Finite Group Databasebeta

← #15765794

Subgroups — #15765794

Order 3328.

664 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125593C211yesmaximal, characteristic
2#13123175C211yesmaximal, characteristic, complemented
3#13114904C211yesmaximal, characteristic, complemented
4#13113407C211yesmaximal, characteristic, complemented
5#13113404C211yesmaximal, characteristic
6#13112703C211yesmaximal, characteristic, complemented
7C13×#2854C211yesmaximal, characteristic
8C2×C13×#123—21no—
9C2×C13×#121C2211yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C2×#88178C2211yescharacteristic
12C13×#390—21no—
13C13×#389—21no—
14C13×#388—22no—
15C13×#386—21no—
16C13×#380C2211yescharacteristic
17#11718879—21no—
18#11718873C2211yescharacteristic
19#11718872—21no—
20#11718871—21no—
21C2×C22⋊#1055C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23#11718702—22no—
24#11718701—21no—
25#11718695—21no—
26#11718632—21no—
27#11718594—22no—
28#11718590—21no—
29#11718589—21no—
30#11718129—22no—
31#11718116—22no—
32#11718044—22no—
33C22×D4×C13—21no—
34C22×D4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13D411yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C22×Dic26D411yescharacteristic
39C13×#123—42no—
40C13×#123—42no—
41C13×#121—21no—
42C13×#121—21no—
43C13×#121—21no—
44C13×#121—21no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C42×C13—21no—
53C2×C42×C13—21no—
54C2×C42×C13—21no—
55C2×C42×C13—21no—
56C2×C42×C13—21no—
57C2×C42×C13—21no—
58C2×C22⋊Dic13—21no—
59C2×C22⋊Dic13—21no—
60C2×#6105—22no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13D411yescharacteristic
63#88178—21no—
64#88178—21no—
65#88178—21no—
66#88178—21no—
67C2×#6101—22no—
68C2×#6101—21no—
69C22×#1055—21no—
70C22×#1055D412yes—
71C13×#95—22no—
72C13×#95D412yes—
73#88072—22no—
74#88071—22no—
75#88071—22no—
76#88071—22no—
77#88071D412yes—
78C22⋊#1055—21no—
79C22⋊#1055—21no—
80C22⋊#1055—21no—
81C22⋊#1055—21no—
82#88050—22no—
83#88048—22no—
84#10323—131nomaximal, Sylow
85C24×C13—21no—
86C24×C13C2×D411yescharacteristic
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—42no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—42no—
108C22×C4×C13—42no—
109C22×C4×C13SD1612yescomplemented
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×Dic13—21no—
117C22×Dic13—22no—
118C22×Dic13—21no—
119C2×Dic26—21no—
120C2×Dic26—21no—
121C2×Dic26—42no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4—44no—
126C13×C22⋊C4—44no—
127C13×C22⋊C4—44no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C42×C13—41no—
133C42×C13—41no—
134C42×C13—41no—
135C42×C13—41no—
136C22⋊Dic13—41no—
137C22⋊Dic13—41no—
138C22⋊Dic13—41no—
139C22⋊Dic13—41no—
140#6105—82no—
141C4⋊Dic13—21no—
142C4⋊Dic13—21no—
143C4⋊Dic13—42no—
144#6101—44no—
145#6101—41no—
146#6101—41no—
147C2×#1055—22no—
148C2×#1055—42no—
149C2×#1055—42no—
150C2×#1055—41no—
151#3187—131no—
152#2855—131no—
153#2854D1311yescharacteristic
154#1817—131no—
155#1520—131no—
156#1519—131no—
157#1289—131no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—42no—
161C23×C13—42no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13#12011yescharacteristic
166C23×C13#12011yescharacteristic
167C23×C13#12111yescharacteristic
168C23×C13C2×SD1611yescharacteristic
169C23×C13#13511yescharacteristic
170C23×C13AGL(1,ℤ/8)11yescharacteristic
171C23×C13#13711yescharacteristic
172D4×C13—42no—
173D4×C13—81no—
174D4×C13—81no—
175D4×C13—81no—
176D4×C13—81no—
177D4×C13—81no—
178C2×C4×C13—22no—
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—41no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13#12111yescharacteristic
206C2×C4×C13#12111yescharacteristic
207C2×C4×C13#12711yescharacteristic
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—42no—
215Dic26—42no—
216Dic26—81no—
217#1055—42no—
218#1055—81no—
219C2×#123—21no—
220C2×C22⋊Q8—131no—
221C2×#121C2×D1311yescharacteristic
222C22×C42C2×D1311yescharacteristic
223#483—261no—
224#481—261no—
225#465—262no—
226#450—261no—
227#448—261no—
228C2×C22⋊C8—131no—
229C2×C22⋊C8—131no—
230#391—261no—
231#390—21no—
232#389—21no—
233#389—261no—
234#388—22no—
235#387—262no—
236#386—21no—
237#385—261no—
238#381—261no—
239#380—131no—
240#380C2×D1311yescharacteristic
241#336—262no—
