Finite Group Databasebeta

← C2×#13125357 #16732532

Subgroups — C2×#13125357 #16732532

Order 3328.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2C2×#11719433C211yesmaximal, characteristic
3#13125357C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718363C211yesmaximal, characteristic, complemented
6C2×#11718537C212yesmaximal, complemented
7C2×#11718517C212yesmaximal, complemented
8C2×#11718741C211yesmaximal, characteristic, complemented
9C2×#11718541C212yesmaximal
10C2×#11718521C212yesmaximal
11C2×D13×#97C211yesmaximal, characteristic
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#125C2211yescharacteristic
15C2×#88200—21no—
16C2×Q8×Dic13—21no—
17C22×C8×D13C2212yes—
18#11719433—24no—
19#11719433C2218yes—
20#11719393—24no—
21#11719393C2218yes—
22C2×#88151—21no—
23C2×#88150—21no—
24C2×#88150—21no—
25C2×#88146C2211yescharacteristic
26C2×#88146C2212yes—
27C2×#88146C2211yescharacteristic
28C2×#88144C2212yes—
29C2×#88142C2211yescharacteristic
30C2×#88142C2211yescharacteristic
31C2×#88141—21no—
32C2×#88141—21no—
33C2×#88141—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88124C2211yescharacteristic
36C2×#88123C2211yescharacteristic
37C13×#501C2218yescomplemented
38C2×C13×#107C2212yes—
39C2×C13×#106C2212yes—
40C2×C13×#97C2211yescharacteristic
41C2×#88058C2212yes—
42C2×#88057C2212yes—
43C2×#88055C2212yes—
44#11718741C2218yescomplemented
45#11718726C2218yescomplemented
46C2×#88048C2212yes—
47C2×#88048C2212yes—
48C2×#88047C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718541C22116yes—
52#11718537C22116yescomplemented
53#11718521C22116yes—
54#11718517C22116yescomplemented
55D13×#97C2218yes—
56#11718363C2218yescomplemented
57C22×Q8×C13—21no—
58C22×C4×D13D411yescharacteristic
59C22×C4×D13D411yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×Dic26—21no—
62C22×Dic26—21no—
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⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2312yes—
75C2×C42×C13C2311yescharacteristic
76#88200—28no—
77Q8×Dic13—28no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13C2312yes—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—22no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2312yes—
98C2×C8×D13Q8116yescomplemented
99C2×C8×D13C2318yes—
100#88151—28no—
101#88150—28no—
102#88150—28no—
103#88146—24no—
104#88146—22no—
105#88146—22no—
106#88146C2318yes—
107#88146C2314yes—
108#88146C2314yes—
109#88144—24no—
110#88144C2318yes—
111#88142—22no—
112#88142—22no—
113#88142C2314yes—
114#88142C2314yes—
115#88141—28no—
116#88141—28no—
117#88141—28no—
118C42×D13D414yes—
119C42×D13C2314yes—
120#88124—22no—
121#88124C2314yes—
122#88123—22no—
123#88123C2314yes—
124C13×#107C2318yes—
125C13×#106C2318yes—
126C13×#97C2314yes—
127#88058C2318yes—
128#88057C2318yes—
129#88055C2318yes—
130#88048C2318yes—
131#88048C2318yes—
132#88047C2318yes—
133#88047C2318yes—
134#88043C2314yes—
135C2×#3162—131nomaximal, Sylow
136C23×D13C2×D411yescharacteristic
137C2×Q8×C13—24no—
138C2×Q8×C13—44no—
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—21no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13C2×D414yes—
154C2×C4×D13C2×D414yes—
155C2×C4×D13C2×D412yes—
156C2×C4×D13C2×Q818yes—
157C2×C4×D13C2412yes—
158C2×Dic26—24no—
159C2×Dic26—24no—
160C2×Dic26—24no—
161C2×Dic26—44no—
162C2×Dic26—44no—
163C2×Dic26—44no—
164C2×C8×C13C2×Q818yes—
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—22no—
172C13×C4⋊C4C2412yes—
173C13×C4⋊C4C2414yes—
174C13×C4⋊C4C2412yes—
175C42×C13C2×D412yes—
176C42×C13C2412yes—
177#6103—24no—
178#6103—24no—
179#6103—28no—
180C4⋊Dic13—22no—
