Finite Group Databasebeta

← #16799368

Subgroups — #16799368

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#423C211yesmaximal, characteristic
2C4×#88237C211yesmaximal, characteristic
3#13131015C214yesmaximal, complemented
4#13131014C214yesmaximal, complemented
5#13130523C214yesmaximal
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13—21no—
8C2×#88237C2212yes—
9C2×D13⋊M16C2212yes—
10C2×C13×C4⋊Q8C411yescharacteristic, complemented
11C2×#88198—21no—
12D13×C4⋊Q8—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8—21no—
16D13×C4⋊Q8C412yescomplemented
17D13×C4⋊Q8C412yescomplemented
18D13×C4⋊Q8C2212yes—
19D13×C4⋊Q8C2212yes—
20C2×C4⋊C4×D13—21no—
21C2×C4⋊C4×D13C2212yes—
22C2×#88142—21no—
23C2×#88142C412yescomplemented
24C2×C42×D13C2211yescharacteristic
25C2×#88123C411yescharacteristic, complemented
26C4×C22⋊#261—21no—
27C4×C22⋊#261—21no—
28#11719129—21no—
29#11719129—21no—
30C4×C4⋊#261C2212yes—
31C4×C4⋊#261C2212yes—
32#11719057—21no—
33C42×#261—21no—
34#11719053—21no—
35#11719052—21no—
36D13⋊(C4⋊C8)C2212yes—
37D13⋊(C4⋊C8)C2212yes—
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×#6122—22no—
53#88237—24no—
54#88237Q818yescomplemented
55C2×C4⋊#261C2314yes—
56C2×C4×#261—22no—
57C2×C4×#261—22no—
58C2×C4×#261—22no—
59D13⋊M16—28no—
60C2×#6118—22no—
61C2×D13⋊C8C2314yes—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8C2×C412yes—
65C13×C4⋊Q8C2×C412yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2×C412yes—
68C2×C42×C13C2×C411yescharacteristic
69#88198—22no—
70#88198—22no—
71#88198—22no—
72#88198—22no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13C2×C412yes—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C4⋊C4×D13—22no—
81C4⋊C4×D13—22no—
82C4⋊C4×D13—22no—
83C4⋊C4×D13—22no—
84C4⋊C4×D13—22no—
85C4⋊C4×D13—22no—
86C4⋊C4×D13C2×C414yes—
87C4⋊C4×D13C2314yes—
88#88142—22no—
89#88142—22no—
90#88142—22no—
91#88142—22no—
92#88142—22no—
93#88142—22no—
94#88142C2×C414yes—
95#88142C2×C414yes—
96C42×D13C2×C411yescharacteristic
97C42×D13C2×C411yescharacteristic
98C42×D13D411yescharacteristic
99C42×D13D411yescharacteristic
100C42×D13D411yescharacteristic
101C42×D13D411yescharacteristic
102C42×D13C2311yescharacteristic
103C42×D13C2311yescharacteristic
104#88123—21no—
105#88123—21no—
106#88123C2×C412yes—
107#88123C2×C412yes—
108(C2×#261)⋊C4—22no—
109(C2×#261)⋊C4—22no—
110#88112—22no—
111#88112—22no—
112C4⋊#1057—22no—
113C4⋊#1057—22no—
114#21313—131nomaximal, Sylow
115C23×D13C2×D411yescharacteristic
116C22×#261—24no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—44no—
120C22×C4×C13—22no—
121C22×C4×C13C22⋊C411yescharacteristic
122C22×C4×C13C22⋊C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×Dic13—22no—
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C22⋊C411yescharacteristic
127C22×Dic13C2×D411yescharacteristic
128Q8×D13—48no—
129Q8×D13—48no—
130Q8×D13—48no—
131Q8×D13—48no—
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—24no—
135C2×C4×D13—24no—
136C2×C4×D13—48no—
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13C22⋊C411yescharacteristic
140C2×C4×D13C22⋊C411yescharacteristic
141C2×C4×D13C22×C411yescharacteristic
142C2×C4×D13C2×D411yescharacteristic
143C2×C4×D13C2×D411yescharacteristic
144C2×C4×D13C2×D411yescharacteristic
145C2×C4×D13C2×D411yescharacteristic
146C2×C4×D13C2×D411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2×Q814yes—
149C2×C4×D13#4114yes—
150C2×C4×D13C2411yescharacteristic
151C2×Dic26—22no—
152C2×Dic26—22no—
153C2×Dic26—24no—
154C2×Dic26—24no—
155C2×Dic26—48no—
156C2×Dic26—44no—
157C22⋊#261—28no—
158#6122—44no—
159C2×#1057—24no—
160C4⋊#261—24no—
161C4⋊#261C2×Q818yescomplemented
162C4×#261—28no—
163C4×#261—44no—
164C4×#261—44no—
165#6118—44no—
