Finite Group Databasebeta

← #16800810

Subgroups — #16800810

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#432C211yesmaximal, characteristic
2#13131283C211yesmaximal, characteristic
3#13131020C214yesmaximal, complemented
4#13131014C214yesmaximal, complemented
5#13130739C214yesmaximal
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13—21no—
8C2×C13×C4⋊Q8C411yescharacteristic, complemented
9C2×#88198—21no—
10D13×C4⋊Q8—21no—
11D13×C4⋊Q8—21no—
12D13×C4⋊Q8—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8C412yescomplemented
15D13×C4⋊Q8C412yescomplemented
16D13×C4⋊Q8C2212yes—
17D13×C4⋊Q8C2212yes—
18C2×C4⋊C4×D13—21no—
19C2×C4⋊C4×D13C2212yes—
20C2×#88142—21no—
21C2×#88142C412yescomplemented
22C2×C42×D13C2211yescharacteristic
23C2×#88123C411yescharacteristic, complemented
24#11719136C2212yes—
25#11719135—21no—
26C4×C22⋊#261—21no—
27#11719130—21no—
28#11719128—21no—
29D13⋊(C22⋊C8)C2212yes—
30#11719061—21no—
31#11719060C2212yes—
32C4×C4⋊#261C2212yes—
33#11719057—21no—
34#11719055—21no—
35#11719054—21no—
36D13⋊(C4⋊C8)C2212yes—
37#11719047C2212yes—
38#11718246C22116yes—
39C22×Q8×C13—21no—
40C2×Q8×D13—22no—
41C2×Q8×D13—22no—
42C2×Q8×D13—22no—
43C2×Q8×D13—22no—
44C2×Q8×D13—48no—
45C22×C4×D13—22no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×Dic26—21no—
50C22×Dic26—22no—
51C2×C22⋊#261—22no—
52C2×C4⋊#261C2314yes—
53C2×C4×#261—22no—
54C2×D13⋊C8C2314yes—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8C2×C412yes—
58C13×C4⋊Q8C2×C412yes—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4C2×C412yes—
61C2×C42×C13C2×C411yescharacteristic
62#88198—22no—
63#88198—22no—
64#88198—22no—
65#88198—22no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13C2×C412yes—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×C4×Dic13C2×C411yescharacteristic
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13D411yescharacteristic
73C4⋊C4×D13—22no—
74C4⋊C4×D13—22no—
75C4⋊C4×D13—22no—
76C4⋊C4×D13—22no—
77C4⋊C4×D13—22no—
78C4⋊C4×D13—22no—
79C4⋊C4×D13C2×C414yes—
80C4⋊C4×D13C2314yes—
81#88142—22no—
82#88142—22no—
83#88142—22no—
84#88142—22no—
85#88142—22no—
86#88142—22no—
87#88142C2×C414yes—
88#88142C2×C414yes—
89C42×D13C2×C411yescharacteristic
90C42×D13C2×C411yescharacteristic
91C42×D13D411yescharacteristic
92C42×D13D411yescharacteristic
93C42×D13D411yescharacteristic
94C42×D13D411yescharacteristic
95C42×D13C2311yescharacteristic
96C42×D13C2311yescharacteristic
97#88123—21no—
98#88123—21no—
99#88123C2×C412yes—
100#88123C2×C412yes—
101C22⋊#1057—22no—
102(C2×#261)⋊C4—22no—
103(C2×#261)⋊C4—22no—
104(C2×#261)⋊C4—22no—
105(C2×#261)⋊C4—22no—
106#88112—22no—
107#88111—22no—
108#88110—22no—
109#88110—22no—
110C4⋊#1057—22no—
111#21840—131nomaximal, Sylow
112C23×D13C2×D411yescharacteristic
113C22×#261—24no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13—44no—
117C22×C4×C13—22no—
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×Dic13—22no—
