Finite Group Databasebeta

← #15935510

Subgroups — #15935510

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118686C211yesmaximal, characteristic
2#13116207C211yesmaximal, characteristic
3#13116171C211yesmaximal, characteristic, complemented
4#13116169C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic
6#13115788C211yesmaximal, characteristic, complemented
7#13115571C211yesmaximal, characteristic, complemented
8#13115463C211yesmaximal, characteristic
9#13115456C211yesmaximal, characteristic
10#13115421C211yesmaximal, characteristic, complemented
11#13115421C211yesmaximal, characteristic, complemented
12#13115402C211yesmaximal, characteristic, complemented
13#13115096C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×#88150—21no—
18C2×C4×D52C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C13×#389—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30#11718655—21no—
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718600C2211yescharacteristic
40#11718600C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718334—21no—
46#11718329—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×Dic26—21no—
62C13×#125—22no—
63C13×#125—22no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95#88150—44no—
96C4×D52—22no—
97C4×D52—41no—
98#88123—22no—
99#88123—41no—
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#88049—22no—
110#88049—22no—
111#88049—41no—
112#88049Q814yescomplemented
113#88048—22no—
114#88048—22no—
115#88048—41no—
116#88047—22no—
117C4⋊#1055—41no—
118#88043—41no—
119#27026—131nomaximal, Sylow
120C23×D13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52C2×Q812yes—
141C2×C4×D13—42no—
142C2×C4×D13—42no—
143C2×C4×D13—81no—
144C2×Dic26—42no—
145C2×Dic26—42no—
146C2×Dic26—81no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—81no—
158C13×C4⋊C4C2×Q812yes—
159C13×C4⋊C4#4112yes—
160C13×C4⋊C4#4112yes—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—42no—
168C42×C13—81no—
169C42×C13—81no—
170#6103—42no—
171#6103—42no—
172#6103—42no—
173#6103—42no—
174#6103—81no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—42no—
181C4⋊Dic13#4112yes—
182#6101—42no—
183#6101—42no—
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—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055C2×Q812yes—
196#2452—131no—
197#2370D1311yescharacteristic, complemented
198#2065—131no—
199#2059—131no—
200#2058—131no—
201#2025—131no—
202#1988—131no—
203#1943—131no—
204#1926—131no—
205#1925—131no—
206#1920—131no—
207#1920—131no—
208#1917—131no—
209#1864—131no—
210#1762—131no—
211C23×C13C22×D411yescharacteristic
212C22×D13—22no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
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—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
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—41no—
248C2×C4×C13AGL(1,ℤ/8)12yes—
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—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264D52—22no—
265D52—22no—
266D52—41no—
267D52—41no—
268C4×D13—84no—
269Dic26—84no—
270#1055—22no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274C2×C4⋊Q8—131no—
275C2×#125C2×D1311yescharacteristic
276C2×C22⋊Q8—261no—
277C2×C4×D4—131no—
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×#106—131no—
282C2×C4⋊C8—131no—
283C2×#102—131no—
284C2×#102—131no—
285C2×#102—131no—
286C2×#102—131no—
287C2×#97—131no—
288#396—261no—
289#393—261no—
290#390—131no—
291#390—131no—
292#389—21no—
293#389—131no—
294#389—131no—
295#389C2×D1311yescharacteristic
296#389C2×D1311yescharacteristic
297#387—21no—
298#387—21no—
299#385—261no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C2×D1311yescharacteristic
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C4⋊C4C2×D1311yescharacteristic
304C4×C4⋊C4C2×D1311yescharacteristic
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—
315#336—131no—
316#336—131no—
317C22×C13#52511yescharacteristic
318C22×C13#54611yescharacteristic
319C22×C13D4×Q811yescharacteristic
320C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C13#57511yescharacteristic
322C22×C13#57711yescharacteristic
