Finite Group Databasebeta

← #15919174

Subgroups — #15919174

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718716C211yesmaximal, characteristic, complemented
2C2×#11718742C211yesmaximal, characteristic, complemented
3#13120657C211yesmaximal, characteristic, complemented
4#13116079C212yesmaximal, complemented
5#13116072C212yesmaximal, complemented
6#13115657C211yesmaximal, characteristic, complemented
7#13115648C211yesmaximal, characteristic, complemented
8#13114776C212yesmaximal
9#13114771C212yesmaximal, complemented
10#13114602C211yesmaximal, characteristic, complemented
11C2×C13×#536C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C23×Q8×C13C2211yescharacteristic
14C13×#536—24no—
15C13×#536—24no—
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C13×#124C2211yescharacteristic
20C2×C13×#123—21no—
21C2×C13×#123—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×#117C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31C2×#88075C2212yes—
32C2×#88072C2212yes—
33C2×#88072C2212yes—
34#11718873C2212yes—
35C2×C22⋊#1055C2212yes—
36#11718742—24no—
37#11718716—24no—
38#11718647—21no—
39#11718640—21no—
40#11718610—21no—
41#11718608—21no—
42#11718597C2211yescharacteristic
43#11718589C2212yes—
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718116C2212yes—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—24no—
50C2×C13×#41—42no—
51C22×Q8×C13—22no—
52C22×Q8×C13—22no—
53C22×Q8×C13—21no—
54C22×Q8×C13—24no—
55C22×Q8×C13—42no—
56C22×Q8×C13C2311yescharacteristic
57C22×Q8×C13C2311yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×Dic26—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8D414yes—
69C13×#124—22no—
70C13×#124—22no—
71C13×#124—22no—
72C13×#124D414yes—
73C13×#123—28no—
74C13×#123—28no—
75C13×C22⋊Q8—28no—
76C13×C22⋊Q8—28no—
77C13×#117—22no—
78C13×#117—22no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4D411yescharacteristic
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C22⋊Dic13—22no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2312yes—
97C2×#6101—22no—
98C22×#1055C2312yes—
99C22×#1055C2312yes—
100#88123—22no—
101#88123—22no—
102#88075—24no—
103#88075—24no—
104#88075—24no—
105#88075—42no—
106#88075—42no—
107#88075—42no—
108#88072—24no—
109#88072—42no—
110#88071—22no—
111#88071—21no—
112#88071—21no—
113#88071—22no—
114C22⋊#1055—24no—
115#88043—22no—
116C4×#1055—22no—
117#25866—131nomaximal, Sylow
118C24×C13—21no—
119C24×C13C2×D411yescharacteristic
120C13×#41—48no—
121C13×#41—48no—
122C2×Q8×C13—24no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—22no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—22no—
132C2×Q8×C13—48no—
133C2×Q8×C13—48no—
134C2×Q8×C13—42no—
135C2×Q8×C13—42no—
136C2×Q8×C13C2×D412yes—
137C2×Q8×C13C2×D412yes—
138C2×Q8×C13C2×D412yes—
139C2×D4×C13—24no—
140C2×D4×C13—21no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—42no—
144C2×D4×C13—42no—
145C2×D4×C13C2×D412yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13#4114yes—
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—22no—
166C22×Dic13—22no—
167C2×Dic26—42no—
168C2×Dic26—82no—
169C13×C4⋊C4—24no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C22⋊C4—24no—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—24no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13C2×D412yes—
184C42×C13C2×D412yes—
185C22⋊Dic13—82no—
186C4⋊Dic13—22no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189C4⋊Dic13—22no—
190C4⋊Dic13—42no—
191#6101—82no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#536D1311yescharacteristic
199C2×#489—131no—
200C2×#487—131no—
201#2628—131no—
202#2043—132no—
203#2042—132no—
204#1960—131no—
205#1958—131no—
206#1788—132no—
207#1787—132no—
208#1750—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13#12412yes—
219C23×C13C22×D411yescharacteristic
220Q8×C13—24no—
221Q8×C13—24no—
222Q8×C13—24no—
223Q8×C13—48no—
224Q8×C13—42no—
225Q8×C13—42no—
226Q8×C13—42no—
227D4×C13—24no—
228D4×C13—48no—
229D4×C13—42no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—48no—
244C2×C4×C13—48no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13#12012yes—
252C2×C4×C13#12012yes—
253C2×C4×C13#12412yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4112yes—
257C2×C4×C13H(5,𝔽2)12yes—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264Dic26—84no—
265#1055—42no—
266#1055—42no—
267C22×#41C2×D1311yescharacteristic
268C23×Q8C2×D1311yescharacteristic
269#536—24no—
270#536—24no—
271C2×C4⋊Q8—131no—
272C2×C4⋊Q8C2×D1311yescharacteristic
273C2×C4⋊Q8C2×D1311yescharacteristic
274C2×#124C2×D1311yescharacteristic
275C2×#124C2×D1311yescharacteristic
276C2×#123—21no—
277C2×#123—21no—
278C2×C22⋊Q8—21no—
279C2×C22⋊Q8—21no—
280C2×#117C2×D1311yescharacteristic
281#489—264no—
282#487—264no—
283C2×#103—132no—
284C2×#103—132no—
285C2×#103—132no—
286C2×#103—132no—
287C2×#103—132no—
288C2×#103—132no—
289C2×#102—132no—
290C2×#102—132no—
