Finite Group Databasebeta

← C2×#13129171 #16770600

Subgroups — C2×#13129171 #16770600

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#13129171C2132yesmaximal, direct product factor
2C2×#11719377C214yesmaximal, complemented
3C2×#11719427C211yesmaximal, characteristic, complemented
4C2×#11719248C212yesmaximal, complemented
5C2×#11719234C214yesmaximal, complemented
6C2×#11719316C214yesmaximal, complemented
7C2×#11719224C214yesmaximal, complemented
8C2×#11719308C214yesmaximal, complemented
9C2×#11719380C214yesmaximal, complemented
10C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
11C2×#11719262C212yesmaximal, complemented
12C2×C13×#555C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2212yes—
14C22×#6129C2214yes—
15C13×#555C22116yescomplemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#124C2214yes—
18C2×C13×#121C2214yes—
19C2×C4×D4×C13C2212yes—
20C2×C13×#117C2214yes—
21C2×#88198C2212yes—
22C2×#88198C2214yes—
23C2×#88192C2212yes—
24C2×#88190C2212yes—
25C2×#88190C2214yes—
26C2×#88189C2218yes—
27C2×D4×Dic13C2214yes—
28C2×C4×C22⋊D13C2214yes—
29C2×#88180C2214yes—
30C22×C4⋊Dic13C2214yes—
31C2×#88178C2214yes—
32D13×C4⋊Q8C22116yescomplemented
33#11719427C22116yescomplemented
34#11719380C22164yescomplemented
35#11719377C22164yescomplemented
36#11719316C22164yescomplemented
37#11719308C22164yescomplemented
38#11719262C22132yescomplemented
39#11719248C22132yescomplemented
40#11719234C22164yescomplemented
41#11719224C22164yescomplemented
42C2×#88151C2212yes—
43C2×C4⋊C4×D13C2214yes—
44C2×#88144C2212yes—
45C2×#88144C2214yes—
46C2×#88142C2214yes—
47C2×#88142C2214yes—
48C2×#88141C2214yes—
49C2×#88137C2218yes—
50C2×#88137C2214yes—
51C2×#88133C2214yes—
52C2×#88133C2218yes—
53C2×#88132C2218yes—
54C2×#88132C2218yes—
55C2×#88132C2218yes—
56C2×#88126C2214yes—
57C2×C42×D13C2211yescharacteristic
58C2×#88124C2218yes—
59C2×#88123C2214yes—
60C2×#88123C2211yescharacteristic
61C2×C4×Dic26C2212yes—
62C22×Q8×C13C2312yes—
63C22×D4×C13C2312yes—
64C22×D4×C13C2314yes—
65C23×C4×C13C2314yes—
66C22×C22⋊D13C2314yes—
67C23×Dic13C2318yes—
68C2×Q8×D13—48no—
69C2×Q8×D13C23116yes—
70C2×#6129—416no—
71C2×#6129C23132yes—
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2312yes—
74C22×C4×D13C2314yes—
75C22×Dic26C2312yes—
76C22×Dic26C2312yes—
77C22×Dic26C2314yes—
78C22×Dic26C2314yes—
79C13×C4⋊Q8C2318yes—
80C13×#124C23132yes—
81C13×#121C23132yes—
82C4×D4×C13C23116yes—
83C13×#117C23132yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C22⋊C4C2318yes—
87C2×C13×C22⋊C4C2314yes—
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2314yes—
90C2×C22⋊Dic13C2314yes—
91C2×C22⋊Dic13C2314yes—
92C2×C22⋊Dic13C2318yes—
93C2×C22⋊Dic13C2314yes—
94#88198C23132yes—
95#88198C23116yes—
96#88192C23116yes—
97#88190C23116yes—
98#88190C23132yes—
99#88189C23164yes—
100D4×Dic13C23132yes—
101C4×C22⋊D13C23132yes—
102C2×#6103C2314yes—
103#88180C23132yes—
104C2×C4⋊Dic13C2312yes—
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2318yes—
107C2×C4⋊Dic13C2314yes—
108C2×C4⋊Dic13C2314yes—
109C2×C4⋊Dic13C23132yes—
110#88178C23132yes—
111C2×#6101C2314yes—
