Finite Group Databasebeta

← #15881289

Subgroups — #15881289

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718371C211yesmaximal, characteristic
2C2×#11718371C211yesmaximal, characteristic
3C2×C4×#6095C211yesmaximal, characteristic
4C4⋊C4×Dic26C211yesmaximal, characteristic, complemented
5#13117747C211yesmaximal, characteristic
6#13115574C211yesmaximal, characteristic, complemented
7#13115569C211yesmaximal, characteristic, complemented
8#13115107C211yesmaximal, characteristic, complemented
9#13115100C211yesmaximal, characteristic
10#13115093C211yesmaximal, characteristic, complemented
11#13115086C211yesmaximal, characteristic
12#13115004C211yesmaximal, characteristic, complemented
13#13114852C211yesmaximal, characteristic, complemented
14#13114837C211yesmaximal, characteristic
15C13×#1771C211yesmaximal, characteristic, complemented
16C22×#6095C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88061C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88058C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88057C2211yescharacteristic
35C2×#88057C2211yescharacteristic
36C2×#88056C2211yescharacteristic
37C2×#88056C2211yescharacteristic
38C2×#88056C2211yescharacteristic
39#11718650—21no—
40#11718650—21no—
41#11718637—21no—
42C4⋊C4×Dic13—21no—
43#11718597C2211yescharacteristic
44#11718596C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718371—24no—
50#11718371C418yescomplemented
51C4×#6095—24no—
52#11718328—21no—
53D13×#95—21no—
54#11718308—21no—
55#11718308—21no—
56C13×#336C2211yescharacteristic
57C13×#336C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718143C2211yescharacteristic
61#11718143C2211yescharacteristic
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×Dic26C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×#6103—21no—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×#6095C2×C414yes—
98C2×#6095D414yes—
99C2×#6095Q814yes—
100C4×D52—22no—
101C4×D52—22no—
102C4×D52—22no—
103C4×D52—41no—
104C4×D52—41no—
105C4×D52C2×C414yes—
106C4×Dic26—22no—
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—41no—
110C4×Dic26—41no—
111C4×Dic26C2×C414yescomplemented
112C13×C4⋊C8—22no—
113C13×#97—22no—
114C13×#97C2×C414yescomplemented
115C4×C8×C13—22no—
116C13×#95D411yescharacteristic
117C13×#95D411yescharacteristic
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88061—22no—
125#88061—22no—
126#88061C2×C414yes—
127#88058—22no—
128#88058—41no—
129#88058C2×C414yescomplemented
130#88057—22no—
131#88057—41no—
132#88056—22no—
133#88056—22no—
134#88056C2×C414yescomplemented
135#22678—131nomaximal, Sylow
136C23×D13—21no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52C22×C412yes—
155C2×D52C2×D412yes—
156C2×D52C2×Q812yes—
157C2×C4×D13—24no—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C2×C4×D13—42no—
162C2×C4×D13—81no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C2×C4×D13—81no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26C22×C412yes—
170C2×Dic26C2×D412yes—
171C2×Dic26C2×Q812yes—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13C22×C412yes—
181C2×C8×C13C22×C412yes—
182C2×C8×C13C2×D412yes—
183C2×C8×C13C2×Q812yes—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—41no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13C22×C412yes—
191C42×C13#4112yes—
192#6103—24no—
193#6103—42no—
194#6103—42no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—42no—
206C4⋊Dic13—81no—
207C4⋊Dic13C22×C412yes—
208C4⋊Dic13C22×C412yes—
209#6101—24no—
210#6101—42no—
211#6101—42no—
212#6101—81no—
213#6101—81no—
214#6101—81no—
215#6101—81no—
216C4×Dic13—24no—
217C4×Dic13—42no—
218C4×Dic13—42no—
219#6095C4⋊C4116yescomplemented
220C2×#440—131no—
221C2×#440—131no—
222C2×C4×SD16—131no—
223Q8×C4⋊C4—131no—
224#2349—131no—
225#1943—131no—
226#1942—131no—
