Finite Group Databasebeta

← #15875229

Subgroups — #15875229

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124618C211yesmaximal, characteristic
2#13123771C211yesmaximal, characteristic, complemented
3#13123481C211yesmaximal, characteristic
4#13115611C211yesmaximal, characteristic, complemented
5#13115583C212yesmaximal, complemented
6#13115541C212yesmaximal
7#13115482C212yesmaximal
8#13115433C212yesmaximal, complemented
9#13114857C211yesmaximal, characteristic
10C4⋊C4×#1055C211yesmaximal, characteristic, complemented
11C13×#1986C211yesmaximal, characteristic, complemented
12C13×#533C2211yescharacteristic
13C4×#6127C2211yescharacteristic
14C4×C13×M16C2211yescharacteristic
15C4×C13×C4⋊C4C2211yescharacteristic
16#11718790C2211yescharacteristic
17#11718790C2211yescharacteristic
18C2×#88062C2212yes—
19#11718780C2211yescharacteristic
20#11718780C2211yescharacteristic
21#11718755C411yescharacteristic, complemented
22#11718752C411yescharacteristic, complemented
23#11718748C411yescharacteristic, complemented
24#11718745C411yescharacteristic, complemented
25#11718727C412yescomplemented
26#11718724C412yescomplemented
27#11718685—21no—
28#11718685—21no—
29Q8×#1055—21no—
30Q8×#1055—21no—
31#11718663C2212yes—
32#11718660C2212yes—
33#11718659C2212yes—
34#11718658C2212yes—
35C2×#88045C2212yes—
36#11718585C2211yescharacteristic
37C2×C4⋊#1055C2211yescharacteristic
38C2×C4×#1055C2212yes—
39C2×C4×#1055C2211yescharacteristic
40#11718370—21no—
41#11718370—21no—
42#11718346—21no—
43#11718346—21no—
44C13×#339C2212yes—
45C13×#339C2212yes—
46#11718150C2212yes—
47#11718116C2212yes—
48#11718115C2212yes—
49C2×#6127C2311yescharacteristic
50C2×C13×M16C2311yescharacteristic
51C2×C13×M16C2311yescharacteristic
52C13×C4⋊Q8C2×C411yescharacteristic
53C13×C4⋊Q8C2×C411yescharacteristic
54C13×#125C2×C412yes—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C4×Q8×C13—21no—
58C4×Q8×C13—21no—
59C13×#117C2312yes—
60C2×C13×C4⋊C4—21no—
61C2×C42×C13C2312yes—
62C2×C42×C13C2311yescharacteristic
63C4×C22⋊D13—21no—
64C4×C22⋊D13—21no—
65#88180C2311yescharacteristic
66C2×#6099C2312yes—
67C22×#1055C2312yes—
68C22×#1055C2311yescharacteristic
69C22×#1055C2311yescharacteristic
70C4×D52C2×C411yescharacteristic
71C4×D52C2×C411yescharacteristic
72#88126—21no—
73C42×D13—21no—
74C4×Dic26C2×C411yescharacteristic
75C4×Dic26C2×C411yescharacteristic
76C13×#97—21no—
77C4×C8×C13—21no—
78C13×#95—21no—
79#88062—42no—
80#88060—21no—
81#88060—21no—
82#88060—21no—
83#88060—21no—
84#88054—21no—
85#88054—21no—
86#88054—21no—
87#88054—21no—
88#88050C2×C412yes—
89#88050C2×C412yes—
90#88049C2×C412yes—
91#88049C2×C412yes—
92#88048C2×C412yes—
93#88048C2×C412yes—
94#88047C2×C412yes—
95#88047C2×C412yes—
96#88045—42no—
97C4⋊#1055—21no—
98C4⋊#1055—21no—
99C4⋊#1055—22no—
100C4⋊#1055—22no—
101C4⋊#1055C2×C412yes—
102C4⋊#1055C2×C411yescharacteristic
103C4⋊#1055C2×C411yescharacteristic