112C2×#6101C2314yes—
113C2×#6101C2318yes—
114C2×#6101C2318yes—
115C2×#6101C2318yes—
116C2×C4×Dic13C2314yes—
117C2×C4×Dic13C2311yescharacteristic
118C2×C4×Dic13C2312yes—
119C2×C4×Dic13C2314yes—
120#88151C23116yes—
121C4⋊C4×D13C23132yes—
122#88144C23116yes—
123#88144C23132yes—
124#88142C23132yes—
125#88142C23132yes—
126#88141C23132yes—
127#88137C23164yes—
128#88137C23132yes—
129#88133C23164yes—
130#88133C23132yes—
131#88132C23164yes—
132#88132C23164yes—
133#88132C23164yes—
134#88126C23132yes—
135C42×D13C2318yes—
136#88124C23164yes—
137#88123C2318yes—
138#88123C23132yes—
139C4×Dic26C23116yes—
140C2×#3544—131nomaximal, Sylow
141C24×C13C2414yes—
142C23×D13C2411yescharacteristic
143C2×Q8×C13—44no—
144C2×Q8×C13C2418yes—
145C2×D4×C13—28no—
146C2×D4×C13—48no—
147C2×D4×C13C2418yes—
148C2×D4×C13C24116yes—
149C22×C4×C13—216no—
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2414yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C24116yes—
154C22×C4×C13C2412yes—
155C2×C22⋊D13—216no—
156C2×C22⋊D13C24116yes—
157C22×Dic13—416no—
158C22×Dic13C2414yes—
159C22×Dic13C2412yes—
160C22×Dic13C2411yescharacteristic
161C22×Dic13C2414yes—
162C22×Dic13C2414yes—
163C22×Dic13C24132yes—
164Q8×D13—432no—
165#6129—464no—
166C2×C4×D13—216no—
167C2×C4×D13—24no—
168C2×C4×D13—28no—
169C2×C4×D13C2414yes—
170C2×C4×D13C2418yes—
171C2×C4×D13C24116yes—
172C2×Dic26—28no—
173C2×Dic26—48no—
174C2×Dic26—48no—
175C2×Dic26—44no—
176C2×Dic26C2418yes—
177C2×Dic26C2418yes—
178C2×Dic26C24116yes—
179C2×Dic26C24116yes—
180C13×C4⋊C4C24116yes—
181C13×C4⋊C4C2418yes—
182C13×C22⋊C4C24132yes—
183C13×C22⋊C4C24116yes—
184C42×C13C2414yes—
185C42×C13C24116yes—
186C22⋊Dic13C24116yes—
187C22⋊Dic13C24116yes—
188C22⋊Dic13C24132yes—
189C22⋊Dic13C24116yes—
190#6103C24116yes—
191C4⋊Dic13C2418yes—
192C4⋊Dic13C24116yes—
193C4⋊Dic13C24132yes—
194C4⋊Dic13C24116yes—
195C4⋊Dic13C24116yes—
196#6101C24116yes—
197#6101C24116yes—
198#6101C24132yes—
199#6101C24132yes—
200#6101C24132yes—
201C4×Dic13C24116yes—
202C4×Dic13C2414yes—
203C4×Dic13C2418yes—
204C4×Dic13C24116yes—
205#3544—1332no—
206C2×#563—134no—
207C2×Q82—131no—
208C2×#555D1311yescharacteristic, complemented
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×C13—28no—
218C23×C13—28no—
219C23×C13—28no—
220C23×C13C2518yes—
221C23×C13C2511yescharacteristic
222C22×D13—24no—
223C22×D13H(5,𝔽2)14yes—
224C22×D13C2512yes—
225Q8×C13—48no—
226D4×C13—216no—
227D4×C13—416no—
228C2×C4×C13—28no—
229C2×C4×C13—22no—
230C2×C4×C13—28no—
231C2×C4×C13—232no—
232C2×C4×C132−1+418yes—
233C2×C4×C13C2512yes—
234C2×C4×C13C2518yes—
235C2×C4×C13C2518yes—
236C2×C4×C13C2514yes—
237C22⋊D13—232no—
238C2×Dic13—22no—
239C2×Dic13—28no—
240C2×Dic13—28no—
241C2×Dic13—28no—
242C2×Dic13—24no—
243C2×Dic13—432no—
244C2×Dic13C2518yes—
245C2×Dic13C2514yes—
246C2×Dic13C2512yes—
247C2×Dic13C2518yes—
248C2×Dic13C2518yes—
249C4×D13—232no—
250C4×D13—28no—
251C4×D13—216no—
252Dic26—216no—
253Dic26—416no—
254Dic26—416no—
255Dic26—48no—
256C22×#41—134no—
257C23×Q8—132no—
258#563—1364no—
259Q82—1316no—
260#555C2×D13116yescomplemented
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—134no—
