Finite Group Databasebeta

← #16799360

Subgroups — #16799360

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D13⋊M16C211yesmaximal, characteristic
2#13131285C211yesmaximal, characteristic
3#13131012C214yesmaximal, complemented
4#13131011C214yesmaximal, complemented
5#13130515C214yesmaximal
6C2×#11719433C211yesmaximal, characteristic
7C2×#88237C2212yes—
8C2×D13⋊M16C2212yes—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88200—21no—
11C2×Q8×Dic13—21no—
12#11719433—21no—
13#11719433—21no—
14#11719433—21no—
15#11719433—21no—
16#11719433C412yescomplemented
17#11719433C412yescomplemented
18#11719433C2212yes—
19#11719433C2212yes—
20C2×#88151—21no—
21C2×#88146C2212yes—
22C2×#88144C412yescomplemented
23C2×#88141—21no—
24C2×C42×D13C2211yescharacteristic
25C2×#88123C411yescharacteristic, complemented
26#11719136—21no—
27#11719136—21no—
28C4×#6122—21no—
29C4×#6122—21no—
30#11719060—21no—
31#11719059—21no—
32C4×C4⋊#261C2212yes—
33C4×C4⋊#261C2212yes—
34C4×#6118C2212yes—
35C4×#6118C2212yes—
36#11719047—21no—
37C4×D13⋊C8—21no—
38#11718247C22116yes—
39C22×Q8×C13—21no—
40C22×C4×D13D411yescharacteristic
41C22×C4×D13D411yescharacteristic
42C22×C4×D13C2311yescharacteristic
43C22×Dic26—21no—
44C2×C22⋊#261—22no—
45C2×#6122—22no—
46#88237—28no—
47C2×C4⋊#261—22no—
48C2×C4⋊#261—22no—
49C2×C4⋊#261—22no—
50C2×C4×#261C2314yes—
51D13⋊M16—24no—
52D13⋊M16Q818yescomplemented
53C2×#6118C2314yes—
54C2×D13⋊C8—22no—
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#88200—22no—
63#88200—22no—
64#88200—22no—
65#88200—22no—
66Q8×Dic13—22no—
67Q8×Dic13—22no—
68Q8×Dic13—22no—
69Q8×Dic13—22no—
70C2×#6103—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13C2×C412yes—
74C2×#6101—22no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79#88151—22no—
80#88151—22no—
81#88151—22no—
82#88151—22no—
83#88146—22no—
84#88146—22no—
85#88146C2×C414yes—
86#88146C2314yes—
87#88144—22no—
88#88144—22no—
89#88144C2×C414yes—
90#88144C2×C414yes—
91#88141—22no—
92#88141—22no—
93#88141—22no—
94#88141—22no—
95C42×D13C2×C411yescharacteristic
96C42×D13C2×C411yescharacteristic
97C42×D13D411yescharacteristic
98C42×D13D411yescharacteristic
99C42×D13D411yescharacteristic
100C42×D13D411yescharacteristic
101C42×D13C2311yescharacteristic
102C42×D13C2311yescharacteristic
103#88123—21no—
104#88123—21no—
105#88123C2×C412yes—
106#88123C2×C412yes—
107(C2×#261)⋊C4—22no—
108(C2×#261)⋊C4—22no—
109#88110—22no—
110#88110—22no—
111C4×#1057—22no—
112C4×#1057—22no—
113#21306—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
127C2×C4×D13—42no—
128C2×C4×D13—42no—
129C2×C4×D13C22⋊C411yescharacteristic
130C2×C4×D13C22⋊C411yescharacteristic
131C2×C4×D13C22⋊C411yescharacteristic
132C2×C4×D13C22⋊C411yescharacteristic
133C2×C4×D13C22×C411yescharacteristic
134C2×C4×D13C2×D411yescharacteristic
