Finite Group Databasebeta

← #15868269

Subgroups — #15868269

Order 3328.

1222 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719184C211yesmaximal, characteristic
2#13117234C211yesmaximal, characteristic, complemented
3#13115821C212yesmaximal, complemented
4#13115672C212yesmaximal
5#13115294C214yesmaximal, complemented
6C4×#88046C214yesmaximal, complemented
7C4×C13×#117C211yesmaximal, characteristic, complemented
8C2×C13×#117C2212yes—
9C22×C42×C13C2211yescharacteristic
10C2×#88184C2211yescharacteristic
11C2×#88183C2212yes—
12C2×C4×C22⋊D13C2212yes—
13C2×#88178C2211yescharacteristic
14#11719184—21no—
15#11719184—21no—
16#11719184—21no—
17#11719184—21no—
18#11719184—21no—
19#11719184—21no—
20#11719184—21no—
21#11719184—21no—
22C2×#88130C412yescomplemented
23C2×#88129C411yescharacteristic, complemented
24C2×C4×D52C411yescharacteristic, complemented
25C2×#88126C412yescomplemented
26C2×#88124C411yescharacteristic, complemented
27C2×C4×Dic26C411yescharacteristic, complemented
28C4×C13×C4⋊C4—21no—
29C4×C13×C4⋊C4—21no—
30C4×C13×C22⋊C4C2212yes—
31C4×C13×C22⋊C4C2212yes—
32C13×#376—21no—
33C43×C13—21no—
34#11718873C2212yes—
35#11718872C2212yes—
36C4×C22⋊Dic13C2212yes—
37C2×#88046C2218yes—
38#11718598—21no—
39#11718597—21no—
40C4×C4⋊Dic13—21no—
41#11718593—21no—
42#11718119C2218yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C22×C22⋊D13C2312yes—
47C22×D52C2×C411yescharacteristic
48C22×C4×D13C2×C412yes—
49C22×Dic26C2×C411yescharacteristic
50C13×#117—28no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C22⋊C4C2314yes—
53C2×C42×C13—22no—
54C2×C42×C13—22no—
55C2×C42×C13—22no—
56C2×C42×C13C2×C411yescharacteristic
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C2×C42×C13C2×C411yescharacteristic
60C2×C42×C13D411yescharacteristic
61C2×C42×C13D411yescharacteristic
62C2×C42×C13D411yescharacteristic
63C2×C42×C13D411yescharacteristic
64C2×C42×C13D411yescharacteristic
65C2×C42×C13D411yescharacteristic
66C2×C42×C13D411yescharacteristic
67C2×C42×C13D411yescharacteristic
68C2×C22⋊Dic13C2314yes—
69C2×C22⋊Dic13C2312yes—
70#88184—21no—
71#88184—21no—
72#88184—21no—
73#88184—21no—
74#88183—22no—
75#88183—22no—
76#88183—22no—
77#88183—22no—
78C4×C22⋊D13—22no—
79C4×C22⋊D13—22no—
80C4×C22⋊D13—22no—
81C4×C22⋊D13—22no—
82C2×#6103C2×C412yes—
83C2×#6103C2×C412yes—
84C2×#6103C2×C412yes—
85C2×#6103C2×C412yes—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×C4⋊Dic13C2×C411yescharacteristic
89#88178—21no—
90#88178—21no—
91#88178—21no—
92#88178—21no—
93C2×#6101C2×C412yes—
94C2×#6101C2×C412yes—
95C2×#6101C2×C412yes—
96C2×#6101C2×C412yes—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2×C412yes—
99#88130—22no—
100#88130—22no—
101#88130—22no—
102#88130—22no—
103#88129—21no—
104#88129—21no—
105#88129—21no—
106#88129—21no—
107C4×D52—21no—
108C4×D52—21no—
109C4×D52—21no—
110C4×D52—21no—
111#88126—22no—
112#88126—22no—
113#88126—22no—
114#88126—22no—
115#88124—21no—
116#88124—21no—
117#88124—21no—
118#88124—21no—
119C4×Dic26—21no—
120C4×Dic26—21no—
121C4×Dic26—21no—
122C4×Dic26—21no—
123C13×#95—22no—
124C13×#95—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88046—216no—
130#21421—131nomaximal, Sylow
131C24×C13C2411yescharacteristic
