Finite Group Databasebeta

← #15799641

Subgroups — #15799641

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718322C211yesmaximal, characteristic
2C2×#11718641C211yesmaximal, characteristic
3C2×#11718644C211yesmaximal, characteristic
4C2×#11718633C211yesmaximal, characteristic
5C2×#11718637C211yesmaximal, characteristic
6C2×#11718637C212yesmaximal
7#13113100C212yesmaximal
8#13113099C212yesmaximal
9#13113064C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic
11C2×C13×#398C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×#6101C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C13×#398—24no—
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36#11718644—24no—
37#11718641—24no—
38#11718637—28no—
39#11718637—24no—
40#11718633—24no—
41#11718322—24no—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—42no—
62C2×C4⋊Dic13—24no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—24no—
67C2×C4⋊Dic13—42no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—22no—
71C2×#6101—22no—
72C2×#6101—24no—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—42no—
84C2×#6101—42no—
85C2×#6101—42no—
86C2×#6101—42no—
87C2×#6101D414yes—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13D414yes—
92C2×C4×Dic13Q818yes—
93C13×#95—24no—
94C13×#95D414yes—
95#88071—24no—
96#88071—22no—
97#88071—22no—
98#88071—24no—
99#88071—24no—
100#88071D414yes—
101#88071Q818yes—
102#15145—131nomaximal, Sylow
103C24×C13C2411yescharacteristic
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D414yes—
133C22×C4×C13C2×Q814yes—
134C22×C4×C13C2×Q814yes—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13C2×D412yes—
161C22×Dic13C2×D414yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13C2×Q814yes—
166C22×Dic13C2×Q814yes—
167C22×Dic13C2×Q814yes—
168C22×Dic13C2×Q814yes—
169C22×Dic13#4112yes—
170C22×Dic13#4114yes—
171C13×C4⋊C4—48no—
172C13×C4⋊C4—44no—
173C13×C4⋊C4—44no—
174C4⋊Dic13—48no—
175C4⋊Dic13—44no—
176#6101—28no—
177#6101—48no—
178#6101—48no—
179#6101—48no—
180#6101—44no—
181#6101—48no—
182#6101—44no—
183C4×Dic13—216no—
184C4×Dic13—28no—
185C2×#398—131no—
186C2×#398—131no—
187C2×#398—131no—
188C2×#398D1311yescharacteristic
189C2×#389—131no—
190C2×#384—132no—
191C2×#384—131no—
192#1444—132no—
193#1444—132no—
194C4⋊#95—132no—
195C4×#95—131no—
196C23×C13C22×D411yescharacteristic
197C23×C13C22×D411yescharacteristic
198C23×C13C22×D411yescharacteristic
199C23×C13C22×D411yescharacteristic
200C23×C13C22×Q812yes—
201C23×C13C22×Q812yes—
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4112yes—
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C13H(5,𝔽2)11yescharacteristic
206C23×C132−1+412yes—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13#12714yes—
237C2×C4×C13C4⋊Q818yes—
238C2×Dic13—24no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—41no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13#12114yes—
268C2×Dic13C22⋊Q818yes—
269C2×Dic13#12314yes—
270C2×Dic13#12518yes—
271C2×Dic13C4⋊Q818yes—
272C2×Dic13C4⋊Q814yes—
273C2×Dic13C4⋊Q814yes—
274C22×C4⋊C4—131no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—132no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4C2×D1311yescharacteristic
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C4⋊C4C2×D1312yes—
286C22×C42—132no—
287C22×C42—131no—
288#398—24no—
289#398—264no—
290#398—264no—
291#398—264no—
292#389—264no—
293#384—264no—
294#384—268no—
295C2×#95—131no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—131no—
301C2×#95—131no—
302C2×#95C2×D1312yes—
303C2×#95C2×D1311yescharacteristic
304C22×C13C2×#12111yescharacteristic
305C22×C13C2×C22⋊Q812yes—
306C22×C13C2×#12311yescharacteristic
307C22×C13C2×#12512yes—
308C22×C13C2×#12711yescharacteristic
309C22×C13C2×C4⋊Q811yescharacteristic
310C22×C13C2×C4⋊Q812yes—
311C22×C13C2×C4⋊Q811yescharacteristic
312C22×C13C2×C4⋊Q812yes—
313C22×C13#53511yescharacteristic
314C22×C13#53611yescharacteristic
315C22×C13#54412yes—
316C22×C13#54412yes—
317C22×C13D4211yescharacteristic
318C22×C13D4211yescharacteristic
319C22×C13#54712yes—
320C22×C13#54712yes—
321C22×C13D4×Q812yes—
322C22×C13#55011yescharacteristic
323C22×C13#55011yescharacteristic
324C22×C13#55412yes—
325C22×C13#55412yes—
326C22×C13#55712yes—
327C4×C13—28no—
328C4×C13—24no—
329C4×C13—42no—
330C4×C13—81no—
331C4×C13—82no—
332Dic13—28no—
333Dic13—24no—
334Dic13—42no—
335Dic13—81no—
336Dic13—82no—
