Finite Group Databasebeta

← #15872630

Subgroups — #15872630

Order 3328.

1106 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719327C211yesmaximal, characteristic
2C2×#11718379C211yesmaximal, characteristic
3#13117239C211yesmaximal, characteristic
4#13115795C212yesmaximal, complemented
5#13115636C212yesmaximal, complemented
6#13115149C211yesmaximal, characteristic
7#13115148C211yesmaximal, characteristic
8#13115146C211yesmaximal, characteristic
9#13114850C212yesmaximal, complemented
10#13114849C212yesmaximal, complemented
11C13×#1873C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2211yescharacteristic
13C2×C13×#117C2211yescharacteristic
14C2×Q8×Dic13C2211yescharacteristic
15C2×#88198C2211yescharacteristic
16C2×#88180C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19#11719327—24no—
20#11719327C418yescomplemented
21C2×#88143—21no—
22C2×#88142C2211yescharacteristic
23C2×#88141—21no—
24C2×#88141C2211yescharacteristic
25C2×#88132—21no—
26C2×#88131—21no—
27C2×C13×#103C2212yes—
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×#88075C2212yes—
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88056C2212yes—
32C2×#88054C2212yes—
33C2×C8×Dic13C2212yes—
34#11718638C2212yes—
35#11718637C2212yes—
36C2×#88050C2212yes—
37#11718603—21no—
38#11718603—21no—
39C4×#6101—21no—
40C4×#6101—21no—
41#11718379—24no—
42C13×#340C2212yes—
43#11718143C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46C22×Q8×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13D411yescharacteristic
49C23×Dic13D411yescharacteristic
50C22×Dic26—21no—
51C22×Dic26C2311yescharacteristic
52C22×C8×C13C2312yes—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8C2×C414yes—
55C13×#117—42no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64Q8×Dic13—22no—
65Q8×Dic13C2×C414yes—
66#88198—22no—
67#88198C2×C414yes—
68#88180—42no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13C2312yes—
71C2×C4⋊Dic13C2311yescharacteristic
72#88178—22no—
73#88178C2×C414yes—
74C2×#6101—21no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×#6101—21no—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13C2×C414yes—
85C2×C4×Dic13D411yescharacteristic
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D414yes—
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2312yes—
91#88143—28no—
92#88142—22no—
93#88142C2×C414yes—
94#88141—28no—
95#88141—22no—
96#88141C2×C414yes—
97#88132—28no—
98#88131—28no—
99C13×#103—42no—
100C13×C22⋊C8—22no—
101#88075—42no—
102#88071—22no—
103#88071—22no—
104C22⋊#1055—22no—
105#88056—42no—
106#88054—24no—
107C8×Dic13—24no—
108#88050—42no—
109#21864—131nomaximal, Sylow
110C24×C13C2×D411yescharacteristic
111C2×Q8×C13—21no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13C22×C412yes—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2411yescharacteristic
124C22×Dic13—24no—
125C22×Dic13—24no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13C22⋊C414yes—
130C22×Dic13C22⋊C414yes—
131C22×Dic13C2×D411yescharacteristic
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C2×Dic26—22no—
136C2×Dic26—22no—
137C2×Dic26—21no—
138C2×Dic26—24no—
139C2×Dic26—44no—
140C2×Dic26C22×C412yes—
141C2×C8×C13—22no—
142C2×C8×C13—22no—
143C2×C8×C13—22no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4C22×C412yes—
149C13×C22⋊C4—24no—
150C13×C22⋊C4—42no—
151C42×C13—42no—
152C22⋊Dic13—24no—
153C22⋊Dic13—42no—
154C4⋊Dic13—21no—
