Finite Group Databasebeta

← C2×#13126037 #16735028

Subgroups — C2×#13126037 #16735028

Order 3328.

1770 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
1C2×#11719433C211yesmaximal, characteristic
2C2×D13×#125C211yesmaximal, characteristic
3#13126037C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718363C211yesmaximal, characteristic, complemented
6C2×#11718743C211yesmaximal, characteristic, complemented
7C2×#11718470C212yesmaximal
8C2×#11718466C212yesmaximal
9C2×#11718457C212yesmaximal, complemented
10C2×#11718460C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic
12C2×C13×#491C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#125C2211yescharacteristic
15C2×#88200C2212yes—
16C2×Q8×Dic13C2212yes—
17#11719433—24no—
18#11719433C2218yes—
19D13×#125—24no—
20D13×#125C2218yes—
21C2×#88151—21no—
22C2×#88146—21no—
23C2×C4⋊C4×D13—21no—
24C2×C4⋊C4×D13—21no—
25C2×C4⋊C4×D13C2211yescharacteristic
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×#88144—21no—
28C2×#88144C2211yescharacteristic
29C2×#88144C2211yescharacteristic
30C2×#88143—21no—
31C2×#88143—21no—
32C2×#88141—21no—
33C2×C42×D13C2211yescharacteristic
34C2×#88124C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#491C2218yescomplemented
37C2×C13×#103C2212yes—
38C2×C13×#103C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88075C2212yes—
41C2×#88075C2212yes—
42C2×#88060C2212yes—
43C2×#88058C2212yes—
44C2×#88057C2212yes—
45C2×#88054C2212yes—
46#11718743C2218yescomplemented
47#11718726C2218yescomplemented
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718470C22116yes—
52#11718466C22116yes—
53#11718460C22116yescomplemented
54#11718457C22116yescomplemented
55#11718366C2218yes—
56#11718363C2218yescomplemented
57C22×Q8×C13C2312yes—
58C22×C4×D13—21no—
59C22×C4×D13—21no—
60C22×C4×D13D411yescharacteristic
61C22×C4×D13D411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×Dic26—21no—
64C22×C8×C13C2312yes—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8C2314yes—
67C13×#125—22no—
68C13×#125C2314yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76#88200—24no—
77#88200C2318yes—
78Q8×Dic13—24no—
79Q8×Dic13C2318yes—
80C2×#6103—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13C2312yes—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—22no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13D411yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C22×#1055C2312yes—
100#88151—28no—
101#88146—28no—
102C4⋊C4×D13—28no—
103C4⋊C4×D13—28no—
104C4⋊C4×D13—22no—
105C4⋊C4×D13—22no—
106C4⋊C4×D13C2314yes—
107C4⋊C4×D13C2314yes—
108#88144—28no—
109#88144—22no—
110#88144—22no—
111#88144C2314yes—
112#88144C2314yes—
113#88143—28no—
114#88143—28no—
115#88141—28no—
116C42×D13D414yes—
117C42×D13C2314yes—
118#88124—22no—
119#88124C2314yes—
120#88123—22no—
121#88123C2314yes—
122C13×#103C2318yes—
123C13×#103C2318yes—
124C13×#97C2314yes—
125#88075C2318yes—
126#88075C2318yes—
127#88060C2318yes—
128#88058C2318yes—
129#88057C2318yes—
130#88054C2318yes—
131#88048C2318yes—
132#88047C2318yes—
133#88043C2314yes—
134C2×#3236—131nomaximal, Sylow
135C23×D13C2×D411yescharacteristic
136C2×Q8×C13—22no—
137C2×Q8×C13—28no—
138C2×Q8×C13C2414yes—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C2×C4×D13—24no—
152C2×C4×D13—24no—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—42no—
156C2×C4×D13—44no—
157C2×C4×D13—44no—
158C2×C4×D13C2×D412yes—
159C2×C4×D13C2×D414yes—
160C2×C4×D13C2×D414yes—
161C2×C4×D13C2412yes—
162C2×Dic26—24no—
163C2×Dic26—44no—
164C2×C8×C13—24no—
165C2×C8×C13C2414yes—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—24no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4C2412yes—
