Finite Group Databasebeta

← #15794264

Subgroups — #15794264

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2C2×#11718311C211yesmaximal, characteristic
3C2×C42×Dic13C211yesmaximal, characteristic
4#13113071C211yesmaximal, characteristic
5#13113070C212yesmaximal
6#13113069C211yesmaximal, characteristic
7#13113068C211yesmaximal, characteristic
8#13113067C212yesmaximal
9#13113064C212yesmaximal
10#13113064C212yesmaximal
11C13×#1436C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×#88143—24no—
25C2×#88143—24no—
26C2×#88143C418yescomplemented
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C42×Dic13—24no—
39#11718311—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C42×C13—22no—
55C2×C42×C13—24no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13C2×C414yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101C2×C414yes—
71C2×#6101C2×C414yes—
72C2×#6101C2×C414yes—
73C2×#6101C2×C414yes—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13C2×C414yes—
82C2×C4×Dic13D414yes—
83C2×C4×Dic13D414yes—
84C2×C4×Dic13Q818yes—
85#88143—232no—
86C13×#95—22no—
87C13×#95—24no—
88C13×#95—24no—
89#88071—22no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#14709—131nomaximal, Sylow
98C24×C13C2411yescharacteristic
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
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×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×Q814yes—
126C22×C4×C13#4114yes—
127C22×C4×C13#4114yes—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13C22×C412yes—
150C22×Dic13C22×C412yes—
151C22×Dic13C22×C412yes—
152C22×Dic13C22×C412yes—
153C22×Dic13C2×D412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×D412yes—
157C22×Dic13C2×Q814yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13#4114yes—
160C22×Dic13#4114yes—
161C22×Dic13#4114yes—
162C13×C4⋊C4—28no—
163C42×C13—28no—
164C4⋊Dic13—28no—
165#6101—28no—
166#6101—28no—
167#6101—28no—
168#6101—28no—
169#6101—48no—
170C4×Dic13—216no—
171C4×Dic13—28no—
172C4×Dic13—216no—
173C4×Dic13C22⋊C4116yes—
174C22×#125—131no—
175C2×#382—131no—
176C2×C43—131no—
177#1436—131no—
178#1436—132no—
179#1436—132no—
180#1436—131no—
181#1436—131no—
182#1436D1311yescharacteristic
183C4⋊#95—132no—
184C4⋊#95—132no—
185C23×C13C23×C411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×Q812yes—
189C23×C13C2×#4112yes—
190C23×C13C2×#4112yes—
191C23×C13C2×#4112yes—
192C23×C13C2×#4112yes—
193C23×C13C2×#4112yes—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
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×C13C2×C22⋊C414yes—
222C2×C4×C13#12518yescomplemented
223C2×Dic13—22no—
224C2×Dic13—22no—
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—24no—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—24no—
238C2×Dic13—42no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13C2×C22⋊C414yes—
251C2×Dic13C2×C22⋊C414yes—
252C2×Dic13C4×Q818yes—
253C2×Dic13C22⋊Q818yes—
254C2×Dic13#12414yes—
255C2×Dic13#12518yescomplemented
256C2×Dic13C4⋊Q814yes—
257C2×#125—138no—
258C2×#125—264no—
259C2×#125—264no—
260C22×C4⋊C4—131no—
261C22×C4⋊C4—131no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—131no—
265C22×C4⋊C4—132no—
266C22×C4⋊C4C2×D1311yescharacteristic
267C22×C42—131no—
268C22×C42—132no—
269C22×C42—132no—
270C22×C42—131no—
271C22×C42C2×D1311yescharacteristic
272#382—264no—
273C2×#95—132no—
274C2×#95—132no—
275C2×#95—132no—
276C2×#95—132no—
277C2×#95—132no—
278C2×#95—132no—
279C2×#95—132no—
280C2×#95—131no—
281C2×#95C2×D1312yes—
282C2×#95C2×D1312yes—
283C2×#95C2×D1311yescharacteristic
284C43—264no—
285C22×C13C22×C22⋊C411yescharacteristic
286C22×C13C2×C4×Q812yes—
287C22×C13C4×#4111yescharacteristic
288C22×C13C4×#4111yescharacteristic
289C22×C13C4×#4112yes—
290C22×C13C2×C22⋊Q812yes—
291C22×C13#52512yes—
292C22×C13#52511yescharacteristic
293C22×C13#52511yescharacteristic
294C22×C13C2×#12411yescharacteristic
295C22×C13C2×#12512yes—
296C22×C13C2×#12512yes—
297C22×C13#52912yes—
298C22×C13#52912yes—
299C22×C13#52912yes—
300C22×C13#52912yes—
301C22×C13C2×C4⋊Q811yescharacteristic
302C22×C13#53212yes—
303C22×C13#53212yes—
304C22×C13#53312yes—
305C22×C13#53312yes—
306C4×C13—28no—
307C4×C13—24no—
308C4×C13—42no—
309C4×C13—42no—
310C4×C13—82no—
311Dic13—28no—
312Dic13—24no—
