Finite Group Databasebeta

← #15875181

Subgroups — #15875181

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×#11718668C211yesmaximal, characteristic
2#13117584C211yesmaximal, characteristic, complemented
3#13115784C211yesmaximal, characteristic, complemented
4#13115604C211yesmaximal, characteristic, complemented
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic
8#13115522C211yesmaximal, characteristic
9#13115460C211yesmaximal, characteristic
10#13115453C211yesmaximal, characteristic
11#13115425C211yesmaximal, characteristic, complemented
12#13115404C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic
14#13114693C211yesmaximal, characteristic, complemented
15C13×#2319C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88123C2211yescharacteristic
18C13×#390C2211yescharacteristic
19C13×#390C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#388—21no—
23C13×#388—21no—
24C13×#381—21no—
25C13×#380—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C13×#376C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718668C418yescomplemented
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718315—21no—
47#11718315—21no—
48#11718307—21no—
49#11718307—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×Dic26—21no—
63C4×D4×C13—22no—
64C4×D4×C13C2×C414yes—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92#88123—22no—
93#88123C2×C414yes—
94C13×#95—21no—
95C13×#95—21no—
96C13×#95—21no—
97C13×#95D411yescharacteristic
98C13×#95D411yescharacteristic
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101#88072—41no—
102#88072—41no—
103#88072C2×C414yes—
104#88072C2×C414yes—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
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
120C24×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13C22×C412yes—
127C22×C4×C13—21no—
128C22×C4×C13—24no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—81no—
132C22×C4×C13—81no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C2×Dic26—24no—
145C2×Dic26—81no—
146C2×Dic26—81no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—81no—
153C13×C4⋊C4—81no—
154C13×C4⋊C4C22×C412yes—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—81no—
157C13×C22⋊C4—81no—
158C13×C22⋊C4—81no—
159C13×C22⋊C4—81no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—81no—
165C42×C13C22×C412yes—
166C42×C13#4112yes—
167C4⋊Dic13—24no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13C22×C412yes—
175C4⋊Dic13C22×C412yes—
176#6101—81no—
177#6101—81no—
178C4×Dic13—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#2331—131no—
194#2319D1311yescharacteristic
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
215D4×C13—22no—
216D4×C13—22no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
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—21no—
235C2×C4×C13—21no—
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×C13—84no—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C4×D412yes—
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×C4×C132−1+411yescharacteristic
253C2×Dic13—22no—
254C2×Dic13—22no—
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—
265Dic26—84no—
266#1055—22no—
267#1055—22no—
268#1055—41no—
269#1055—41no—
270C2×C4⋊Q8—131no—
271C2×C4×D4C2×D1311yescharacteristic
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—261no—
286#391—261no—
287#390C2×D1311yescharacteristic
288#390C2×D1311yescharacteristic
289#389—131no—
290#389—131no—
291#389C2×D1311yescharacteristic
292#389C2×D1311yescharacteristic
293#388—21no—
294#388—21no—
295#387—261no—
296#387—261no—
297#382—131no—
298#381—21no—
299#380—21no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
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×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—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13#51911yescharacteristic
338C4×C13#52011yescharacteristic
339C4×C13#54111yescharacteristic
340C4×C13#54211yescharacteristic
341Dic13—42no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—261no—
346C22×D4C22×D1311yescharacteristic
347C23×C4—21no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C4⋊Q8—134no—
353C4⋊Q8—262no—
354C4×D4—22no—
355C4×D4C4×D1314yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
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—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42—261no—
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—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95C22⋊D1311yescharacteristic
401#95C22⋊D1311yescharacteristic
402#95C22⋊D1311yescharacteristic
403#95C22⋊D1311yescharacteristic
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—264no—
414C2×Q8—1041no—
415C2×Q8—1041no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D1312yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
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—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—132no—
459C4⋊C4—132no—
460C4⋊C4—264no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C4⋊C4C2×C4×D1312yes—
470C22⋊C4—24no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—1041no—
481C42—1041no—
482C42C2×C4×D1312yes—
483C42#612712yes—
484C13#2212711yescharacteristic, complemented, Sylow
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×C22⋊D1311yescharacteristic
493Q8—1044no—
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—21no—
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—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—262no—
525C2×C4—262no—
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×C4C4×C22⋊D1312yes—
537C2×C4C4×C22⋊D1312yes—
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C2×#612711yescharacteristic
540C2×C4#8825611yescharacteristic
541C2×C4#8825711yescharacteristic
542C2×C4#8825711yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—262no—
545C8—262no—
546C8—521no—
547C8—521no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×C4×C22⋊D1311yescharacteristic
556C22#1171953011yescharacteristic
557C22#1171953811yescharacteristic
558C22#1171954011yescharacteristic
559C22#1171954011yescharacteristic
560C22#1171954111yescharacteristic
561C22#1171954311yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—522no—
572C4—522no—
573C4—1041no—
574C4—1041no—
575C4#1171922111yescharacteristic
576C4#1171922311yescharacteristic
577C4#1171922811yescharacteristic
578C4#1171923911yescharacteristic
579C2—82no—
580C2#1311751811yescharacteristic
581C2#1312367511yescharacteristic
582C2#1312368611yescharacteristic
583C2#1312608311yescharacteristic
584C2#1312611311yescharacteristic
585C2#1312624111yescharacteristic
586C2#1312629211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2319C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2319D13
hypocenterC13#22127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13117584C2semidirect
3. #13115784C2semidirect
4. #13115604C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
11. #13115425C2semidirect
12. #13115404C2semidirect
14. #13114693C2semidirect
32. #11718668C4semidirect
484. C13#22127semidirect

Maximal subgroups

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

subgroupindex
C2×#117186682
#131175842
#131157842
#131156042
#131155712
#131155662
#131155362
#131155222
#131154602
#131154532
#131154252
#131154042
#131148462
#131146932
C13×#23192
#2212713