227#1865—131no—
228#1864—131no—
229#1863—131no—
230#1862—131no—
231#1847—131no—
232#1805—131no—
233#1802—131no—
234#1771D1311yescharacteristic, complemented
235C23×C13C22×D411yescharacteristic
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
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—21no—
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×C13C4×D412yes—
259C2×C4×C13C4×D412yes—
260C2×C4×C13#13712yes—
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C22×Q811yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13H(5,𝔽2)11yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288D52—22no—
289D52—22no—
290D52—22no—
291D52C2×C4⋊C414yes—
292C4×D13—84no—
293C4×D13—84no—
294C4×D13—84no—
295Dic26—22no—
296Dic26—22no—
297Dic26—22no—
298Dic26C2×C4⋊C414yes—
299C8×C13—22no—
300C8×C13—41no—
301C8×C13—41no—
302C8×C13C2×C4⋊C414yes—
303C22×SD16—131no—
304C2×C4×Q8—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×D4—131no—
308C2×C4×D4—131no—
309C2×C4×D4—131no—
310#440—138no—
311#440—264no—
312C4×SD16—264no—
313C2×#107—131no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#106—131no—
317C2×#106—131no—
318C2×C4⋊C8C2×D1311yescharacteristic
319C2×#103—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#102—131no—
323C2×#102—131no—
324C2×#102—131no—
325C2×#97C2×D1311yescharacteristic
326C2×#97C2×D1311yescharacteristic
327C2×C4×C8C2×D1311yescharacteristic
328#389—131no—
329#389—131no—
330#389—131no—
331#389—131no—
332#389—261no—
333#389—261no—
334#385—261no—
335#385—261no—
336#384—131no—
337#384—261no—
338#382—131no—
339#380—261no—
340C4×C4⋊C4—261no—
341C4×C4⋊C4C2×D1311yescharacteristic
342C2×#95—261no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#336C2×D1311yescharacteristic
348#336C2×D1311yescharacteristic
349C22×C13C2×C4×D411yescharacteristic
350C22×C13D4211yescharacteristic
351C22×C13D4×Q811yescharacteristic
352C22×C13C2×#13711yescharacteristic
353C22×C13#57511yescharacteristic
354C22×C13#57611yescharacteristic
355C22×C13#57711yescharacteristic
356C2×D13—24no—
357C2×D13—42no—
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—42no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13C22×C4⋊C411yescharacteristic
370C4×C13#52011yescharacteristic
371C4×C13#54711yescharacteristic
372C4×C13#55411yescharacteristic
373Dic13—24no—
374Dic13—42no—
375Dic13—42no—
376Dic13—81no—
377Dic13—81no—
378Dic13—81no—
379Dic13—81no—
380C22×Q8—131no—
381C22×D4—131no—
382C23×C4—261no—
383C23×C4—261no—
384C23×C4—261no—
385C2×SD16—134no—
386C2×SD16—134no—
387C2×SD16—134no—
388C22×C8C22×D1311yescharacteristic
389C22×C8C22×D1311yescharacteristic
390C22×C8C22×D1311yescharacteristic
391C22×C8C22×D1311yescharacteristic
392C4×Q8—134no—
393C4×Q8—262no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—521no—
397C4×Q8—521no—
398C4×D4—134no—
399C4×D4—262no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4—521no—
403C4×D4—521no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4D5211yescharacteristic
420C2×C4⋊C4D5211yescharacteristic
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430#107—134no—
431#107—262no—
432#107—521no—
433#106—262no—
434#106—521no—
435C4⋊C8—22no—
436#103—134no—
437#103—262no—
438#103—262no—
439#102—134no—
440#102—262no—
441#102—262no—
442#97—22no—
443#97C4×D1314yescomplemented
444C4×C8—22no—
445#95—261no—
446#95—261no—
447#95—261no—
448#95—261no—
449#95—261no—
450#95—261no—
451#95D5211yescharacteristic
452#95D5211yescharacteristic
453C2×C13D4×C4⋊C411yescharacteristic
454C2×C13C4×#13711yescharacteristic
455C2×C13#294611yescharacteristic
456C2×C13#326611yescharacteristic
457C2×C13#326811yescharacteristic
458C2×C13#338511yescharacteristic
459C2×C13#338811yescharacteristic
460D13—44no—
461C24—261no—
462C2×Q8—132no—
463C2×Q8—132no—
