Finite Group Databasebeta

← #15879784

Subgroups — #15879784

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719289C211yesmaximal, characteristic
2C2×#11718685C211yesmaximal, characteristic, complemented
3#13115768C211yesmaximal, characteristic
4#13115768C211yesmaximal, characteristic
5#13115759C211yesmaximal, characteristic, complemented
6#13115655C211yesmaximal, characteristic, complemented
7#13115650C211yesmaximal, characteristic
8#13115645C211yesmaximal, characteristic
9#13114848C211yesmaximal, characteristic, complemented
10#13114843C211yesmaximal, characteristic
11#13114838C211yesmaximal, characteristic, complemented
12#13114669C211yesmaximal, characteristic, complemented
13#13114664C211yesmaximal, characteristic
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2355C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200—21no—
18#11719289—24no—
19#11719289C418yescomplemented
20C2×#88152—21no—
21C2×#88152—21no—
22C2×#88146—21no—
23C2×#88129C2211yescharacteristic
24C2×#88129C2211yescharacteristic
25C2×C4×D52C2211yescharacteristic
26C2×#88123C2211yescharacteristic
27C2×C4×Dic26C2211yescharacteristic
28C2×C4×Dic26C2211yescharacteristic
29C13×#391—21no—
30C13×#387—21no—
31C13×#387—21no—
32C13×#384C2211yescharacteristic
33C13×#382C2211yescharacteristic
34C13×#382C2211yescharacteristic
35C4×C13×C4⋊C4—21no—
36C4×C13×C4⋊C4C2211yescharacteristic
37C4×C13×C4⋊C4C2211yescharacteristic
38C4×C13×C4⋊C4C2211yescharacteristic
39#11718685—24no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88050C2211yescharacteristic
45C2×#88050C2211yescharacteristic
46C2×#88050C2211yescharacteristic
47C2×#88050C2211yescharacteristic
48C2×#88049C2211yescharacteristic
49C2×#88049C2211yescharacteristic
50C2×#88049C2211yescharacteristic
51C2×#88049C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×C4⋊#1055C2211yescharacteristic
55C2×#88043C2211yescharacteristic
56C2×#88043C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13D411yescharacteristic
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×Dic26C2311yescharacteristic
66C22×Dic26C2311yescharacteristic
67C4×Q8×C13C2×C414yes—
68C4×Q8×C13D414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84#88200—28no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88152—28no—
102#88152—28no—
103#88146—28no—
104#88129—22no—
105#88129—22no—
106#88129C2×C414yes—
107#88129C2×C414yes—
108C4×D52—22no—
109C4×D52C2×C414yes—
110#88123—22no—
111#88123C2×C414yes—
112C4×Dic26—22no—
113C4×Dic26—22no—
114C4×Dic26C2×C414yes—
115C4×Dic26C2×C414yes—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119C13×#95—21no—
120C13×#95—21no—
121C13×#95—21no—
122C13×#95—21no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88050—41no—
128#88050—41no—
129#88050—41no—
130#88050—41no—
131#88049—22no—
132#88049—22no—
133#88049—41no—
134#88049—41no—
135C4⋊#1055—22no—
136C4⋊#1055—22no—
137C4⋊#1055—22no—
138#88043—22no—
139#88043—22no—
140C4×#1055—22no—
141#22548—131nomaximal, Sylow
142C23×D13—21no—
143C2×Q8×C13—41no—
144C2×Q8×C13—41no—
145C2×Q8×C13C22⋊C414yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52C22×C412yes—
166C2×C4×D13—24no—
167C2×C4×D13—42no—
168C2×C4×D13—42no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26—21no—
177C2×Dic26—21no—
178C2×Dic26—21no—
179C2×Dic26C22×C412yes—
180C2×Dic26C22×C412yes—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—42no—
189C13×C4⋊C4—81no—
190C13×C4⋊C4C22⋊C414yes—
191C13×C4⋊C4C22⋊C414yes—
192C13×C4⋊C4C22⋊C414yes—
193C13×C4⋊C4#4112yes—
194C42×C13—42no—
195C42×C13—81no—
196C42×C13—81no—
197C42×C13C22×C412yes—
198C42×C13C22×C412yes—
199C42×C13C22×C412yes—
200C42×C13C2×D412yes—
201C42×C13C2×D412yes—
202C42×C13C2×D412yes—
203#6103—24no—
204#6103—24no—
205#6103—24no—
206#6103—24no—
207#6103—24no—
208C4⋊Dic13—24no—
209C4⋊Dic13—24no—
210C4⋊Dic13—21no—
