Finite Group Databasebeta

← #16792915

Subgroups — #16792915

Order 3328.

1210 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#13131687C212yesmaximal, complemented
2#13130099C212yesmaximal, complemented
3#13130092C212yesmaximal, complemented
4#13130087C212yesmaximal, complemented
5#13130084C212yesmaximal, complemented
6#13130072C212yesmaximal, complemented
7C2×#11718285C212yesmaximal, complemented
8C2×#11719532C211yesmaximal, characteristic
9C22×C13×#41C411yescharacteristic
10#11719532—28no—
11C2×Q8×Dic13C411yescharacteristic
12C2×Q8×Dic13C2211yescharacteristic
13C2×D4×Dic13C411yescharacteristic
14C2×D4×Dic13C411yescharacteristic
15C2×D4×Dic13C411yescharacteristic
16C2×D4×Dic13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×#88180C411yescharacteristic
20C2×#88180C411yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×C4⋊Dic13C411yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25#11719169C2214yes—
26C2×C22⋊#1057C2214yes—
27#11719144—28no—
28#11719128C2214yes—
29#11718305C2214yes—
30#11718285C2214yes—
31#11718285C2214yes—
32#11718285C2214yes—
33C2×C13×#41—24no—
34C2×C13×#41—24no—
35C2×C13×#41—24no—
36C22×Q8×C13C2×C411yescharacteristic
37C22×D4×C13C2×C411yescharacteristic
38C22×D4×C13C2×C411yescharacteristic
39C22×D4×C13C2×C411yescharacteristic
40C23×C4×C13C2×C411yescharacteristic
41C23×C4×C13C2×C411yescharacteristic
42C23×C4×C13C2×C411yescharacteristic
43C23×Dic13C2×C411yescharacteristic
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C23×Dic13C2×C411yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×#6122—24no—
50C22×#1057—24no—
51C2×C22⋊Dic13C2×C411yescharacteristic
52C2×C22⋊Dic13C2×C411yescharacteristic
53C2×C22⋊Dic13C2×C411yescharacteristic
54C2×C22⋊Dic13C2×C411yescharacteristic
55C2×C22⋊Dic13C2×C411yescharacteristic
56C2×C22⋊Dic13C2311yescharacteristic
57Q8×Dic13—24no—
58Q8×Dic13—24no—
59D4×Dic13—24no—
60D4×Dic13—24no—
61D4×Dic13—24no—
62D4×Dic13—24no—
63D4×Dic13—24no—
64D4×Dic13D418yes—
65#88180—24no—
66#88180—24no—
67#88180—24no—
68C2×C4⋊Dic13—24no—
69C2×C4⋊Dic13—24no—
70C2×C4⋊Dic13—24no—
71C2×C4⋊Dic13C2×C411yescharacteristic
72C2×C4⋊Dic13C2×C411yescharacteristic
73C2×C4⋊Dic13C2×C411yescharacteristic
74C2×C4⋊Dic13C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C22⋊#1057—24no—
88C22⋊#1057—24no—
89C22⋊#1057C2318yes—
90#88112—24no—
91#88110—24no—
92#17368—131nomaximal, Sylow
93C24×C13C22×C411yescharacteristic
94C24×C13C22×C411yescharacteristic
95C24×C13C22×C411yescharacteristic
96C13×#41—232no—
97C2×Q8×C13—22no—
98C2×Q8×C13—22no—
99C2×Q8×C13—22no—
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—22no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13C22⋊C414yes—
108C2×D4×C13M1614yescomplemented
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13M1614yescomplemented
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—81no—
127C22×Dic13—81no—
128C22×Dic13—81no—
129C22×Dic13—81no—
130C22×Dic13—81no—
131C22×Dic13—81no—
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C2×D414yes—
140C22×Dic13C2×D414yes—
141C22×Dic13C2411yescharacteristic
142#6122—84no—
143C2×#1057—28no—
144C2×#1057—84no—
145C22⋊Dic13—22no—
146C22⋊Dic13—22no—
147C22⋊Dic13—22no—
148C22⋊Dic13—22no—
149C22⋊Dic13C22⋊C414yes—
150C22⋊Dic13C22⋊C414yes—
151C4⋊Dic13—22no—
152C4⋊Dic13—22no—
153C4⋊Dic13—22no—
154C4⋊Dic13—22no—
155C4⋊Dic13—22no—
156C4⋊Dic13—22no—
157C4⋊Dic13—22no—
158C4⋊Dic13—22no—
159C4⋊Dic13—22no—
