Finite Group Databasebeta

← #15875175

Subgroups — #15875175

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
1C2×#11718748C211yesmaximal, characteristic
2#13117480C211yesmaximal, characteristic
3#13115785C211yesmaximal, characteristic, complemented
4#13115602C211yesmaximal, characteristic, complemented
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115532C211yesmaximal, characteristic
8#13115518C211yesmaximal, characteristic
9#13115463C211yesmaximal, characteristic
10#13115456C211yesmaximal, characteristic
11#13115428C211yesmaximal, characteristic, complemented
12#13115407C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic
14#13114693C211yesmaximal, characteristic, complemented
15C13×#2331C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#391—21no—
19C13×#391—21no—
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#387—21no—
24C13×#382C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C13×#376C2211yescharacteristic
28#11718748C418yescomplemented
29C2×#88049C2211yescharacteristic
30C2×#88049C2211yescharacteristic
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718600C2211yescharacteristic
38#11718600C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718330—21no—
47#11718330—21no—
48#11718328—21no—
49#11718325—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×Q8×C13—21no—
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C13×C4⋊Q8—22no—
64C13×C4⋊Q8C2×C414yes—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×#6103—21no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C4×D52—22no—
93C4×D52C2×C414yes—
94C13×#95—21no—
95C13×#95—21no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95D411yescharacteristic
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88049—41no—
108#88049—41no—
109#88049C2×C414yes—
110#88049C2×C414yes—
111#88048—41no—
112#88047—41no—
113#88047C2×C414yes—
114#88047C2×C414yes—
115C4⋊#1055—22no—
116C4⋊#1055C2×C414yes—
117#88043—41no—
118C4×#1055—41no—
119#22127—131nomaximal, Sylow
120C23×D13—21no—
121C2×Q8×C13—24no—
122C2×Q8×C13—81no—
123C2×Q8×C13—81no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52C22×C412yes—
144C2×C4×D13—24no—
145C2×C4×D13—81no—
146C2×C4×D13—81no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—81no—
155C13×C4⋊C4—81no—
156C13×C4⋊C4C22×C412yes—
157C13×C4⋊C4C22×C412yes—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—81no—
163C42×C13—81no—
164C42×C13C22×C412yes—
165C42×C13#4112yes—
166#6103—24no—
167#6103—81no—
168#6103—81no—
169#6103—81no—
170#6103—81no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13C22×C412yes—
177#6101—81no—
178#6101—81no—
179C4×Dic13—81no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191C2×#1055C22×C412yes—
192C2×#474—131no—
193#2331D1311yescharacteristic, complemented
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×C13C22×D411yescharacteristic
208C22×D13—22no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215Q8×C13—84no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D412yes—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×C4×C132−1+411yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×Dic13—22no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261D52—22no—
262D52—22no—
263D52—41no—
264D52—41no—
265C4×D13—84no—
266#1055—22no—
267#1055—22no—
268#1055—41no—
269#1055—41no—
270C2×C4⋊Q8C2×D1311yescharacteristic
271C2×C4×D4—131no—
272#474—138no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#107—131no—
276C2×#106—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×#97—131no—
284C2×C4×C8—131no—
285#391—21no—
286#391—21no—
287#390—131no—
288#390—131no—
289#389—131no—
290#389—131no—
291#389C2×D1311yescharacteristic
292#389C2×D1311yescharacteristic
293#388—261no—
294#388—261no—
295#387—21no—
296#387—21no—
297#382C2×D1311yescharacteristic
298#381—261no—
299#380—261no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4C2×D1311yescharacteristic
302C4×C4⋊C4C2×D1311yescharacteristic
303#376C2×D1311yescharacteristic
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×C13C2×C4×D411yescharacteristic
315C22×C13#53611yescharacteristic
316C22×C13#53711yescharacteristic
