Finite Group Databasebeta

← #15791429

Subgroups — #15791429

Order 3328.

1614 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88198C211yesmaximal, characteristic
2C2×#11718891C211yesmaximal, characteristic
3#13113106C212yesmaximal
4#13113090C212yesmaximal
5#13113086C212yesmaximal
6#13113071C212yesmaximal
7#13113069C212yesmaximal
8#13113060C212yesmaximal
9C2×C13×#391C211yesmaximal, characteristic
10C23×Q8×C13C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C2×#88198—24no—
15C2×#88198—24no—
16C2×#88198C418yescomplemented
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C13×#391—24no—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25#11718891—24no—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C22×Q8×C13—41no—
37C22×Q8×C13—41no—
38C22×Q8×C13—41no—
39C22×Q8×C13—41no—
40C22×Q8×C13C2×C414yes—
41C22×Q8×C13D414yes—
42C22×Q8×C13D414yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2312yes—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—41no—
55C22×Dic26—41no—
56C22×Dic26—41no—
57C22×Dic26—41no—
58C22×Dic26C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—41no—
61C2×C13×C4⋊C4—41no—
62C2×C42×C13—22no—
63C2×C42×C13—41no—
64C2×C42×C13—41no—
65#88198—232no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—41no—
68C2×C4⋊Dic13—41no—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101C2×C418yes—
74C2×#6101C2×C418yes—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—41no—
79C2×C4×Dic13—41no—
80C2×C4×Dic13C2×C414yes—
81C13×#95—24no—
82C13×#95—24no—
83#88071—24no—
84#88071—24no—
85#88071—24no—
86#88071—24no—
87#88071—24no—
88#88071—42no—
89#88071—42no—
90#88071—42no—
91#88071—42no—
92#88071Q818yescomplemented
93#14450—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C2×Q8×C13—44no—
96C2×Q8×C13—44no—
97C2×Q8×C13—44no—
98C2×Q8×C13—44no—
99C2×Q8×C13—44no—
100C2×Q8×C13—44no—
101C2×Q8×C13C22⋊C4116yes—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
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×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×Q814yes—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
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×Dic13C22×C414yes—
161C22×Dic13C22×C414yes—
162C22×Dic13C2×Q814yes—
163C22×Dic13C2×Q814yes—
164C22×Dic13#4114yes—
165C2×Dic26—28no—
166C2×Dic26—44no—
167C2×Dic26—44no—
168C2×Dic26—44no—
169C2×Dic26—44no—
170C2×Dic26—44no—
171C2×Dic26—44no—
172C13×C4⋊C4—44no—
173C42×C13—44no—
174C4⋊Dic13—44no—
175#6101—216no—
176#6101—216no—
177C4×Dic13—28no—
178C4×Dic13—44no—
179C22×C4⋊Q8—131no—
180C2×#391—131no—
181C2×#391D1311yescharacteristic
182#1446—132no—
183#1441—132no—
184#1441—132no—
185#1436—132no—
186#1436—132no—
187#1434—132no—
188C23×C13C23×C411yescharacteristic
189C23×C13C22×D411yescharacteristic
190C23×C13C22×D411yescharacteristic
191C23×C13C22×Q812yes—
192C23×C13C2×#4112yes—
193C23×C13H(5,𝔽2)11yescharacteristic
194C23×C13H(5,𝔽2)11yescharacteristic
195C23×C13H(5,𝔽2)11yescharacteristic
196C23×C13H(5,𝔽2)11yescharacteristic
197C23×C132−1+412yes—
198C23×C132−1+412yes—
199Q8×C13—416no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13C2×C22⋊C414yes—
233C2×C4×C13C2×C22⋊C414yes—
234C2×C4×C13C2×C22⋊C414yes—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13C4×Q818yes—
263Dic26—416no—
264C23×Q8—131no—
265C23×Q8C2×D1311yescharacteristic
266C2×C4⋊Q8—138no—
267C2×C4⋊Q8—264no—
268C2×C4⋊Q8—264no—
269C22×C4⋊C4—132no—
270C22×C4⋊C4—132no—
271C22×C4⋊C4—131no—
272C22×C4⋊C4C2×D1311yescharacteristic
273C22×C42—131no—
274C22×C42—131no—
275C22×C42C2×D1311yescharacteristic
276#391—24no—
277#391—264no—
278C2×#95—132no—
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—132no—
288C2×#95C2×D1312yes—
289C2×#95C2×D1312yes—
290C22×C13C22×C22⋊C411yescharacteristic
291C22×C13C2×C4×Q812yes—
292C22×C13#51811yescharacteristic
293C22×C13#51811yescharacteristic
294C22×C13#51912yes—
295C22×C13#53411yescharacteristic
296C22×C13#53411yescharacteristic
297C22×C13#53411yescharacteristic
298C22×C13#53411yescharacteristic
299C22×C13#54212yes—
300C22×C13#54212yes—
301C22×C13#54412yes—
302C22×C13#54412yes—
303C22×C13#54812yes—
304C22×C13#54812yes—
305C22×C13D4×Q812yes—
306C22×C13D4×Q812yes—
307C22×C13#55412yes—
308C22×C13#55511yescharacteristic
309C22×C13Q8211yescharacteristic
310C22×C13#56311yescharacteristic
311C22×C13#56312yes—
