Finite Group Databasebeta

← #16794763

Subgroups — #16794763

Order 3328.

1178 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131512C211yesmaximal, characteristic
2#13131512C211yesmaximal, characteristic
3#13130365C214yesmaximal, complemented
4#13130351C214yesmaximal, complemented
5#13130345C214yesmaximal, complemented
6C22×#88142C211yesmaximal, characteristic
7C23×Dic26—21no—
8C22×C13×C4⋊C4C411yescharacteristic
9C22×C4⋊Dic13C411yescharacteristic
10C22×#6101—21no—
11C22×C4×Dic13C2211yescharacteristic
12C2×#88142—21no—
13C2×#88142—21no—
14C2×#88142—21no—
15C2×#88142—21no—
16C2×#88142—21no—
17C2×#88142—21no—
18C2×#88142C412yes—
19C2×#88142C412yes—
20C2×#88142C412yes—
21C2×#88142C2212yes—
22C2×#88142C2212yes—
23C2×#88142C2212yes—
24#11719169—21no—
25#11719169—21no—
26#11719130—21no—
27#11719130—21no—
28#11719129C2212yes—
29#11719129C2212yes—
30#11719128C2212yes—
31#11719128C2212yes—
32#11719125C2212yes—
33#11719125C2212yes—
34C4×#6122—21no—
35C4×#6122—21no—
36#11719119—21no—
37#11719119—21no—
38#11718245C22116yescomplemented
39C23×C4×C13—21no—
40C23×C4×C13C2×C411yescharacteristic
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C23×Dic13D411yescharacteristic
44C22×Dic26—22no—
45C22×Dic26—22no—
46C22×Dic26—22no—
47C22×Dic26—22no—
48C22×Dic26—22no—
49C22×Dic26—22no—
50C22×Dic26—48no—
51C2×#6122—22no—
52C2×#6122—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2×C412yes—
57C2×C13×C4⋊C4C2×C412yes—
58C2×C13×C4⋊C4C2×C412yes—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13C2×C412yes—
63C2×C4⋊Dic13C2×C412yes—
64C2×C4⋊Dic13C2×C412yes—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—22no—
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13D411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83#88142—22no—
84#88142—22no—
85#88142—22no—
86#88142—22no—
87#88142—22no—
88#88142—22no—
89#88142—22no—
90#88142—22no—
91#88142—22no—
92#88142—22no—
93#88142—22no—
94#88142—22no—
95#88142C2×C414yes—
96#88142C2×C414yes—
97#88142C2×C414yes—
98#88142C2314yes—
99C22⋊#1057—22no—
100C22⋊#1057—22no—
101C22⋊#1057—22no—
102C22⋊#1057—22no—
103#88112C2314yes—
104#88112C2314yes—
105#88110—22no—
106#88110—22no—
107C4⋊#1057—22no—
108C4⋊#1057—22no—
109C4×#1057—22no—
110C4×#1057—22no—
111#17742—131nomaximal, Sylow
112C24×C13C22⋊C411yescharacteristic
113C22×C4×C13—24no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—44no—
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×Dic13—24no—
125C22×Dic13—24no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—44no—
130C22×Dic13C22⋊C411yescharacteristic
131C22×Dic13C22⋊C411yescharacteristic
132C22×Dic13C22⋊C411yescharacteristic
133C22×Dic13C22⋊C411yescharacteristic
134C22×Dic13C22⋊C411yescharacteristic
135C22×Dic13C22⋊C411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C2×Dic26—24no—
143C2×Dic26—24no—
144C2×Dic26—24no—
145C2×Dic26—24no—
146C2×Dic26—48no—
147C2×Dic26—48no—
148C2×Dic26—48no—
149C2×Dic26—48no—
150C2×Dic26—48no—
151C2×Dic26—48no—
152#6122—44no—
153#6122—44no—
154C2×#1057—24no—
155C2×#1057—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4C22×C414yes—
160C4⋊Dic13—22no—
161C4⋊Dic13—22no—
162C4⋊Dic13—22no—
163C4⋊Dic13C22×C414yes—
164#6101—24no—
165#6101—24no—
166#6101—24no—
167#6101—24no—
168C4×Dic13C22⋊C411yescharacteristic
169C4×Dic13C22⋊C411yescharacteristic
170C4×Dic13C22⋊C411yescharacteristic
171C4×Dic13C22⋊C411yescharacteristic
172C4×Dic13C22⋊C411yescharacteristic
173C4×Dic13C22⋊C411yescharacteristic
174C4×Dic13C22×C411yescharacteristic