173C13×C4⋊C4C2412yes—
174C42×C13C2×D412yes—
175C42×C13C2412yes—
176#6103—28no—
177C4⋊Dic13—22no—
178C4⋊Dic13—24no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—24no—
182C4⋊Dic13—24no—
183C4⋊Dic13—28no—
184C4⋊Dic13C2412yes—
185C4⋊Dic13C2412yes—
186C4⋊Dic13C2414yes—
187#6101—24no—
188#6101—24no—
189#6101—28no—
190#6101—24no—
191#6101—24no—
192#6101—24no—
193#6101—24no—
194C4×Dic13—28no—
195C4×Dic13C2×D412yes—
196C4×Dic13C2×D414yes—
197C4×Dic13C2×D414yes—
198C4×Dic13C2412yes—
199C2×#1055—24no—
200C2×#1055C2414yes—
201C2×#533—131no—
202C22×#125—131no—
203#3236—1316no—
204C2×#501—131no—
205C2×#501—131no—
206C2×#491—131no—
207C2×#491D1311yescharacteristic, complemented
208C2×#484—132no—
209C2×#483—132no—
210C2×#479—132no—
211C2×#479—132no—
212C2×#432—131no—
213C23×C13C22×D411yescharacteristic
214C22×D13—22no—
215C22×D13—22no—
216C22×D13#13714yes—
217C22×D13C22×D412yes—
218Q8×C13—28no—
219Q8×C13—44no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—44no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13C22×D412yes—
229C2×C4×C13C22×D412yes—
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C132−1+414yes—
232C2×C4×C13C2511yescharacteristic
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—42no—
240C2×Dic13—44no—
241C2×Dic13—42no—
242C2×Dic13C22×D412yes—
243C2×Dic13C22×D412yes—
244C2×Dic13C22×D412yes—
245C4×D13—28no—
246C4×D13—24no—
247C4×D13—24no—
248C4×D13—44no—
249C4×D13—48no—
250C4×D13—48no—
251Dic26—48no—
252C8×C13—24no—
253#1055—24no—
254#533—138no—
255#533—264no—
256C2×C4⋊Q8—131no—
257C2×C4⋊Q8C2×D1311yescharacteristic
258C2×#125—138no—
259C2×#125—131no—
260C2×#125—131no—
261C2×#125—131no—
262C2×#125—261no—
263C2×#125—261no—
264C2×#125—261no—
265C2×#125—264no—
266C2×#125C2×D1311yescharacteristic
267C2×C22⋊Q8—132no—
268C2×C22⋊Q8—261no—
269C2×C4×Q8—132no—
270C2×C4×Q8—261no—
271C2×#117—261no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—131no—
274C22×C4⋊C4—261no—
275C22×C4⋊C4—261no—
276C22×C42—131no—
277#501—138no—
278#501—138no—
279#491—138no—
280#491C2×D1318yescomplemented
281#484—1316no—
282#483—1316no—
283#479—1316no—
284#479—1316no—
285#432—138no—
286C2×#107—132no—
287C2×#107—132no—
288C2×#106—132no—
289C2×#106—132no—
290C2×C4⋊C8—132no—
291C2×#103—132no—
292C2×#103—132no—
293C2×#103C2×D1312yes—
294C2×#103C2×D1312yes—
295C2×C22⋊C8—132no—
296C2×#97—131no—
297C2×#97C2×D1311yescharacteristic
298C22×C13#53612yes—
299C22×C13C2×#13712yes—
300C22×C13#57512yes—
301C22×C13C23×D411yescharacteristic
302C2×D13—22no—
303C2×D13—28no—
304C2×D13—22no—
305C2×D13C2×#13714yes—
306C4×C13—22no—
307C4×C13—22no—
308C4×C13—44no—
309C4×C13—42no—
310C4×C13—42no—
311C4×C13#53612yes—
312C4×C13C2×2−1+412yes—
313Dic13—22no—
314Dic13—22no—
315Dic13—22no—
316Dic13—42no—
317Dic13—44no—
318Dic13—42no—
319C22×Q8—261no—
320C22×Q8C22×D1312yes—
321C23×C4—131no—
322C23×C4—131no—
323C23×C4—131no—
324C23×C4—261no—
325C23×C4—261no—
326C22×C8—132no—
327C22×C8C22×D1312yes—
328C4⋊Q8—22no—
329C4⋊Q8—134no—
330C4⋊Q8—262no—
331C4⋊Q8C22×D1314yes—
332#125—22no—
333#125—134no—
334#125—134no—
335#125—134no—
336#125—268no—
337#125—268no—
338#125—262no—
339#125—262no—
340#125—268no—
341#125—262no—
342#125C22×D1314yes—
343C22⋊Q8—138no—
344C22⋊Q8—268no—
345C22⋊Q8—264no—
346C4×Q8—138no—
347C4×Q8—268no—
348C4×Q8—264no—
349#117—268no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—132no—
357C2×C4⋊C4—134no—
358C2×C4⋊C4—134no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—268no—
362C2×C4⋊C4—268no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C22⋊C4—262no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—134no—
