Finite Group Databasebeta

← #15923331

Subgroups — #15923331

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718692C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic
3#13118612C211yesmaximal, characteristic
4#13116380C211yesmaximal, characteristic
5#13116338C211yesmaximal, characteristic
6#13116245C211yesmaximal, characteristic
7#13116082C211yesmaximal, characteristic
8#13115525C211yesmaximal, characteristic
9#13115402C211yesmaximal, characteristic
10#13115177C211yesmaximal, characteristic
11#13115177C211yesmaximal, characteristic
12#13115177C211yesmaximal, characteristic
13#13115104C211yesmaximal, characteristic
14#13115103C211yesmaximal, characteristic
15Q8×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C22×#6107C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#389—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#384—21no—
28C13×#384C2211yescharacteristic
29C4×C13×C4⋊C4—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33#11718692—24no—
34#11718691—24no—
35#11718645—21no—
36#11718642—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718321—21no—
52#11718316—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×Dic26C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—41no—
69C4×Q8×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×#6107—22no—
89C2×#6107—22no—
90C2×#6107—22no—
91C2×#6107—22no—
92C2×#6107—22no—
93C2×#6107D414yes—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105#88123—22no—
106#88123—41no—
107C4×Dic26—22no—
108C4×Dic26—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88075—22no—
114#88075—22no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88050—22no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88050—41no—
128#88048—22no—
129#88048—41no—
130C4⋊#1055—22no—
131#88043—22no—
132#26187—131nomaximal, Sylow
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13C2×D412yes—
137C2×Q8×C13#4112yes—
138C2×Q8×C13#4112yes—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26C2×D412yes—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4—81no—
180C13×C4⋊C4#4112yes—
181C42×C13—24no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—42no—
189C42×C13—42no—
190#6107—28no—
191#6107—44no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—42no—
197C4⋊Dic13—42no—
198#6101—42no—
199#6101—42no—
200C4×Dic13—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055C2×D412yes—
213C2×#462—131no—
214C2×#441—131no—
215#2446—131no—
216Q8×C4⋊C4D1311yescharacteristic
217#2096—131no—
218#2088—131no—
219#2072—131no—
220#2043—131no—
221#1935—131no—
222#1917—131no—
223#1878—131no—
224#1878—131no—
225#1878—131no—
226#1865—131no—
227#1865—131no—
228C23×C13C22×D411yescharacteristic
229Q8×C13—22no—
230Q8×C13—22no—
231Q8×C13—22no—
232Q8×C13#12314yes—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13#13712yes—
262C2×C4×C13#13712yes—
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13H(5,𝔽2)11yescharacteristic
268C2×C4×C132−1+411yescharacteristic
269C2×Dic13—22no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281Dic26—22no—
282Dic26—22no—
283Dic26—41no—
284Dic26—41no—
285Dic26—41no—
286Dic26—41no—
287Dic26—41no—
288Dic26—41no—
289#1055—22no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293C22×Q16—131no—
294C22×Q16—131no—
295C2×C4⋊Q8—131no—
296C2×C4×Q8—131no—
297C2×C4×Q8C2×D1311yescharacteristic
298C2×C4×Q8C2×D1311yescharacteristic
299C2×C4×Q8C2×D1311yescharacteristic
300#462—264no—
301#441—264no—
302C2×#106—131no—
303C2×#106—131no—
304C2×C4⋊C8—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×#103—131no—
313C2×#97—131no—
314#400—261no—
315#398—261no—
316#391—131no—
317#391—131no—
318#391—131no—
319#389—21no—
320#389—21no—
321#389—131no—
322#389C2×D1311yescharacteristic
323#389C2×D1311yescharacteristic
324#387—261no—
325#387—261no—
326#384—21no—
327#384C2×D1311yescharacteristic
328C4×C4⋊C4—21no—
329C4×C4⋊C4C2×D1311yescharacteristic
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338C22×C13#52511yescharacteristic
339C22×C13D4211yescharacteristic