317C22×C13#57611yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C22×C13#57811yescharacteristic
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—81no—
325C2×D13—81no—
326C2×D13—81no—
327C2×D13—81no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13#51911yescharacteristic
339C4×C13#52011yescharacteristic
340C4×C13#54111yescharacteristic
341C4×C13#54211yescharacteristic
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—21no—
346C22×D4—131no—
347C23×C4—261no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C4⋊Q8—22no—
353C4⋊Q8C4×D1314yes—
354C4×D4—134no—
355C4×D4—262no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—261no—
376C2×C42C22×D1311yescharacteristic
377C2×C42C22×D1311yescharacteristic
378C2×C42C22×D1311yescharacteristic
379#107—134no—
380#107—134no—
381#107—521no—
382#106—521no—
383C4⋊C8—134no—
384C4⋊C8—262no—
385#102—134no—
386#102—134no—
387#102—521no—
388#102—521no—
389#97—521no—
390C4×C8—521no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95C22⋊D1311yescharacteristic
401#95C22⋊D1311yescharacteristic
402#95C22⋊D1311yescharacteristic
403#95C22⋊D1311yescharacteristic
404C2×C13#232311yescharacteristic
405C2×C13#294711yescharacteristic
406C2×C13#294811yescharacteristic
407C2×C13#324111yescharacteristic
408C2×C13#324311yescharacteristic
409C2×C13#325711yescharacteristic
410C2×C13#326211yescharacteristic
411D13—82no—
412C24—261no—
413C2×Q8—24no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—132no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—261no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1041no—
431C22×C4—1041no—
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—132no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4C2×C4×D1312yes—
469C4⋊C4C2×C4×D1312yes—
470C22⋊C4—264no—
471C22⋊C4—1041no—
472C22⋊C4—1041no—
473C22⋊C4—1041no—
474C22⋊C4—1041no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—1041no—
482C42C2×C4×D1312yes—
483C42#612712yes—
484C13#2212711yescharacteristic, complemented, Sylow
485C23—262no—
486C23—521no—
487C23—521no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23—521no—
492C23C22×C22⋊D1311yescharacteristic
493Q8—84no—
494D4—262no—
495D4—262no—
496D4—521no—
497D4—521no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—262no—
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—1044no—
536C2×C4C4×C22⋊D1312yes—
537C2×C4C4×C22⋊D1312yes—
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C2×#612711yescharacteristic
540C2×C4#8825411yescharacteristic
541C2×C4#8825411yescharacteristic
542C2×C4#8825611yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—262no—
545C8—262no—
546C8—521no—
547C8—521no—
548C22—522no—
549C22—522no—
550C22—522no—
551C22—1041no—
552C22—1041no—
553C22—1041no—
554C22—1041no—
555C22C2×C4×C22⋊D1311yescharacteristic
556C22#1171952111yescharacteristic
557C22#1171953811yescharacteristic
558C22#1171954011yescharacteristic
559C22#1171954011yescharacteristic
560C22#1171954211yescharacteristic
561C22#1171954311yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—522no—
573C4—1041no—
574C4—1041no—
575C4#1171927711yescharacteristic
576C4#1171927911yescharacteristic
577C4#1171928711yescharacteristic
578C4#1171928811yescharacteristic
579C2—1042no—
580C2#1311751211yescharacteristic
581C2#1312367911yescharacteristic
582C2#1312368611yescharacteristic
583C2#1312608911yescharacteristic
584C2#1312611911yescharacteristic
585C2#1312624711yescharacteristic
586C2#1312629211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2331C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2331D13
hypocenterC13#22127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #13115785C2semidirect
4. #13115602C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
11. #13115428C2semidirect
12. #13115407C2semidirect
14. #13114693C2semidirect
15. C13×#2331C2semidirect
28. #11718748C4semidirect
193. #2331D13semidirect
484. C13#22127semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131174802
#131157852
#131156022
#131155712
#131155662
#131155322
#131155182
#131154632
#131154562
#131154282
#131154072
#131148432
#131146932
C13×#23312
#2212713