211C4⋊Dic13C22×C412yes—
212#6101—24no—
213#6101—24no—
214C4×Dic13—24no—
215C4×Dic13—24no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055#4112yes—
228C2×#556—131no—
229C2×#446—131no—
230#2355D1311yescharacteristic, complemented
231#1983—131no—
232#1983—131no—
233#1981—131no—
234#1960—131no—
235#1959—131no—
236#1958—131no—
237#1805—131no—
238#1804—131no—
239#1803—131no—
240#1763—131no—
241#1762—131no—
242C4×#103—131no—
243C23×C13C22×D411yescharacteristic
244C22×D13—22no—
245C22×D13—41no—
246C22×D13—41no—
247C22×D13—41no—
248C22×D13—41no—
249C22×D13—41no—
250C22×D13—41no—
251Q8×C13—44no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13C2×C22⋊C412yes—
277C2×C4×C13C2×C22⋊C412yes—
278C2×C4×C13C2×C22⋊C412yes—
279C2×C4×C13C2×C22⋊C412yes—
280C2×C4×C13C2×C22⋊C412yes—
281C2×C4×C13C2×C22⋊C412yes—
282C2×C4×C13C23×C411yescharacteristic
283C2×C4×C13C22×D411yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×C4×C132−1+411yescharacteristic
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297D52—22no—
298D52—22no—
299D52—41no—
300D52—41no—
301C4×D13—48no—
302Dic26—22no—
303Dic26—22no—
304Dic26—22no—
305Dic26—22no—
306Dic26—41no—
307Dic26—41no—
308Dic26—41no—
309Dic26—41no—
310#1055—22no—
311#1055—41no—
312#1055—41no—
313#1055—41no—
314#556—138no—
315#556—264no—
316C2×C4⋊Q8—131no—
317C2×#126—261no—
318C2×#126—261no—
319C2×#124—131no—
320C2×#124—131no—
321C2×C22⋊Q8—261no—
322C2×C4×Q8—131no—
323C2×C4×Q8—131no—
324C2×C4×Q8C2×D1311yescharacteristic
325C2×C4×D4—131no—
326C2×#117—261no—
327#446—264no—
328C2×C4⋊C8—131no—
329C2×C4⋊C8—131no—
330C2×C4⋊C8—131no—
331C2×#103—131no—
332C2×#103—131no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#102—131no—
340C2×#102—131no—
341C2×#102—131no—
342C2×#102—131no—
343C2×#97—131no—
344C2×#97—131no—
345C2×C4×C8—131no—
346#391—21no—
347#387—21no—
348#387—21no—
349#384C2×D1311yescharacteristic
350#382C2×D1311yescharacteristic
351#382C2×D1311yescharacteristic
352C4×C4⋊C4—21no—
353C4×C4⋊C4C2×D1311yescharacteristic
354C4×C4⋊C4C2×D1311yescharacteristic
355C4×C4⋊C4C2×D1311yescharacteristic
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360C22×C13C22×C22⋊C411yescharacteristic
361C22×C13#54811yescharacteristic
362C22×C13#55011yescharacteristic
363C22×C13#57511yescharacteristic
364C22×C13#57511yescharacteristic
365C22×C13#57711yescharacteristic
366C22×C13#57811yescharacteristic
367C2×D13—42no—
368C2×D13—42no—
369C2×D13—42no—
370C2×D13—81no—
371C2×D13—81no—
372C2×D13—81no—
373C2×D13—81no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—42no—
381C4×C13—81no—
382C4×C13—81no—
383C4×C13—81no—
384C4×C13C4×#4111yescharacteristic
385C4×C13#52011yescharacteristic
386C4×C13#54811yescharacteristic
387C4×C13#55011yescharacteristic
388Dic13—42no—
389Dic13—42no—
390Dic13—42no—
391C22×Q8—131no—
392C22×Q8—131no—
393C22×Q8C22⋊D1311yescharacteristic
394C22×D4—131no—
395C23×C4—261no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C4⋊Q8—134no—
401C4⋊Q8—262no—
402#126—268no—
403#126—268no—
404#124—134no—
405#124—134no—
406#124—262no—
407#124—262no—
408C22⋊Q8—268no—
409C4×Q8—134no—
410C4×Q8—134no—
411C4×Q8—262no—
412C4×Q8—262no—
413C4×Q8C4×D1314yes—
414C4×Q8D5214yes—
415C4×D4—134no—
416C4×D4—262no—
417#117—268no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4C22⋊D1311yescharacteristic
426C2×C4⋊C4C22⋊D1311yescharacteristic
427C2×C4⋊C4C22⋊D1311yescharacteristic
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C22⋊C4—261no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—261no—
441C2×C42—261no—
442C2×C42C22×D1311yescharacteristic
443C2×C42C22×D1311yescharacteristic
444C2×C42C22×D1311yescharacteristic
445C4⋊C8—262no—
446C4⋊C8—262no—
447C4⋊C8—262no—
448#103—262no—
449#103—262no—
450#103—262no—
451#103—262no—
452#103—521no—
453#103—521no—
454#103—521no—
455#103—521no—
456#102—262no—
457#102—262no—