464C2×Q8—132no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×D4—132no—
469C2×D4—132no—
470C2×D4—132no—
471C2×D4—261no—
472C2×D4—261no—
473C2×D4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—264no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—522no—
483C22×C4—522no—
484C22×C4—522no—
485C22×C4—522no—
486C22×C4—1041no—
487C22×C4—1041no—
488C22×C4—1041no—
489C22×C4—1041no—
490C22×C4C2×D5211yescharacteristic
491C22×C4C2×D5211yescharacteristic
492C22×C4C2×D5211yescharacteristic
493C22×C4C2×D5211yescharacteristic
494C22×C4C2×D5211yescharacteristic
495C22×C4C2×D5211yescharacteristic
496C22×C4C23×D1311yescharacteristic
497SD16—1316no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×C4×D1312yes—
507C2×C8C2×C4×D1312yes—
508C2×C8D4×D1312yes—
509C2×C8Q8×D1312yes—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—132no—
513C4⋊C4—132no—
514C4⋊C4—264no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—522no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4—1041no—
529C4⋊C4—1041no—
530C4⋊C4—1041no—
531C4⋊C4—1041no—
532C4⋊C4—1041no—
533C22⋊C4—264no—
534C22⋊C4—522no—
535C22⋊C4—522no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—264no—
541C42—522no—
542C42—522no—
543C42C2×C4×D1312yes—
544C42#612712yes—
545C13#2267811yescharacteristic, complemented, Sylow
546C23—262no—
547C23—262no—
548C23—262no—
549C23—521no—
550C23—521no—
551C23—521no—
552C23—521no—
553C23C22×D5211yescharacteristic
554Q8—134no—
555Q8—262no—
556Q8—262no—
557Q8—262no—
558D4—134no—
559D4—262no—
560D4—262no—
561D4—262no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
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—521no—
597C2×C4—521no—
598C2×C4—1044no—
599C2×C4—1044no—
600C2×C4—1044no—
601C2×C4C4×D5212yes—
602C2×C4C4×D5212yes—
603C2×C4#8816312yes—
604C2×C4C22×C4×D1311yescharacteristic
605C2×C4C2×#612711yescharacteristic
606C2×C4C2×D4×D1311yescharacteristic
607C2×C4C2×Q8×D1311yescharacteristic
608C2×C4#8825611yescharacteristic
609C2×C4#8825711yescharacteristic
610C8—22no—
611C8—41no—
612C8—41no—
613C8C4⋊C4×D1314yes—
614C22—264no—
615C22—522no—
616C22—522no—
617C22—522no—
618C22—522no—
619C22—522no—
620C22—522no—
621C22C2×C4×D5211yescharacteristic
622C22D4×D5211yescharacteristic
623C22Q8×D5211yescharacteristic
624C22C2×#8816311yescharacteristic
625C22#1171945311yescharacteristic
626C22#1171945611yescharacteristic
627C22#1171945711yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—264no—
635C4—522no—
636C4—522no—
637C4—1041no—
638C4—1041no—
639C4—1041no—
640C4—1041no—
641C4C2×C4⋊C4×D1311yescharacteristic
642C4#1171922811yescharacteristic
643C4#1171925611yescharacteristic
644C4#1171928411yescharacteristic
645C2—524no—
646C2C4⋊C4×D5211yescharacteristic
647C2C4×#8816311yescharacteristic
648C2#1312367011yescharacteristic
649C2#1312635111yescharacteristic
650C2#1312638111yescharacteristic
651C2#1312774811yescharacteristic
652C2#1312778311yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1771C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1771D13
hypocenterC13#22678
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic26C2semidirect
6. #13115574C2semidirect
7. #13115569C2semidirect
8. #13115107C2semidirect
10. #13115093C2semidirect
12. #13115004C2semidirect
13. #13114852C2semidirect
15. C13×#1771C2semidirect
50. #11718371C4semidirect
111. C4×Dic26C2×C4semidirect
114. C13×#97C2×C4semidirect
129. #88058C2×C4semidirect
134. #88056C2×C4semidirect
219. #6095C4⋊C4semidirect
234. #1771D13semidirect
443. #97C4×D13semidirect
545. C13#22678semidirect

Maximal subgroups

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

subgroupindex
C2×#117183712
C2×C4×#60952
C4⋊C4×Dic262
#131177472
#131155742
#131155692
#131151072
#131151002
#131150932
#131150862
#131150042
#131148522
#131148372
C13×#17712
#2267813