Finite Group Databasebeta

← #16799398

Subgroups — #16799398

Order 3328.

1202 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131285C211yesmaximal, characteristic
2C4×#88237C211yesmaximal, characteristic
3#13131026C214yesmaximal
4#13131025C214yesmaximal
5#13130536C214yesmaximal
6C2×#11719433C211yesmaximal, characteristic
7C2×#88237C2212yes—
8C2×#88237C2212yes—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88200C2212yes—
11C2×Q8×Dic13C412yescomplemented
12#11719433—21no—
13#11719433—21no—
14#11719433—21no—
15#11719433—21no—
16#11719433—21no—
17#11719433—21no—
18#11719433—21no—
19#11719433—21no—
20C2×#88151C2212yes—
21C2×#88146C2212yes—
22C2×#88144C412yescomplemented
23C2×#88141C412yescomplemented
24C2×C42×D13C2211yescharacteristic
25C2×#88123C411yescharacteristic, complemented
26#11719136C2212yes—
27#11719136C2212yes—
28C4×C22⋊#261C2212yes—
29C4×C22⋊#261C2212yes—
30#11719060—21no—
31#11719059—21no—
32C4×C4⋊#261—21no—
33C4×C4⋊#261—21no—
34C4×C4⋊#261—21no—
35C4×C4⋊#261—21no—
36#11719057—21no—
37C42×#261—21no—
38#11718289C22116yes—
39C22×Q8×C13C2×C412yes—
40C22×C4×D13C2311yescharacteristic
41C22×C4×D13C2311yescharacteristic
42C22×C4×D13C2311yescharacteristic
43C22×Dic26C2×C412yes—
44C2×C22⋊#261C2314yes—
45C2×C22⋊#261C2314yes—
46#88237—24no—
47#88237—28no—
48#88237Q818yescomplemented
49C2×C4⋊#261—22no—
50C2×C4⋊#261—22no—
51C2×C4⋊#261—22no—
52C2×C4⋊#261—22no—
53C2×C4×#261—22no—
54C2×C4×#261—22no—
55C2×C4×#261—22no—
56C2×C4×#261—22no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C2×C13×C4⋊C4C2×C412yes—
62C2×C13×C4⋊C4C2×C412yes—
63C2×C42×C13C2×C411yescharacteristic
64#88200—22no—
65#88200—22no—
66#88200—22no—
67#88200—22no—
68Q8×Dic13—22no—
69Q8×Dic13—22no—
70Q8×Dic13—22no—
71Q8×Dic13—22no—
72C2×#6103C2314yes—
73C2×C4⋊Dic13C2×C412yes—
74C2×C4⋊Dic13C2×C412yes—
75C2×C4⋊Dic13C2×C414yes—
76C2×#6101C2×C414yes—
77C2×C4×Dic13C2×C414yes—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81#88151—22no—
82#88151—22no—
83#88151—22no—
84#88151—22no—
85#88146—22no—
86#88146—22no—
87#88146—22no—
88#88146—22no—
89#88144—22no—
90#88144—22no—
91#88144—22no—
92#88144—22no—
93#88141—22no—
94#88141—22no—
95#88141—22no—
96#88141—22no—
97C42×D13D411yescharacteristic
98C42×D13D411yescharacteristic
99C42×D13D411yescharacteristic
100C42×D13D411yescharacteristic
101C42×D13D411yescharacteristic
102C42×D13D411yescharacteristic
103C42×D13D411yescharacteristic
104C42×D13D411yescharacteristic
105#88123—21no—
106#88123—21no—
107#88123—21no—
108#88123—21no—
109(C2×#261)⋊C4—22no—
110(C2×#261)⋊C4—22no—
111(C2×#261)⋊C4—22no—
112(C2×#261)⋊C4—22no—
113#21332—131nomaximal, Sylow
114C23×D13C2411yescharacteristic
115C22×#261—24no—
116C22×#261—24no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—44no—
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C414yes—
123C22×C4×C13C22×C411yescharacteristic
124C22×Dic13C22×C414yes—
125C22×Dic13C22×C411yescharacteristic
126C22×Dic13C22×C411yescharacteristic
127C22×Dic13C22×C411yescharacteristic
128C2×C4×D13—42no—
129C2×C4×D13—42no—
130C2×C4×D13C2×D411yescharacteristic
131C2×C4×D13C2×D411yescharacteristic
132C2×C4×D13C2×D411yescharacteristic
133C2×C4×D13C2×D411yescharacteristic
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×D411yescharacteristic
141C2×C4×D13C2×D411yescharacteristic
142C2×C4×D13C2×Q814yes—
143C2×C4×D13#4114yes—
144C2×Dic26—22no—
145C2×Dic26—22no—
146C2×Dic26—44no—
147C22⋊#261—24no—
148C22⋊#261—28no—
149C22⋊#261C2×Q818yes—
150C4⋊#261—28no—
151C4⋊#261—44no—
152C4⋊#261—44no—
153C4⋊#261—44no—
154C4×#261—28no—
155C4×#261—44no—
156C4×#261—44no—
157C4×#261—44no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C42×C13C22⋊C411yescharacteristic
