Finite Group Databasebeta

← #15918768

Subgroups — #15918768

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C211yesmaximal, characteristic
2C2×#11718726C211yesmaximal, characteristic, complemented
3C2×#11718725C211yesmaximal, characteristic, complemented
4#13116174C211yesmaximal, characteristic, complemented
5#13116174C211yesmaximal, characteristic, complemented
6#13116169C211yesmaximal, characteristic, complemented
7#13116164C211yesmaximal, characteristic, complemented
8#13115804C211yesmaximal, characteristic, complemented
9#13115796C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic
11#13115033C211yesmaximal, characteristic
12#13115028C211yesmaximal, characteristic
13#13115023C211yesmaximal, characteristic
14#13114602C211yesmaximal, characteristic
15C13×#2629C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20#11719224—24no—
21#11719224—24no—
22C2×#88144—21no—
23C2×#88142—21no—
24C2×#88132—21no—
25C2×#88132—21no—
26C2×#88124C2211yescharacteristic
27C2×#88124C2211yescharacteristic
28C2×#88123C2211yescharacteristic
29C2×#88123C2211yescharacteristic
30C13×#398—21no—
31C13×#398—21no—
32C13×#396—21no—
33C13×#396—21no—
34C13×#389C2211yescharacteristic
35C13×#389C2211yescharacteristic
36C13×#384C2211yescharacteristic
37C13×#380C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718726—24no—
42#11718725—24no—
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48C2×#88047C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C22×Dic26—21no—
66C22×Dic26—21no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#117—22no—
70C13×#117—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—21no—
90#88180—22no—
91#88180—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×#6101—21no—
104C2×#6101—21no—
105C2×C4×Dic13—21no—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110#88144—28no—
111#88142—28no—
112#88132—28no—
113#88132—28no—
114#88124—22no—
115#88124—22no—
116#88124—22no—
117#88124D414yes—
118#88123—22no—
119#88123—22no—
120#88123—22no—
121#88123D414yes—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95—21no—
126C22⋊#1055Q814yescomplemented
127C22⋊#1055Q814yescomplemented
128#88048—22no—
129#88048—22no—
130#88048—22no—
131#88048—22no—
132#88047—22no—
133#88047—22no—
134#88047—22no—
135#88047—22no—
136#88043—22no—
137C4×#1055—22no—
138#25822—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×Q812yes—
154C22×C4×C13C2×Q812yes—
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—24no—
161C22×Dic13—81no—
162C22×Dic13—81no—
163C2×Dic26—24no—
164C2×Dic26—24no—
165C2×Dic26—81no—
166C2×Dic26—81no—
167C2×Dic26—81no—
168C2×Dic26—81no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4—81no—
182C13×C4⋊C4—81no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4—81no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—81no—
188C13×C22⋊C4—81no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13C2×D412yes—
192C42×C13C2×D412yes—
193C22⋊Dic13—24no—
194C4⋊Dic13—24no—
195C4⋊Dic13—24no—
196C4⋊Dic13—24no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C2×D412yes—
202C4⋊Dic13C2×D412yes—
203C4⋊Dic13C2×D412yes—
204C4⋊Dic13C2×D412yes—
205#6101—24no—
206#6101—24no—
207#6101—24no—
208#6101—24no—
209C4×Dic13—24no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055C2×Q812yes—
219C2×#1055C2×Q812yes—
220C2×#1055C2×Q812yes—
221C2×#1055C2×Q812yes—
222C2×#544—131no—
223C2×#501—131no—
224C2×#499—131no—
225#2629D1311yescharacteristic
226#2059—131no—
227#2059—131no—
228#2058—131no—
229#2057—131no—
230#1992—131no—
231#1990—131no—
232#1854—131no—
233#1854—131no—
234#1853—131no—
235#1852—131no—
236#1750—131no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13C4⋊Q812yes—
244C23×C13C22×D411yescharacteristic
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
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—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
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#12012yes—
274C2×C4×C13#12012yes—
275C2×C4×C13C4⋊Q812yes—
276C2×C4×C13C22×D411yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C22×Q811yescharacteristic
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C132−1+411yescharacteristic
281C2×C4×C132−1+411yescharacteristic
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—84no—
295Dic26—84no—
296Dic26—84no—
297#1055—22no—
298#1055—22no—
299#1055—22no—
300#1055—22no—
301#544—264no—
302#544—264no—
303C2×C4⋊Q8—131no—
304C2×C4⋊Q8—131no—
305C2×C4⋊Q8—261no—
306C2×#125—131no—
307C2×#125—131no—
308C2×#125—261no—
309C2×#125C2×D1311yescharacteristic
310C2×C22⋊Q8—261no—
311C2×C22⋊Q8—261no—
312C2×#117—131no—
313C2×#117C2×D1311yescharacteristic
314C22×C4⋊C4—131no—
315#501—264no—
316#499—264no—
317C2×#107—131no—
318C2×#107—131no—
319C2×#107—131no—
320C2×#107—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×#106—131no—
324C2×#106—131no—
325C2×C22⋊C8—131no—
326C2×C22⋊C8—131no—
327C2×#97—131no—
328C2×C4×C8—131no—
329#398—21no—
330#398—21no—
331#396—21no—
332#396—21no—
