Finite Group Databasebeta

← #15863494

Subgroups — #15863494

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718658C211yesmaximal, characteristic
2#13117445C211yesmaximal, characteristic
3#13115005C211yesmaximal, characteristic, complemented
4#13115002C211yesmaximal, characteristic, complemented
5#13114966C211yesmaximal, characteristic, complemented
6#13114963C211yesmaximal, characteristic, complemented
7#13114867C211yesmaximal, characteristic
8#13114867C211yesmaximal, characteristic
9#13114863C211yesmaximal, characteristic
10#13114859C211yesmaximal, characteristic
11#13114734C211yesmaximal, characteristic, complemented
12#13114734C211yesmaximal, characteristic, complemented
13C4×#88047C211yesmaximal, characteristic, complemented
14C4×#88048C211yesmaximal, characteristic, complemented
15C13×#2314C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C22×#6099C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C13×#388—21no—
20C13×#388—21no—
21C13×#387—21no—
22C13×#387—21no—
23C13×#384C2211yescharacteristic
24C13×#382C2211yescharacteristic
25C13×#380C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718873C2211yescharacteristic
30#11718873C2211yescharacteristic
31#11718658C418yescomplemented
32#11718642—21no—
33#11718642—21no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718612—21no—
43#11718612—21no—
44#11718597C2211yescharacteristic
45#11718596C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C13×#117C2×C414yes—
62C13×#117Q814yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×#6099—22no—
90C2×#6099—22no—
91C2×#6099C2×C414yes—
92C22×#1055—22no—
93C22×#1055—22no—
94C22×#1055C2×C414yes—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88048—22no—
112#88048—22no—
113#88048—22no—
114#88048—22no—
115#88047—22no—
116#88047—22no—
117#88047—22no—
118#88047—22no—
119#88043C2×C414yes—
120#88043C2×C414yes—
121C4×#1055C2×C414yes—
122C4×#1055C2×C414yes—
123#20822—131nomaximal, Sylow
124C24×C13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×Q812yes—
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
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—81no—
154C13×C4⋊C4—81no—
155C13×C4⋊C4C4⋊C414yes—
156C13×C4⋊C4C4⋊C414yes—
157C13×C22⋊C4—81no—
158C13×C22⋊C4—81no—
159C13×C22⋊C4C4⋊C414yes—
160C13×C22⋊C4C4⋊C414yes—
161C42×C13—81no—
162C42×C13—81no—
163C42×C13C22×C412yes—
164C42×C13C22×C412yes—
165C42×C13C2×Q812yes—
166C42×C13C2×Q812yes—
167C22⋊Dic13—81no—
168C22⋊Dic13—81no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—81no—
178C4⋊Dic13—81no—
179C4×Dic13—81no—
180C4×Dic13—81no—
181#6099—28no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—28no—
187C2×#1055C22×C412yes—
188C2×#1055C22×C412yes—
189C2×#1055C22×C412yes—
190C2×#1055C22×C412yes—
191C2×#1055#4112yes—
192C2×#1055#4112yes—
193C2×#1055#4112yes—
194C2×#1055#4112yes—
195C2×#405—131no—
196#2314—131no—
197#2314D1311yescharacteristic
198#1847—131no—
199#1847—131no—
200#1835—131no—
201#1834—131no—
202#1809—131no—
203#1809—131no—
204#1808—131no—
205#1807—131no—
206#1776—131no—
207#1776—131no—
208C4×#107—131no—
209C4×#106—131no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13C2×C4⋊C412yes—
217C23×C13C22×D411yescharacteristic
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
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×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C2×C4⋊C412yes—
245C2×C4×C13C2×C4⋊C412yes—
246C2×C4×C13C2×C4⋊C412yes—
247C2×C4×C13C2×C4⋊C412yes—
248C2×C4×C13C2×C4⋊C412yes—
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
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—
265C2×Dic13—41no—
266C2×Dic13—41no—
267#1055—22no—
268#1055—22no—
269#1055#11714yes—
270#1055#11714yes—
271C22×M16—131no—
272C23×C8—131no—
273C2×#117C2×D1311yescharacteristic
274C2×#107—131no—
275C2×#107—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×#106—131no—
282#405—138no—
283C2×#97—131no—
284C2×#97—131no—
285C2×C4×C8—131no—
286C2×C4×C8—131no—
287#388—21no—
288#388—21no—
289#388—261no—
290#388—261no—
291#387—21no—
292#387—21no—
293#387—261no—
294#387—261no—
295#384—131no—
296#384C2×D1311yescharacteristic
297#382—131no—
298#382C2×D1311yescharacteristic
299#380—131no—
300#380—131no—
301#380C2×D1311yescharacteristic
302#380C2×D1311yescharacteristic
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4C2×D1311yescharacteristic
306C4×C4⋊C4C2×D1311yescharacteristic