135C2×C4×D13C2×D411yescharacteristic
136C2×C4×D13C2×D411yescharacteristic
137C2×C4×D13C2×D411yescharacteristic
138C2×C4×D13C2×D411yescharacteristic
139C2×C4×D13C2×D411yescharacteristic
140C2×C4×D13C2×Q814yes—
141C2×C4×D13#4114yes—
142C2×C4×D13C2411yescharacteristic
143C2×Dic26—22no—
144C2×Dic26—22no—
145C2×Dic26—44no—
146C22⋊#261—44no—
147#6122—28no—
148C2×#1057—24no—
149C4⋊#261—44no—
150C4⋊#261—44no—
151C4⋊#261—44no—
152C4×#261—28no—
153#6118—24no—
154#6118C2×Q818yescomplemented
155D13⋊C8—28no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4C22×C414yes—
160C42×C13C22⋊C411yescharacteristic
161C42×C13C22⋊C411yescharacteristic
162C42×C13C22×C411yescharacteristic
163C42×C13C22×C411yescharacteristic
164#6103—24no—
165#6103—24no—
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—24no—
170C4⋊Dic13—24no—
171C4⋊Dic13C22×C414yes—
172#6101—24no—
173#6101—24no—
174C4×Dic13—24no—
175C4×Dic13—24no—
176C4×Dic13C22⋊C411yescharacteristic
177C4×Dic13C22⋊C411yescharacteristic
178C4×Dic13C22⋊C411yescharacteristic
179C4×Dic13C22⋊C411yescharacteristic
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22×C411yescharacteristic
183C4×Dic13C22×C411yescharacteristic
184C4×Dic13C2×D411yescharacteristic
185C4×Dic13C2×D411yescharacteristic
186C4×Dic13C2×D411yescharacteristic
187C4×Dic13C2×D411yescharacteristic
188C2×#533—131no—
189C2×C4×M16—131no—
190#2285—131no—
191#1986—134no—
192#1986—134no—
193#1733—134no—
194C23×C13C2×C22⋊C411yescharacteristic
195C22×D13—41no—
196C22×D13—41no—
197C22×D13C2×C22⋊C411yescharacteristic
198C22×D13#12412yes—
199C22×D13C4⋊Q812yes—
200C22×D13C22×D411yescharacteristic
201C2×#261—44no—
202C2×#261—44no—
203C2×#261—44no—
204Q8×C13—44no—
205Q8×C13—44no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—44no—
210C2×C4×C13C2×C22⋊C411yescharacteristic
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13C4×Q814yes—
216C2×C4×C13C23×C411yescharacteristic
217C2×Dic13—24no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—44no—
221C2×Dic13C2×C22⋊C411yescharacteristic
222C2×Dic13C2×C22⋊C411yescharacteristic
223C2×Dic13C2×C22⋊C411yescharacteristic
224C2×Dic13C2×C22⋊C411yescharacteristic
225C2×Dic13C2×C22⋊C411yescharacteristic
226C2×Dic13C22⋊Q814yes—
227C2×Dic13C22×D411yescharacteristic
228C4×D13—22no—
229C4×D13—22no—
230C4×D13—22no—
231C4×D13—22no—
232C4×D13—41no—
233C4×D13—41no—
234C4×D13—41no—
235C4×D13—41no—
236C4×D13C4×Q814yes—
237C4×D13C22⋊Q814yes—
238C4×D13#12412yes—
239C4×D13C4⋊Q812yes—
240C4×D13C22×Q812yes—
241C4×D13C2×#4112yes—
242Dic26—44no—
243Dic26—44no—
244#1057—28no—
245C22×M16—132no—
246#533—132no—
247#533—132no—
248#533—132no—
249#533—132no—
250#533—261no—
251#533—261no—
252#533—261no—
253#533—261no—
254C2×C4⋊Q8—131no—
255C2×C4⋊Q8#26111yescharacteristic, complemented