333#389C2×D1311yescharacteristic
334#389C2×D1311yescharacteristic
335#384C2×D1311yescharacteristic
336#380C2×D1311yescharacteristic
337#380C2×D1311yescharacteristic
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#336—131no—
347#336—131no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13C2×#12011yescharacteristic
356C22×C13C2×C4⋊Q811yescharacteristic
357C22×C13#53611yescharacteristic
358C22×C13#57611yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57711yescharacteristic
361C22×C13#57811yescharacteristic
362C4×C13—22no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13—81no—
370C4×C13—81no—
371C4×C13D4×Q811yescharacteristic
372C4×C13D4×Q811yescharacteristic
373C4×C13D4×Q811yescharacteristic
374C4×C13D4×Q811yescharacteristic
375Dic13—42no—
376Dic13—42no—
377Dic13—42no—
378Dic13—42no—
379C22×Q8—261no—
380C22×Q8—261no—
381C23×C4—261no—
382C23×C4C22×D1311yescharacteristic
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C22×C8—131no—
387C4⋊Q8—134no—
388C4⋊Q8—262no—
389C4⋊Q8—262no—
390C4⋊Q8—268no—
391C4⋊Q8—262no—
392#125—22no—
393#125—22no—
394#125—134no—
395#125—262no—
396#125—262no—
397#125—268no—
398#125—262no—
399C22⋊Q8—268no—
400C22⋊Q8—268no—
401#117—22no—
402#117—22no—
403#117—262no—
404#117—262no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4C22⋊D1311yescharacteristic
425C2×C4⋊C4C22⋊D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C4⋊C4C22×D1311yescharacteristic
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C22⋊C4C22⋊D1311yescharacteristic
435C2×C42—261no—
436C2×C42C22×D1311yescharacteristic
437C2×C42C22×D1311yescharacteristic
438#107—262no—
439#107—262no—
440#107—262no—
441#107—262no—
442#106—262no—
443#106—262no—
444#106—262no—
445#106—262no—
446C22⋊C8—134no—
447C22⋊C8—134no—
448#97—262no—
449C4×C8—262no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454C2×C13—42no—
455C2×C13#243411yescharacteristic
456C2×C13#301211yescharacteristic
457C2×C13#301311yescharacteristic
458C2×C13#316311yescharacteristic
459C2×C13#316411yescharacteristic
460C2×C13#324111yescharacteristic
461C2×C13#324211yescharacteristic
462C24C2×C22⋊D1311yescharacteristic
463C2×Q8—264no—
464C2×Q8—264no—
465C2×Q8—1041no—
466C2×Q8—1041no—
467C2×Q8—1041no—
468C2×Q8—1041no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—264no—
482C22×C4—1041no—
483C22×C4—1041no—
484C22×C4Q8×D1312yes—
485C22×C4Q8×D1312yes—
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C23×D1311yescharacteristic
492C2×C8—132no—
493C2×C8—132no—
494C2×C8—132no—
495C2×C8—132no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—81no—
517C4⋊C4—81no—
518C4⋊C4—81no—
519C4⋊C4—81no—
520C4⋊C4—132no—
521C4⋊C4—132no—
522C4⋊C4—132no—
523C4⋊C4—132no—
524C4⋊C4—264no—
525C4⋊C4—264no—
526C4⋊C4—264no—
527C4⋊C4—264no—
528C4⋊C4—264no—
529C4⋊C4—264no—
530C4⋊C4—264no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C22⋊C4—264no—
540C42—21no—
541C42—21no—
542C42—264no—
543C42D4×D1312yes—
544C42D4×D1312yes—
545C13#2582211yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23#8819812yes—
553C23C22×C22⋊D1311yescharacteristic
554Q8—1044no—
555Q8—1044no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—1044no—
597C2×C4#8819112yes—
598C2×C4#8819112yes—
599C2×C4#8819812yes—
600C2×C4C2×D4×D1311yescharacteristic
601C2×C4C2×D4×D1311yescharacteristic
602C2×C4C2×Q8×D1311yescharacteristic
603C2×C4C2×Q8×D1311yescharacteristic
604C2×C4#8825711yescharacteristic
605C2×C4#8825711yescharacteristic
606C8—262no—
607C8—262no—
608C8—262no—
609C8—262no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22C2×#8819111yescharacteristic
618C22C2×#8819811yescharacteristic
619C22#1171953011yescharacteristic
620C22#1171954011yescharacteristic
621C22#1171954111yescharacteristic
622C22#1171954211yescharacteristic
623C22#1171954311yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—522no—
634C4—522no—
635C4—522no—
636C4—522no—
637C4#1171933711yescharacteristic
638C4#1171933711yescharacteristic
639C4#1171933711yescharacteristic
640C4#1171933711yescharacteristic
641C2—42no—
642C2#1311848111yescharacteristic
643C2#1312413711yescharacteristic
644C2#1312414811yescharacteristic
645C2#1312536211yescharacteristic
646C2#1312537011yescharacteristic
647C2#1312608311yescharacteristic
648C2#1312609811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2629C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2629D13
hypocenterC13#25822
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
2. C2×#11718726C2semidirect
3. C2×#11718725C2semidirect
4. #13116174C2semidirect
5. #13116174C2semidirect
6. #13116169C2semidirect
7. #13116164C2semidirect
8. #13115804C2semidirect
9. #13115796C2semidirect
126. C22⋊#1055Q8semidirect
127. C22⋊#1055Q8semidirect
545. C13#25822semidirect

Maximal subgroups

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

subgroupindex
C2×#117192242
C2×#117187262
C2×#117187252
#131161742
#131161692
#131161642
#131158042
#131157962
#131150332
#131150282
#131150232
#131146022
C13×#26292
#2582213