Finite Group Databasebeta

← #15875185

Subgroups — #15875185

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117585C211yesmaximal, characteristic, complemented
2#13117479C211yesmaximal, characteristic
3#13115785C211yesmaximal, characteristic, complemented
4#13115606C211yesmaximal, characteristic, complemented
5#13115575C211yesmaximal, characteristic, complemented
6#13115570C211yesmaximal, characteristic, complemented
7#13115535C211yesmaximal, characteristic
8#13115521C211yesmaximal, characteristic
9#13115465C211yesmaximal, characteristic
10#13115458C211yesmaximal, characteristic
11#13115430C211yesmaximal, characteristic, complemented
12#13115409C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic
14#13114695C211yesmaximal, characteristic, complemented
15C2×C13×#474C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C13×#474C418yescomplemented
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24#11718891—21no—
25#11718891—21no—
26#11718882C2211yescharacteristic
27#11718882C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30#11718873—21no—
31#11718872—21no—
32C2×#88058C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718646C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718646C2211yescharacteristic
40#11718642—21no—
41#11718642—21no—
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718612—21no—
45#11718612—21no—
46#11718597C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718593C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8C2×C414yes—
67C4×D4×C13—22no—
68C4×D4×C13C2×C414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C13×#107C2×C414yes—
95C13×#107C2×C414yes—
96C13×C4⋊C8C2×C414yes—
97C13×#102C2×C414yes—
98C13×#102C2×C414yes—
99#88072—41no—
100#88072—41no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88071D411yescharacteristic
113#88071D411yescharacteristic
114#88058—41no—
115#88057—41no—
116#88055—41no—
117C8×Dic13—41no—
118C4⋊#1055—22no—
119#22127—131nomaximal, Sylow
120C24×C13—21no—
121C2×Q8×C13—24no—
122C2×Q8×C13—81no—
123C2×Q8×C13—81no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C22×C412yes—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—24no—
134C22×C4×C13—81no—
135C22×C4×C13—81no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13C22×C412yes—
152C2×C8×C13C22×C412yes—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4C22×C412yes—
158C13×C4⋊C4C22×C412yes—
159C13×C4⋊C4C22×C412yes—
160C13×C22⋊C4—24no—
161C42×C13C22×C412yes—
162C42×C13#4112yes—
163C22⋊Dic13—81no—
164C22⋊Dic13—81no—
165C22⋊Dic13—81no—
166C22⋊Dic13—81no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—81no—
176C4⋊Dic13—81no—
177C4⋊Dic13—81no—
178C4⋊Dic13—81no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—81no—
184C4×Dic13—81no—
185C4×Dic13—81no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#474D1311yescharacteristic
193#2331—131no—
194#2319—131no—
195#1987—131no—
196#1949—131no—
197#1943—131no—
198#1942—131no—
199#1936—131no—
200#1934—131no—
201#1926—131no—
202#1925—131no—
203#1921—131no—
204#1918—131no—
205#1804—131no—
206#1768—131no—
207C23×C13—22no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13C22×D411yescharacteristic
215Q8×C13—84no—
216D4×C13—22no—
217D4×C13—22no—
218D4×C13—41no—
219D4×C13—41no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—84no—
234C2×C4×C13C4×D412yes—
235C2×C4×C13C4×D412yes—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C8×C13—22no—
267C8×C13—22no—
268#1055—41no—
269#1055—41no—
270C2×C4⋊Q8C2×D1311yescharacteristic
271C2×C4×D4C2×D1311yescharacteristic
272#474Dic1318yescomplemented
273C2×#107—131no—
274C2×#107C2×D1311yescharacteristic
275C2×#107C2×D1311yescharacteristic
276C2×#106—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8C2×D1311yescharacteristic
279C2×#102—131no—
280C2×#102—131no—
281C2×#102C2×D1311yescharacteristic
282C2×#102C2×D1311yescharacteristic
283C2×#97—131no—
284C2×C4×C8—131no—
285#391—261no—
286#391—261no—
287#390—131no—
288#390—131no—
289#389—131no—
290#389—131no—
291#389—131no—
292#389—131no—
293#388—261no—
294#388—261no—
295#387—261no—
296#387—261no—
297#382—131no—
298#381—261no—
299#380—261no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303#376—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#336—131no—