163C42×C13C22⋊C411yescharacteristic
164C42×C13C22⋊C411yescharacteristic
165C42×C13C22⋊C411yescharacteristic
166#6103—24no—
167#6103—24no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—24no—
173C4⋊Dic13—24no—
174#6101—24no—
175#6101—24no—
176C4×Dic13—24no—
177C4×Dic13—24no—
178C4×Dic13C22⋊C411yescharacteristic
179C4×Dic13C22⋊C411yescharacteristic
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22⋊C411yescharacteristic
186C4×Dic13C22⋊C411yescharacteristic
187C4×Dic13C22⋊C411yescharacteristic
188C4×Dic13C22⋊C411yescharacteristic
189C4×Dic13C22⋊C411yescharacteristic
190C2×#533—131no—
191#2285—131no—
192C4×#117—131no—
193#1996—134no—
194#1996—134no—
195#1740—134no—
196C23×C13C23×C411yescharacteristic
197C22×D13—41no—
198C22×D13—41no—
199C22×D13C22×D411yescharacteristic
200C22×D13C22×D411yescharacteristic
201C22×D13C22×Q812yes—
202C22×D13C2×#4112yes—
203C2×#261—28no—
204C2×#261—44no—
205C2×#261—44no—
206C2×#261—44no—
207C2×#261—44no—
208C2×#261—44no—
209Q8×C13—44no—
210Q8×C13—44no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—24no—
214C2×C4×C13—44no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
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×Dic13—24no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—44no—
226C2×Dic13C2×C22⋊C411yescharacteristic
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13C2×C22⋊C411yescharacteristic
231C2×Dic13C2×C22⋊C411yescharacteristic
232C2×Dic13C4×Q814yes—
233C4×D13—22no—
234C4×D13—22no—
235C4×D13—22no—
236C4×D13—22no—
237C4×D13—41no—
238C4×D13—41no—
239C4×D13—41no—
240C4×D13—41no—
241C4×D13C22⋊Q814yes—
242C4×D13C22⋊Q814yes—
243C4×D13#12412yes—
244C4×D13#12412yes—
245C4×D13C4⋊Q812yes—
246C4×D13C4⋊Q812yes—
247Dic26—44no—
248Dic26—44no—
249#533—261no—
250#533—261no—
251#533—261no—
252#533—261no—
253#533—261no—
254#533—261no—
255#533—261no—
256#533—261no—
257C2×C4⋊Q8—131no—
258C2×C4⋊Q8#26111yescharacteristic, complemented
259C2×#125—132no—
260C2×C22⋊Q8—132no—
261C2×C22⋊Q8—132no—
262C2×C4×Q8—132no—
263C2×C4×Q8—132no—
264C2×#117—132no—
265C2×#117—132no—
266C2×#117—132no—
267C22×C42—131no—
268#384—261no—
269#382—261no—
270#380—132no—
271#380—132no—
272C4×C4⋊C4—261no—
273C4×C4⋊C4—261no—
274C4×C4⋊C4—261no—
275C4×C4⋊C4—261no—
276C4×C22⋊C4—132no—
277C4×C22⋊C4—132no—
278#376—261no—
279C43—261no—
280#342—1316no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13C22×C22⋊C411yescharacteristic
284C22×C13C2×C4×Q812yes—
285C2×D13—21no—
286C2×D13—21no—
287C2×D13—21no—
288C2×D13—21no—
289C2×D13—42no—
290C2×D13—42no—
291C2×D13C2×C22⋊Q812yes—
292C2×D13C2×#12411yescharacteristic
293C2×D13C2×C4⋊Q811yescharacteristic
294#261—48no—
295#261—84no—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—44no—
299C4×C13#39112yes—
300C4×C13#39112yes—
301C4×C13#41012yes—
302C4×C13#41012yes—
303Dic13—21no—
304Dic13—21no—
305Dic13—21no—
306Dic13—21no—
307Dic13—44no—
308Dic13#39112yes—
309Dic13#39112yes—
310C22×Q8—132no—
311C22×Q8C2×#26112yes—
312C23×C4—131no—
313C23×C4—131no—
314C23×C4—131no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—261no—
320C4⋊Q8—261no—
321C4⋊Q8—261no—
322C4⋊Q8—261no—
323#125—262no—
324#125—262no—
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—138no—
344#117—262no—
345#117—262no—
346#117—262no—
347#117—262no—
348#117—264no—
349#117—268no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—134no—
352C2×C4⋊C4—134no—
353C2×C4⋊C4—132no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4C2×#26112yes—
359C2×C4⋊C4C2×#26112yes—
360C2×C22⋊C4—134no—
361C2×C22⋊C4—134no—
362C2×C22⋊C4—134no—
363C2×C42—131no—
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—134no—
375C2×C42—262no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42C2×#26111yescharacteristic
