Finite Group Databasebeta

← #15873455

Subgroups — #15873455

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic
2#13117242C211yesmaximal, characteristic
3#13117240C211yesmaximal, characteristic
4#13115606C211yesmaximal, characteristic, complemented
5#13115604C211yesmaximal, characteristic, complemented
6#13115602C211yesmaximal, characteristic, complemented
7#13115038C211yesmaximal, characteristic
8#13115036C211yesmaximal, characteristic
9#13115034C211yesmaximal, characteristic
10#13115032C211yesmaximal, characteristic
11#13114994C211yesmaximal, characteristic, complemented
12#13114991C211yesmaximal, characteristic, complemented
13#13114962C211yesmaximal, characteristic, complemented
14#13114962C211yesmaximal, characteristic, complemented
15C13×#1949C211yesmaximal, characteristic, complemented
16C2×#88146C2211yescharacteristic
17C2×#88146C2211yescharacteristic
18C2×#88126—21no—
19C2×C42×D13C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C13×#382C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30C2×C8×Dic13C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718648C2211yescharacteristic
33#11718637C2211yescharacteristic
34#11718637C2211yescharacteristic
35#11718637C2211yescharacteristic
36#11718637C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×#6101—21no—
44C2×C4⋊#1055C2211yescharacteristic
45#11718494C418yescomplemented
46#11718328—21no—
47#11718328—21no—
48#11718328—21no—
49#11718311—21no—
50#11718310—21no—
51#11718310—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13D411yescharacteristic
61C22×C4×D13D411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×#6101—21no—
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95#88146—41no—
96#88146—41no—
97#88146—41no—
98#88146—41no—
99#88126—44no—
100C42×D13C2×C414yes—
101C42×D13Q814yes—
102C13×#107—41no—
103C13×#106—41no—
104C13×C4⋊C8C2×C414yes—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88060C2×C414yes—
114#88060C2×C414yes—
115#88058—41no—
116#88057—41no—
117C8×Dic13C2×C414yes—
118C8×Dic13C2×C414yes—
119#88048—41no—
120#88048—41no—
121#88047—41no—
122#88047—41no—
123C4⋊#1055C2×C414yes—
124#21984—131nomaximal, Sylow
125C23×D13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13C4⋊C414yes—
149C2×C4×D13C4⋊C414yes—
150C2×C4×D13C22×C412yes—
151C2×C4×D13C2×Q812yes—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C22×C412yes—
157C2×C8×C13C22×C412yes—
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—21no—
165C13×C4⋊C4—21no—
166C42×C13—42no—
167C42×C13C22×C412yes—
168C42×C13C2×Q812yes—
169#6103—42no—
170#6103—42no—
171#6103—42no—
172#6103—42no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181#6101—42no—
182#6101—42no—
183#6101—42no—
184#6101—42no—
185#6101—42no—
186#6101—42no—
187#6101—42no—
188#6101—42no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13C4⋊C414yes—
193C4×Dic13C4⋊C414yes—
194C4×Dic13C22×C412yes—
195C4×Dic13C2×Q812yes—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C412yes—
201C2×#1055C22×C412yes—
202C2×#431—131no—
203#2285—131no—
204#2285—131no—
205#1949—131no—
206#1949—131no—
207#1949—131no—
208#1949D1311yescharacteristic, complemented
209#1854—131no—
210#1854—131no—
211#1854—131no—
212#1854—131no—
213#1845—131no—
214#1844—131no—
215#1834—131no—
216#1834—131no—
217C23×C13C22×D411yescharacteristic
218C22×D13—21no—
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—21no—
224C22×D13C2×C4⋊C412yes—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
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—41no—
241C2×C4×C13C2×C4⋊C412yes—
242C2×C4×C13C2×C4⋊C412yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13H(5,𝔽2)11yescharacteristic
246C2×C4×C13H(5,𝔽2)11yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×C4×C132−1+411yescharacteristic
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
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×Dic13C2×C4⋊C412yes—
264C2×Dic13C2×C4⋊C412yes—
265C2×Dic13C2×C4⋊C412yes—
266C2×Dic13#13512yes—
267C2×Dic13#13512yes—
268C2×Dic13AGL(1,ℤ/8)12yes—
269C2×Dic13#13712yes—
270C4×D13—22no—
271C4×D13—22no—
272C4×D13—22no—
273C4×D13—22no—
274C4×D13—28no—
275C4×D13—28no—
276C8×C13—22no—
277C8×C13—22no—
278#1055—22no—
279#1055—22no—
280C2×#117—131no—
281C2×#117—131no—
282C2×#117—261no—
283C22×C42—131no—
284#431—138no—
285C2×#107—131no—
286C2×#107—131no—
287C2×#107—131no—
288C2×#107C2×D1311yescharacteristic
289C2×#106—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×#106C2×D1311yescharacteristic
293C2×C4⋊C8—131no—
294C2×C4⋊C8C2×D1311yescharacteristic
295C2×C22⋊C8—131no—
296C2×C22⋊C8—131no—
297C2×C4×C8—131no—
298C2×C4×C8—131no—
299#384—131no—
300#384—131no—
301#384—131no—
302#384—131no—
303#382—131no—
304#382—261no—
305#382C2×D1311yescharacteristic
306#380—131no—
307#380—131no—
308#380—261no—
309#380—261no—
310#380—261no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—261no—