122C22×Dic13C22⋊C411yescharacteristic
123C22×Dic13C22⋊C411yescharacteristic
124C22×Dic13C2×D411yescharacteristic
125Q8×D13—48no—
126Q8×D13—48no—
127Q8×D13—48no—
128Q8×D13—48no—
129C2×C4×D13—24no—
130C2×C4×D13—24no—
131C2×C4×D13—24no—
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—48no—
135C2×C4×D13C22⋊C411yescharacteristic
136C2×C4×D13C22⋊C411yescharacteristic
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13C22×C411yescharacteristic
140C2×C4×D13C2×D411yescharacteristic
141C2×C4×D13C2×D411yescharacteristic
142C2×C4×D13C2×D411yescharacteristic
143C2×C4×D13C2×D411yescharacteristic
144C2×C4×D13C2×D411yescharacteristic
145C2×C4×D13C2×D411yescharacteristic
146C2×C4×D13C2411yescharacteristic
147C2×Dic26—22no—
148C2×Dic26—22no—
149C2×Dic26—24no—
150C2×Dic26—24no—
151C2×Dic26—48no—
152C2×Dic26—44no—
153C22⋊#261—44no—
154C2×#1057—24no—
155C4⋊#261—28no—
156C4×#261—44no—
157D13⋊C8—28no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4C22×C414yes—
162C42×C13C22⋊C411yescharacteristic
163C42×C13C22⋊C411yescharacteristic
164C42×C13C22×C411yescharacteristic
165C42×C13C22×C411yescharacteristic
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13C22×C414yes—
170#6101—24no—
171#6101—24no—
172#6101—24no—
173#6101—24no—
174C4×Dic13C22⋊C411yescharacteristic
175C4×Dic13C22⋊C411yescharacteristic
176C4×Dic13C22⋊C411yescharacteristic
177C4×Dic13C22⋊C411yescharacteristic
178C4×Dic13C22⋊C411yescharacteristic
179C4×Dic13C22⋊C411yescharacteristic
180C4×Dic13C22×C411yescharacteristic
181C4×Dic13C22×C411yescharacteristic
182C4×Dic13C2×D411yescharacteristic
183C4×Dic13C2×D411yescharacteristic
184C4×Dic13C2×D411yescharacteristic
185C4×Dic13C2×D411yescharacteristic
186C22×C4⋊Q8—131no—
187C2×#432—131no—
188#2283—131no—
189#1993—134no—
190#1987—134no—
191#1823—134no—
192C23×C13C2×C22⋊C411yescharacteristic
193C22×D13—22no—
194C22×D13—22no—
195C22×D13C2×C22⋊C411yescharacteristic
196C22×D13AGL(1,ℤ/8)14yes—
197C22×D13C22×D411yescharacteristic
198C2×#261—44no—
199C2×#261—44no—
200C2×#261—44no—
201Q8×C13—44no—
202Q8×C13—44no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—24no—
207C2×C4×C13—44no—
208C2×C4×C13C2×C22⋊C411yescharacteristic
209C2×C4×C13C2×C22⋊C411yescharacteristic
210C2×C4×C13C2×C22⋊C411yescharacteristic
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C23×C411yescharacteristic
214C2×Dic13—22no—
215C2×Dic13—22no—
216C2×Dic13—22no—
217C2×Dic13—24no—
218C2×Dic13—44no—
219C2×Dic13C2×C22⋊C411yescharacteristic
220C2×Dic13C2×C22⋊C411yescharacteristic
221C2×Dic13C2×C22⋊C411yescharacteristic
222C2×Dic13C2×C22⋊C411yescharacteristic
223C2×Dic13C2×C22⋊C411yescharacteristic
224C2×Dic13C22×D411yescharacteristic
225C4×D13—22no—
226C4×D13—22no—
227C4×D13—22no—
228C4×D13—22no—
229C4×D13—22no—
230C4×D13—22no—
231C4×D13—22no—
232C4×D13—22no—
233C4×D13—22no—
234C4×D13—22no—
235C4×D13—48no—
236C4×D13—48no—
237C4×D13#13714yes—
238C4×D132−1+414yes—
239Dic26—48no—
