Finite Group Databasebeta

← #15920526

Subgroups — #15920526

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118532C211yesmaximal, characteristic
2#13117707C211yesmaximal, characteristic
3#13116396C211yesmaximal, characteristic, complemented
4#13116328C211yesmaximal, characteristic, complemented
5#13116325C211yesmaximal, characteristic, complemented
6#13116162C211yesmaximal, characteristic, complemented
7#13115786C211yesmaximal, characteristic, complemented
8#13115591C211yesmaximal, characteristic, complemented
9#13115409C211yesmaximal, characteristic, complemented
10#13115405C211yesmaximal, characteristic, complemented
11#13115013C211yesmaximal, characteristic
12#13114923C211yesmaximal, characteristic
13#13114863C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#1852C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C2×#88178—21no—
19C23×#1055C2211yescharacteristic
20C2×#88142C2211yescharacteristic
21C2×#88131—21no—
22C2×C13×#107C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C13×#380C2211yescharacteristic
26#11718873C2211yescharacteristic
27#11718871—21no—
28C4×C22⋊Dic13C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31#11718646C2211yescharacteristic
32#11718645—21no—
33#11718640—21no—
34#11718637C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39#11718634C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718604—21no—
43#11718315—21no—
44#11718315—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×Dic26—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—41no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13D411yescharacteristic
75C2×C22⋊Dic13D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13Q814yescomplemented
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84#88178—44no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055—22no—
96C22×#1055—22no—
97C22×#1055—41no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88142—22no—
101#88142—41no—
102#88131—44no—
103C13×#107—22no—
104C13×#107—41no—
105C13×C22⋊C8—22no—
106C13×#95—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071D411yescharacteristic
115#88071D411yescharacteristic
116#88054—22no—
117#88054—41no—
118#88047—22no—
119#88047—41no—
120#25988—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
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—21no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—81no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×Q812yes—
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—24no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—42no—
143C22×Dic13—42no—
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C2×Dic26—42no—
149C2×Dic26—42no—
150C2×Dic26—81no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4#4112yes—
166C13×C22⋊C4—42no—
167C22⋊Dic13—22no—
168C22⋊Dic13—42no—
169C22⋊Dic13D814yes—
170C4⋊Dic13—24no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—42no—
178C4⋊Dic13C2×Q812yes—
179C4⋊Dic13C2×Q812yes—
180#6101—42no—
181#6101—42no—
182#6101—42no—
183#6101—42no—
184#6101—42no—
185#6101—81no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—44no—
198C2×#1055#4112yes—
199#2440—131no—
200#2344—131no—
201#2099—131no—
202#2086—131no—
203#2086—131no—
204#2057—131no—
205#1988—131no—
206#1947—131no—
207#1918—131no—
208#1918—131no—
209#1852D1311yescharacteristic
210#1850—131no—
211#1823—131no—
212#1808—131no—
213C2×#340—131no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C22⋊Q812yes—
219C23×C13C2×D812yes—
220C23×C13#13712yes—
221C23×C13C22×D411yescharacteristic
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
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—84no—
241C2×C4×C13C22⋊Q812yes—
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13H(5,𝔽2)11yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—48no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13C2×D812yes—
272C2×Dic13C2×D812yes—
273Dic26—84no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—22no—
277#1055—41no—
278C23×C8—131no—
279C2×C4⋊Q8—131no—
280C2×C22⋊Q8—261no—
281C2×#117—261no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4C2×D1311yescharacteristic
284C2×#107—131no—
285C2×#107—131no—
286C2×#107C2×D1311yescharacteristic
287C2×#107C2×D1311yescharacteristic
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×C22⋊C8C2×D1311yescharacteristic
291#398—261no—
292#395—261no—
293#389—131no—
294#389—131no—
295#389—131no—
296#389—131no—
297#387—261no—
298#387—261no—
299#385—261no—
300#384—131no—
301#381—261no—
302#380—131no—
303#380C2×D1311yescharacteristic
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C22⋊C4—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340C2×D1311yescharacteristic