272C2×C4⋊Q8—131no—
273C2×C4⋊Q8—134no—
274C2×C4⋊Q8C2×D1311yescharacteristic
275#529—1332no—
276C2×#126—134no—
277C2×#126—138no—
278C2×#125—132no—
279C2×#125—134no—
280C2×#125—138no—
281C2×#124—132no—
282C2×#124—134no—
283C2×#124C2×D1314yes—
284C2×#123—138no—
285C2×#123—134no—
286C2×#123—138no—
287C2×C22⋊Q8—134no—
288C2×C22⋊Q8—132no—
289C2×C22⋊Q8—138no—
290C2×C22⋊Q8—138no—
291C2×C22⋊Q8—138no—
292C2×#121—132no—
293C2×#121C2×D1314yes—
294C2×C4×Q8—134no—
295C2×C4×Q8—132no—
296C2×C4×D4—134no—
297C2×C4×D4—134no—
298C2×C4×D4C2×D1312yes—
299C2×#117—134no—
300C2×#117—134no—
301C2×#117C2×D1314yes—
302C22×C4⋊C4—134no—
303C22×C4⋊C4—134no—
304C22×C42—131no—
305C22×C13—28no—
306C22×C13—28no—
307C22×C13—28no—
308C22×C13—416no—
309C22×C13C2×H(5,𝔽2)12yes—
310C22×C13C2×2−1+414yes—
311C22×C13C2611yescharacteristic
312C2×D13—24no—
313C2×D13—28no—
314C2×D13C2×H(5,𝔽2)14yes—
315C4×C13—28no—
316C4×C13—22no—
317C4×C13—28no—
318C4×C13C2×2−1+418yes—
319Dic13—22no—
320Dic13—28no—
321Dic13—28no—
322Dic13—28no—
323Dic13—24no—
324C2×#41—1332no—
325C2×#41—5216no—
326C22×Q8—1316no—
327C22×Q8—132no—
328C22×Q8—132no—
329C22×Q8—134no—
330C22×Q8—134no—
331C22×Q8—528no—
332C22×Q8C22×D1312yes—
333C22×D4—134no—
334C22×D4C22×D1312yes—
335C22×D4C22×D1314yes—
336C23×C4—138no—
337C23×C4—134no—
338C23×C4—132no—
339C23×C4—131no—
340C23×C4C22×D1314yes—
341C4⋊Q8—1316no—
342C4⋊Q8—1332no—
343C4⋊Q8—1332no—
344C4⋊Q8—1332no—
345C4⋊Q8—138no—
346C4⋊Q8—1332no—
347C4⋊Q8C22×D1318yes—
348#126—1332no—
349#126—1364no—
350#125—1316no—
351#125—1332no—
352#125—1364no—
353#124—1316no—
354#124—1332no—
355#124C22×D13132yes—
356#123—1364no—
357#123—1332no—
358#123—1364no—
359C22⋊Q8—1332no—
360C22⋊Q8—1316no—
361C22⋊Q8—1364no—
362C22⋊Q8—1364no—
363C22⋊Q8—1364no—
364#121—1316no—
365#121C22×D13132yes—
366C4×Q8—1332no—
367C4×Q8—1316no—
368C4×D4—1332no—
369C4×D4—1332no—
370C4×D4C22×D13116yes—
371#117—1332no—
372#117—1332no—
373#117C22×D13132yes—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—132no—
376C2×C4⋊C4—138no—
377C2×C4⋊C4—138no—
378C2×C4⋊C4—1332no—
379C2×C4⋊C4—138no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—138no—
385C2×C4⋊C4—1332no—
386C2×C4⋊C4C22×D1314yes—
387C2×C4⋊C4C22×D1312yes—
388C2×C22⋊C4—134no—
389C2×C22⋊C4—134no—
390C2×C22⋊C4—138no—
391C2×C22⋊C4—134no—
392C2×C22⋊C4—134no—
393C2×C22⋊C4C22×D1318yes—
394C2×C22⋊C4C22×D1314yes—
395C2×C42—132no—
396C2×C42—134no—
397C2×C42—134no—
398C2×C42—131no—
399C2×C42—138no—
400C2×C42C22×D1314yes—
401C2×C42C22×D1311yescharacteristic
402C2×C13—48no—
403C2×C13#354414yescomplemented
404C2×C13C22×H(5,𝔽2)11yescharacteristic
405C2×C13C22×2−1+412yes—
406D13—24no—
407C24—131no—
408C24C23×D1314yes—
409#41—5264no—
410C2×Q8—44no—
411C2×Q8—138no—
412C2×Q8—138no—
413C2×Q8—1316no—
414C2×Q8—1316no—
415C2×Q8—268no—
416C2×Q8—528no—
417C2×Q8—524no—
418C2×Q8—528no—
419C2×Q8—5232no—
420C2×Q8C23×D1318yes—
421C2×D4—28no—
422C2×D4—48no—
423C2×D4—1316no—
424C2×D4—2616no—
425C2×D4C23×D1318yes—
426C2×D4C23×D13116yes—
427C22×C4—216no—
428C22×C4—134no—
429C22×C4—132no—
430C22×C4—131no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—1332no—
