Finite Group Databasebeta

← #15785326

Subgroups — #15785326

Order 3328.

1710 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×#11718311C211yesmaximal, characteristic
3C2×C4×#6101C211yesmaximal, characteristic
4#13113106C212yesmaximal
5#13113102C212yesmaximal
6#13113071C211yesmaximal, characteristic
7#13113069C211yesmaximal, characteristic
8#13113068C211yesmaximal, characteristic
9#13113064C212yesmaximal
10#13113064C212yesmaximal
11C13×#1436C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×#88141—24no—
24C2×#88141—24no—
25C2×#88141C418yescomplemented
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C4×#6101—24no—
39#11718311—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×Dic26—24no—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—24no—
55C22×Dic26C2×C414yes—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4C2×C414yes—
59C2×C42×C13—22no—
60C2×C42×C13—42no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101C2×C414yes—
71C2×#6101C2×C414yes—
72C2×#6101Q818yescomplemented
73C2×C4×Dic13—22no—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—42no—
79C2×C4×Dic13C2×C414yes—
80C2×C4×Dic13C2×C414yes—
81C2×C4×Dic13C2×C414yes—
82C2×C4×Dic13D414yes—
83C2×C4×Dic13D414yes—
84#88141—232no—
85C13×#95—22no—
86C13×#95—24no—
87C13×#95—42no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071—42no—
95#88071—42no—
96#88071—42no—
97#13925—131nomaximal, Sylow
98C24×C13C2411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—21no—
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—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×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×Q814yes—
127C22×C4×C13#4114yes—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—22no—
137C22×Dic13—22no—
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×Dic13—22no—
150C22×Dic13C22×C412yes—
151C22×Dic13C22×C412yes—
152C22×Dic13C22×C412yes—
153C22×Dic13C22×C412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×D412yes—
157C22×Dic13C2×D412yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13C2×Q814yes—
160C22×Dic13#4114yes—
161C22×Dic13#4114yes—
162C2×Dic26—216no—
163C2×Dic26—216no—
164C2×Dic26—28no—
165C2×Dic26—28no—
166C2×Dic26—28no—
167C13×C4⋊C4—28no—
168C42×C13—44no—
169#6101—28no—
170#6101—28no—
171#6101—216no—
172#6101—48no—
173C4×Dic13—28no—
174C4×Dic13—28no—
175C4×Dic13—44no—
176C4×Dic13C22⋊C4116yes—
177C22×C4×Q8—131no—
178C2×#382—131no—
179C2×C4×C4⋊C4—131no—
180#1446—132no—
181#1445—132no—
182#1436—131no—
183#1436—131no—
184#1436—131no—
185#1436D1311yescharacteristic
186C4⋊#95—132no—
187C4⋊#95—132no—
188C23×C13C23×C411yescharacteristic
189C23×C13C22×D411yescharacteristic
190C23×C13C22×D411yescharacteristic
191C23×C13C22×Q812yes—
192C23×C13C2×#4112yes—
193C23×C13C2×#4112yes—
194C23×C13C2×#4112yes—
195C23×C13H(5,𝔽2)12yes—
196C23×C132−1+412yes—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
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×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13C2×C22⋊C414yes—
225C2×C4×C13#11714yes—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—22no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13C2×C22⋊C414yes—
254C2×Dic13C2×C22⋊C414yes—
255C2×Dic13#11714yes—
256C2×Dic13C4×Q818yes—
257C2×Dic13C22⋊Q818yes—
258C2×Dic13#12414yes—
259C2×Dic13C4⋊Q814yes—
260Dic26—232no—
261C23×Q8—131no—
262C2×C4×Q8—138no—
263C2×C4×Q8—264no—
264C2×C4×Q8—264no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—132no—
269C22×C4⋊C4C2×D1311yescharacteristic
270C22×C42—131no—
271C22×C42—131no—
272C22×C42—131no—
273C22×C42—131no—
274C22×C42C2×D1311yescharacteristic
275#382—264no—
276C4×C4⋊C4—264no—
277C2×#95—132no—
278C2×#95—132no—
279C2×#95—132no—
280C2×#95—131no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95C2×D1312yes—
287C2×#95C2×D1311yescharacteristic
288C2×#95C2×D1312yes—
289C22×C13C22×C22⋊C411yescharacteristic
290C22×C13C2×#11711yescharacteristic
291C22×C13C2×#11711yescharacteristic
292C22×C13C2×C4×Q812yes—
293C22×C13#52012yes—
294C22×C13C2×C22⋊Q812yes—
295C22×C13#52512yes—
296C22×C13#52512yes—
297C22×C13C2×#12411yescharacteristic
298C22×C13C2×C4⋊Q811yescharacteristic
299C22×C13#53511yescharacteristic
300C22×C13#53611yescharacteristic
301C22×C13#53712yes—
302C22×C13#55412yes—
303C22×C13#55412yes—
304C22×C13#55612yes—
305C22×C13#55612yes—
306C22×C13#55712yes—