155C4⋊Dic13—24no—
156C4⋊Dic13—22no—
157C4⋊Dic13—22no—
158C4⋊Dic13C22×C412yes—
159#6101—24no—
160#6101—24no—
161#6101—24no—
162#6101—24no—
163#6101—24no—
164#6101—44no—
165#6101—44no—
166C4×Dic13—24no—
167C4×Dic13—24no—
168C4×Dic13—42no—
169C4×Dic13C22⋊C414yes—
170C4×Dic13C22⋊C414yes—
171C4×Dic13C22×C412yes—
172C4×Dic13C22×C412yes—
173C4×Dic13C2×D412yes—
174C4×Dic13C2×D412yes—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#533—131no—
179C2×#431—131no—
180#2285—131no—
181#1990—132no—
182#1956—132no—
183#1873—131no—
184#1873—131no—
185#1873—131no—
186#1873D1311yescharacteristic
187#1805—132no—
188#1805—132no—
189C23×C13—21no—
190C23×C13—21no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13C2×C22⋊C412yes—
194C23×C13C22×D411yescharacteristic
195Q8×C13—24no—
196Q8×C13—42no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13C2×C22⋊C412yes—
210C2×C4×C13C23×C411yescharacteristic
211C2×C4×C13C22×D411yescharacteristic
212C2×C4×C13H(5,𝔽2)12yes—
213C2×C4×C132−1+412yes—
214C2×Dic13—22no—
215C2×Dic13—22no—
216C2×Dic13—28no—
217C2×Dic13—28no—
218C2×Dic13—22no—
219C2×Dic13—22no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13C2×C22⋊C412yes—
227C2×Dic13C2×C22⋊C412yes—
228C2×Dic13C2×C22⋊C412yes—
229C2×Dic13C2×C22⋊C412yes—
230C2×Dic13#13514yes—
231C2×Dic13#13714yes—
232Dic26—24no—
233Dic26—42no—
234Dic26—48no—
235C8×C13—42no—
236#1055—42no—
237#533—138no—
238#533—264no—
239C2×C4⋊Q8—131no—
240C2×C4⋊Q8—131no—
241C2×#125—261no—
242C2×C22⋊Q8—131no—
243C2×C22⋊Q8—261no—
244C2×C22⋊Q8C2×D1311yescharacteristic
245C2×C4×Q8—131no—
246C2×C4×Q8—131no—
247C2×C4×Q8—261no—
248C2×#117—131no—
249C2×#117—261no—
250C2×#117C2×D1311yescharacteristic
251C22×C42—131no—
252#431—264no—
253C2×C4⋊C8—132no—
254C2×#103—132no—
255C2×#103—132no—
256C2×#103—132no—
257C2×#103C2×D1312yes—
258C2×C22⋊C8—131no—
259C2×C22⋊C8C2×D1311yescharacteristic
260C2×C4×C8—132no—
261#384—132no—
262#382—132no—
263#380—261no—
264#380—261no—
265C4×C4⋊C4—261no—
266C4×C4⋊C4—261no—
267#340—132no—
268#340—132no—
269#340—132no—
270#340C2×D1312yes—
271C22×C13—22no—
272C22×C13—22no—
273C22×C13—22no—
274C22×C13—42no—
275C22×C13—42no—
276C22×C13C22×C22⋊C411yescharacteristic
277C22×C13#53511yescharacteristic
278C22×C13#53611yescharacteristic
279C22×C13C2×#13512yes—
280C22×C13C2×#13712yes—
281C4×C13—22no—
282C4×C13—42no—
283C4×C13—42no—
284C4×C13—82no—
285C4×C13#52012yes—
286C4×C13#53712yes—
287Dic13—22no—
288Dic13—22no—
289Dic13—42no—
290Dic13—42no—
291Dic13—82no—
292Dic13#41614yes—
293Dic13#41914yes—
294C22×Q8—131no—
295C22×Q8—261no—
296C22×Q8C22×D1311yescharacteristic
297C23×C4—131no—
298C23×C4—131no—
299C23×C4C22×D1311yescharacteristic
300C22×C8—132no—
301C22×C8C22×D1312yes—
302C4⋊Q8—134no—
303C4⋊Q8—134no—
304C4⋊Q8—262no—
305C4⋊Q8—262no—
306#125—268no—
307C22⋊Q8—22no—
308C22⋊Q8—134no—
309C22⋊Q8—268no—
310C22⋊Q8—262no—
311C22⋊Q8C4×D1314yes—
312C4×Q8—134no—
313C4×Q8—134no—
314C4×Q8—262no—
315C4×Q8—268no—
316C4×Q8—262no—
317#117—42no—
318#117—268no—
319#117—522no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—132no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4—261no—
325C2×C4⋊C4—261no—
326C2×C4⋊C4—261no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—261no—
329C2×C4⋊C4—262no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4C22×D1312yes—
332C2×C4⋊C4C22×D1311yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—261no—
336C2×C22⋊C4—261no—
337C2×C42—21no—
