋊C4—1316no—
459C22⋊C4—1316no—
460C22⋊C4—1332no—
461C22⋊C4—1316no—
462C22⋊C4—1332no—
463C22⋊C4—1316no—
464C22⋊C4—1316no—
465C42—138no—
466C42—134no—
467C42—1316no—
468C42C23×D1314yes—
469C42C23×D13116yes—
470C42C23×D13116yes—
471C13C2×#354411yescharacteristic, complemented, Sylow
472C23—134no—
473C23—132no—
474C23—138no—
475C23—264no—
476C23—268no—
477C23—268no—
478C23—268no—
479C23C24×D1311yescharacteristic
480Q8—216no—
481Q8—48no—
482Q8—416no—
483Q8—5216no—
484Q8—528no—
485D4—2632no—
486D4—2616no—
487D4—5216no—
488C2×C4—28no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—28no—
492C2×C4—134no—
493C2×C4—138no—
494C2×C4—132no—
495C2×C4—138no—
496C2×C4—268no—
497C2×C4—2632no—
498C2×C4—268no—
499C2×C4—264no—
500C2×C4—268no—
501C2×C4—262no—
502C2×C4—2616no—
503C2×C4—2632no—
504C2×C4—5232no—
505C2×C4#8825418yes—
506C2×C4C24×D1312yes—
507C2×C4C24×D1318yes—
508C2×C4C24×D1318yes—
509C2×C4C24×D1318yes—
510C2×C4C24×D1314yes—
511C22—134no—
512C22—264no—
513C22—268no—
514C22—268no—
515C22—268no—
516C22—268no—
517C22—5216no—
518C22C2×#8825414yes—
519C22D13×H(5,𝔽2)12yes—
520C22C25×D1311yescharacteristic
521C4—28no—
522C4—22no—
523C4—28no—
524C4—28no—
525C4—268no—
526C4—262no—
527C4—264no—
528C4—268no—
529C4C2×#8825418yes—
530C2—264no—
531C2—528no—
532C2#1312918114yesdirect product factor
533C2C2×D13×H(5,𝔽2)11yescharacteristic
534C2C22×#8825412yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×Q82×C13C2
socleC23×C13C25
hypercenterC2×Q82D13
hypocenterC13C2×#3544
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. #13129181C2direct (N × H)
2. C2×#11719440C2semidirect
3. C2×#11719439C2semidirect
4. C2×#11719284C2semidirect
5. C2×#11719286C2semidirect
6. C2×#11719431C2semidirect
7. C2×#11719434C2semidirect
8. C2×#11719287C2semidirect
9. C2×#11719429C2semidirect
10. C2×D13×C4⋊Q8C2semidirect
11. C2×#11719285C2semidirect
12. C2×Q82×C13C2semidirect
15. Q82×C13C22semidirect
28. #11719440C22semidirect
29. #11719439C22semidirect
30. #11719434C22semidirect
31. #11719431C22semidirect
32. #11719429C22semidirect
33. D13×C4⋊Q8C22semidirect
34. #11719287C22semidirect
35. #11719286C22semidirect
36. #11719285C22semidirect
37. #11719284C22semidirect
207. C2×Q82D13semidirect
259. Q82C2×D13semidirect
402. C2×C13#3544semidirect
471. C13C2×#3544semidirect
532. C2#13129181direct (N × H)

Maximal subgroups

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

subgroupindex
#131291812
C2×#117194402
C2×#117194392
C2×#117192842
C2×#117192862
C2×#117194312
C2×#117194342
C2×#117192872
C2×#117194292
C2×D13×C4⋊Q82
C2×#117192852
C2×Q82×C132
C2×#354413