318#340C2×D1311yescharacteristic
319#336—131no—
320#336—131no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13#47414yes—
328C22×C13C2×C22⋊Q811yescharacteristic
329C22×C13#54611yescharacteristic
330C22×C13#54711yescharacteristic
331C22×C13C22×D811yescharacteristic
332C22×C13C2×#13711yescharacteristic
333C22×C13#57711yescharacteristic
334C22×C13#57811yescharacteristic
335C4×C13—22no—
336C4×C13—42no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13#53311yescharacteristic
341C4×C13#54411yescharacteristic
342C4×C13#55111yescharacteristic
343C4×C13#55211yescharacteristic
344Dic13—22no—
345Dic13—22no—
346Dic13—41no—
347Dic13—41no—
348Dic13—42no—
349Dic13—42no—
350Dic13—81no—
351Dic13—81no—
352C22×Q8—261no—
353C23×C4—21no—
354C23×C4—261no—
355C23×C4C22×D1311yescharacteristic
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—262no—
359C22×C8—262no—
360C22×C8—521no—
361C22×C8C22×D1311yescharacteristic
362C22×C8C22×D1311yescharacteristic
363C4⋊Q8—262no—
364C4⋊Q8—521no—
365C22⋊Q8—524no—
366#117—524no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—131no—
390C2×C22⋊C4—131no—
391C2×C22⋊C4—261no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—261no—
395C2×C42—261no—
396#107—22no—
397#107—41no—
398#107—262no—
399#107—521no—
400C4⋊C8—262no—
401C4⋊C8—521no—
402C22⋊C8—22no—
403#95—21no—
404#95—131no—
405#95—131no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413C2×C13—24no—
414C2×C13#243811yescharacteristic
415C2×C13C2×#47411yescharacteristic
416C2×C13#308211yescharacteristic
417C2×C13#329411yescharacteristic
418C2×C13#331211yescharacteristic
419C2×C13#333411yescharacteristic
420C2×C13#334411yescharacteristic
421C24D4×D1311yescharacteristic
422C2×Q8—522no—
423C2×Q8—522no—
424C2×Q8—1041no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4#612712yes—
448C22×C4D4×D1311yescharacteristic
449C22×C4Q8×D1312yes—
450C22×C4C23×D1311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—132no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—524no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—264no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—522no—
487C4⋊C4—1041no—
488C4⋊C4#612912yes—
489C22⋊C4—42no—
490C22⋊C4—134no—
491C22⋊C4—262no—
492C22⋊C4—522no—
493C42—261no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—522no—
498C42—522no—
499C13#2598811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#8815012yes—
505C23D8×D1312yes—
506C23#8817212yes—
507C23C2×D4×D1311yescharacteristic
508Q8—1044no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
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—132no—
529C2×C4—132no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—528no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4#8815012yes—
554C2×C4C2×#612711yescharacteristic
555C2×C4C2×#612911yescharacteristic
556C2×C4#8825111yescharacteristic
557C2×C4C2×Q8×D1311yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—41no—
561C8—41no—
562C8—262no—
563C8—521no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1171855114yes—
571C22C2×#8815011yescharacteristic
572C22#1171929611yescharacteristic
573C22#1171936011yescharacteristic
574C22C2×D8×D1311yescharacteristic
575C22C2×#8817211yescharacteristic
576C22#1171948011yescharacteristic
577C22#1171948411yescharacteristic
578C4—22no—
579C4—42no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—262no—
584C4—262no—
585C4—521no—
586C4—522no—
587C4—522no—
588C4—521no—
589C4—1041no—
590C4—1041no—
591C4#1171924611yescharacteristic
592C4#1171926111yescharacteristic
593C4#1171932711yescharacteristic
594C4#1171932811yescharacteristic
595C2—24no—
596C2#1311851611yescharacteristic
597C2C2×#1171855111yescharacteristic
598C2#1312467611yescharacteristic
599C2#1312664211yescharacteristic
600C2#1312689111yescharacteristic
601C2#1312717811yescharacteristic
602C2#1312728911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1852C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1852D13
hypocenterC13#25988
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
3. #13116396C2semidirect
4. #13116328C2semidirect
5. #13116325C2semidirect
6. #13116162C2semidirect
7. #13115786C2semidirect
8. #13115591C2semidirect
9. #13115409C2semidirect
10. #13115405C2semidirect
79. C2×C4⋊Dic13Q8semidirect
499. C13#25988semidirect

Maximal subgroups

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

subgroupindex
#131185322
#131177072
#131163962
#131163282
#131163252
#131161622
#131157862
#131155912
#131154092
#131154052
#131150132
#131149232
#131148632
C2×#117181212
C13×#18522
#2598813