323C22×C13#57711yescharacteristic
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—42no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—81no—
331C4×C13—22no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—81no—
341C4×C13#53311yescharacteristic
342C4×C13#54211yescharacteristic
343C4×C13#55411yescharacteristic
344C4×C13#55611yescharacteristic
345Dic13—42no—
346Dic13—81no—
347Dic13—81no—
348C22×Q8—261no—
349C22×D4—131no—
350C23×C4—261no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—131no—
354C22×C8—131no—
355C4⋊Q8—262no—
356C4⋊Q8—521no—
357#125—22no—
358#125—22no—
359C22⋊Q8—524no—
360C4×D4—262no—
361C4×D4—521no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4C22⋊D1311yescharacteristic
373C2×C4⋊C4C22⋊D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389#107—262no—
390#106—262no—
391#106—262no—
392#106—521no—
393C4⋊C8—521no—
394#102—134no—
395#102—262no—
396#102—262no—
397#102—521no—
398#97—521no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—261no—
405#95—261no—
406#95C22⋊D1311yescharacteristic
407#95C22⋊D1311yescharacteristic
408C2×C13#246511yescharacteristic
409C2×C13#311511yescharacteristic
410C2×C13#312511yescharacteristic
411C2×C13#331011yescharacteristic
412C2×C13#332611yescharacteristic
413C2×C13#338411yescharacteristic
414C2×C13#338811yescharacteristic
415D13—82no—
416C24—261no—
417C2×Q8—522no—
418C2×Q8—522no—
419C2×Q8—1041no—
420C2×D4—132no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—522no—
434C22×C4—522no—
435C22×C4—1041no—
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—132no—
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—261no—
454C2×C8—261no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—132no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C4⋊C4—522no—
475C4⋊C4#612712yes—
476C4⋊C4#612712yes—
477C4⋊C4Q8×D1312yes—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C22⋊C4—1041no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—81no—
491C42—81no—
492C13#2702611yescharacteristic, complemented, Sylow
493C23—262no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23—521no—
498C23—521no—
499C23—521no—
500C23C22×C22⋊D1311yescharacteristic
501Q8—1044no—
502D4—262no—
503D4—262no—
504D4—521no—
505D4—521no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—262no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—1044no—
545C2×C4#8820312yes—
546C2×C4C2×#612711yescharacteristic
547C2×C4C2×#612711yescharacteristic
548C2×C4C2×Q8×D1311yescharacteristic
549C2×C4#8825411yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4#8825611yescharacteristic
552C8—262no—
553C8—521no—
554C8—521no—
555C8—521no—
556C22—522no—
557C22—522no—
558C22—522no—
559C22—1041no—
560C22—1041no—
561C22—1041no—
562C22—1041no—
563C22#1171949611yescharacteristic
564C22Q8×C22⋊D1311yescharacteristic
565C22C2×#8820311yescharacteristic
566C22#1171952711yescharacteristic
567C22#1171953411yescharacteristic
568C22#1171954111yescharacteristic
569C22#1171954211yescharacteristic
570C4—22no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—522no—
581C4—1041no—
582C4—1041no—
583C4#1171927311yescharacteristic
584C4#1171928311yescharacteristic
585C4#1171928411yescharacteristic
586C4#1171928711yescharacteristic
587C2—1042no—
588C2#1311885111yescharacteristic
589C2#1312498711yescharacteristic
590C2#1312511311yescharacteristic
591C2#1312685111yescharacteristic
592C2#1312708311yescharacteristic
593C2#1312773511yescharacteristic
594C2#1312777511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2370D13
hypocenterC13#27026
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #13116171C2semidirect
4. #13116169C2semidirect
6. #13115788C2semidirect
7. #13115571C2semidirect
10. #13115421C2semidirect
11. #13115421C2semidirect
12. #13115402C2semidirect
15. C13×#2370C2semidirect
112. #88049Q8semidirect
197. #2370D13semidirect
492. C13#27026semidirect

Maximal subgroups

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

subgroupindex
#131186862
#131162072
#131161712
#131161692
#131159792
#131157882
#131155712
#131154632
#131154562
#131154212
#131154022
#131150962
#131146642
C13×#23702
#2702613