291C2×C22⋊C8—132no—
292C2×#97—131no—
293C2×C4×C8—131no—
294#400—261no—
295#399—261no—
296#395—261no—
297#393—261no—
298#389—132no—
299#382—131no—
300#380—132no—
301#336—132no—
302C22×C13—24no—
303C22×C13—22no—
304C22×C13—42no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—82no—
311C22×C13—82no—
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×#12411yescharacteristic
314C22×C13#53511yescharacteristic
315C22×C13#57712yes—
316C22×C13#57812yes—
317C4×C13—22no—
318C4×C13—22no—
319C4×C13—22no—
320C4×C13—42no—
321C4×C13—42no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13#54612yes—
326C4×C13#54612yes—
327Dic13—82no—
328Dic13—82no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—24no—
332C2×#41—42no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—21no—
336C22×Q8—24no—
337C22×Q8—42no—
338C22×Q8—261no—
339C22×Q8C22×D1311yescharacteristic
340C22×Q8C22×D1311yescharacteristic
341C22×Q8C22×D1311yescharacteristic
342C22×D4—21no—
343C22×D4C22×D1311yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4C22×D1311yescharacteristic
347C22×C8—132no—
348C22×C8—132no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—262no—
353C4⋊Q8—262no—
354C4⋊Q8C22⋊D1314yes—
355#124—22no—
356#124—22no—
357#124—22no—
358#124C22⋊D1314yes—
359#123—28no—
360#123—28no—
361C22⋊Q8—28no—
362C22⋊Q8—28no—
363#117—22no—
364#117—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—132no—
370C2×C4⋊C4—132no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4C22⋊D1311yescharacteristic
374C2×C4⋊C4C22⋊D1311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—262no—
380C2×C22⋊C4C22⋊D1311yescharacteristic
381C2×C22⋊C4C22⋊D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383C2×C42C22×D1311yescharacteristic
384#103—264no—
385#103—264no—
386#103—264no—
387#103—522no—
388#103—522no—
389#103—522no—
390#102—264no—
391#102—522no—
392C22⋊C8—264no—
393#97—262no—
394C4×C8—262no—
395#95—262no—
396#95—261no—
397#95—261no—
398#95—262no—
399C2×C13—42no—
400C2×C13—82no—
401C2×C13#243511yescharacteristic
402C2×C13#301011yescharacteristic
403C2×C13#301111yescharacteristic
404C2×C13#313712yes—
405C2×C13#322512yes—
406C24—21no—
407C24C2×C22⋊D1311yescharacteristic
408#41—48no—
409#41—48no—
410C2×Q8—24no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—48no—
421C2×Q8—48no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—522no—
425C2×Q8—1042no—
426C2×Q8C2×C22⋊D1312yes—
427C2×Q8C2×C22⋊D1312yes—
428C2×Q8C2×C22⋊D1312yes—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4C2×C22⋊D1312yes—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4#612914yes—
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C23×D1311yescharacteristic
457C2×C8—262no—
458C2×C8—262no—
459C2×C8—262no—
460C2×C8—262no—
461C2×C8—262no—
462C2×C8—262no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—262no—
473C4⋊C4—522no—
474C4⋊C4—1042no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—1042no—
482C42—21no—
483C42—21no—
484C42C2×C22⋊D1312yes—
485C42C2×C22⋊D1312yes—
486C13#2586611yescharacteristic, complemented, Sylow
487C23—21no—
488C23—22no—
489C23—22no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—42no—
495C23—42no—
496C23#8819012yes—
497C23C22×C22⋊D1311yescharacteristic
498Q8—24no—
499Q8—24no—
500Q8—24no—
501Q8—48no—
502Q8—42no—
503Q8—42no—
504Q8—42no—
505Q8—1044no—
506D4—24no—
507D4—48no—
508D4—42no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—48no—
523C2×C4—48no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4#8819012yes—
537C2×C4#8820712yes—
538C2×C4#8820712yes—
539C2×C4C2×#612912yes—
540C2×C4#8825112yes—
541C2×C4C22×C22⋊D1311yescharacteristic
542C2×C4C22×C22⋊D1311yescharacteristic
543C8—522no—
544C8—522no—
545C22—22no—
546C22—24no—
547C22—41no—
548C22—41no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—82no—
554C22—82no—
555C22C2×#8819011yescharacteristic
556C22#1171951011yescharacteristic
557C22#1171954212yes—
558C22#1171954312yes—
559C22C2×#8820711yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—1042no—
569C4—1042no—
570C4#1171951112yes—
571C4#1171951112yes—
572C2—42no—
573C2—82no—
574C2#1311848311yescharacteristic
575C2#1312412211yescharacteristic
576C2#1312413111yescharacteristic
577C2#1312520112yes—
578C2#1312594512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#536C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenterC2×#536D13
hypocenterC13#25866
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#11718716C2semidirect
2. C2×#11718742C2semidirect
3. #13120657C2semidirect
4. #13116079C2semidirect
5. #13116072C2semidirect
6. #13115657C2semidirect
7. #13115648C2semidirect
9. #13114771C2semidirect
10. #13114602C2semidirect
486. C13#25866semidirect

Maximal subgroups

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

subgroupindex
C2×#117187162
C2×#117187422
#131206572
#131160792
#131160722
#131156572
#131156482
#131147762
#131147712
#131146022
C2×C13×#5362
#2586613