Finite Group Databasebeta

← #16800803

Subgroups — #16800803

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2#13131285C211yesmaximal, characteristic
3#13131017C214yesmaximal, complemented
4#13131015C214yesmaximal, complemented
5#13130739C214yesmaximal
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13—21no—
8C2×#88237—21no—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88198—21no—
11D13×C4⋊Q8—21no—
12D13×C4⋊Q8—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8C412yescomplemented
16D13×C4⋊Q8C412yescomplemented
17D13×C4⋊Q8C2212yes—
18D13×C4⋊Q8C2212yes—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13C2212yes—
21C2×#88142—21no—
22C2×#88142C412yescomplemented
23C2×C42×D13C2211yescharacteristic
24C2×#88123C411yescharacteristic, complemented
25#11719136—21no—
26#11719136C2212yes—
27#11719125—21no—
28D13⋊(C22⋊C8)C2212yes—
29#11719119—21no—
30#11719060—21no—
31#11719059C2212yes—
32C4×C4⋊#261—21no—
33C4×C4⋊#261C2212yes—
34#11719051—21no—
35D13⋊(C4⋊C8)C2212yes—
36#11719049—21no—
37C4×D13⋊C8C2212yes—
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—44no—
45C2×Q8×D13—44no—
46C22×C4×D13—22no—
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D411yescharacteristic
49C22×C4×D13C2311yescharacteristic
50C22×Dic26—21no—
51C22×Dic26—22no—
52C2×C22⋊#261—22no—
53#88237—44no—
54C2×C4⋊#261—22no—
55C2×C4⋊#261—22no—
56C2×C4⋊#261C2314yes—
57C2×C4×#261—22no—
58C2×D13⋊C8C2314yes—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8C2×C412yes—
62C13×C4⋊Q8C2×C412yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2×C412yes—
65C2×C42×C13C2×C411yescharacteristic
66#88198—22no—
67#88198—22no—
68#88198—22no—
69#88198—22no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13C2×C412yes—
72C2×#6101—22no—
73C2×#6101—22no—
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C4⋊C4×D13—22no—
78C4⋊C4×D13—22no—
79C4⋊C4×D13—22no—
80C4⋊C4×D13—22no—
81C4⋊C4×D13—22no—
82C4⋊C4×D13—22no—
83C4⋊C4×D13C2×C414yes—
84C4⋊C4×D13C2314yes—
85#88142—22no—
86#88142—22no—
87#88142—22no—
88#88142—22no—
89#88142—22no—
90#88142—22no—
91#88142C2×C414yes—
92#88142C2×C414yes—
93C42×D13C2×C411yescharacteristic
94C42×D13C2×C411yescharacteristic
95C42×D13D411yescharacteristic
96C42×D13D411yescharacteristic
97C42×D13D411yescharacteristic
98C42×D13D411yescharacteristic
99C42×D13C2311yescharacteristic
100C42×D13C2311yescharacteristic
101#88123—21no—
102#88123—21no—
103#88123C2×C412yes—
104#88123C2×C412yes—
105C22⋊#1057—22no—
106(C2×#261)⋊C4—22no—
107(C2×#261)⋊C4—22no—
108#88112—22no—
109#88111—22no—
110C4⋊#1057—22no—
111C4×#1057—22no—
112C4×#1057—22no—
113#21833—131nomaximal, Sylow
114C23×D13C2×D411yescharacteristic
115C22×#261—24no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—44no—
119C22×C4×C13—22no—
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22⋊C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×Dic13—22no—
124C22×Dic13C22⋊C411yescharacteristic
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C2×D411yescharacteristic
127Q8×D13—48no—
128Q8×D13—48no—
129Q8×D13—44no—
130Q8×D13—44no—
131Q8×D13—44no—
132Q8×D13—44no—
133C2×C4×D13—24no—
134C2×C4×D13—24no—
135C2×C4×D13—24no—
136C2×C4×D13—24no—
137C2×C4×D13—44no—
138C2×C4×D13—44no—
139C2×C4×D13C22⋊C411yescharacteristic
140C2×C4×D13C22⋊C411yescharacteristic
141C2×C4×D13C22⋊C411yescharacteristic
142C2×C4×D13C22⋊C411yescharacteristic
143C2×C4×D13D814yes—
144C2×C4×D13SD1614yes—
145C2×C4×D13C22×C411yescharacteristic
146C2×C4×D13C2×D411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13C2×D411yescharacteristic
150C2×C4×D13C2×D411yescharacteristic
151C2×C4×D13C2×D411yescharacteristic
152C2×C4×D13C2411yescharacteristic
153C2×Dic26—22no—
154C2×Dic26—22no—
155C2×Dic26—24no—
156C2×Dic26—24no—
157C2×Dic26—44no—
158C2×Dic26—48no—
159C22⋊#261—44no—
160C2×#1057—24no—
161C4⋊#261—28no—