240Dic26—48no—
241Dic26—44no—
242Dic26—44no—
243#1057—44no—
244C23×Q8—261no—
245C2×C4⋊Q8—132no—
246C2×C4⋊Q8—132no—
247C2×C4⋊Q8—132no—
248C2×C4⋊Q8—132no—
249C2×C4⋊Q8—132no—
250C2×C4⋊Q8—131no—
251C2×C4⋊Q8—261no—
252C2×C4⋊Q8—261no—
253C2×C4⋊Q8—261no—
254C2×C4⋊Q8—261no—
255C2×C4⋊Q8—261no—
256C2×C4⋊Q8—261no—
257C2×C4⋊Q8#26111yescharacteristic, complemented
258C22×C4⋊C4—132no—
259C22×C4⋊C4—261no—
260C22×C42—131no—
261#432—261no—
262#432—261no—
263#432—261no—
264#432—261no—
265C2×C4⋊C8—132no—
266C2×C22⋊C8—132no—
267C2×#97—132no—
268#383—261no—
269#382—132no—
270#381—261no—
271#380—132no—
272C4×C4⋊C4—132no—
273C4×C22⋊C4—261no—
274#376—261no—
275#340—1316no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13#41812yes—
279C22×C13C22×C22⋊C411yescharacteristic
280C2×D13—21no—
281C2×D13—21no—
282C2×D13—28no—
283C2×D13#41812yes—
284C2×D13#53612yes—
285C2×D13C2×AGL(1,ℤ/8)12yes—
286C2×D13C2×#13712yes—
287#261—84no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—44no—
293C4×C13#41912yes—
294C4×C13#51912yes—
295Dic13—21no—
296Dic13—21no—
297Dic13—21no—
298Dic13—21no—
299Dic13—44no—
300Dic13#41912yes—
301Dic13#53612yes—
302C22×Q8—21no—
303C22×Q8—262no—
304C22×Q8—262no—
305C22×Q8—262no—
306C22×Q8—262no—
307C22×Q8—262no—
308C22×Q8—261no—
309C22×Q8—528no—
310C23×C4—131no—
311C23×C4—131no—
312C23×C4—131no—
313C23×C4—262no—
314C22×C8—134no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—134no—
318C4⋊Q8—134no—
319C4⋊Q8—132no—
320C4⋊Q8—132no—
321C4⋊Q8—262no—
322C4⋊Q8—262no—
323C4⋊Q8—262no—
324C4⋊Q8—262no—
325C4⋊Q8—262no—
326C4⋊Q8—262no—
327C4⋊Q8—262no—
328C4⋊Q8—262no—
329C4⋊Q8—262no—
330C4⋊Q8—262no—
331C4⋊Q8—261no—
332C4⋊Q8—261no—
333C4⋊Q8C2×#26112yes—
334C4⋊Q8C2×#26112yes—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—132no—
337C2×C4⋊C4—134no—
338C2×C4⋊C4—134no—
339C2×C4⋊C4—134no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—262no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4C2×#26112yes—
350C2×C22⋊C4—262no—
351C2×C42—131no—
352C2×C42—131no—
353C2×C42—131no—
354C2×C42—131no—
355C2×C42—131no—
356C2×C42—131no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—131no—
360C2×C42—131no—
361C2×C42—131no—
362C2×C42—262no—
363C2×C42C2×#26111yescharacteristic
364C4⋊C8—262no—
365C4⋊C8—262no—
366C22⋊C8—262no—
367C22⋊C8—262no—
368#97—262no—
369#97—262no—
370#95—262no—
371#95—262no—
372#95—262no—
373#95—262no—
374C2×C13—22no—
375C2×C13#231011yescharacteristic
376C2×C13C2×#41811yescharacteristic
377C2×C13C2×#41911yescharacteristic
378D13—22no—
379D13#323814yes—
380C24—131no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—264no—
385C2×Q8—264no—
386C2×Q8—262no—
387C2×Q8—262no—
388C2×Q8—524no—
389C2×Q8—528no—
390C2×Q8—528no—
391C2×Q8—528no—
392C2×Q8—528no—
393C2×Q8—528no—
394C22×C4—22no—
395C22×C4—131no—
396C22×C4—131no—
397C22×C4—131no—
398C22×C4—131no—
399C22×C4—131no—
400C22×C4—131no—
401C22×C4—131no—
402C22×C4—131no—
403C22×C4—131no—