256C2×#125—132no—
257C2×C22⋊Q8—261no—
258C2×C22⋊Q8—261no—
259C2×C4×Q8—261no—
260C2×C4×Q8—261no—
261C2×#117—132no—
262C2×#117—132no—
263C22×C42—131no—
264C4×M16—132no—
265C4×M16—132no—
266C4×M16—261no—
267C4×M16—261no—
268C2×#97—261no—
269C2×C4×C8—261no—
270#384—261no—
271#382—261no—
272#380—261no—
273#380—261no—
274C4×C4⋊C4—132no—
275C4×C4⋊C4—132no—
276#339—1316no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13#39112yes—
280C22×C13C22×C22⋊C411yescharacteristic
281C2×D13—21no—
282C2×D13—21no—
283C2×D13—21no—
284C2×D13—21no—
285C2×D13—42no—
286C2×D13—42no—
287C2×D13#39112yes—
288C2×D13C2×#12411yescharacteristic
289C2×D13C2×C4⋊Q811yescharacteristic
290#261—84no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—44no—
294C4×C13#39112yes—
295C4×C13#42112yes—
296C4×C13#42112yes—
297C4×C13C2×C4×Q812yes—
298Dic13—21no—
299Dic13—21no—
300Dic13—21no—
301Dic13—21no—
302Dic13—44no—
303Dic13#39112yes—
304Dic13C2×C22⋊Q812yes—
305C22×Q8—21no—
306C22×Q8—261no—
307C23×C4—131no—
308C23×C4—131no—
309C23×C4—131no—
310C2×M16—134no—
311C2×M16—138no—
312C2×M16—262no—
313C2×M16—264no—
314C22×C8—262no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—132no—
318C4⋊Q8—132no—
319C4⋊Q8—261no—
320C4⋊Q8—261no—
321C4⋊Q8C2×#26112yes—
322C4⋊Q8C2×#26112yes—
323#125—134no—
324#125—134no—
325#125—262no—
326#125—262no—
327C22⋊Q8—262no—
328C22⋊Q8—262no—
329C22⋊Q8—262no—
330C22⋊Q8—262no—
331C22⋊Q8—262no—
332C22⋊Q8—262no—
333C22⋊Q8—262no—
334C22⋊Q8—262no—
335C4×Q8—262no—
336C4×Q8—262no—
337C4×Q8—262no—
338C4×Q8—262no—
339C4×Q8—262no—
340C4×Q8—262no—
341C4×Q8—262no—
342C4×Q8—262no—
343#117—134no—
344#117—134no—
345#117—262no—
346#117—262no—
347#117—268no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—132no—
350C2×C4⋊C4—262no—
351C2×C4⋊C4—262no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4C2×#26112yes—
357C2×C22⋊C4—262no—
358C2×C22⋊C4—262no—
359C2×C42—131no—
360C2×C42—131no—
361C2×C42—131no—
362C2×C42—131no—
363C2×C42—131no—
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—134no—
371C2×C42—262no—
372C2×C42C2×#26111yescharacteristic
373#97—262no—
374#97—262no—
375C4×C8—262no—
376C4×C8—262no—
377#95—262no—
378#95—262no—
379C2×C13—22no—
380C2×C13C2×#39111yescharacteristic
381C2×C13C2×#42111yescharacteristic
382C2×C13C2×#42111yescharacteristic
383D13—21no—
384D13—21no—
385D13—22no—
386C24—131no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—44no—
390C2×Q8—262no—
391C2×Q8—262no—
392C2×Q8—524no—
393C22×C4—22no—
394C22×C4—131no—
395C22×C4—134no—
396C22×C4—134no—
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—131no—
411C22×C4—262no—
412C22×C4—264no—
413C22×C4—522no—
414C22×C4—522no—
415C22×C4C22⋊#26111yescharacteristic
416C22×C4C22⋊#26111yescharacteristic
417C22×C4C22×#26111yescharacteristic
418M16—138no—