162C4⋊#261—44no—
163C4⋊#261—44no—
164C4×#261—44no—
165D13⋊C8—28no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4C22×C414yes—
170C42×C13C22⋊C411yescharacteristic
171C42×C13C22⋊C411yescharacteristic
172C42×C13C22×C411yescharacteristic
173C42×C13C22×C411yescharacteristic
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13—22no—
177C4⋊Dic13C22×C414yes—
178#6101—24no—
179#6101—24no—
180#6101—24no—
181#6101—24no—
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22⋊C411yescharacteristic
186C4×Dic13C22⋊C411yescharacteristic
187C4×Dic13C22⋊C411yescharacteristic
188C4×Dic13C22×C411yescharacteristic
189C4×Dic13C22×C411yescharacteristic
190C4×Dic13C2×D411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C22×C4⋊Q8—131no—
195C2×#431—131no—
196#2285—131no—
197#1990—134no—
198#1988—134no—
199#1823—134no—
200C23×C13C2×C22⋊C411yescharacteristic
201C22×D13—22no—
202C22×D13—22no—
203C22×D13C2×C22⋊C411yescharacteristic
204C22×D13C2×D812yes—
205C22×D13C2×SD1612yes—
206C22×D13C22×D411yescharacteristic
207C2×#261—44no—
208C2×#261—44no—
209C2×#261—44no—
210Q8×C13—44no—
211Q8×C13—44no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—24no—
215C2×C4×C13—44no—
216C2×C4×C13#10214yes—
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13C23×C411yescharacteristic
223C2×Dic13—22no—
224C2×Dic13—22no—
225C2×Dic13—24no—
226C2×Dic13—44no—
227C2×Dic13#10214yes—
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13C2×C22⋊C411yescharacteristic
231C2×Dic13C2×C22⋊C411yescharacteristic
232C2×Dic13C2×C22⋊C411yescharacteristic
233C2×Dic13C22×D411yescharacteristic
234C4×D13—22no—
235C4×D13—22no—
236C4×D13—22no—
237C4×D13—22no—
238C4×D13—22no—
239C4×D13—22no—
240C4×D13—44no—
241C4×D13—44no—
242C4×D13—48no—
243C4×D13#10214yes—
244C4×D13#10214yes—
245C4×D13C2×D812yes—
246C4×D13C2×D812yes—
247C4×D13C2×SD1612yes—
248C4×D13C2×SD1612yes—
249C4×D13#13714yes—
250C4×D132−1+414yes—
251Dic26—44no—
252Dic26—44no—
253Dic26—48no—
254Dic26—48no—
255#1057—44no—
256C23×Q8—261no—
257C2×C4⋊Q8—132no—
258C2×C4⋊Q8—132no—
259C2×C4⋊Q8—132no—
260C2×C4⋊Q8—132no—
261C2×C4⋊Q8—132no—
262C2×C4⋊Q8—131no—
263C2×C4⋊Q8—261no—
264C2×C4⋊Q8—261no—
265C2×C4⋊Q8—261no—
266C2×C4⋊Q8—261no—
267C2×C4⋊Q8—261no—
268C2×C4⋊Q8—261no—
269C2×C4⋊Q8#26111yescharacteristic, complemented
270C2×#117—261no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—261no—
273C22×C42—131no—
274#431—261no—
275#431—261no—
276#431—261no—
277#431—261no—
278C2×C4⋊C8—132no—
279C2×C22⋊C8—132no—
280C2×C4×C8—132no—
281#384—132no—
282#382—261no—
283#380—132no—
284#380—261no—
285C4×C4⋊C4—132no—
286C4×C4⋊C4—261no—
287#340—1316no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13C2×#10212yes—
291C22×C13C22×C22⋊C411yescharacteristic
292C2×D13—21no—
293C2×D13—21no—
294C2×D13—24no—
295C2×D13—24no—
296C2×D13C2×#10212yes—
297C2×D13#53612yes—
298C2×D13C22×D811yescharacteristic
299C2×D13C22×SD1611yescharacteristic
300C2×D13C2×#13712yes—
301#261—84no—
302C4×C13—21no—
303C4×C13—21no—
304C4×C13—44no—
305C4×C13C2×#10212yes—
306C4×C13C2×#10212yes—
307C4×C13#41912yes—
308C4×C13#51912yes—
309Dic13—21no—
310Dic13—21no—
311Dic13—44no—
312Dic13C2×#10212yes—
313Dic13C2×#10212yes—
314Dic13#41912yes—
315Dic13#53612yes—
316C22×Q8—21no—
317C22×Q8—262no—
318C22×Q8—262no—
319C22×Q8—262no—
320C22×Q8—262no—
321C22×Q8—262no—
322C22×Q8—261no—
323C22×Q8—524no—
324C22×Q8—524no—
325C23×C4—131no—
326C23×C4—131no—
327C23×C4—131no—
328C23×C4—262no—
329C22×C8—134no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—134no—
333C4⋊Q8—134no—
334C4⋊Q8—132no—
335C4⋊Q8—132no—
336C4⋊Q8—262no—
337C4⋊Q8—262no—
338C4⋊Q8—262no—
339C4⋊Q8—262no—
340C4⋊Q8—262no—
341C4⋊Q8—262no—
342C4⋊Q8—262no—
343C4⋊Q8—262no—
344C4⋊Q8—262no—
345C4⋊Q8—262no—
346C4⋊Q8—261no—
347C4⋊Q8—261no—
348C4⋊Q8C2×#26112yes—
349C4⋊Q8C2×#26112yes—
350#117—524no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—132no—