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13C22×C4⋊C411yescharacteristic
323C22×C13#53211yescharacteristic
324C22×C13#53211yescharacteristic
325C22×C13#57611yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57811yescharacteristic
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—22no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13C2×#11711yescharacteristic
339C4×C13C2×#11711yescharacteristic
340C4×C13#53311yescharacteristic
341C4×C13#53311yescharacteristic
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345Dic13—81no—
346C23×C4C22×D1311yescharacteristic
347C2×M16—134no—
348C2×M16—262no—
349C2×M16—262no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—134no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—262no—
356C22×C8—262no—
357#117Dic2614yes—
358#117C4×D1314yes—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22⋊D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4C22⋊D1311yescharacteristic
378C2×C22⋊C4C22⋊D1311yescharacteristic
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42C22×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385#107—262no—
386#107—262no—
387#107—262no—
388#107—262no—
389#106—262no—
390#106—262no—
391#106—262no—
392#106—262no—
393#97—134no—
394#97—134no—
395C4×C8—134no—
396C4×C8—134no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409C2×C13—42no—
410C2×C13#228511yescharacteristic
411C2×C13#291211yescharacteristic
412C2×C13#291311yescharacteristic
413C2×C13#317811yescharacteristic
414C2×C13#317811yescharacteristic
415C2×C13#317911yescharacteristic
416C2×C13#317911yescharacteristic
417C24C2×C22⋊D1311yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4C2×Dic2612yes—
431C22×C4C2×C4×D1312yes—
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438M16—268no—
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—132no—
442C2×C8—132no—
443C2×C8—132no—
444C2×C8—132no—
445C2×C8—132no—
446C2×C8—132no—
447C2×C8—268no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—1041no—
471C4⋊C4—1041no—
472C4⋊C4#610114yes—
473C4⋊C4#610114yes—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—1041no—
477C22⋊C4—1041no—
478C22⋊C4#610114yes—
479C22⋊C4#610114yes—
480C42—81no—
481C42—81no—
482C42—1041no—
483C42—1041no—
484C42C2×Dic2612yes—
485C42C2×Dic2612yes—
486C42C2×C4×D1312yes—
487C42C2×C4×D1312yes—
488C13#2082211yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×#610112yes—
496C23C22×C22⋊D1311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
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—521no—
524C2×C4—521no—
525C2×C4—521no—
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×C4C2×#610112yes—
536C2×C4C2×#610112yes—
537C2×C4C2×#610112yes—
538C2×C4C2×#610112yes—
539C2×C4C2×#610112yes—
540C2×C4C22×Dic2611yescharacteristic
541C2×C4C22×C4×D1311yescharacteristic
542C2×C4#41×D1311yescharacteristic
543C2×C4#41×D1311yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C8—134no—
547C8—134no—
548C8—262no—
549C8—262no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C22×#610111yescharacteristic
558C22#1171953711yescharacteristic
559C22#1171953711yescharacteristic
560C22#1171954011yescharacteristic
561C22#1171954111yescharacteristic
562C22#1171954211yescharacteristic
563C22#1171954311yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—1041no—
574C4—1041no—
575C4—1041no—
576C4—1041no—
577C4#1171922211yescharacteristic
578C4#1171922211yescharacteristic
579C4D13×#11711yescharacteristic
580C4D13×#11711yescharacteristic
581C2—42no—
582C2#1311723911yescharacteristic
583C2#1312342911yescharacteristic
584C2#1312343411yescharacteristic
585C2#1312549811yescharacteristic
586C2#1312550611yescharacteristic
587C2#1312551311yescharacteristic
588C2#1312552111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2314C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#2314D13
hypocenterC13#20822
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13115005C2semidirect
4. #13115002C2semidirect
5. #13114966C2semidirect
6. #13114963C2semidirect
11. #13114734C2semidirect
12. #13114734C2semidirect
13. C4×#88047C2semidirect
14. C4×#88048C2semidirect
31. #11718658C4semidirect
488. C13#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#117186582
#131174452
#131150052
#131150022
#131149662
#131149632
#131148672
#131148632
#131148592
#131147342
C4×#880472
C4×#880482
C13×#23142
#2082213