313Dic13—42no—
314Dic13—42no—
315Dic13—82no—
316Dic13#39118yes—
317C23×C4—131no—
318C23×C4—131no—
319C23×C4—132no—
320C23×C4—131no—
321C23×C4—131no—
322C23×C4—132no—
323C23×C4C22×D1312yes—
324C23×C4C22×D1311yescharacteristic
325C23×C4C22×D1311yescharacteristic
326C23×C4C22×D1311yescharacteristic
327C23×C4C22×D1312yes—
328#125—2632no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—134no—
332C2×C4⋊C4—134no—
333C2×C4⋊C4—134no—
334C2×C4⋊C4—134no—
335C2×C4⋊C4—134no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—262no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—264no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4C4×D1314yes—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—134no—
353C2×C42—134no—
354C2×C42—134no—
355C2×C42—138no—
356C2×C42—264no—
357C2×C42—264no—
358C2×C42—264no—
359C2×C42—264no—
360C2×C42—264no—
361C2×C42—264no—
362C2×C42—262no—
363#95—24no—
364#95—22no—
365#95—24no—
366#95—264no—
367#95—264no—
368#95—264no—
369#95—264no—
370#95—264no—
371#95—264no—
372#95—262no—
373#95—264no—
374C2×C13C2×#39111yescharacteristic
375C2×C13#229711yescharacteristic
376C2×C13#229711yescharacteristic
377C2×C13C4×#12512yes—
378C2×C13C4×#12512yes—
379C2×C13#285112yes—
380C2×C13#285112yes—
381C2×C13#285912yes—
382C2×C13#286112yes—
383C24C23×D1311yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—132no—
406C22×C4—132no—
407C22×C4—132no—
408C22×C4—134no—
409C22×C4—134no—
410C22×C4—132no—
411C22×C4—132no—
412C22×C4—132no—
413C22×C4—134no—
414C22×C4—134no—
415C22×C4—134no—
416C22×C4—132no—
417C22×C4—132no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4C2×C4×D1312yes—
440C22×C4C2×C4×D1312yes—
441C22×C4C2×C4×D1312yes—
442C22×C4#612714yes—
443C22×C4D4×D1312yes—
444C22×C4D4×D1312yes—
445C22×C4#612914yes—
446C22×C4Q8×D1314yes—
447C4⋊C4—28no—
448C4⋊C4—268no—
449C4⋊C4—268no—
450C4⋊C4—268no—
451C4⋊C4—268no—
452C4⋊C4—268no—
453C4⋊C4—528no—
454C42—28no—
455C42—1316no—
456C42—2616no—
457C42—2616no—
458C42—268no—
459C13#1470911yescharacteristic, complemented, Sylow
460C23C22×C4×D1311yescharacteristic
461C23C2×#612712yes—
462C23C2×D4×D1311yescharacteristic
463C23C2×D4×D1311yescharacteristic
464C23C2×#612912yes—
465C23C2×Q8×D1312yes—
466C23#41×D1312yes—
467C23#41×D1312yes—
468C23#41×D1312yes—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—134no—
497C2×C4—134no—
498C2×C4—138no—
499C2×C4—138no—
500C2×C4—134no—
501C2×C4—134no—
502C2×C4—138no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—264no—
506C2×C4—264no—
507C2×C4—264no—
508C2×C4—264no—
509C2×C4—264no—
510C2×C4—264no—
511C2×C4—264no—
512C2×C4—264no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—264no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—521no—
521C2×C4—522no—
522C2×C4—521no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4C22⋊C4×D1314yes—
531C2×C4#8814318yescomplemented
532C22C4×#612711yescharacteristic
533C22C2×C22⋊C4×D1311yescharacteristic
534C22C2×#8814312yes—
535C22#1171922711yescharacteristic
536C22#1171923312yes—
537C22C4×#612912yes—
538C22#1171924312yes—
539C22#1171925212yes—
540C22#1171925312yes—
541C22C4×Q8×D1312yes—
542C22#1171928312yes—
543C22#1171929111yescharacteristic
544C22#1171930112yes—
545C22#1171932712yes—
546C22D13×C22⋊Q812yes—
547C22#1171935412yes—
548C22#1171936111yescharacteristic
549C22D13×#12411yescharacteristic
550C22D13×#12512yes—
551C22#1171941112yes—
552C22D13×C4⋊Q811yescharacteristic
553C4—28no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4—138no—
559C4—268no—
560C4—264no—
561C4—522no—
562C4—522no—
563C4—1042no—
564C2D13×#39111yescharacteristic
565C2#1311732111yescharacteristic
566C2#1311732211yescharacteristic
567C2C4×#8814312yes—
568C2#1311739312yes—
569C2#1312314212yes—
570C2#1312314312yes—
571C2#1312319512yes—
572C2#1312320512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1436D13
hypocenterC13#14709
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
26. C2×#88143C4semidirect
222. C2×C4×C13#125semidirect
255. C2×Dic13#125semidirect
459. C13#14709semidirect
531. C2×C4#88143semidirect

Maximal subgroups

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

subgroupindex
C22×#881432
C2×#117183112
C2×C42×Dic132
#131130712
#131130702
#131130692
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