380#95—262no—
381#95—262no—
382#95—262no—
383#95—262no—
384C2×C13—22no—
385C2×C13C2×#39111yescharacteristic
386C2×C13C2×#41011yescharacteristic
387C2×C13C2×#41011yescharacteristic
388D13—22no—
389D13—21no—
390D13—21no—
391C24—131no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—262no—
396C2×Q8—262no—
397C2×Q8—524no—
398C22×C4—131no—
399C22×C4—134no—
400C22×C4—134no—
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—131no—
412C22×C4—131no—
413C22×C4—131no—
414C22×C4—131no—
415C22×C4—134no—
416C22×C4—264no—
417C22×C4—264no—
418C22×C4—522no—
419C22×C4—522no—
420C22×C4C22×#26111yescharacteristic
421C22×C4C22×#26111yescharacteristic
422C22×C4C22×#26114yes—
423C22×C4C22×#26111yescharacteristic
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—264no—
429C4⋊C4—264no—
430C4⋊C4—264no—
431C4⋊C4—264no—
432C4⋊C4—268no—
433C4⋊C4—262no—
434C4⋊C4—262no—
435C4⋊C4—262no—
436C4⋊C4—262no—
437C4⋊C4—524no—
438C4⋊C4—524no—
439C4⋊C4—524no—
440C22⋊C4—138no—
441C22⋊C4—264no—
442C22⋊C4—264no—
443C22⋊C4—264no—
444C22⋊C4—268no—
445C42—131no—
446C42—131no—
447C42—131no—
448C42—131no—
449C42—131no—
450C42—131no—
451C42—131no—
452C42—131no—
453C42—131no—
454C42—131no—
455C42—131no—
456C42—131no—
457C42—264no—
458C42—264no—
459C42—268no—
460C42—524no—
461C42—524no—
462C42—524no—
463C42C22⋊#26111yescharacteristic
464C42C22⋊#26111yescharacteristic
465C42C22⋊#26111yescharacteristic
466C42C22⋊#26111yescharacteristic
467C13#2133211yescharacteristic, complemented, Sylow
468C23—131no—
469C23—131no—
470C23—132no—
471C23—132no—
472C23—521no—
473C23—521no—
474C23C23×#26111yescharacteristic
475Q8—44no—
476Q8—44no—
477Q8—524no—
478Q8—524no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—44no—
483C2×C4—134no—
484C2×C4—131no—
485C2×C4—131no—
486C2×C4—134no—
487C2×C4—132no—
488C2×C4—134no—
489C2×C4—132no—
490C2×C4—132no—
491C2×C4—132no—
492C2×C4—131no—
493C2×C4—131no—
494C2×C4—131no—
495C2×C4—131no—
496C2×C4—262no—
497C2×C4—262no—
498C2×C4—262no—
499C2×C4—262no—
500C2×C4—268no—
501C2×C4—264no—
502C2×C4—521no—
503C2×C4—521no—
504C2×C4—521no—
505C2×C4—521no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—524no—
509C2×C4—524no—
510C2×C4—524no—
511C2×C4—524no—
512C2×C4—524no—
513C2×C4—524no—
514C2×C4Q8×#26114yes—
515C2×C4C2×C22⋊#26111yescharacteristic
516C2×C4C2×C22⋊#26111yescharacteristic
517C2×C4C2×C22⋊#26111yescharacteristic
518C2×C4C2×C22⋊#26111yescharacteristic
519C2×C4C2×C22⋊#26111yescharacteristic
520C2×C4C2×C22⋊#26111yescharacteristic
521C22—21no—
522C22—21no—
523C22—132no—
524C22—131no—
525C22—131no—
526C22—261no—
527C22—261no—
528C22—261no—
529C22—261no—
530C22—522no—
531C22—522no—
532C22C2×Q8×#26112yes—
533C22C22×C22⋊#26111yescharacteristic
534C4—21no—
535C4—21no—
536C4—44no—
537C4—132no—
538C4—132no—
539C4—261no—
540C4—261no—
541C4—261no—
542C4—261no—
543C4—528no—
544C4—524no—
545C4—1044no—
546C4#1171914212yes—
547C4#1171915612yes—
548C4(C2×#261)⋊Q812yes—
549C4(C2×#261)⋊Q812yes—
550C2—22no—
551C2—262no—
552C2—261no—
553C2—261no—
554C2C2×(C2×#261)⋊Q811yescharacteristic
555C2C2×#1171914211yescharacteristic
556C2C2×#1171915611yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radical, cosocleC23×D13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13#21332
LCSG ▷ C23×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
9. C2×C13×C4⋊Q8C4semidirect
11. C2×Q8×Dic13C4semidirect
22. C2×#88144C4semidirect
23. C2×#88141C4semidirect
25. C2×#88123C4semidirect
48. #88237Q8semidirect
258. C2×C4⋊Q8#261semidirect
467. C13#21332semidirect

Maximal subgroups

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

subgroupindex
#131312852
C4×#882372
#131310262
#131310252
#131305362
C2×#117194332
#2133213