313#336—131no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13C2×C4×D411yescharacteristic
322C22×C13#53611yescharacteristic
323C22×C13#53711yescharacteristic
324C22×C13#57611yescharacteristic
325C22×C13#57611yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57811yescharacteristic
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—42no—
333C4×C13#51911yescharacteristic
334C4×C13#52011yescharacteristic
335C4×C13#54111yescharacteristic
336C4×C13#54211yescharacteristic
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—21no—
346C22×D4C22×D1311yescharacteristic
347C23×C4—21no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C4⋊Q8—22no—
353C4⋊Q8C2×Dic1314yes—
354C4×D4—22no—
355C4×D4C2×Dic1314yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—261no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—261no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42C22×D1311yescharacteristic
379#107—521no—
380#107C2×Dic1314yes—
381#107C2×Dic1314yes—
382#106—521no—
383C4⋊C8—262no—
384C4⋊C8C2×Dic1314yes—
385#102—521no—
386#102—521no—
387#102C2×Dic1314yes—
388#102C2×Dic1314yes—
389#97—521no—
390C4×C8—521no—
391#95—131no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404C2×C13—82no—
405C2×C13#232311yescharacteristic
406C2×C13#294711yescharacteristic
407C2×C13#294811yescharacteristic
408C2×C13#324111yescharacteristic
409C2×C13#324311yescharacteristic
410C2×C13#325711yescharacteristic
411C2×C13#326211yescharacteristic
412C24—21no—
413C2×Q8—24no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C22×Dic1312yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4D4×D1311yescharacteristic
437C22×C4D4×D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8C22×Dic1312yes—
450C2×C8C22×Dic1312yes—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—1041no—
464C4⋊C4—1041no—
465C4⋊C4—1041no—
466C4⋊C4—1041no—
467C4⋊C4C22×Dic1312yes—
468C4⋊C4C22×Dic1312yes—
469C4⋊C4C22×Dic1312yes—
470C22⋊C4—24no—
471C22⋊C4—1041no—
472C22⋊C4—1041no—
473C22⋊C4—1041no—
474C22⋊C4—1041no—
475C42—261no—
476C42—261no—
477C42—261no—
478C42—261no—
479C42—1041no—
480C42—1041no—
481C42—1041no—
482C42#612912yes—
483C42C22×Dic1312yes—
484C13#2212711yescharacteristic, complemented, Sylow
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C2×D4×D1311yescharacteristic
493Q8—84no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—84no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4D4×Dic1312yes—
537C2×C4D4×Dic1312yes—
538C2×C4C2×#612911yescharacteristic
539C2×C4#8825411yescharacteristic
540C2×C4#8825411yescharacteristic
541C2×C4#8825611yescharacteristic
542C2×C4#8825711yescharacteristic
543C2×C4C23×Dic1311yescharacteristic
544C8—22no—
545C8—22no—
546C8—521no—
547C8—521no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22#1171933311yescharacteristic
556C22#1171933411yescharacteristic
557C22#1171946211yescharacteristic
558C22#1171946211yescharacteristic
559C22#1171948311yescharacteristic
560C22#1171948411yescharacteristic
561C22C2×D4×Dic1311yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—521no—
568C4—521no—
569C4—521no—
570C4—521no—
571C4—1041no—
572C4—1041no—
573C4—1041no—
574C4—1041no—
575C4#1171933011yescharacteristic
576C4#1171934811yescharacteristic
577C4#1171951711yescharacteristic
578C4#1171953211yescharacteristic
579C2—82no—
580C2#1311752011yescharacteristic
581C2#1312368011yescharacteristic
582C2#1312368811yescharacteristic
583C2#1312609611yescharacteristic
584C2#1312611611yescharacteristic
585C2#1312625411yescharacteristic
586C2#1312629611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#474C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#474D13
hypocenterC13#22127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #13117585C2semidirect
3. #13115785C2semidirect
4. #13115606C2semidirect
5. #13115575C2semidirect
6. #13115570C2semidirect
11. #13115430C2semidirect
12. #13115409C2semidirect
14. #13114695C2semidirect
18. C13×#474C4semidirect
272. #474Dic13semidirect
484. C13#22127semidirect

Maximal subgroups

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

subgroupindex
#131175852
#131174792
#131157852
#131156062
#131155752
#131155702
#131155352
#131155212
#131154652
#131154582
#131154302
#131154092
#131148462
#131146952
C2×C13×#4742
#2212713