132C23×D13C22×C412yes—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C2×C22⋊D13—22no—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—28no—
158C22×Dic13—24no—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C412yes—
161C22×Dic13C22×C412yes—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—42no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—44no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—42no—
171C13×C4⋊C4—28no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4#4118yes—
174C42×C13—28no—
175C42×C13—44no—
176C42×C13—44no—
177C42×C13C22⋊C411yescharacteristic
178C42×C13C22⋊C411yescharacteristic
179C42×C13C22⋊C411yescharacteristic
180C42×C13C22⋊C411yescharacteristic
181C42×C13C22⋊C411yescharacteristic
182C42×C13C22⋊C411yescharacteristic
183C42×C13C22⋊C411yescharacteristic
184C42×C13C22⋊C411yescharacteristic
185C42×C13C22⋊C411yescharacteristic
186C42×C13C22⋊C411yescharacteristic
187C42×C13C22⋊C411yescharacteristic
188C42×C13C22⋊C411yescharacteristic
189C42×C13C22⋊C411yescharacteristic
190C42×C13C22⋊C411yescharacteristic
191C42×C13C22⋊C411yescharacteristic
192C42×C13C22⋊C411yescharacteristic
193C22⋊Dic13—22no—
194C22⋊Dic13—22no—
195C22⋊Dic13—28no—
196#6103—22no—
197#6103—22no—
198#6103—22no—
199#6103—22no—
200#6103—22no—
201#6103—22no—
202#6103—22no—
203#6103—22no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—44no—
209#6101—22no—
210#6101—22no—
211#6101—22no—
212#6101—22no—
213#6101—22no—
214#6101—22no—
215#6101—22no—
216#6101—22no—
217C4×Dic13—22no—
218C4×Dic13—22no—
219C4×Dic13—44no—
220C2×#529—131no—
221#2283—131no—
222C4×#117D1311yescharacteristic, complemented
223#1996—132no—
224#1964—132no—
225#1899—134no—
226C4×#99—134no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13C23×C411yescharacteristic
230C23×C13C22×D411yescharacteristic
231C23×C13C22×D411yescharacteristic
232C23×C13C2×#4114yes—
233C22×D13—22no—
234C22×D13—24no—
235C22×D13—42no—
236C22×D13—42no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—28no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—44no—
257C2×C4×C13—44no—
258C2×C4×C13C2×C22⋊C411yescharacteristic
259C2×C4×C13C2×C22⋊C411yescharacteristic
260C2×C4×C13C2×C22⋊C411yescharacteristic
261C2×C4×C13C2×C22⋊C411yescharacteristic
262C2×C4×C13C2×C22⋊C411yescharacteristic
263C2×C4×C13C2×C22⋊C411yescharacteristic
264C2×C4×C13C2×C22⋊C411yescharacteristic
265C2×C4×C13C2×C22⋊C411yescharacteristic
266C2×C4×C13C2×C22⋊C411yescharacteristic
267C2×C4×C13C2×C22⋊C411yescharacteristic
268C2×C4×C13C2×C22⋊C411yescharacteristic
269C2×C4×C13C2×C22⋊C411yescharacteristic
270C22⋊D13—44no—
271C22⋊D13—44no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—44no—
279C2×Dic13—44no—
280C2×Dic13—44no—
281D52—42no—
282D52—42no—
283C4×D13—44no—
284C4×D13—44no—
285Dic26—42no—
286Dic26—42no—
287#529—261no—
288#529—261no—
289#529—261no—
290#529—261no—
291#529—261no—
292#529—261no—
293#529—261no—
294#529—261no—
295C2×#126—132no—
296C2×#125—131no—
297C2×#124—131no—
298C2×#123—132no—
299C2×C22⋊Q8—131no—
300C2×#121—131no—
301C2×C4×Q8—131no—
302C2×C4×D4—132no—
303C2×C4×D4—131no—
304C2×#117—132no—
305C2×#117C2×D1312yes—
306C22×C42C2×D1311yescharacteristic
307C2×#99—138no—
308#383—261no—
309#382—261no—
310#381—132no—
311#380—132no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—21no—
314C4×C4⋊C4—261no—