160C4⋊Dic13C22⋊C414yes—
161C4×Dic13—22no—
162C4×Dic13—22no—
163C4×Dic13—22no—
164C4×Dic13—22no—
165C4×Dic13—22no—
166C4×Dic13C2×D414yes—
167C2×#520—131no—
168#2973—132no—
169#1467—132no—
170#1465—132no—
171#1464—132no—
172#1463—132no—
173#1459—132no—
174C2×#324—132no—
175C23×C13—21no—
176C23×C13—21no—
177C23×C13—21no—
178C23×C13—21no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13C2×C22⋊C412yes—
186C23×C13C2×C22⋊C412yes—
187C23×C13C2×M1612yes—
188C23×C13C2×M1612yes—
189C23×C13C2×M1612yes—
190C23×C13C23×C411yescharacteristic
191Q8×C13—28no—
192D4×C13—28no—
193D4×C13—28no—
194D4×C13—28no—
195C2×C4×C13—28no—
196C2×C4×C13—28no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—28no—
206C2×C4×C13C2×C22⋊C412yes—
207C2×C4×C13C2×M1612yes—
208C2×C4×C13C2×M1612yes—
209C2×C4×C13C2×M1612yes—
210C2×Dic13—21no—
211C2×Dic13—21no—
212C2×Dic13—21no—
213C2×Dic13—21no—
214C2×Dic13—44no—
215C2×Dic13—44no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13—82no—
225C2×Dic13—82no—
226C2×Dic13—82no—
227C2×Dic13—82no—
228C2×Dic13C2×C22⋊C412yes—
229C2×Dic13C2×C22⋊C412yes—
230C2×Dic13C2×C22⋊C412yes—
231C2×Dic13C22×D412yes—
232#1057—48no—
233C22×#41#26111yescharacteristic
234#520—268no—
235C2×C4×Q8—131no—
236C2×C4×Q8—131no—
237C2×C4×D4—131no—
238C2×C4×D4—131no—
239C2×C4×D4—131no—
240C2×C4×D4—131no—
241C2×C4×D4—131no—
242C2×C4×D4—131no—
243C2×#117—131no—
244C2×#117—131no—
245C2×#117—131no—
246C22×C4⋊C4—131no—
247C22×C4⋊C4—131no—
248C22×C4⋊C4—131no—
249#435—268no—
250#432—134no—
251#407—134no—
252C2×C22⋊C8—134no—
253#324—134no—
254#324—134no—
255#324—134no—
256#323—134no—
257C22×C13—21no—
258C22×C13—22no—
259C22×C13—21no—
260C22×C13—22no—
261C22×C13—22no—
262C22×C13—22no—
263C22×C13—22no—
264C22×C13—22no—
265C22×C13—42no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13#40714yes—
274C22×C13C22×C22⋊C411yescharacteristic
275C22×C13C22×M1611yescharacteristic
276C22×C13C22×M1611yescharacteristic
277C4×C13—22no—
278C4×C13—22no—
279C4×C13—22no—
280C4×C13—22no—
281Dic13—22no—
282Dic13—22no—
283Dic13—22no—
284Dic13—22no—
285Dic13—41no—
286Dic13—41no—
287Dic13—41no—
288Dic13—41no—
289C2×#41—24no—
290C2×#41—24no—
291C2×#41—24no—
292C22×Q8C2×#26111yescharacteristic
293C22×D4C2×#26111yescharacteristic
294C22×D4C2×#26111yescharacteristic
295C22×D4C2×#26111yescharacteristic
296C23×C4—131no—
297C23×C4—131no—
298C23×C4—131no—
299C23×C4—131no—
300C23×C4—131no—
301C23×C4—131no—
302C23×C4C2×#26111yescharacteristic
303C23×C4C2×#26111yescharacteristic
304C23×C4C2×#26111yescharacteristic
305C2×M16—264no—
306C22×C8—264no—
307C4×Q8—264no—
308C4×Q8—264no—
309C4×D4—138no—
310C4×D4—264no—
311C4×D4—264no—
312C4×D4—264no—
313C4×D4—264no—
314C4×D4—264no—
315#117—264no—
316#117—264no—
317#117—264no—
318C2×C4⋊C4—131no—
319C2×C4⋊C4—131no—
320C2×C4⋊C4—131no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—131no—
323C2×C4⋊C4—131no—
324C2×C4⋊C4—131no—
325C2×C4⋊C4—131no—
326C2×C4⋊C4—131no—
327C2×C4⋊C4—131no—
328C2×C4⋊C4—264no—
329C2×C4⋊C4—264no—
330C2×C4⋊C4—264no—
331C2×C22⋊C4—131no—
332C2×C22⋊C4—131no—
333C2×C22⋊C4—131no—
334C2×C22⋊C4—131no—
335C2×C22⋊C4—131no—
336C2×C22⋊C4—131no—
337C2×C42—131no—
338C2×C42—131no—
339C2×C42—131no—
340C2×C42—131no—
341C2×C42—131no—
342C2×C42—131no—
343C4⋊C8—264no—
344C22⋊C8—138no—
345C22⋊C8—264no—
346C22⋊C8—264no—
347#97—264no—
348C2×C13—21no—
349C2×C13—21no—
350C2×C13—24no—
351C2×C13—42no—
352C2×C13—42no—
353C2×C13C2×#40711yescharacteristic