337Dic13#39818yescomplemented
338C23×C4—131no—
339C23×C4—132no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—132no—
343C23×C4—131no—
344C23×C4C22×D1312yes—
345C23×C4C22×D1311yescharacteristic
346C23×C4C22×D1311yescharacteristic
347C23×C4C22×D1311yescharacteristic
348C23×C4C22×D1312yes—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—134no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—264no—
362C2×C4⋊C4—264no—
363C2×C4⋊C4—264no—
364C2×C4⋊C4—264no—
365C2×C4⋊C4—264no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—264no—
369C2×C4⋊C4—264no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—264no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—522no—
380C2×C4⋊C4—522no—
381C2×C4⋊C4—522no—
382C2×C4⋊C4—522no—
383C2×C4⋊C4—522no—
384C2×C42—134no—
385C2×C42—138no—
386C2×C42—264no—
387C2×C42—264no—
388C2×C42—264no—
389#95—24no—
390#95—134no—
391#95—138no—
392#95—262no—
393#95—262no—
394#95—264no—
395#95—264no—
396#95—264no—
397#95C22⋊D1314yes—
398C2×C13C2×#39811yescharacteristic
399C2×C13#244012yes—
400C2×C13#244012yes—
401C2×C13#250111yescharacteristic
402C2×C13#250211yescharacteristic
403C2×C13#254111yescharacteristic
404C2×C13#254611yescharacteristic
405C2×C13#255212yes—
406C2×C13#255212yes—
407C2×C13#266011yescharacteristic
408C2×C13#286811yescharacteristic
409C24C23×D1311yescharacteristic
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—134no—
437C22×C4—134no—
438C22×C4—132no—
439C22×C4—134no—
440C22×C4—132no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—262no—
446C22×C4—261no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—261no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—262no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—261no—
469C22×C4—262no—
470C22×C4D4×D1312yes—
471C22×C4D4×D1312yes—
472C22×C4D4×D1312yes—
473C22×C4Q8×D1314yes—
474C22×C4Q8×D1314yes—
475C22×C4C2×C22⋊D1312yes—
476C22×C4C2×C22⋊D1314yes—
477C4⋊C4—48no—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C4⋊C4—268no—
481C4⋊C4—528no—
482C4⋊C4—528no—
483C4⋊C4—528no—
484C4⋊C4—524no—
485C4⋊C4—528no—
486C4⋊C4—528no—
487C4⋊C4—524no—
488C4⋊C4—524no—
489C42—2616no—
490C42—268no—
491C13#1514511yescharacteristic, complemented, Sylow
492C23C2×D4×D1311yescharacteristic
493C23C2×D4×D1311yescharacteristic
494C23C2×D4×D1311yescharacteristic
495C23#8825111yescharacteristic
496C23C2×Q8×D1312yes—
497C23C2×Q8×D1312yes—
498C23#41×D1312yes—
499C23#41×D1311yescharacteristic
500C23#8825611yescharacteristic
501C23#8825712yes—
502C23C22×C22⋊D1311yescharacteristic
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—134no—
533C2×C4—134no—
534C2×C4—138no—
535C2×C4—134no—
536C2×C4—138no—
537C2×C4—138no—
538C2×C4—134no—
539C2×C4—262no—
540C2×C4—264no—
541C2×C4—264no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—521no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—522no—
568C2×C4#8819414yes—
569C2×C4#8819818yes—
570C22#1171930411yescharacteristic
571C22D13×#12111yescharacteristic
572C22#1171931211yescharacteristic
573C22#1171931411yescharacteristic
574C22#1171932812yes—
575C22D13×C22⋊Q812yes—
576C22#1171933712yes—
577C22#1171934112yes—
578C22#1171935311yescharacteristic
579C22D13×#12311yescharacteristic
580C22#1171936012yes—
581C22#1171939012yes—
582C22D13×#12512yes—
583C22#1171939412yes—
584C22#1171939512yes—
585C22D13×C4⋊Q812yes—
586C22D13×C4⋊Q811yescharacteristic
587C22D13×C4⋊Q811yescharacteristic
588C22D4×C22⋊D1311yescharacteristic
589C22C2×#8819411yescharacteristic
590C22C2×#8819812yes—
591C22#1171952912yes—
592C22#1171953911yescharacteristic
593C4—28no—
594C4—24no—
595C4—42no—
596C4—82no—
597C4—81no—
598C4—138no—
599C4—268no—
600C4—264no—
601C4—522no—
602C4—1042no—
603C4—1041no—
604C2D13×#39811yescharacteristic
605C2#1311853312yes—
606C2#1311853512yes—
607C2#1311930511yescharacteristic
608C2#1311930911yescharacteristic
609C2#1311977911yescharacteristic
610C2#1311982011yescharacteristic
611C2#1311986612yes—
612C2#1311986812yes—
613C2#1312095911yescharacteristic
614C2#1312323211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC2×C13×#398C2
hypercenterC2×#398D13
hypocenterC13#15145
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
337. Dic13#398semidirect
491. C13#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#117183222
C2×#117186412
C2×#117186442
C2×#117186332
C2×#117186372
#131131002
#131130992
#131130642
#95×Dic132
C2×C13×#3982
#1514513