312C22×C13#56311yescharacteristic
313C4×C13—24no—
314C4×C13—24no—
315C4×C13—24no—
316C4×C13—44no—
317C4×C13—82no—
318Dic13—28no—
319Dic13—44no—
320Dic13—44no—
321Dic13—82no—
322C22×Q8—41no—
323C22×Q8—41no—
324C22×Q8—41no—
325C22×Q8—41no—
326C22×Q8—134no—
327C22×Q8—262no—
328C22×Q8—262no—
329C22×Q8—521no—
330C22×Q8—521no—
331C22×Q8—521no—
332C22×Q8—521no—
333C22×Q8C4×D1314yes—
334C22×Q8D5214yes—
335C22×Q8C22⋊D1314yes—
336C23×C4—132no—
337C23×C4—132no—
338C23×C4—132no—
339C23×C4—132no—
340C23×C4C22×D1312yes—
341C23×C4C22×D1312yes—
342C23×C4C22×D1311yescharacteristic
343C23×C4C22×D1311yescharacteristic
344C23×C4C22×D1311yescharacteristic
345C4⋊Q8—2632no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—138no—
350C2×C4⋊C4—138no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—521no—
357C2×C4⋊C4—521no—
358C2×C42—22no—
359C2×C42—41no—
360C2×C42—41no—
361C2×C42—134no—
362C2×C42—262no—
363C2×C42—262no—
364C2×C42—262no—
365C2×C42—521no—
366C2×C42—521no—
367#95—24no—
368#95—24no—
369#95—138no—
370#95—264no—
371#95—264no—
372#95—264no—
373#95—264no—
374#95—264no—
375#95—522no—
376#95—522no—
377#95—522no—
378#95—522no—
379C2×C13#230811yescharacteristic
380C2×C13#233112yes—
381C2×C13Q8×C22⋊C412yes—
382C2×C13#236911yescharacteristic
383C2×C13#238111yescharacteristic
384C2×C13#272912yes—
385C2×C13#272912yes—
386C2×C13#273111yescharacteristic
387C2×C13#273111yescharacteristic
388C2×C13#273411yescharacteristic
389C2×C13#273411yescharacteristic
390C24C23×D1311yescharacteristic
391C2×Q8—44no—
392C2×Q8—44no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—268no—
398C2×Q8—524no—
399C2×Q8—524no—
400C2×Q8—524no—
401C2×Q8—524no—
402C2×Q8—524no—
403C2×Q8—524no—
404C2×Q8#6103116yes—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—134no—
434C22×C4—134no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4C2×C4×D1312yes—
459C22×C4C2×C4×D1312yes—
460C22×C4C2×C4×D1312yes—
461C22×C4C2×D5212yes—
462C22×C4C2×D5212yes—
463C22×C4C2×D5212yes—
464C22×C4Q8×D1314yes—
465C22×C4C2×C22⋊D1312yes—
466C22×C4C2×C22⋊D1312yes—
467C22×C4C2×C22⋊D1312yes—
468C4⋊C4—44no—
469C4⋊C4—2616no—
470C4⋊C4—2616no—
471C4⋊C4—524no—
472C42—44no—
473C42—268no—
474C42—524no—
475C13#1445011yescharacteristic, complemented, Sylow
476C23C22×C4×D1311yescharacteristic
477C23C22×D5211yescharacteristic
478C23#8825111yescharacteristic
479C23#8825111yescharacteristic
480C23#8825111yescharacteristic
481C23#8825111yescharacteristic
482C23C2×Q8×D1312yes—
483C23#8825412yes—
484C23#41×D1312yes—
485C23#8825712yes—
486C23C22×C22⋊D1311yescharacteristic
487Q8—416no—
488Q8—5216no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—138no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—264no—
528C2×C4—264no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4C2×#610314yes—
550C2×C4C2×#610314yes—
551C2×C4C2×#610314yes—
552C22#1171919111yescharacteristic
553C22#1171919111yescharacteristic
554C22#1171919811yescharacteristic
555C22#1171919811yescharacteristic
556C22C4×Q8×D1312yes—
557C22#1171927712yes—
558C22Q8×D5212yes—
559C22#1171928112yes—
560C22#1171932812yes—
561C22#1171934112yes—
562C22#1171934512yes—
563C22#1171935112yes—
564C22#1171937412yes—
565C22#1171937511yescharacteristic
566C22#1171937711yescharacteristic
567C22#1171942711yescharacteristic
568C22#1171943412yes—
569C22#1171944011yescharacteristic
570C22C22×#610311yescharacteristic
571C22#1171950911yescharacteristic
572C22#1171950911yescharacteristic
573C22Q8×C22⋊D1312yes—
574C22#1171953612yes—
575C4—24no—
576C4—24no—
577C4—24no—
578C4—44no—
579C4—82no—
580C4—268no—
581C4—524no—
582C4—524no—
583C4—1042no—
584C2#1311741111yescharacteristic
585C2#1311757912yes—
586C2Q8×#610312yes—
587C2#1311792411yescharacteristic
588C2#1311801511yescharacteristic
589C2#1312181412yes—
590C2#1312181612yes—
591C2#1312184411yescharacteristic
592C2#1312184511yescharacteristic
593C2#1312186611yescharacteristic
594C2#1312186811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#391D13
hypocenterC13#14450
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
16. C2×#88198C4semidirect
92. #88071Q8semidirect
475. C13#14450semidirect

Maximal subgroups

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

subgroupindex
C22×#881982
C2×#117188912
#131131062
#131130902
#131130862
#131130712
#131130692
#131130602
C2×C13×#3912
#1445013