307C22×C13#55712yes—
308C22×C13#55912yes—
309C22×C13#55912yes—
310C4×C13—24no—
311C4×C13—24no—
312C4×C13—42no—
313C4×C13—44no—
314C4×C13—82no—
315Dic13—24no—
316Dic13—24no—
317Dic13—42no—
318Dic13—44no—
319Dic13—82no—
320Dic13#39118yes—
321C22×Q8—134no—
322C22×Q8—262no—
323C22×Q8—262no—
324C22×Q8—264no—
325C22×Q8—264no—
326C23×C4—131no—
327C23×C4—131no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4—132no—
331C23×C4—132no—
332C23×C4C22×D1312yes—
333C23×C4C22×D1311yescharacteristic
334C23×C4C22×D1312yes—
335C23×C4C22×D1311yescharacteristic
336C23×C4C22×D1311yescharacteristic
337C4×Q8—2632no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—134no—
341C2×C4⋊C4—134no—
342C2×C4⋊C4—138no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—264no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—262no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4C4×D1314yes—
353C2×C42—22no—
354C2×C42—42no—
355C2×C42—134no—
356C2×C42—134no—
357C2×C42—134no—
358C2×C42—134no—
359C2×C42—134no—
360C2×C42—262no—
361C2×C42—262no—
362C2×C42—262no—
363C2×C42—262no—
364C2×C42—262no—
365C2×C42—522no—
366#95—24no—
367#95—22no—
368#95—42no—
369#95—264no—
370#95—264no—
371#95—264no—
372#95—264no—
373#95—264no—
374#95—262no—
375#95—522no—
376#95—522no—
377#95—522no—
378C2×C13#228011yescharacteristic
379C2×C13C2×#39111yescharacteristic
380C2×C13#231111yescharacteristic
381C2×C13#235512yes—
382C2×C13#235512yes—
383C2×C13#258012yes—
384C2×C13#258112yes—
385C2×C13#258412yes—
386C2×C13#259212yes—
387C24C23×D1311yescharacteristic
388C2×Q8—268no—
389C2×Q8—268no—
390C2×Q8—2616no—
391C2×Q8—2616no—
392C2×Q8—268no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
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—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—132no—
418C22×C4—134no—
419C22×C4—134no—
420C22×C4—132no—
421C22×C4—132no—
422C22×C4—132no—
423C22×C4—132no—
424C22×C4—134no—
425C22×C4—132no—
426C22×C4—134no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4C2×C4×D1312yes—
450C22×C4C2×C4×D1312yes—
451C22×C4C2×C4×D1312yes—
452C22×C4#612714yes—
453C22×C4D4×D1312yes—
454C22×C4D4×D1312yes—
455C22×C4Q8×D1314yes—
456C4⋊C4—28no—
457C4⋊C4—268no—
458C4⋊C4—2616no—
459C4⋊C4—268no—
460C4⋊C4—528no—
461C42—44no—
462C42—1316no—
463C42—268no—
464C42—268no—
465C42—524no—
466C13#1392511yescharacteristic, complemented, Sylow
467C23C22×C4×D1311yescharacteristic
468C23C2×#612712yes—
469C23C2×D4×D1311yescharacteristic
470C23C2×D4×D1311yescharacteristic
471C23#8825112yes—
472C23C2×Q8×D1312yes—
473C23#41×D1312yes—
474C23#41×D1312yes—
475C23#8825712yes—
476Q8—2632no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—134no—
505C2×C4—134no—
506C2×C4—138no—
507C2×C4—138no—
508C2×C4—134no—
509C2×C4—134no—
510C2×C4—134no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—264no—
516C2×C4—264no—
517C2×C4—264no—
518C2×C4—264no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—521no—
528C2×C4—522no—
529C2×C4—521no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4#8812614yes—
539C2×C4C22⋊C4×D1314yes—
540C22C2×#8812611yescharacteristic
541C22C2×C22⋊C4×D1311yescharacteristic
542C22#1171921612yes—
543C22D13×#11711yescharacteristic
544C22#1171923812yes—
545C22#1171925112yes—
546C22#1171925212yes—
547C22#1171925212yes—
548C22#1171926412yes—
549C22#1171927212yes—
550C22C4×Q8×D1312yes—
551C22#1171929711yescharacteristic
552C22#1171930212yes—
553C22D13×C22⋊Q812yes—
554C22#1171934112yes—
555C22#1171935311yescharacteristic
556C22#1171936912yes—
557C22D13×#12411yescharacteristic
558C22#1171939012yes—
559C22#1171940712yes—
560C22D13×C4⋊Q811yescharacteristic
561C4—24no—
562C4—24no—
563C4—44no—
564C4—42no—
565C4—82no—
566C4—138no—
567C4—264no—
568C4—264no—
569C4—524no—
570C4—522no—
571C4—1042no—
572C2#1311721711yescharacteristic
573C2D13×#39111yescharacteristic
574C2#1311742311yescharacteristic
575C2#1311778912yes—
576C2#1311779012yes—
577C2#1312019312yes—
578C2#1312020112yes—
579C2#1312022212yes—
580C2#1312032212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1436D13
hypocenterC13#13925
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
25. C2×#88141C4semidirect
72. C2×#6101Q8semidirect
466. C13#13925semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183112
C2×C4×#61012
#131131062
#131131022
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