404C22×C4—131no—
405C22×C4—131no—
406C22×C4—131no—
407C22×C4—131no—
408C22×C4—131no—
409C22×C4—131no—
410C22×C4—264no—
411C22×C4—264no—
412C22×C4—264no—
413C22×C4—264no—
414C22×C4—264no—
415C22×C4—262no—
416C22×C4—264no—
417C22×C4—528no—
418C22×C4C22⋊#26111yescharacteristic
419C22×C4C22⋊#26111yescharacteristic
420C22×C4C22×#26111yescharacteristic
421C2×C8—264no—
422C2×C8—268no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—134no—
427C4⋊C4—264no—
428C4⋊C4—264no—
429C4⋊C4—264no—
430C4⋊C4—264no—
431C4⋊C4—268no—
432C4⋊C4—262no—
433C4⋊C4—262no—
434C4⋊C4—262no—
435C4⋊C4C22×#26114yes—
436C22⋊C4—524no—
437C42—131no—
438C42—131no—
439C42—131no—
440C42—131no—
441C42—131no—
442C42—131no—
443C42—131no—
444C42—131no—
445C42—131no—
446C42—131no—
447C42—131no—
448C42—131no—
449C42—524no—
450C42C22⋊#26111yescharacteristic
451C42C22⋊#26111yescharacteristic
452C42C22×#26111yescharacteristic
453C42C22×#26111yescharacteristic
454C13#2184011yescharacteristic, complemented, Sylow
455C23—131no—
456C23—131no—
457C23—134no—
458C23—262no—
459C23—262no—
460C23C2×C22⋊#26111yescharacteristic
461Q8—44no—
462Q8—44no—
463Q8—524no—
464Q8—524no—
465Q8—528no—
466Q8—528no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—44no—
472C2×C4—131no—
473C2×C4—131no—
474C2×C4—134no—
475C2×C4—134no—
476C2×C4—131no—
477C2×C4—131no—
478C2×C4—131no—
479C2×C4—131no—
480C2×C4—262no—
481C2×C4—262no—
482C2×C4—262no—
483C2×C4—262no—
484C2×C4—262no—
485C2×C4—262no—
486C2×C4—262no—
487C2×C4—262no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—262no—
491C2×C4—262no—
492C2×C4—262no—
493C2×C4—264no—
494C2×C4—528no—
495C2×C4—528no—
496C2×C4—524no—
497C2×C4—524no—
498C2×C4—524no—
499C2×C4—524no—
500C2×C4C2×C22⋊#26111yescharacteristic
501C2×C4C2×C22⋊#26111yescharacteristic
502C2×C4C2×C22⋊#26111yescharacteristic
503C2×C4C2×C22⋊#26111yescharacteristic
504C2×C4C2×C22⋊#26111yescharacteristic
505C2×C4C23×#26111yescharacteristic
506C8—524no—
507C22—21no—
508C22—21no—
509C22—132no—
510C22—132no—
511C22—132no—
512C22—132no—
513C22—268no—
514C22—261no—
515C22—261no—
516C22#1171913812yes—
517C22C22×C22⋊#26111yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—44no—
523C4—132no—
524C4—132no—
525C4—261no—
526C4—261no—
527C4—261no—
528C4—261no—
529C4—524no—
530C4—1044no—
531C4#1171915312yes—
532C4#1171962712yes—
533C2—22no—
534C2—134no—
535C2—262no—
536C2#1313131011yescharacteristic
537C2C2×#1171913811yescharacteristic
538C2C2×#1171915311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13#21840
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13131020C2semidirect
4. #13131014C2semidirect
8. C2×C13×C4⋊Q8C4semidirect
14. D13×C4⋊Q8C4semidirect
15. D13×C4⋊Q8C4semidirect
21. C2×#88142C4semidirect
23. C2×#88123C4semidirect
257. C2×C4⋊Q8#261semidirect
454. C13#21840semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4322
#131312832
#131310202
#131310142
#131307392
C2×D13×C4⋊Q82
#2184013