338C2×C42—134no—
339C2×C42—131no—
340C2×C42—131no—
341C2×C42—134no—
342C2×C42—131no—
343C2×C42—131no—
344C2×C42—261no—
345C2×C42—261no—
346C2×C42—261no—
347C4⋊C8—264no—
348#103—42no—
349#103—522no—
350#103—522no—
351#103—522no—
352C22⋊C8—22no—
353C22⋊C8—262no—
354C4×C8—264no—
355#95—262no—
356#95—262no—
357C2×C13—42no—
358C2×C13#231111yescharacteristic
359C2×C13C2×#41611yescharacteristic
360C2×C13C2×#41911yescharacteristic
361C2×C13#321012yes—
362C2×C13#323112yes—
363C24D4×D1311yescharacteristic
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—132no—
368C2×Q8—264no—
369C2×Q8—261no—
370C2×Q8—262no—
371C2×Q8—262no—
372C2×Q8—524no—
373C2×Q8C2×C4×D1312yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—131no—
380C22×C4—131no—
381C22×C4—134no—
382C22×C4—134no—
383C22×C4—131no—
384C22×C4—131no—
385C22×C4—264no—
386C22×C4—264no—
387C22×C4—261no—
388C22×C4—261no—
389C22×C4—262no—
390C22×C4C2×C4×D1312yes—
391C22×C4D4×D1311yescharacteristic
392C22×C4D4×D1312yes—
393C22×C4C23×D1311yescharacteristic
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C4⋊C4—24no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—132no—
405C4⋊C4—264no—
406C4⋊C4—264no—
407C4⋊C4—264no—
408C4⋊C4—264no—
409C4⋊C4—264no—
410C4⋊C4—264no—
411C4⋊C4—261no—
412C4⋊C4—262no—
413C4⋊C4—262no—
414C4⋊C4—524no—
415C4⋊C4—524no—
416C4⋊C4C2×C4×D1312yes—
417C22⋊C4—24no—
418C22⋊C4—42no—
419C22⋊C4—264no—
420C22⋊C4—522no—
421C42—42no—
422C42—134no—
423C42—134no—
424C42—132no—
425C42—132no—
426C42—132no—
427C42—132no—
428C42—264no—
429C42—264no—
430C42—522no—
431C13#2186411yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—21no—
435C23—21no—
436C23C22⋊C4×D1312yes—
437C23C2×D4×D1311yescharacteristic
438Q8—24no—
439Q8—42no—
440Q8—264no—
441Q8—528no—
442Q8—522no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—132no—
456C2×C4—132no—
457C2×C4—134no—
458C2×C4—134no—
459C2×C4—132no—
460C2×C4—132no—
461C2×C4—268no—
462C2×C4—268no—
463C2×C4—262no—
464C2×C4—262no—
465C2×C4—262no—
466C2×C4—262no—
467C2×C4—522no—
468C2×C4—521no—
469C2×C4—521no—
470C2×C4—522no—
471C2×C4—522no—
472C2×C4—522no—
473C2×C4C22⋊C4×D1312yes—
474C2×C4C22×C4×D1311yescharacteristic
475C2×C4C2×D4×D1311yescharacteristic
476C2×C4#8825112yes—
477C2×C4#8825712yes—
478C8—42no—
479C8—522no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—42no—
484C22—42no—
485C22C2×C22⋊C4×D1311yescharacteristic
486C22#1171929711yescharacteristic
487C22#1171935311yescharacteristic
488C22D13×#13512yes—
489C22D13×#13712yes—
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—134no—
495C4—134no—
496C4—262no—
497C4—262no—
498C4—522no—
499C4—522no—
500C4—1042no—
501C4#1171925112yes—
502C4#1171930212yes—
503C2—42no—
504C2#1311742311yescharacteristic
505C2D13×#41611yescharacteristic
506C2D13×#41911yescharacteristic
507C2#1312579012yes—
508C2#1312599312yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1873C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1873D13
hypocenterC13#21864
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
4. #13115795C2semidirect
5. #13115636C2semidirect
9. #13114850C2semidirect
10. #13114849C2semidirect
20. #11719327C4semidirect
431. C13#21864semidirect

Maximal subgroups

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

subgroupindex
C2×#117193272
C2×#117183792
#131172392
#131157952
#131156362
#131151492
#131151482
#131151462
#131148502
#131148492
C13×#18732
#2186413