Finite Group Databasebeta

← #15789693

Subgroups — #15789693

Order 3328.

1634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718640C211yesmaximal, characteristic
3C2×#11718316C212yesmaximal
4C2×#11718642C211yesmaximal, characteristic
5#13113106C211yesmaximal, characteristic
6#13113095C211yesmaximal, characteristic
7#13113091C212yesmaximal
8#13113087C212yesmaximal
9#13113062C212yesmaximal
10#13113061C211yesmaximal, characteristic
11C13×#1441C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×C4×Dic13C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C2×#88141—28no—
21C2×#88141—24no—
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37#11718642—24no—
38#11718640C418yescomplemented
39#11718316—28no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—24no—
54C22×Dic26—24no—
55C22×Dic26C2×C414yes—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4C2×C414yes—
61C2×C4⋊Dic13—24no—
62C2×C4⋊Dic13—22no—
63C2×#6101—24no—
64C2×#6101—24no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101C2×C418yes—
69C2×C4×Dic13—24no—
70C2×C4×Dic13—24no—
71C2×C4×Dic13—24no—
72C2×C4×Dic13D418yes—
73C2×C4×Dic13D414yes—
74#88141—232no—
75C13×#95—24no—
76C13×#95—22no—
77C13×#95—42no—
78#88071—24no—
79#88071—22no—
80#88071—24no—
81#88071—24no—
82#88071—22no—
83#88071—22no—
84#88071—22no—
85#88071—24no—
86#88071—42no—
87#88071—42no—
88#88071C2×C414yes—
89#88071C2×C418yes—
90#14302—131nomaximal, Sylow
91C24×C13C2411yescharacteristic
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
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×C13C22×C412yes—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C2×D414yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13#4112yes—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—21no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—21no—
150C22×Dic13C22×C414yes—
151C22×Dic13C22×C414yes—
152C22×Dic13C2×D412yes—
153C22×Dic13C2×D414yes—
154C22×Dic13C2×D414yes—
155C22×Dic13C2×D412yes—
156C22×Dic13#4114yes—
157C2×Dic26—28no—
158C2×Dic26—216no—
159C2×Dic26—28no—
160C2×Dic26—28no—
161C2×Dic26—216no—
162C13×C4⋊C4—28no—
163C13×C4⋊C4—28no—
164C4⋊Dic13—44no—
165#6101—216no—
166#6101—216no—
167C4×Dic13—216no—
168C4×Dic13—28no—
169C22×C4×Q8—131no—
170C2×#395—131no—
171C2×#387—132no—
172C2×#387—131no—
173#1446—131no—
174#1442—132no—
175#1442—131no—
176#1441—132no—
177#1441D1311yescharacteristic
178#1434—131no—
179#1434—132no—
180C23×C13C23×C411yescharacteristic
181C23×C13C22×D411yescharacteristic
182C23×C13C22×D412yes—
183C23×C13C2×#4111yescharacteristic
184C23×C13C2×#4112yes—
185C23×C13H(5,𝔽2)11yescharacteristic
186C23×C132−1+412yes—
187C23×C132−1+411yescharacteristic
188C23×C132−1+411yescharacteristic
189C23×C132−1+412yes—
190C23×C132−1+411yescharacteristic
191C2×C4×C13—24no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13C4×D414yes—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—24no—
228C2×Dic13—24no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—42no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—42no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13C4×D418yes—
255C2×Dic13#12014yes—
256Dic26—232no—
257C23×Q8—131no—
258C2×C4×Q8—264no—
259C2×C4×Q8—268no—
260C22×C4⋊C4—132no—
261C22×C4⋊C4—132no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4C2×D1311yescharacteristic
264C22×C4⋊C4C2×D1311yescharacteristic
265C22×C42—132no—
266C22×C42—131no—
267#395—138no—
268#387—268no—
269#387—264no—
270C2×#95—132no—
271C2×#95—131no—
272C2×#95—132no—
273C2×#95—131no—
274C2×#95—132no—
275C2×#95—131no—
276C2×#95—131no—
277C2×#95—132no—
278C2×#95—132no—
279C2×#95—131no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95C2×D1311yescharacteristic
283C2×#95C2×D1312yes—
284C2×#95C2×D1312yes—
285C22×C13C2×C4×D411yescharacteristic
286C22×C13C2×C4×D412yes—
287C22×C13#51911yescharacteristic
288C22×C13#51912yes—
289C22×C13#52011yescharacteristic
290C22×C13C2×#12011yescharacteristic
291C22×C13#52512yes—
292C22×C13#52511yescharacteristic
293C22×C13#53612yes—
294C22×C13#53611yescharacteristic
295C22×C13#53611yescharacteristic
296C22×C13#53612yes—
297C22×C13#53612yes—
298C22×C13#53611yescharacteristic
299C22×C13#53712yes—
300C22×C13#53711yescharacteristic
301C22×C13#54111yescharacteristic
302C22×C13#54112yes—
303C22×C13#54112yes—
304C22×C13#54112yes—
305C22×C13#54112yes—
306C22×C13#54211yescharacteristic
307C22×C13#54212yes—
308C4×C13—24no—
309C4×C13—42no—
310C4×C13—44no—
311C4×C13—42no—