434C22×C4—138no—
435C22×C4—134no—
436C22×C4—1316no—
437C22×C4—264no—
438C22×C4—2616no—
439C22×C4—268no—
440C22×C4—5216no—
441C22×C4C23×D13116yes—
442C22×C4C23×D1311yescharacteristic
443C22×C4C23×D1314yes—
444C22×C4C23×D1314yes—
445C22×C4C23×D1312yes—
446C4⋊C4—1316no—
447C4⋊C4—138no—
448C4⋊C4—1332no—
449C4⋊C4—1332no—
450C4⋊C4—1332no—
451C4⋊C4—1316no—
452C4⋊C4—1316no—
453C4⋊C4—1316no—
454C4⋊C4—1316no—
455C4⋊C4—1332no—
456C4⋊C4C23×D13116yes—
457C4⋊C4C23×D1318yes—
458C22⋊C4—1316no—
459C22⋊C4—1316no—
460C22⋊C4—1332no—
461C22⋊C4—1316no—
462C22⋊C4—1316no—
463C22⋊C4C23×D13132yes—
464C22⋊C4C23×D13116yes—
465C42—138no—
466C42—134no—
467C42—1316no—
468C42—1316no—
469C42C23×D1314yes—
470C42C23×D13116yes—
471C13C2×#354411yescharacteristic, complemented, Sylow
472C23—28no—
473C23—28no—
474C23—28no—
475C23—134no—
476C23—132no—
477C23—264no—
478C23C24×D1318yes—
479C23C24×D1311yescharacteristic
480Q8—48no—
481Q8—2616no—
482Q8—5216no—
483Q8—528no—
484Q8—5216no—
485D4—216no—
486D4—416no—
487D4—2632no—
488C2×C4—28no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—232no—
492C2×C4—138no—
493C2×C4—134no—
494C2×C4—132no—
495C2×C4—138no—
496C2×C4—138no—
497C2×C4—268no—
498C2×C4—2632no—
499C2×C4—264no—
500C2×C4—268no—
501C2×C4—268no—
502C2×C4—262no—
503C2×C4—268no—
504C2×C4—2616no—
505C2×C4—5232no—
506C2×C4#8825718yes—
507C2×C4C24×D1312yes—
508C2×C4C24×D1318yes—
509C2×C4C24×D1318yes—
510C2×C4C24×D1314yes—
511C22—28no—
512C22—28no—
513C22—28no—
514C22—416no—
515C22—134no—
516C22—264no—
517C22—268no—
518C22C2×#8825714yes—
519C22D13×H(5,𝔽2)12yes—
520C22C25×D1311yescharacteristic
521C4—28no—
522C4—22no—
523C4—28no—
524C4—268no—
525C4—262no—
526C4—268no—
527C4—264no—
528C4—268no—
529C4C2×#8825718yes—
530C2—48no—
531C2—264no—
532C2#1312917114yesdirect product factor
533C2C2×D13×H(5,𝔽2)11yescharacteristic
534C2C22×#8825712yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#555C2
socleC23×C13C25
hypercenterC2×#555D13
hypocenterC13C2×#3544
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13129171C2direct (N × H)
2. C2×#11719377C2semidirect
3. C2×#11719427C2semidirect
4. C2×#11719248C2semidirect
5. C2×#11719234C2semidirect
6. C2×#11719316C2semidirect
7. C2×#11719224C2semidirect
8. C2×#11719308C2semidirect
9. C2×#11719380C2semidirect
10. C2×D13×C4⋊Q8C2semidirect
11. C2×#11719262C2semidirect
12. C2×C13×#555C2semidirect
15. C13×#555C22semidirect
32. D13×C4⋊Q8C22semidirect
33. #11719427C22semidirect
34. #11719380C22semidirect
35. #11719377C22semidirect
36. #11719316C22semidirect
37. #11719308C22semidirect
38. #11719262C22semidirect
39. #11719248C22semidirect
40. #11719234C22semidirect
41. #11719224C22semidirect
208. C2×#555D13semidirect
260. #555C2×D13semidirect
403. C2×C13#3544semidirect
471. C13C2×#3544semidirect
532. C2#13129171direct (N × H)

Maximal subgroups

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

subgroupindex
#131291712
C2×#117193772
C2×#117194272
C2×#117192482
C2×#117192342
C2×#117193162
C2×#117192242
C2×#117193082
C2×#117193802
C2×D13×C4⋊Q82
C2×#117192622
C2×C13×#5552
C2×#354413