354C2×C13#288311yescharacteristic
355C2×C13#288911yescharacteristic
356C24C22×#26111yescharacteristic
357C24C22×#26111yescharacteristic
358C24C22×#26111yescharacteristic
359#41—232no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4#612214yescomplemented
371C2×D4C22⋊#26114yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—134no—
381C22×C4—134no—
382C22×C4—131no—
383C22×C4—131no—
384C22×C4—131no—
385C22×C4—131no—
386C22×C4—131no—
387C22×C4—131no—
388C22×C4—131no—
389C22×C4—131no—
390C22×C4—262no—
391C22×C4—262no—
392C22×C4—262no—
393C22×C4—262no—
394C22×C4—1041no—
395C22×C4—1041no—
396C22×C4—1041no—
397C22×C4—1041no—
398C22×C4—1041no—
399C22×C4—1041no—
400C22×C4#612214yescomplemented
401C22×C4C22×#26111yescharacteristic
402C22×C4C22×#26111yescharacteristic
403C22×C4C22×#26111yescharacteristic
404C22×C4C22×#26111yescharacteristic
405M16—1044no—
406C2×C8—268no—
407C2×C8—1044no—
408C4⋊C4—134no—
409C4⋊C4—262no—
410C4⋊C4—262no—
411C4⋊C4—262no—
412C4⋊C4—262no—
413C4⋊C4—262no—
414C4⋊C4—262no—
415C4⋊C4—262no—
416C4⋊C4—262no—
417C4⋊C4—262no—
418C22⋊C4—134no—
419C22⋊C4—134no—
420C22⋊C4—262no—
421C22⋊C4—262no—
422C22⋊C4—262no—
423C22⋊C4—262no—
424C42—134no—
425C42—262no—
426C42—262no—
427C42—262no—
428C42—262no—
429C42—262no—
430C13#1736811yescharacteristic, complemented, Sylow
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C2×#612212yes—
442C23C2×#612212yes—
443C23C2×#612212yes—
444C23C2×C22⋊#26112yes—
445C23C2×C22⋊#26112yes—
446C23C23×#26111yescharacteristic
447Q8—28no—
448D4—28no—
449D4—28no—
450D4—28no—
451C2×C4—28no—
452C2×C4—28no—
453C2×C4—28no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—132no—
463C2×C4—132no—
464C2×C4—132no—
465C2×C4—132no—
466C2×C4—261no—
467C2×C4—261no—
468C2×C4—261no—
469C2×C4—261no—
470C2×C4—524no—
471C2×C4—524no—
472C2×C4—521no—
473C2×C4—521no—
474C2×C4—521no—
475C2×C4—521no—
476C2×C4—521no—
477C2×C4—521no—
478C2×C4—521no—
479C2×C4—521no—
480C2×C4—1042no—
481C2×C4—1042no—
482C2×C4—1042no—
483C2×C4—1042no—
484C2×C4C2×#612212yes—
485C2×C4C2×#612212yes—
486C2×C4C2×#612212yes—
487C2×C4C2×C22⋊#26112yes—
488C8—528no—
489C22—21no—
490C22—22no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—41no—
504C22—41no—
505C22#1171916914yes—
506C22C22×#612211yescharacteristic
507C22C22×#612211yescharacteristic
508C22C22×C22⋊#26111yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—262no—
514C4—262no—
515C4—262no—
516C4—262no—
517C4—521no—
518C4—521no—
519C4—521no—
520C4—521no—
521C2—21no—
522C2—21no—
523C2—24no—
524C2—42no—
525C2—42no—
526C2C2×#1171916911yescharacteristic
527C2#1313143611yescharacteristic
528C2#1313144811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
Fitting, prime radicalC22×C13×#41C4
socleC22×C13C22×C22⋊C4
cosocleC22×Dic13C24
hypercenterC22×#41#261
hypocenterC13#17368
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×D4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #13131687C2semidirect
2. #13130099C2semidirect
3. #13130092C2semidirect
4. #13130087C2semidirect
5. #13130084C2semidirect
6. #13130072C2semidirect
7. C2×#11718285C2semidirect
108. C2×D4×C13M16semidirect
117. C22×C4×C13M16semidirect
370. C2×D4#6122semidirect
400. C22×C4#6122semidirect
430. C13#17368semidirect

Maximal subgroups

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

subgroupindex
#131316872
#131300992
#131300922
#131300872
#131300842
#131300722
C2×#117182852
C2×#117195322
#1736813