166D13⋊C8—28no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4C22×C414yes—
171C42×C13C22⋊C411yescharacteristic
172C42×C13C22⋊C411yescharacteristic
173C42×C13C22×C411yescharacteristic
174C42×C13C22×C411yescharacteristic
175C4⋊Dic13—22no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13C22×C414yes—
179#6101—24no—
180#6101—24no—
181#6101—24no—
182#6101—24no—
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22⋊C411yescharacteristic
186C4×Dic13C22⋊C411yescharacteristic
187C4×Dic13C22⋊C411yescharacteristic
188C4×Dic13C22⋊C411yescharacteristic
189C4×Dic13C22×C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C22×C4⋊Q8—131no—
196C2×#423—131no—
197C4×#117—131no—
198#1988—134no—
199#1987—134no—
200#1736—134no—
201C23×C13C2×C22⋊C411yescharacteristic
202C22×D13—22no—
203C22×D13—22no—
204C22×D13C2×C22⋊C411yescharacteristic
205C22×D13C22⋊Q814yes—
206C22×D13C22×D411yescharacteristic
207C2×#261—28no—
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×C13C2×C22⋊C411yescharacteristic
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C4×Q814yes—
222C2×C4×C13C23×C411yescharacteristic
223C2×Dic13—22no—
224C2×Dic13—22no—
225C2×Dic13—24no—
226C2×Dic13—44no—
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13C2×C22⋊C411yescharacteristic
231C2×Dic13C2×C22⋊C411yescharacteristic
232C2×Dic13#12412yes—
233C2×Dic13C4⋊Q812yes—
234C2×Dic13C22×D411yescharacteristic
235C4×D13—22no—
236C4×D13—22no—
237C4×D13—22no—
238C4×D13—22no—
239C4×D13—22no—
240C4×D13—22no—
241C4×D13—48no—
242C4×D13—48no—
243C4×D13C4×Q814yes—
244C4×D13C22⋊Q814yes—
245C4×D13#12412yes—
246C4×D13C4⋊Q812yes—
247C4×D13AGL(1,ℤ/8)14yes—
248C4×D13#13714yes—
249C4×D13C22×Q812yes—
250C4×D13C2×#4112yes—
251Dic26—48no—
252Dic26—44no—
253Dic26—44no—
254Dic26—48no—
255#1057—44no—
256C23×Q8—261no—
257C22×M16—132no—
258C2×C4⋊Q8—132no—
259C2×C4⋊Q8—132no—
260C2×C4⋊Q8—132no—
261C2×C4⋊Q8—132no—
262C2×C4⋊Q8—132no—
263C2×C4⋊Q8—131no—
264C2×C4⋊Q8—261no—
265C2×C4⋊Q8—261no—
266C2×C4⋊Q8—261no—
267C2×C4⋊Q8—261no—
268C2×C4⋊Q8—261no—
269C2×C4⋊Q8—261no—
270C2×C4⋊Q8#26111yescharacteristic, complemented
271C2×#117—132no—
272C22×C4⋊C4—132no—
273C22×C4⋊C4—261no—
274C22×C42—131no—
275#423—261no—
276#423—261no—
277#423—261no—
278#423—261no—
279C2×C4⋊C8—132no—
280C2×C4⋊C8—132no—
281C4×C4⋊C4—132no—
282C4×C4⋊C4—132no—
283C4×C22⋊C4—261no—
284C4×C22⋊C4—261no—
285#376—261no—
286C43—261no—
287#340—1316no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13#39112yes—
291C22×C13C22×C22⋊C411yescharacteristic
292C2×D13—21no—
293C2×D13—21no—
294C2×D13—28no—
295C2×D13#39112yes—
296C2×D13C2×C22⋊Q812yes—
297C2×D13C2×AGL(1,ℤ/8)12yes—
298C2×D13C2×#13712yes—
299#261—48no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—44no—
303C4×C13#39112yes—
304C4×C13#41812yes—
305C4×C13#41912yes—
306C4×C13C2×C4×Q812yes—
307Dic13—21no—
308Dic13—21no—
309Dic13—44no—
310Dic13#39112yes—
311Dic13#41812yes—
312Dic13#41912yes—
313Dic13C2×#12411yescharacteristic
314Dic13C2×C4⋊Q811yescharacteristic
315C22×Q8—21no—
316C22×Q8—262no—
317C22×Q8—262no—
318C22×Q8—262no—
319C22×Q8—262no—
320C22×Q8—262no—
321C22×Q8—261no—
322C22×Q8—528no—
323C23×C4—131no—
324C23×C4—131no—
325C23×C4—131no—
326C23×C4—262no—
327C2×M16—262no—
328C2×M16—262no—
329C2×M16—268no—
330C22×C8—134no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—134no—
334C4⋊Q8—134no—
335C4⋊Q8—132no—
336C4⋊Q8—132no—
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—262no—
347C4⋊Q8—261no—
348C4⋊Q8—261no—
349C4⋊Q8C2×#26112yes—
350C4⋊Q8C2×#26112yes—
351#117—138no—
352#117—264no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—134no—
355C2×C4⋊C4—132no—
356C2×C4⋊C4—134no—
357C2×C4⋊C4—134no—