312C4×C13—82no—
313Dic13—24no—
314Dic13—28no—
315Dic13—44no—
316Dic13—42no—
317Dic13—81no—
318Dic13—81no—
319C22×Q8—134no—
320C22×Q8—264no—
321C22×Q8—264no—
322C22×Q8—262no—
323C22×Q8—262no—
324C23×C4—132no—
325C23×C4—131no—
326C23×C4—131no—
327C23×C4—132no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4C22×D1312yes—
331C23×C4C22×D1311yescharacteristic
332C23×C4C22×D1311yescharacteristic
333C23×C4C22×D1312yes—
334C23×C4C22×D1311yescharacteristic
335C4×Q8—2632no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—138no—
341C2×C4⋊C4—264no—
342C2×C4⋊C4—264no—
343C2×C4⋊C4—264no—
344C2×C4⋊C4—264no—
345C2×C4⋊C4—264no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4C4×D1314yes—
349C2×C42—138no—
350C2×C42—134no—
351C2×C42—264no—
352C2×C42—264no—
353C2×C42—264no—
354#95—24no—
355#95—22no—
356#95—42no—
357#95—138no—
358#95—134no—
359#95—264no—
360#95—262no—
361#95—262no—
362#95—262no—
363#95—264no—
364#95—264no—
365#95—264no—
366#95—262no—
367#95—522no—
368#95—522no—
369C2×C13C4×#12011yescharacteristic
370C2×C13#232312yes—
371C2×C13#232311yescharacteristic
372C2×C13#232712yes—
373C2×C13#232711yescharacteristic
374C2×C13#261411yescharacteristic
375C2×C13#261611yescharacteristic
376C2×C13#263411yescharacteristic
377C2×C13#263412yes—
378C2×C13#263711yescharacteristic
379C2×C13#263712yes—
380C24C23×D1311yescharacteristic
381C2×Q8—2616no—
382C2×Q8—268no—
383C2×Q8—2616no—
384C2×Q8—268no—
385C2×Q8—268no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—134no—
412C22×C4—132no—
413C22×C4—134no—
414C22×C4—134no—
415C22×C4—134no—
416C22×C4—134no—
417C22×C4—132no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—261no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—261no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—261no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—261no—
434C22×C4—262no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—262no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4C2×C4×D1312yes—
446C22×C4C2×C4×D1312yes—
447C22×C4C2×C4×D1312yes—
448C22×C4D4×D1314yes—
449C22×C4D4×D1312yes—
450C22×C4#612912yes—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—2616no—
454C4⋊C4—2616no—
455C4⋊C4—524no—
456C42—268no—
457C42—2616no—
458C13#1430211yescharacteristic, complemented, Sylow
459C23C22×C4×D1311yescharacteristic
460C23C2×D4×D1311yescharacteristic
461C23C2×D4×D1312yes—
462C23C2×#612911yescharacteristic
463C23#8825111yescharacteristic
464C23#8825411yescharacteristic
465C23#8825412yes—
466C23#41×D1312yes—
467C23#8825711yescharacteristic
468C23#8825711yescharacteristic
469C23#8825712yes—
470Q8—2632no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—138no—
502C2×C4—134no—
503C2×C4—264no—
504C2×C4—262no—
505C2×C4—264no—
506C2×C4—264no—
507C2×C4—264no—
508C2×C4—264no—
509C2×C4—264no—
510C2×C4—262no—
511C2×C4—264no—
512C2×C4—264no—
513C2×C4—264no—
514C2×C4—264no—
515C2×C4—264no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—521no—
534C2×C4—522no—
535C2×C4#8813514yes—
536C22C2×#8813511yescharacteristic
537C22#1171920911yescharacteristic
538C22#1171922111yescharacteristic
539C22C4×D4×D1312yes—
540C22#1171927712yes—
541C22D13×#12011yescharacteristic
542C22#1171930212yes—
543C22#1171930811yescharacteristic
544C22#1171931112yes—
545C22#1171931311yescharacteristic
546C22#1171933011yescharacteristic
547C22#1171933012yes—
548C22#1171933311yescharacteristic
549C22#1171933312yes—
550C22#1171934512yes—
551C22#1171935312yes—
552C22#1171936111yescharacteristic
553C22#1171938011yescharacteristic
554C22#1171940112yes—
555C22#1171940112yes—
556C22#1171940612yes—
557C22#1171942912yes—
558C22#1171942911yescharacteristic
559C4—24no—
560C4—44no—
561C4—42no—
562C4—42no—
563C4—82no—
564C4—264no—
565C4—268no—
566C4—522no—
567C4—524no—
568C4—1041no—
569C4—1041no—
570C2#1311734111yescharacteristic
571C2#1311751312yes—
572C2#1311751411yescharacteristic
573C2#1311755112yes—
574C2#1311755411yescharacteristic
575C2#1312055611yescharacteristic
576C2#1312056411yescharacteristic
577C2#1312071411yescharacteristic
578C2#1312071712yes—
579C2#1312074711yescharacteristic
580C2#1312074912yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14302
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
38. #11718640C4semidirect
458. C13#14302semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117186402
C2×#117183162
C2×#117186422
#131131062
#131130952
#131130912
#131130872
#131130622
#131130612
C13×#14412
#1430213