419M16—264no—
420M16—268no—
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—262no—
432C4⋊C4—262no—
433C4⋊C4—262no—
434C4⋊C4—524no—
435C4⋊C4—524no—
436C4⋊C4—524no—
437C4⋊C4C22×#26114yes—
438C22⋊C4—264no—
439C22⋊C4—264no—
440C22⋊C4—524no—
441C42—131no—
442C42—131no—
443C42—131no—
444C42—131no—
445C42—131no—
446C42—131no—
447C42—131no—
448C42—131no—
449C42—131no—
450C42—131no—
451C42—131no—
452C42—131no—
453C42—264no—
454C42—264no—
455C42—268no—
456C42C22⋊#26111yescharacteristic
457C42C22⋊#26111yescharacteristic
458C42C22×#26111yescharacteristic
459C42C22×#26111yescharacteristic
460C13#2130611yescharacteristic, complemented, Sylow
461C23—131no—
462C23—131no—
463C23—132no—
464C23—132no—
465C23—521no—
466C23—521no—
467C23C2×C22⋊#26111yescharacteristic
468Q8—44no—
469Q8—44no—
470Q8—524no—
471Q8—524no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—44no—
476C2×C4—131no—
477C2×C4—131no—
478C2×C4—134no—
479C2×C4—132no—
480C2×C4—132no—
481C2×C4—134no—
482C2×C4—132no—
483C2×C4—134no—
484C2×C4—132no—
485C2×C4—131no—
486C2×C4—131no—
487C2×C4—131no—
488C2×C4—131no—
489C2×C4—262no—
490C2×C4—262no—
491C2×C4—262no—
492C2×C4—262no—
493C2×C4—264no—
494C2×C4—521no—
495C2×C4—521no—
496C2×C4—521no—
497C2×C4—521no—
498C2×C4—521no—
499C2×C4—521no—
500C2×C4—524no—
501C2×C4—524no—
502C2×C4—524no—
503C2×C4—524no—
504C2×C4Q8×#26114yes—
505C2×C4C2×C22⋊#26111yescharacteristic
506C2×C4C2×C22⋊#26111yescharacteristic
507C2×C4C2×C22⋊#26111yescharacteristic
508C2×C4C2×C22⋊#26111yescharacteristic
509C2×C4C2×C22⋊#26111yescharacteristic
510C2×C4C23×#26111yescharacteristic
511C8—268no—
512C22—21no—
513C22—21no—
514C22—131no—
515C22—131no—
516C22—132no—
517C22—261no—
518C22—261no—
519C22—261no—
520C22—261no—
521C22—522no—
522C22—522no—
523C22(C2×#261)⋊Q812yes—
524C22C22×C22⋊#26111yescharacteristic
525C4—21no—
526C4—21no—
527C4—44no—
528C4—132no—
529C4—132no—
530C4—261no—
531C4—261no—
532C4—261no—
533C4—261no—
534C4—524no—
535C4—1044no—
536C4#1171914012yes—
537C4#1171915512yes—
538C4(C2×#261)⋊Q812yes—
539C4C2×Q8×#26112yes—
540C2—22no—
541C2—261no—
542C2—261no—
543C2—262no—
544C2C2×(C2×#261)⋊Q811yescharacteristic
545C2C2×#1171914011yescharacteristic
546C2C2×#1171915511yescharacteristic
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#21306
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. #13131012C2semidirect
4. #13131011C2semidirect
9. C2×C13×C4⋊Q8C4semidirect
16. #11719433C4semidirect
17. #11719433C4semidirect
22. C2×#88144C4semidirect
25. C2×#88123C4semidirect
52. D13⋊M16Q8semidirect
154. #6118C2×Q8semidirect
255. C2×C4⋊Q8#261semidirect
460. C13#21306semidirect

Maximal subgroups

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

subgroupindex
C4×D13⋊M162
#131312852
#131310122
#131310112
#131305152
C2×#117194332
#2130613