353C2×C4⋊C4—134no—
354C2×C4⋊C4—134no—
355C2×C4⋊C4—134no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4C2×#26112yes—
368C2×C22⋊C4—262no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—262no—
381C2×C42C2×#26111yescharacteristic
382C4⋊C8—262no—
383C4⋊C8—262no—
384C22⋊C8—262no—
385C22⋊C8—262no—
386C4×C8—262no—
387C4×C8—262no—
388#95—262no—
389#95—262no—
390C2×C13—22no—
391C2×C13#231011yescharacteristic
392C2×C13C22×#10211yescharacteristic
393C2×C13C2×#41911yescharacteristic
394D13—22no—
395D13#322612yes—
396D13#322912yes—
397C24—131no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—44no—
401C2×Q8—264no—
402C2×Q8—264no—
403C2×Q8—262no—
404C2×Q8—262no—
405C2×Q8—528no—
406C2×Q8—524no—
407C2×Q8—524no—
408C2×Q8—528no—
409C2×Q8—528no—
410C2×Q8—524no—
411C2×Q8—524no—
412C2×Q8—524no—
413C22×C4—22no—
414C22×C4—131no—
415C22×C4—134no—
416C22×C4—134no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—264no—
432C22×C4—264no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—262no—
436C22×C4—264no—
437C22×C4—524no—
438C22×C4—524no—
439C22×C4C22⋊#26111yescharacteristic
440C22×C4C22⋊#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442C2×C8—264no—
443C2×C8—268no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—134no—
448C4⋊C4—264no—
449C4⋊C4—264no—
450C4⋊C4—264no—
451C4⋊C4—264no—
452C4⋊C4—268no—
453C4⋊C4—262no—
454C4⋊C4—262no—
455C4⋊C4—262no—
456C4⋊C4—524no—
457C4⋊C4—524no—
458C4⋊C4C22×#26114yes—
459C22⋊C4—524no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—131no—
464C42—131no—
465C42—131no—
466C42—131no—
467C42—131no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—131no—
472C42—524no—
473C42C22⋊#26111yescharacteristic
474C42C22⋊#26111yescharacteristic
475C42C22×#26111yescharacteristic
476C42C22×#26111yescharacteristic
477C13#2183311yescharacteristic, complemented, Sylow
478C23—131no—
479C23—131no—
480C23—132no—
481C23—132no—
482C23—262no—
483C23—262no—
484C23C2×C22⋊#26111yescharacteristic
485Q8—44no—
486Q8—44no—
487Q8—528no—
488Q8—528no—
489Q8—524no—
490Q8—524no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—44no—
495C2×C4—131no—
496C2×C4—131no—
497C2×C4—131no—
498C2×C4—131no—
499C2×C4—134no—
500C2×C4—134no—
501C2×C4—132no—
502C2×C4—132no—
503C2×C4—134no—
504C2×C4—134no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—134no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—264no—
519C2×C4—524no—
520C2×C4—524no—
521C2×C4—528no—
522C2×C4—524no—
523C2×C4—524no—
524C2×C4—524no—
525C2×C4—524no—
526C2×C4#8811514yes—
527C2×C4C2×C22⋊#26111yescharacteristic
528C2×C4C2×C22⋊#26111yescharacteristic
529C2×C4C2×C22⋊#26111yescharacteristic
530C2×C4C2×C22⋊#26111yescharacteristic
531C2×C4C2×C22⋊#26111yescharacteristic
532C2×C4C23×#26111yescharacteristic
533C8—524no—
534C22—21no—
535C22—21no—
536C22—132no—
537C22—131no—
538C22—131no—
539C22—132no—
540C22—132no—
541C22—264no—
542C22—264no—
543C22—261no—
544C22—261no—
545C22C2×#8811512yes—
546C22C22×C22⋊#26111yescharacteristic
547C4—21no—
548C4—21no—
549C4—44no—
550C4—132no—
551C4—132no—
552C4—132no—
553C4—132no—
554C4—261no—
555C4—261no—
556C4—524no—
557C4—1044no—
558C4C2×#8811512yes—
559C4C2×#8811512yes—
560C4#1171915312yes—
561C4#1171962712yes—
562C2—22no—
563C2—132no—
564C2—132no—
565C2—262no—
566C2#1313131011yescharacteristic
567C2C22×#8811511yescharacteristic
568C2C2×#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#21833
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. #13131017C2semidirect
4. #13131015C2semidirect
9. C2×C13×C4⋊Q8C4semidirect
15. D13×C4⋊Q8C4semidirect
16. D13×C4⋊Q8C4semidirect
22. C2×#88142C4semidirect
24. C2×#88123C4semidirect
269. C2×C4⋊Q8#261semidirect
477. C13#21833semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131312852
#131310172
#131310152
#131307392
C2×D13×C4⋊Q82
#2183313