315C4×C22⋊C4—132no—
316C4×C22⋊C4C2×D1312yes—
317C4×C22⋊C4C2×D1312yes—
318#376—21no—
319#376—261no—
320C43—21no—
321#342—138no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—44no—
329C22×C13C22×C22⋊C411yescharacteristic
330C22×C13C4×#4112yes—
331C22×C13#52512yes—
332C22×C13#53212yes—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—84no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—21no—
346C4×C13—21no—
347C4×C13—48no—
348C4×C13#41012yes—
349C4×C13#41012yes—
350Dic13—42no—
351Dic13—42no—
352Dic13—42no—
353Dic13—84no—
354C22×Q8—131no—
355C22×D4—132no—
356C22×D4—131no—
357C23×C4—132no—
358C23×C4C22×D1311yescharacteristic
359C23×C4C22×D1311yescharacteristic
360C23×C4C22×D1311yescharacteristic
361#126—262no—
362#126—262no—
363#126—262no—
364#126—262no—
365#125—261no—
366#125—261no—
367#125—261no—
368#125—261no—
369#124—261no—
370#124—261no—
371#124—261no—
372#124—261no—
373#123—262no—
374#123—262no—
375#123—262no—
376#123—262no—
377C22⋊Q8—261no—
378C22⋊Q8—261no—
379C22⋊Q8—261no—
380C22⋊Q8—261no—
381#121—261no—
382#121—261no—
383#121—261no—
384#121—261no—
385C4×Q8—261no—
386C4×Q8—261no—
387C4×Q8—261no—
388C4×Q8—261no—
389C4×D4—262no—
390C4×D4—262no—
391C4×D4—262no—
392C4×D4—262no—
393C4×D4—261no—
394C4×D4—261no—
395C4×D4—261no—
396C4×D4—261no—
397#117—28no—
398#117—262no—
399#117—262no—
400#117—262no—
401#117—262no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—132no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—132no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—132no—
409C2×C4⋊C4—262no—
410C2×C22⋊C4—132no—
411C2×C22⋊C4—132no—
412C2×C22⋊C4—132no—
413C2×C22⋊C4—132no—
414C2×C22⋊C4—132no—
415C2×C22⋊C4—134no—
416C2×C22⋊C4C22×D1314yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—132no—
421C2×C42—262no—
422C2×C42C4×D1311yescharacteristic
423C2×C42C4×D1311yescharacteristic
424C2×C42C4×D1311yescharacteristic
425C2×C42C4×D1311yescharacteristic
426C2×C42D5211yescharacteristic
427C2×C42D5211yescharacteristic
428C2×C42D5211yescharacteristic
429C2×C42D5211yescharacteristic
430C2×C42C22⋊D1311yescharacteristic
431C2×C42C22⋊D1311yescharacteristic
432C2×C42C22⋊D1311yescharacteristic
433C2×C42C22⋊D1311yescharacteristic
434#99—2616no—
435#95—22no—
436#95—22no—
437#95—262no—
438#95—262no—
439#95—262no—
440#95—262no—
441C2×C13—22no—
442C2×C13—22no—
443C2×C13—22no—
444C2×C13#229711yescharacteristic
445C2×C13C2×#41011yescharacteristic
446C2×C13C2×#41011yescharacteristic
447D13—82no—
448C24—132no—
449C24C23×D1311yescharacteristic
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8—522no—
453C2×D4—262no—
454C2×D4—268no—
455C2×D4—262no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—522no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—264no—
469C22×C4—524no—
470C22×C4C2×C4×D1311yescharacteristic
471C22×C4C2×C4×D1311yescharacteristic
472C22×C4C2×C4×D1311yescharacteristic
473C22×C4C2×C4×D1311yescharacteristic
474C22×C4C2×C4×D1311yescharacteristic
475C22×C4C2×C4×D1311yescharacteristic
476C22×C4C2×D5211yescharacteristic
477C22×C4C2×D5211yescharacteristic
478C22×C4C2×D5211yescharacteristic
479C22×C4C2×D5211yescharacteristic
480C22×C4C2×D5211yescharacteristic
481C22×C4C2×D5211yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C4⋊C4—28no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—262no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—262no—