175C4×Dic13C22×C411yescharacteristic
176C4×Dic13C22×C411yescharacteristic
177C4×Dic13C2×D411yescharacteristic
178C4×Dic13C2×D411yescharacteristic
179C4×Dic13C2×D411yescharacteristic
180C4×Dic13C2×D411yescharacteristic
181C4×Dic13C2×D411yescharacteristic
182C4×Dic13C2×D411yescharacteristic
183C4×Dic13C2411yescharacteristic
184C22×C4⋊Q8—131no—
185#2920—131no—
186#2920—131no—
187#1556—134no—
188#1549—134no—
189#1546—134no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13C2×C22⋊C411yescharacteristic
194C23×C13C2×C22⋊C411yescharacteristic
195C23×C13C2×C22⋊C411yescharacteristic
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—24no—
202C2×C4×C13—44no—
203C2×C4×C13—44no—
204C2×C4×C13—44no—
205C2×C4×C13#10114yes—
206C2×C4×C13C2×C22⋊C411yescharacteristic
207C2×C4×C13C2×C22⋊C411yescharacteristic
208C2×C4×C13C2×C22⋊C411yescharacteristic
209C2×C4×C13C23×C411yescharacteristic
210C2×Dic13—22no—
211C2×Dic13—22no—
212C2×Dic13—22no—
213C2×Dic13—22no—
214C2×Dic13—22no—
215C2×Dic13—22no—
216C2×Dic13—22no—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—22no—
220C2×Dic13—24no—
221C2×Dic13—44no—
222C2×Dic13—44no—
223C2×Dic13—44no—
224C2×Dic13C2×C22⋊C411yescharacteristic
225C2×Dic13C2×C22⋊C411yescharacteristic
226C2×Dic13C2×C22⋊C411yescharacteristic
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13AGL(1,ℤ/8)14yes—
231C2×Dic13#13714yes—
232C2×Dic13C22×D411yescharacteristic
233C2×Dic13C22×D411yescharacteristic
234Dic26—48no—
235Dic26—48no—
236Dic26—48no—
237Dic26—48no—
238#1057—44no—
239#1057—44no—
240C23×Q8—261no—
241C2×C4⋊Q8—132no—
242C2×C4⋊Q8—132no—
243C2×C4⋊Q8—132no—
244C2×C4⋊Q8—132no—
245C2×C4⋊Q8—132no—
246C2×C4⋊Q8—132no—
247C2×C4⋊Q8—261no—
248C2×C4⋊Q8—261no—
249C2×C4⋊Q8—261no—
250C2×C4⋊Q8—261no—
251C2×C4⋊Q8—261no—
252C2×C4⋊Q8—261no—
253C22×C4⋊C4—131no—
254C22×C4⋊C4—261no—
255C22×C4⋊C4#26111yescharacteristic
256C22×C42—131no—
257#432—132no—
258#432—132no—
259#432—261no—
260#432—261no—
261#431—132no—
262#431—132no—
263#431—261no—
264#431—261no—
265#423—132no—
266#423—132no—
267#407—261no—
268#407—261no—
269C4×M16—261no—
270C4×M16—261no—
271#332—1316no—
272C22×C13—28no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13C2×#10112yes—
280C22×C13#41812yes—
281C22×C13#41912yes—
282C22×C13C22×C22⋊C411yescharacteristic
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—44no—
286C4×C13C2×#10112yes—
287C4×C13C2×#10112yes—
288Dic13—21no—
289Dic13—21no—
290Dic13—21no—
291Dic13—21no—
292Dic13—44no—
293Dic13#41812yes—
294Dic13#41912yes—
295Dic13C2×AGL(1,ℤ/8)12yes—
296Dic13C2×#13712yes—
297C22×Q8—262no—
298C22×Q8—262no—
299C22×Q8—262no—
300C22×Q8—262no—
301C22×Q8—262no—
302C22×Q8—262no—
303C22×Q8—528no—
304C23×C4—21no—
305C23×C4—131no—
306C23×C4—131no—
307C23×C4—261no—
308C23×C4C2×#26111yescharacteristic
309C2×M16—262no—
310C2×M16—262no—
311C4⋊Q8—134no—
312C4⋊Q8—134no—
313C4⋊Q8—134no—
314C4⋊Q8—134no—
315C4⋊Q8—262no—
316C4⋊Q8—262no—
317C4⋊Q8—262no—
318C4⋊Q8—262no—
319C4⋊Q8—262no—
320C4⋊Q8—262no—
321C4⋊Q8—262no—
322C4⋊Q8—262no—
323C4⋊Q8—262no—
324C4⋊Q8—262no—
325C4⋊Q8—262no—
326C4⋊Q8—262no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—132no—
331C2×C4⋊C4—132no—
332C2×C4⋊C4—132no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—262no—
335C2×C4⋊C4—262no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—261no—
340C2×C4⋊C4—261no—
341C2×C4⋊C4—261no—
342C2×C4⋊C4C2×#26112yes—
343C2×C4⋊C4C2×#26112yes—
344C2×C4⋊C4C2×#26112yes—
345C2×C42—131no—
346C2×C42—131no—
347C2×C42—131no—
348C2×C42—131no—
349C2×C42—131no—