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—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—261no—
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×C42—262no—
382C2×C42—262no—
383C2×C42C2×#26111yescharacteristic
384C4⋊C8—262no—
385C4⋊C8—262no—
386C4⋊C8—262no—
387C4⋊C8—262no—
388#95—262no—
389#95—262no—
390C2×C13—22no—
391C2×C13C2×#39111yescharacteristic
392C2×C13C2×#41811yescharacteristic
393C2×C13C2×#41911yescharacteristic
394D13—22no—
395D13#307914yes—
396C24—131no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—44no—
400C2×Q8—264no—
401C2×Q8—264no—
402C2×Q8—262no—
403C2×Q8—262no—
404C2×Q8—524no—
405C2×Q8—528no—
406C2×Q8—528no—
407C2×Q8—528no—
408C2×Q8—528no—
409C2×Q8—528no—
410C22×C4—22no—
411C22×C4—131no—
412C22×C4—134no—
413C22×C4—134no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—131no—
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—264no—
429C22×C4—264no—
430C22×C4—264no—
431C22×C4—264no—
432C22×C4—264no—
433C22×C4—262no—
434C22×C4—528no—
435C22×C4C22⋊#26111yescharacteristic
436C22×C4C22⋊#26111yescharacteristic
437C22×C4C22×#26111yescharacteristic
438M16—524no—
439M16—524no—
440C2×C8—264no—
441C2×C8—268no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—138no—
446C4⋊C4—134no—
447C4⋊C4—264no—
448C4⋊C4—264no—
449C4⋊C4—264no—
450C4⋊C4—264no—
451C4⋊C4—264no—
452C4⋊C4—262no—
453C4⋊C4—262no—
454C4⋊C4—262no—
455C4⋊C4C22×#26114yes—
456C22⋊C4—268no—
457C42—131no—
458C42—131no—
459C42—131no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—131no—
464C42—131no—
465C42—131no—
466C42—131no—
467C42—131no—
468C42—131no—
469C42—268no—
470C42—524no—
471C42—524no—
472C42C22⋊#26111yescharacteristic
473C42C22⋊#26111yescharacteristic
474C42C22×#26111yescharacteristic
475C42C22×#26111yescharacteristic
476C13#2131311yescharacteristic, complemented, Sylow
477C23—131no—
478C23—131no—
479C23—134no—
480C23—262no—
481C23—262no—
482C23C2×C22⋊#26111yescharacteristic
483Q8—44no—
484Q8—44no—
485Q8—524no—
486Q8—528no—
487Q8—528no—
488Q8—524no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—44no—
493C2×C4—131no—
494C2×C4—131no—
495C2×C4—131no—
496C2×C4—131no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—134no—
502C2×C4—134no—
503C2×C4—134no—
504C2×C4—134no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—268no—
518C2×C4—264no—
519C2×C4—528no—
520C2×C4—528no—
521C2×C4—524no—
522C2×C4—524no—
523C2×C4—524no—
524C2×C4Q8×#26114yes—
525C2×C4C2×C22⋊#26111yescharacteristic
526C2×C4C2×C22⋊#26111yescharacteristic
527C2×C4C2×C22⋊#26111yescharacteristic
528C2×C4C2×C22⋊#26111yescharacteristic
529C2×C4C2×C22⋊#26111yescharacteristic
530C2×C4C23×#26111yescharacteristic
531C8—524no—
532C22—21no—
533C22—21no—
534C22—132no—
535C22—132no—
536C22—132no—
537C22—132no—
538C22—268no—
539C22—261no—
540C22—261no—
541C22(C2×#261)⋊Q812yes—
542C22C22×C22⋊#26111yescharacteristic
543C4—21no—
544C4—21no—
545C4—44no—
546C4—131no—
547C4—131no—
548C4—132no—
549C4—132no—
550C4—132no—
551C4—261no—
552C4—261no—
553C4—528no—
554C4—524no—
555C4#1171913812yes—
556C4#1171915312yes—
557C4(C2×#261)⋊Q812yes—
558C4C2×Q8×#26112yes—
559C2—22no—
560C2—134no—
561C2—262no—
562C2C2×(C2×#261)⋊Q811yescharacteristic
563C2C2×#1171913811yescharacteristic
564C2C2×#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#21313
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. #13131015C2semidirect
4. #13131014C2semidirect
10. C2×C13×C4⋊Q8C4semidirect
16. D13×C4⋊Q8C4semidirect
17. D13×C4⋊Q8C4semidirect
23. C2×#88142C4semidirect
25. C2×#88123C4semidirect
54. #88237Q8semidirect
161. C4⋊#261C2×Q8semidirect
270. C2×C4⋊Q8#261semidirect
476. C13#21313semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4232
C4×#882372
#131310152
#131310142
#131305232
C2×D13×C4⋊Q82
#2131313