242#328—262no—
243#327—262no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—82no—
255C22×C13—82no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13#39211yescharacteristic
260C22×C13#44811yescharacteristic
261C22×C13#44911yescharacteristic
262C22×C13#45011yescharacteristic
263C22×C13#45211yescharacteristic
264C22×C13#46511yescharacteristic
265C22×C13#46811yescharacteristic
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—42no—
270C4×C13—42no—
271C4×C13—82no—
272C4×C13—81no—
273C4×C13#45812yes—
274Dic13—82no—
275Dic13—81no—
276Dic13—81no—
277C22×Q8—131no—
278C22×D4—21no—
279C22×D4C22⋊D1311yescharacteristic
280C23×C4C22⋊D1311yescharacteristic
281C23×C4C22⋊D1311yescharacteristic
282C23×C4C22×D1311yescharacteristic
283C2×SD16—262no—
284C22×C8—132no—
285C22×C8—261no—
286#123—42no—
287#123—42no—
288C22⋊Q8—261no—
289C22⋊Q8—261no—
290C22⋊Q8—261no—
291C22⋊Q8—261no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—131no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4C22⋊D1311yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—261no—
308C2×C22⋊C4—261no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315#106—262no—
316#103—262no—
317#102—262no—
318C22⋊C8—261no—
319C22⋊C8—261no—
320C22⋊C8—261no—
321C22⋊C8—261no—
322#95—22no—
323#95—132no—
324#95—262no—
325#95—262no—
326#95—262no—
327#95C22⋊D1312yes—
328C2×C13—21no—
329C2×C13—21no—
330C2×C13—21no—
331C2×C13—21no—
332C2×C13—21no—
333C2×C13—21no—
334C2×C13—161no—
335C2×C13#200011yescharacteristic
336C2×C13#201011yescharacteristic
337C2×C13#202211yescharacteristic
338C24—21no—
339C24C2×C22⋊D1311yescharacteristic
340C2×Q8—261no—
341C2×Q8—261no—
342C2×Q8—522no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—262no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4#610512yescomplemented
369C22×C4D4×D1311yescharacteristic
370C22×C4D4×D1311yescharacteristic
371C22×C4D4×D1311yescharacteristic
372C22×C4#612911yescharacteristic
373C22×C4C2×C22⋊D1311yescharacteristic
374C22×C4C2×C22⋊D1311yescharacteristic
375SD16—1042no—
376C2×C8—262no—
377C2×C8—522no—
378C2×C8—522no—
379C2×C8—521no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—44no—
383C4⋊C4—42no—
384C4⋊C4—261no—
385C4⋊C4—261no—
386C4⋊C4—524no—
387C4⋊C4—522no—
388C4⋊C4—521no—
389C4⋊C4—521no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—521no—
397C22⋊C4—521no—
398C22⋊C4—521no—
399C22⋊C4—521no—
400C42—41no—
401C42—41no—
402C42—41no—
403C42—41no—
404C13#1032311yescharacteristic, complemented, Sylow
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23#8818611yescharacteristic
413C23C2×#610511yescharacteristic
414C23#8819111yescharacteristic
415C23#8819311yescharacteristic
416C23#8820411yescharacteristic
417C23#8820511yescharacteristic
418C23#8820711yescharacteristic
419Q8—522no—
420Q8—1041no—
421D4—42no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—522no—
454C2×C4—522no—
455C2×C4—522no—
456C2×C4—522no—
457C2×C4—522no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4#8819111yescharacteristic
461C2×C4#8819211yescharacteristic
462C2×C4#8819311yescharacteristic
463C2×C4#8819411yescharacteristic
464C8—522no—
465C8—1041no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22#1171869811yescharacteristic
482C22#1171870111yescharacteristic
483C22#1171870211yescharacteristic
484C22#1171870311yescharacteristic
485C22#1171887911yescharacteristic
486C22#1171888411yescharacteristic
487C22#1171890011yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—1042no—
496C4—1041no—
497C4—1041no—
498C4#1171871412yes—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—161no—
506C2#1311583911yescharacteristic
507C2#1311590111yescharacteristic
508C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2854C2
socleC22×C13#392
prime radicalC2×C13×#121C22
hypercenter#2854D13
hypocenterC13#10323
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. #13123175C2semidirect
3. #13114904C2semidirect
4. #13113407C2semidirect
6. #13112703C2semidirect
109. C22×C4×C13SD16semidirect
368. C22×C4#6105semidirect
404. C13#10323semidirect

Maximal subgroups

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

subgroupindex
#131255932
#131231752
#131149042
#131134072
#131134042
#131127032
C13×#28542
#1032313