458#102—521no—
459#102—521no—
460#97—262no—
461#97—262no—
462C4×C8—262no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C2×C13#234111yescharacteristic
471C2×C13#289611yescharacteristic
472C2×C13#289811yescharacteristic
473C2×C13#337611yescharacteristic
474C2×C13#337711yescharacteristic
475C2×C13#340111yescharacteristic
476C2×C13#340211yescharacteristic
477D13—82no—
478C24—261no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—132no—
482C2×Q8—132no—
483C2×Q8—261no—
484C2×Q8—261no—
485C2×Q8—261no—
486C2×Q8—261no—
487C2×Q8—261no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×Q8—261no—
491C2×Q8—261no—
492C2×Q8—261no—
493C2×Q8#610314yes—
494C2×D4—132no—
495C2×D4—261no—
496C2×D4—261no—
497C2×D4—261no—
498C2×D4—261no—
499C2×D4—261no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4—264no—
508C22×C4—522no—
509C22×C4—522no—
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C2×C22⋊D1311yescharacteristic
516C22×C4C23×D1311yescharacteristic
517C2×C8—132no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—132no—
539C4⋊C4—264no—
540C4⋊C4—264no—
541C4⋊C4—264no—
542C4⋊C4—264no—
543C4⋊C4—261no—
544C4⋊C4#610314yes—
545C4⋊C4#610314yes—
546C4⋊C4#610314yes—
547C4⋊C4#613112yes—
548C22⋊C4—264no—
549C22⋊C4—264no—
550C22⋊C4—264no—
551C22⋊C4—264no—
552C22⋊C4—264no—
553C42—42no—
554C42—81no—
555C42—81no—
556C42—264no—
557C42—264no—
558C42C2×C4×D1312yes—
559C42C2×C4×D1312yes—
560C42C2×C4×D1312yes—
561C42C2×D5212yes—
562C42C2×D5212yes—
563C42C2×D5212yes—
564C13#2254811yescharacteristic, complemented, Sylow
565C23—262no—
566C23—521no—
567C23—521no—
568C23—521no—
569C23—521no—
570C23—521no—
571C23—521no—
572C23C22×C22⋊D1311yescharacteristic
573Q8—44no—
574Q8—262no—
575Q8—262no—
576Q8—262no—
577Q8—262no—
578Q8—521no—
579Q8—521no—
580Q8—521no—
581Q8—521no—
582D4—262no—
583D4—262no—
584D4—521no—
585D4—521no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—528no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4C2×#610312yes—
621C2×C4C2×#610312yes—
622C2×C4C2×#610312yes—
623C2×C4C2×#610312yes—
624C2×C4C2×#610312yes—
625C2×C4C2×#610312yes—
626C2×C4C22×C4×D1311yescharacteristic
627C2×C4C22×D5211yescharacteristic
628C2×C4C2×#613111yescharacteristic
629C2×C4#8825411yescharacteristic
630C2×C4#41×D1311yescharacteristic
631C2×C4#8825611yescharacteristic
632C8—262no—
633C8—521no—
634C8—521no—
635C8—521no—
636C22—522no—
637C22—522no—
638C22—522no—
639C22—1041no—
640C22—1041no—
641C22—1041no—
642C22—1041no—
643C22C22×#610311yescharacteristic
644C22#1171952211yescharacteristic
645C22#1171952711yescharacteristic
646C22#1171952711yescharacteristic
647C22#1171953911yescharacteristic
648C22#1171954111yescharacteristic
649C22#1171954311yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—522no—
661C4—522no—
662C4—522no—
663C4C4×#613111yescharacteristic
664C4#1171927911yescharacteristic
665C4#1171928111yescharacteristic
666C4#1171928211yescharacteristic
667C2—1042no—
668C2#1311767411yescharacteristic
669C2#1312335311yescharacteristic
670C2#1312336611yescharacteristic
671C2#1312766311yescharacteristic
672C2#1312767811yescharacteristic
673C2#1312789611yescharacteristic
674C2#1312791111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2355C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2355D13
hypocenterC13#22548
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×#11718685C2semidirect
5. #13115759C2semidirect
6. #13115655C2semidirect
9. #13114848C2semidirect
11. #13114838C2semidirect
12. #13114669C2semidirect
14. C4×#88050C2semidirect
15. C13×#2355C2semidirect
19. #11719289C4semidirect
230. #2355D13semidirect
564. C13#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#117192892
C2×#117186852
#131157682
#131157592
#131156552
#131156502
#131156452
#131148482
#131148432
#131148382
#131146692
#131146642
C4×#880502
C13×#23552
#2254813