181C4⋊Dic13—24no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—28no—
185C4⋊Dic13C2414yes—
186C4⋊Dic13C2412yes—
187C4⋊Dic13C2412yes—
188#6101—24no—
189#6101—24no—
190#6101—24no—
191#6101—24no—
192#6101—28no—
193C4×Dic13—24no—
194C4×Dic13—24no—
195C4×Dic13—28no—
196C4×Dic13C2×D412yes—
197C4×Dic13C2×D414yes—
198C4×Dic13C2×D414yes—
199C4×Dic13C2412yes—
200C2×#1055C2×Q818yes—
201C2×#1055C2414yes—
202C8×D13C2×Q8132yescomplemented
203C2×#533—131no—
204C2×#533—131no—
205#3162—1316no—
206C2×#501—132no—
207C2×#501—132no—
208C2×#501—131no—
209C2×#501—131no—
210C2×#501—131no—
211C2×#501D1311yescharacteristic, complemented
212C2×#427—132no—
213C2×#427—132no—
214C22×#97—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—22no—
218C22×D13C4⋊Q814yes—
219C22×D13C22×D412yes—
220Q8×C13—48no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—44no—
229C2×C4×C13C22×D412yes—
230C2×C4×C13C22×D412yes—
231C2×C4×C13C22×D411yescharacteristic
232C2×C4×C13C22×Q814yes—
233C2×C4×C13C2511yescharacteristic
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—24no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—44no—
242C2×Dic13C4⋊Q814yes—
243C2×Dic13C22×D412yes—
244C2×Dic13C22×D412yes—
245C2×Dic13C22×D412yes—
246C4×D13—44no—
247C4×D13—44no—
248C4×D13C4⋊Q818yes—
249C4×D13C22×Q818yes—
250Dic26—48no—
251Dic26—48no—
252Dic26—48no—
253C8×C13C22×Q818yes—
254#1055C22×Q818yes—
255C23×C8—132no—
256#533—138no—
257#533—138no—
258#533—264no—
259#533—264no—
260C2×C4⋊Q8—131no—
261C2×C4⋊Q8—131no—
262C2×C4⋊Q8—131no—
263C2×C4⋊Q8C2×D1311yescharacteristic
264C2×#125—132no—
265C2×#125—131no—
266C2×#125C2×D1311yescharacteristic
267C2×C22⋊Q8—261no—
268C2×C22⋊Q8—261no—
269C2×C22⋊Q8—261no—
270C2×C22⋊Q8—261no—
271C2×C4×Q8—261no—
272C2×C4×Q8—261no—
273C2×C4×Q8—261no—
274C2×C4×Q8—261no—
275C2×#117—132no—
276C2×#117—131no—
277C2×#117—131no—
278C22×C42—131no—
279#501—138no—
280#501—138no—
281#501—1316no—
282#501—1316no—
283#501—138no—
284#501C2×D1318yescomplemented
285#427—1316no—
286#427—1316no—
287C2×#107—132no—
288C2×#107—132no—
289C2×#107—132no—
290C2×#107C2×D1312yes—
291C2×#106—132no—
292C2×#106—132no—
293C2×#106—132no—
294C2×#106C2×D1312yes—
295C2×#97—132no—
296C2×#97—131no—
297C2×#97—138no—
298C2×#97C2×D1311yescharacteristic
299C22×C13C2×C4⋊Q812yes—
300C22×C13#57512yes—
301C22×C13#57512yes—
302C22×C13C23×D411yescharacteristic
303C2×D13—28no—
304C2×D13—22no—
305C2×D13—22no—
306C2×D13C2×C4⋊Q814yes—
307C4×C13—22no—
308C4×C13—22no—
309C4×C13—42no—
310C4×C13—42no—
311C4×C13—44no—
312C4×C13C2×C4⋊Q812yes—
313C4×C13C23×Q812yes—
314Dic13—22no—
315Dic13—22no—
316Dic13—42no—
317Dic13—42no—
318Dic13—44no—
319Dic13C2×C4⋊Q814yes—
320C22×Q8—21no—
321C22×Q8—261no—
322C22×Q8—261no—
323C22×Q8—261no—
324C23×C4—131no—
325C23×C4—131no—
326C23×C4—131no—
327C22×C8—132no—
328C22×C8—1316no—
329C22×C8—138no—
330C22×C8C22×D1312yes—
331C4⋊Q8—22no—
332C4⋊Q8—134no—
333C4⋊Q8—134no—
334C4⋊Q8—134no—
335C4⋊Q8—262no—
336C4⋊Q8—262no—
337C4⋊Q8—262no—
338C4⋊Q8C22×D1314yes—
339#125—22no—
340#125—138no—
341#125—134no—
342#125—264no—
343#125—262no—
344#125C22×D1314yes—
345C22⋊Q8—268no—
346C22⋊Q8—268no—
347C22⋊Q8—268no—
348C22⋊Q8—268no—
349C4×Q8—268no—
350C4×Q8—268no—
351C4×Q8—268no—
352C4×Q8—268no—
353#117—134no—
354#117—138no—
355#117—134no—
356#117—262no—
357#117—262no—
358#117—264no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—132no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4C22×D1312yes—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—262no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—134no—