496C4⋊C4—262no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—524no—
502C22⋊C4—24no—
503C22⋊C4—262no—
504C22⋊C4—262no—
505C22⋊C4—262no—
506C22⋊C4—262no—
507C22⋊C4—262no—
508C22⋊C4—262no—
509C22⋊C4—262no—
510C22⋊C4—262no—
511C22⋊C4—262no—
512C22⋊C4—262no—
513C22⋊C4—268no—
514C22⋊C4#612718yes—
515C42—28no—
516C42—44no—
517C42—44no—
518C42—262no—
519C42—262no—
520C42—524no—
521C42#610311yescharacteristic
522C42#610311yescharacteristic
523C42#610311yescharacteristic
524C42#610311yescharacteristic
525C42#610311yescharacteristic
526C42#610311yescharacteristic
527C42#610311yescharacteristic
528C42#610311yescharacteristic
529C42#610311yescharacteristic
530C42#610311yescharacteristic
531C42#610311yescharacteristic
532C42#610311yescharacteristic
533C42#610311yescharacteristic
534C42#610311yescharacteristic
535C42#610311yescharacteristic
536C42#610311yescharacteristic
537C13#2142111yescharacteristic, complemented, Sylow
538C23—41no—
539C23—41no—
540C23—262no—
541C23—264no—
542C23—522no—
543C23—522no—
544C23C22×C4×D1311yescharacteristic
545C23C22×D5211yescharacteristic
546C23C2×#612714yes—
547C23C22×C22⋊D1311yescharacteristic
548Q8—522no—
549Q8—522no—
550D4—522no—
551D4—524no—
552D4—524no—
553D4—522no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—28no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—264no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—524no—
580C2×C4—524no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—524no—
584C2×C4—524no—
585C2×C4—524no—
586C2×C4C2×#610311yescharacteristic
587C2×C4C2×#610311yescharacteristic
588C2×C4C2×#610311yescharacteristic
589C2×C4C2×#610311yescharacteristic
590C2×C4C2×#610311yescharacteristic
591C2×C4C2×#610311yescharacteristic
592C2×C4C2×#610311yescharacteristic
593C2×C4C2×#610311yescharacteristic
594C2×C4C2×#610311yescharacteristic
595C2×C4C2×#610311yescharacteristic
596C2×C4C2×#610311yescharacteristic
597C2×C4C2×#610311yescharacteristic
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—44no—
605C22—522no—
606C22—522no—
607C22—522no—
608C22—1044no—
609C22C4×#612712yes—
610C22#1171918212yes—
611C22C22×#610311yescharacteristic
612C22#1171949612yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—48no—
624C4—522no—
625C4—522no—
626C4—522no—
627C4—1044no—
628C4#1171866712yes—
629C4#1171866712yes—
630C2—22no—
631C2—22no—
632C2—22no—
633C2—1042no—
634C2#1311732611yescharacteristic
635C2C2×#1171866711yescharacteristic
636C2C2×#1171866711yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC4×C13×#117C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#88184C22
cosocleC24×C13C24
hypercenterC4×#117D13
hypocenterC13#21421
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13117234C2semidirect
3. #13115821C2semidirect
5. #13115294C2semidirect
6. C4×#88046C2semidirect
7. C4×C13×#117C2semidirect
22. C2×#88130C4semidirect
23. C2×#88129C4semidirect
24. C2×C4×D52C4semidirect
25. C2×#88126C4semidirect
26. C2×#88124C4semidirect
27. C2×C4×Dic26C4semidirect
222. C4×#117D13semidirect
537. C13#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#117191842
#131172342
#131158212
#131156722
#131152942
C4×#880462
C4×C13×#1172
#2142113