381C2×C42—134no—
382C2×C42—262no—
383C2×C42C22×D1311yescharacteristic
384#107—138no—
385#107—138no—
386#106—138no—
387#106—138no—
388C4⋊C8—138no—
389#103—138no—
390#103—138no—
391#103C22×D1318yes—
392#103C22×D1318yes—
393C22⋊C8—138no—
394#97—134no—
395#97C22×D1314yes—
396C2×C13#323614yescomplemented
397C2×C13C2×#53611yescharacteristic
398C2×C13C22×#13711yescharacteristic
399C2×C13C2×#57511yescharacteristic
400D13—24no—
401C24—131no—
402C2×Q8—22no—
403C2×Q8—28no—
404C2×Q8—264no—
405C2×Q8—524no—
406C2×Q8C23×D1314yes—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—131no—
413C22×C4—134no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—134no—
417C22×C4—264no—
418C22×C4—264no—
419C22×C4—264no—
420C22×C4—264no—
421C22×C4—262no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—522no—
425C22×C4—524no—
426C22×C4—524no—
427C22×C4D4×D1311yescharacteristic
428C22×C4D4×D1311yescharacteristic
429C22×C4C23×D1311yescharacteristic
430C2×C8—24no—
431C2×C8—134no—
432C2×C8—264no—
433C2×C8C23×D1314yes—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—132no—
441C4⋊C4—132no—
442C4⋊C4—134no—
443C4⋊C4—264no—
444C4⋊C4—264no—
445C4⋊C4—264no—
446C4⋊C4—264no—
447C4⋊C4—264no—
448C4⋊C4—264no—
449C4⋊C4—268no—
450C4⋊C4—268no—
451C4⋊C4—261no—
452C4⋊C4—261no—
453C4⋊C4—262no—
454C4⋊C4—264no—
455C4⋊C4—264no—
456C4⋊C4—264no—
457C4⋊C4C23×D1312yes—
458C4⋊C4C23×D1312yes—
459C22⋊C4—268no—
460C42—134no—
461C42—132no—
462C42—134no—
463C42—132no—
464C42—268no—
465C42D4×D1312yes—
466C42C23×D1312yes—
467C13C2×#323611yescharacteristic, complemented, Sylow
468C23—134no—
469C23—132no—
470C23—262no—
471C23—262no—
472C23C2×D4×D1311yescharacteristic
473Q8—28no—
474Q8—44no—
475Q8—528no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—132no—
485C2×C4—132no—
486C2×C4—132no—
487C2×C4—268no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—262no—
491C2×C4—264no—
492C2×C4—264no—
493C2×C4—264no—
494C2×C4—262no—
495C2×C4—262no—
496C2×C4—524no—
497C2×C4—528no—
498C2×C4—528no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—524no—
502C2×C4C2×D4×D1312yes—
503C2×C4C2×D4×D1312yes—
504C2×C4C2×D4×D1311yescharacteristic
505C2×C4#8825714yes—
506C2×C4C24×D1311yescharacteristic
507C8—24no—
508C8—264no—
509C22—134no—
510C22—262no—
511C22—268no—
512C22—262no—
513C22#1171938012yes—
514C22D13×#13712yes—
515C22#1171948212yes—
516C22C22×D4×D1311yescharacteristic
517C4—22no—
518C4—22no—
519C4—42no—
520C4—42no—
521C4—44no—
522C4—262no—
523C4—262no—
524C4—262no—
525C4—522no—
526C4—522no—
527C4—524no—
528C4#1171938012yes—
529C4C2×#8825712yes—
530C2—264no—
531C2#1312603714yesdirect product factor
532C2C2×#1171938011yescharacteristic
533C2C2×D13×#13711yescharacteristic
534C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#491C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#491D13
hypocenterC13C2×#3236
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. #13126037C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718363C2semidirect
6. C2×#11718743C2semidirect
9. C2×#11718457C2semidirect
10. C2×#11718460C2semidirect
12. C2×C13×#491C2semidirect
36. C13×#491C22semidirect
46. #11718743C22semidirect
47. #11718726C22semidirect
53. #11718460C22semidirect
54. #11718457C22semidirect
56. #11718363C22semidirect
207. C2×#491D13semidirect
280. #491C2×D13semidirect
396. C2×C13#3236semidirect
467. C13C2×#3236semidirect
531. C2#13126037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×D13×#1252
#131260372
C2×#117187262
C2×#117183632
C2×#117187432
C2×#117184702
C2×#117184662
C2×#117184572
C2×#117184602
C2×#117183662
C2×C13×#4912
C2×#323613