382C2×C42—134no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—262no—
386C2×C42C22×D1311yescharacteristic
387#107—138no—
388#107—138no—
389#107—138no—
390#107C22×D1318yes—
391#106—138no—
392#106—138no—
393#106—138no—
394#106C22×D1318yes—
395#97—138no—
396#97—134no—
397#97C22×D1314yes—
398C2×C13#316214yescomplemented
399C2×C13C22×C4⋊Q811yescharacteristic
400C2×C13C2×#57511yescharacteristic
401C2×C13C2×#57511yescharacteristic
402D13—24no—
403C24—131no—
404C2×Q8—24no—
405C2×Q8—44no—
406C2×Q8—264no—
407C2×Q8—264no—
408C2×Q8—264no—
409C2×Q8—524no—
410C2×Q8—524no—
411C2×Q8—524no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—131no—
416C22×C4—132no—
417C22×C4—138no—
418C22×C4—132no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—134no—
422C22×C4—134no—
423C22×C4—261no—
424C22×C4—262no—
425C22×C4—261no—
426C22×C4—522no—
427C22×C4—522no—
428C22×C4D4×D1311yescharacteristic
429C22×C4D4×D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—138no—
432C2×C8—134no—
433C2×C8—1332no—
434C2×C8Q8×D1318yes—
435C2×C8C23×D1314yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—132no—
443C4⋊C4—134no—
444C4⋊C4—132no—
445C4⋊C4—268no—
446C4⋊C4—268no—
447C4⋊C4—264no—
448C4⋊C4—264no—
449C4⋊C4—262no—
450C4⋊C4—261no—
451C4⋊C4—261no—
452C4⋊C4—264no—
453C4⋊C4—264no—
454C4⋊C4—264no—
455C4⋊C4C23×D1312yes—
456C4⋊C4C23×D1314yes—
457C4⋊C4C23×D1312yes—
458C22⋊C4—264no—
459C22⋊C4—264no—
460C22⋊C4—268no—
461C42—134no—
462C42—134no—
463C42—132no—
464C42—132no—
465C42—264no—
466C42—264no—
467C42—268no—
468C42D4×D1312yes—
469C42C23×D1312yes—
470C13C2×#316211yescharacteristic, complemented, Sylow
471C23—134no—
472C23—132no—
473C23—262no—
474C23—262no—
475C23C2×D4×D1311yescharacteristic
476Q8—48no—
477Q8—528no—
478Q8—528no—
479Q8—528no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—134no—
489C2×C4—132no—
490C2×C4—138no—
491C2×C4—138no—
492C2×C4—132no—
493C2×C4—132no—
494C2×C4—262no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—264no—
498C2×C4—262no—
499C2×C4—524no—
500C2×C4—524no—
501C2×C4—522no—
502C2×C4—524no—
503C2×C4—522no—
504C2×C4C2×D4×D1312yes—
505C2×C4C2×D4×D1312yes—
506C2×C4C2×D4×D1311yescharacteristic
507C2×C4C2×Q8×D1314yes—
508C2×C4C24×D1311yescharacteristic
509C8—138no—
510C8C2×Q8×D1318yes—
511C22—134no—
512C22—262no—
513C22—262no—
514C22—268no—
515C22D13×C4⋊Q812yes—
516C22#1171947812yes—
517C22#1171948212yes—
518C22C22×D4×D1311yescharacteristic
519C4—22no—
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—134no—
525C4—262no—
526C4—262no—
527C4—522no—
528C4—524no—
529C4—522no—
530C4D13×C4⋊Q812yes—
531C4C22×Q8×D1312yes—
532C2—264no—
533C2#1312535714yesdirect product factor
534C2C2×D13×C4⋊Q811yescharacteristic
535C2C2×#1171947811yescharacteristic
536C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#501D13
hypocenterC13C2×#3162
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13125357C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718363C2semidirect
6. C2×#11718537C2semidirect
7. C2×#11718517C2semidirect
8. C2×#11718741C2semidirect
12. C2×C13×#501C2semidirect
37. C13×#501C22semidirect
44. #11718741C22semidirect
45. #11718726C22semidirect
52. #11718537C22semidirect
54. #11718517C22semidirect
56. #11718363C22semidirect
98. C2×C8×D13Q8semidirect
202. C8×D13C2×Q8semidirect
211. C2×#501D13semidirect
284. #501C2×D13semidirect
398. C2×C13#3162semidirect
470. C13C2×#3162semidirect
533. C2#13125357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×#117194332
#131253572
C2×#117187262
C2×#117183632
C2×#117185372
C2×#117185172
C2×#117187412
C2×#117185412
C2×#117185212
C2×D13×#972
C2×C13×#5012
C2×#316213