Finite Group Databasebeta

← #15920638

Subgroups — #15920638

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117703C211yesmaximal, characteristic
2#13116403C211yesmaximal, characteristic, complemented
3#13116337C211yesmaximal, characteristic, complemented
4#13116332C211yesmaximal, characteristic, complemented
5#13116171C211yesmaximal, characteristic, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115602C211yesmaximal, characteristic, complemented
8#13115425C211yesmaximal, characteristic, complemented
9#13115411C211yesmaximal, characteristic, complemented
10#13115029C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114920C211yesmaximal, characteristic
13#13114863C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#2442C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C2×#88131—21no—
21C13×#400—21no—
22C13×#398—21no—
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#385—21no—
26C13×#382C2211yescharacteristic
27C13×#380—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88048C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36#11718604—21no—
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718314—21no—
44#11718314—21no—
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C13×#125—22no—
63C13×#125—41no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—41no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13Q814yes—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C22×#1055—22no—
93C22×#1055—22no—
94C22×#1055—41no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88131—44no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113#88048—22no—
114#88048—41no—
115#88047—22no—
116#88047—41no—
117C4⋊#1055—22no—
118C4⋊#1055—41no—
119#25996—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×Q812yes—
138C22×C4×C13#4112yes—
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—24no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—42no—
146C22×Dic13—42no—
147C13×C4⋊C4—21no—
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—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—81no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4#4112yes—
160C13×C22⋊C4—22no—
161C13×C22⋊C4—22no—
162C13×C22⋊C4—42no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C22⋊Dic13—42no—
168C4⋊Dic13—24no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13C2×Q812yes—
176C4⋊Dic13C2×Q812yes—
177#6101—42no—
178#6101—42no—
179C4×Dic13—42no—
180C4×Dic13—42no—
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×#1055—21no—
191C2×#1055—21no—
192C2×#1055—44no—
193C2×#1055#4112yes—
194#2442D1311yescharacteristic
195#2344—131no—
196#2101—131no—
197#2088—131no—
198#2087—131no—
199#2059—131no—
200#1989—131no—
201#1949—131no—
202#1921—131no—
203#1919—131no—
204#1853—131no—
205#1850—131no—
206#1823—131no—
207#1808—131no—
208C2×#340—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C22⋊Q812yes—
214C23×C13#13512yes—
215C23×C13AGL(1,ℤ/8)12yes—
216C23×C13C22×D411yescharacteristic
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
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—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—84no—
248C2×C4×C13C22⋊Q812yes—
249C2×C4×C13C22×Q811yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—48no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268#1055—22no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272C23×C8—131no—
273C2×#125C2×D1311yescharacteristic
274C2×#117—261no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4C2×D1311yescharacteristic
277C2×#107—131no—
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×C4⋊C8—131no—
282C2×C4⋊C8—131no—
283C2×C22⋊C8—131no—
284#400—21no—
285#398—21no—
286#389—131no—
287#389—131no—
288#389C2×D1311yescharacteristic
289#389C2×D1311yescharacteristic
290#387—261no—
291#387—261no—
292#385—21no—
293#382C2×D1311yescharacteristic
294#381—261no—
295#380—21no—
296#380—131no—
297#380C2×D1311yescharacteristic
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C22⋊C4C2×D1311yescharacteristic
301#340—131no—
302#340—131no—
303#340—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#340—131no—
313#336—131no—
314#336—131no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13#47814yes—
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13#54611yescharacteristic
324C22×C13#54711yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57811yescharacteristic
329C4×C13—22no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13#53311yescharacteristic
339C4×C13#54411yescharacteristic
340C4×C13#55111yescharacteristic
341C4×C13#55211yescharacteristic
342Dic13—42no—
343Dic13—42no—
344Dic13—81no—
345Dic13—81no—
346C23×C4—21no—
347C23×C4—261no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—262no—
354C22×C8—262no—
355C22×C8—521no—
356#125—22no—
357#125—41no—
358#117—524no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4C22⋊D1311yescharacteristic
382C2×C22⋊C4C22⋊D1311yescharacteristic
383C2×C42—261no—
384C2×C42—261no—
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#107—262no—
388#107—521no—
389#106—262no—
390#106—521no—
391C4⋊C8—262no—
392C4⋊C8—521no—
393C22⋊C8—262no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95C22⋊D1311yescharacteristic
405#95C22⋊D1311yescharacteristic
406C2×C13—24no—
407C2×C13#243811yescharacteristic
408C2×C13C2×#47811yescharacteristic
409C2×C13#308211yescharacteristic
410C2×C13#329611yescharacteristic
411C2×C13#330811yescharacteristic
412C2×C13#333611yescharacteristic
413C2×C13#334511yescharacteristic
414C24C2×C22⋊D1311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4—264no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—522no—
432C22×C4—522no—
433C22×C4Q8×D1312yes—
434C22×C4#613112yes—
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441C2×C8—132no—
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—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—524no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—132no—
467C4⋊C4—132no—
468C4⋊C4—264no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C4⋊C4#612912yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—42no—
481C22⋊C4—522no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—522no—
487C42—522no—
488C13#2599611yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23#8820012yes—
494C23#8820312yes—
495C23#8820412yes—
496C23C22×C22⋊D1311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
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—41no—
527C2×C4—84no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—528no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4#8820012yes—
542C2×C4C2×#612911yescharacteristic
543C2×C4#8825111yescharacteristic
544C2×C4C2×Q8×D1311yescharacteristic
545C2×C4C2×#613111yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—262no—
549C8—521no—
550C8—521no—
551C8—521no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22#1171872714yes—
559C22#1171951111yescharacteristic
560C22C2×#8820011yescharacteristic
561C22C2×#8820311yescharacteristic
562C22C2×#8820411yescharacteristic
563C22#1171952911yescharacteristic
564C22#1171954111yescharacteristic
565C22#1171954311yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—522no—
576C4—522no—
577C4—1041no—
578C4—1041no—
579C4#1171932711yescharacteristic
580C4#1171932811yescharacteristic
581C4#1171934211yescharacteristic
582C4#1171934711yescharacteristic
583C2—24no—
584C2#1311850811yescharacteristic
585C2C2×#1171872711yescharacteristic
586C2#1312467211yescharacteristic
587C2#1312667111yescharacteristic
588C2#1312682711yescharacteristic
589C2#1312719811yescharacteristic
590C2#1312730011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2442C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2442D13
hypocenterC13#25996
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
2. #13116403C2semidirect
3. #13116337C2semidirect
4. #13116332C2semidirect
5. #13116171C2semidirect
6. #13115794C2semidirect
7. #13115602C2semidirect
8. #13115425C2semidirect
9. #13115411C2semidirect
488. C13#25996semidirect

Maximal subgroups

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

subgroupindex
#131177032
#131164032
#131163372
#131163322
#131161712
#131157942
#131156022
#131154252
#131154112
#131150292
#131150162
#131149202
#131148632
C2×#117181212
C13×#24422
#2599613