340C22×C13#54811yescharacteristic
341C22×C13C2×#13711yescharacteristic
342C22×C13C2×#13711yescharacteristic
343C22×C13#57711yescharacteristic
344C22×C13#57811yescharacteristic
345C4×C13—22no—
346C4×C13—24no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—81no—
354C4×C13—81no—
355C4×C13C2×#12311yescharacteristic
356C4×C13#53911yescharacteristic
357C4×C13#54711yescharacteristic
358C4×C13#55311yescharacteristic
359Dic13—42no—
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363C22×Q8—131no—
364C22×Q8—131no—
365C22×Q8C22×D1311yescharacteristic
366C2×Q16—134no—
367C2×Q16—262no—
368C2×Q16—262no—
369C2×Q16—262no—
370C2×Q16—262no—
371C2×Q16—262no—
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C4⋊Q8—262no—
377C4⋊Q8—521no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×Q8—41no—
384C4×Q8—262no—
385C4×Q8—521no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4C22⋊D1311yescharacteristic
400C2×C4⋊C4C22⋊D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—261no—
408C2×C42C22×D1311yescharacteristic
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411#106—262no—
412#106—521no—
413C4⋊C8—262no—
414#103—262no—
415#103—262no—
416#103—262no—
417#103—262no—
418#103—262no—
419#103—262no—
420#103—262no—
421#103—521no—
422#97—262no—
423#95—21no—
424#95—21no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95C22⋊D1311yescharacteristic
433#95C22⋊D1311yescharacteristic
434C2×C13#244311yescharacteristic
435C2×C13#311311yescharacteristic
436C2×C13#312011yescharacteristic
437C2×C13#327011yescharacteristic
438C2×C13#327811yescharacteristic
439C2×C13#336911yescharacteristic
440C2×C13#337411yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—132no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8#612712yes—
457C2×Q8D4×D1312yes—
458C2×Q8#613112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474Q16—268no—
475Q16—524no—
476C2×C8—132no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—522no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—522no—
510C4⋊C4#612712yes—
511C42—24no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—42no—
520C42—522no—
521C13#2618711yescharacteristic, complemented, Sylow
522C23C22×C22⋊D1311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—262no—
527Q8—262no—
528Q8—521no—
529Q8—521no—
530Q8—521no—
531Q8—521no—
532Q8—521no—
533Q8—521no—
534Q8#8814814yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—262no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4#8819612yes—
576C2×C4#8820512yes—
577C2×C4C2×#612711yescharacteristic
578C2×C4C2×#612711yescharacteristic
579C2×C4C2×D4×D1311yescharacteristic
580C2×C4#8825111yescharacteristic
581C2×C4C2×#613111yescharacteristic
582C2×C4#8825411yescharacteristic
583C8—262no—
584C8—521no—
585C8—521no—
586C8—521no—
587C22#1171949611yescharacteristic
588C22D4×C22⋊D1311yescharacteristic
589C22C2×#8819611yescharacteristic
590C22#1171952211yescharacteristic
591C22C2×#8820511yescharacteristic
592C22#1171954111yescharacteristic
593C22#1171954311yescharacteristic
594C4—22no—
595C4—22no—
596C4—24no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—81no—
603C4—81no—
604C4—522no—
605C4—1041no—
606C4—1041no—
607C4—1041no—
608C4C2×#8814811yescharacteristic
609C4#1171921211yescharacteristic
610C4#1171921911yescharacteristic
611C4#1171922011yescharacteristic
612C2#1311857111yescharacteristic
613C2#1312496611yescharacteristic
614C2#1312505011yescharacteristic
615C2#1312640711yescharacteristic
616C2#1312650211yescharacteristic
617C2#1312757611yescharacteristic
618C2#1312763911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingQ8×C13×C4⋊C4C2
socle, prime radicalC23×C13C22×D4
hypercenterQ8×C4⋊C4D13
hypocenterC13#26187
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
521. C13#26187semidirect

Maximal subgroups

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

subgroupindex
C2×#117186922
C2×#117186912
#131186122
#131163802
#131163382
#131162452
#131160822
#131155252
#131154022
#131151772
#131151042
#131151032
Q8×C13×C4⋊C42
#2618713