350C2×C42—131no—
351C2×C42—131no—
352C2×C42—131no—
353C2×C42—131no—
354C2×C42—131no—
355C2×C42—131no—
356C2×C42—131no—
357C4⋊C8—134no—
358C4⋊C8—134no—
359C4⋊C8—262no—
360C4⋊C8—262no—
361C22⋊C8—262no—
362C22⋊C8—262no—
363C22⋊C8—262no—
364C22⋊C8—262no—
365#97—262no—
366#97—262no—
367C4×C8—262no—
368C4×C8—262no—
369C2×C13—22no—
370C2×C13—22no—
371C2×C13—22no—
372C2×C13C22×#10111yescharacteristic
373C2×C13C2×#41811yescharacteristic
374C2×C13C2×#41911yescharacteristic
375C24C22⋊#26111yescharacteristic
376C2×Q8—264no—
377C2×Q8—264no—
378C2×Q8—264no—
379C2×Q8—264no—
380C2×Q8—528no—
381C2×Q8—528no—
382C2×Q8—528no—
383C2×Q8—528no—
384C2×Q8—528no—
385C2×Q8—528no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—44no—
391C22×C4—131no—
392C22×C4—131no—
393C22×C4—131no—
394C22×C4—131no—
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—264no—
404C22×C4—264no—
405C22×C4—262no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4—524no—
409C22×C4C22⋊#26111yescharacteristic
410C22×C4C22⋊#26111yescharacteristic
411C22×C4C22⋊#26111yescharacteristic
412C22×C4C22×#26111yescharacteristic
413C22×C4C22×#26111yescharacteristic
414C22×C4C22×#26111yescharacteristic
415M16—524no—
416M16—524no—
417C2×C8—264no—
418C2×C8—264no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—134no—
423C4⋊C4—264no—
424C4⋊C4—264no—
425C4⋊C4—264no—
426C4⋊C4—264no—
427C4⋊C4—262no—
428C4⋊C4—262no—
429C4⋊C4—262no—
430C4⋊C4C22×#26114yes—
431C42—131no—
432C42—131no—
433C42—131no—
434C42—131no—
435C42—131no—
436C42—131no—
437C42—131no—
438C42—131no—
439C42—131no—
440C42—131no—
441C42—131no—
442C42—131no—
443C42—131no—
444C42—131no—
445C42—131no—
446C42—131no—
447C13#1774211yescharacteristic, complemented, Sylow
448C23—22no—
449C23—22no—
450C23—22no—
451C23C2×C22⋊#26111yescharacteristic
452C23C2×C22⋊#26111yescharacteristic
453C23C2×C22⋊#26111yescharacteristic
454Q8—528no—
455Q8—528no—
456Q8—528no—
457Q8—528no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—131no—
468C2×C4—131no—
469C2×C4—131no—
470C2×C4—131no—
471C2×C4—134no—
472C2×C4—134no—
473C2×C4—131no—
474C2×C4—131no—
475C2×C4—131no—
476C2×C4—131no—
477C2×C4—262no—
478C2×C4—262no—
479C2×C4—262no—
480C2×C4—262no—
481C2×C4—262no—
482C2×C4—262no—
483C2×C4—262no—
484C2×C4—262no—
485C2×C4—262no—
486C2×C4—262no—
487C2×C4—264no—
488C2×C4—524no—
489C2×C4—524no—
490C2×C4—524no—
491C2×C4#8811314yes—
492C2×C4C2×C22⋊#26111yescharacteristic
493C2×C4C2×C22⋊#26111yescharacteristic
494C2×C4C2×C22⋊#26111yescharacteristic
495C2×C4C23×#26111yescharacteristic
496C8—524no—
497C8—524no—
498C22—28no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22C2×#8811312yes—
506C22#1171913812yes—
507C22#1171915312yes—
508C22C22×C22⋊#26111yescharacteristic
509C4—21no—
510C4—21no—
511C4—44no—
512C4—132no—
513C4—132no—
514C4—132no—
515C4—132no—
516C4—261no—
517C4—261no—
518C4—261no—
519C4—261no—
520C4—524no—
521C4C2×#8811312yes—
522C4C2×#8811312yes—
523C2—22no—
524C2—22no—
525C2—22no—
526C2C22×#8811311yescharacteristic
527C2C2×#1171913811yescharacteristic
528C2C2×#1171915311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C22×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13#17742
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130365C2semidirect
4. #13130351C2semidirect
5. #13130345C2semidirect
38. #11718245C22semidirect
447. C13#17742semidirect

Maximal subgroups

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

subgroupindex
#131315122
#131303652
#131303512
#131303452
C22×#881422
#1774213