313C4×C4⋊C4—261no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4C2×D1311yescharacteristic
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340C2×D1311yescharacteristic
323#340C2×D1311yescharacteristic
324C22×C13C22×C4⋊C411yescharacteristic
325C22×C13#53511yescharacteristic
326C22×C13#53611yescharacteristic
327C22×C13C2×#13511yescharacteristic
328C22×C13C2×#13511yescharacteristic
329C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C13C2×#13711yescharacteristic
331C2×D13—22no—
332C2×D13—22no—
333C2×D13—22no—
334C2×D13—41no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13—81no—
344C4×C13#52011yescharacteristic
345C4×C13#52011yescharacteristic
346C4×C13#54411yescharacteristic
347C4×C13#54411yescharacteristic
348Dic13—22no—
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352Dic13—81no—
353Dic13#42714yes—
354Dic13#42814yes—
355C23×C4—131no—
356C23×C4—131no—
357C23×C4—131no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#117—524no—
363#117—521no—
364#117—521no—
365#117—521no—
366#117—521no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—21no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—134no—
392C2×C42—134no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42C22×D1311yescharacteristic
397#107—41no—
398#107—521no—
399#107—521no—
400#107—521no—
401#106—41no—
402#106—521no—
403#106—521no—
404#106—521no—
405C4⋊C8—134no—
406C4⋊C8C4×D1314yes—
407C22⋊C8—134no—
408C22⋊C8—134no—
409C4×C8—134no—
410C4×C8—134no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419C2×C13#231711yescharacteristic
420C2×C13C2×#42711yescharacteristic
421C2×C13C2×#42811yescharacteristic
422C2×C13#320711yescharacteristic
423C2×C13#321011yescharacteristic
424C2×C13#322811yescharacteristic
425C2×C13#323111yescharacteristic
426D13—42no—
427C24—131no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—134no—
436C22×C4—134no—
437C22×C4—132no—
438C22×C4—132no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4D4×D1311yescharacteristic
452C22×C4D4×D1311yescharacteristic
453C22×C4C23×D1311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—132no—
459C2×C8—132no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8C2×C4×D1312yes—
465C2×C8C2×C4×D1312yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—522no—
487C4⋊C4—522no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C22⋊C4—522no—
493C22⋊C4—522no—
494C42—42no—
495C42—134no—
496C42—134no—
497C42—132no—
498C42—132no—
499C42—522no—
500C42—522no—
501C42—522no—
502C42C2×C4×D1312yes—
503C42Q8×D1312yes—
504C13#2198411yescharacteristic, complemented, Sylow
505C23—132no—
506C23—261no—
507C23—261no—
508C23—261no—
509C23—261no—
510C23—261no—
511C23—261no—
512C23C2×D4×D1311yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
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—41no—
528C2×C4—41no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—268no—
537C2×C4—268no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4C4⋊C4×D1312yes—
557C2×C4C4⋊C4×D1312yes—
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4#8825111yescharacteristic
560C2×C4C2×Q8×D1311yescharacteristic
561C2×C4#8825411yescharacteristic
562C2×C4#8825611yescharacteristic
563C2×C4#8825711yescharacteristic
564C8—22no—
565C8—22no—
566C8—262no—
567C8—262no—
568C22—262no—
569C22—262no—
570C22—262no—
571C22—521no—
572C22—521no—
573C22—521no—
574C22—521no—
575C22C2×C4⋊C4×D1311yescharacteristic
576C22#1171931211yescharacteristic
577C22#1171933311yescharacteristic
578C22D13×#13511yescharacteristic
579C22D13×#13511yescharacteristic
580C22D13×AGL(1,ℤ/8)11yescharacteristic
581C22D13×#13711yescharacteristic
582C4—22no—
583C4—22no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—134no—
589C4—134no—
590C4—262no—
591C4—1041no—
592C4—1041no—
593C4—1041no—
594C4—1041no—
595C4#1171925111yescharacteristic
596C4#1171927911yescharacteristic
597C4#1171939411yescharacteristic
598C4#1171943411yescharacteristic
599C2—522no—
600C2#1311745811yescharacteristic
601C2D13×#42711yescharacteristic
602C2D13×#42811yescharacteristic
603C2#1312576811yescharacteristic
604C2#1312579111yescharacteristic
605C2#1312597111yescharacteristic
606C2#1312599411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1949C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1949D13
hypocenterC13#21984
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13115606C2semidirect
5. #13115604C2semidirect
6. #13115602C2semidirect
11. #13114994C2semidirect
12. #13114991C2semidirect
13. #13114962C2semidirect
14. #13114962C2semidirect
15. C13×#1949C2semidirect
45. #11718494C4semidirect
208. #1949D13semidirect
504. C13#21984semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131172422
#131172402
#131156062
#131156042
#131156022
#131150382
#131150362
#131150342
#131150322
#131149942
#131149912
#131149622
C13×#19492
#2198413