104#88043—22no—
105C4×#1055—22no—
106C4×#1055—42no—
107C4×#1055D411yescharacteristic
108C4×#1055D411yescharacteristic
109C4×#1055D411yescharacteristic
110C4×#1055D411yescharacteristic
111#22130—131nomaximal, Sylow
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13C2411yescharacteristic
118C2×C22⋊D13—21no—
119#6127—21no—
120#6127—21no—
121#6127—21no—
122#6127—21no—
123C2×D52C22×C411yescharacteristic
124C2×C4×D13—21no—
125C2×C4×D13—21no—
126C2×C4×D13—21no—
127C2×Dic26C22×C411yescharacteristic
128C13×M16—21no—
129C13×M16—21no—
130C13×M16—21no—
131C13×M16—21no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4C22×C412yes—
140C13×C4⋊C4C22×C412yes—
141C13×C22⋊C4—22no—
142C42×C13—22no—
143C42×C13—22no—
144C42×C13—22no—
145C42×C13C22×C411yescharacteristic
146C42×C13C22×C411yescharacteristic
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C22⋊Dic13—21no—
150#6103—21no—
151#6103—21no—
152C4⋊Dic13C22×C411yescharacteristic
153C4⋊Dic13C22×C411yescharacteristic
154#6101—21no—
155#6101—21no—
156C4×Dic13—21no—
157C4×Dic13—21no—
158C4×Dic13—21no—
159#6099—22no—
160#6099—22no—
161C2×#1055—21no—
162C2×#1055—22no—
163C2×#1055—22no—
164C2×#1055—21no—
165C2×#1055—21no—
166C2×#1055—21no—
167C2×#1055—22no—
168C2×#1055C22×C412yes—
169C2×#1055C22×C412yes—
170C2×#1055C2×D411yescharacteristic
171C2×#1055C2×D411yescharacteristic
172C2×#1055C2×D411yescharacteristic
173C2×#1055C2×D411yescharacteristic
174#3076—131no—
175#2960—131no—
176#2922—131no—
177#1986D1311yescharacteristic, complemented
178#1950—131no—
179#1945—132no—
180#1937—132no—
181#1929—132no—
182#1922—132no—
183#1806—131no—
184C8×C4⋊C4—131no—
185C23×C13C2×#4111yescharacteristic
186C22×D13—21no—
187Q8×C13—42no—
188Q8×C13—42no—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—41no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13C4×D411yescharacteristic
197C2×C4×C13C4×D411yescharacteristic
198C2×C4×C13C4×D411yescharacteristic
199C2×C4×C13C4×D411yescharacteristic
200C2×C4×C13C23×C411yescharacteristic
201C2×C4×C13C22×D411yescharacteristic
202C2×C4×C13H(5,𝔽2)11yescharacteristic
203C2×C4×C132−1+411yescharacteristic
204C2×C4×C132−1+411yescharacteristic
205C2×C4×C132−1+411yescharacteristic
206C22⋊D13—41no—
207C22⋊D13—41no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—21no—
211D52—21no—
212D52—21no—
213C4×D13—42no—
214C4×D13—41no—
215C4×D13—41no—
216C4×D13—42no—
217Dic26—21no—
218Dic26—21no—
219C8×C13—41no—
220C8×C13—41no—
221#1055—22no—
222#1055—22no—
223#1055—21no—
224#1055—21no—
225#1055—21no—
226#1055—21no—
227#1055—42no—
228#533C2×D1311yescharacteristic
229C4×#41—131no—
230#479—132no—
231#478—132no—
232#477—131no—
233#476—131no—
234#475—131no—
235#474—131no—
236#446—261no—
237#446—261no—
238C8×Q8—261no—
239C8×Q8—261no—
240#433—261no—
241#433—261no—
242#431—261no—
243#431—261no—
244C2×#108—132no—
245#427—132no—
246#424—131no—
247#424—131no—
248#424—132no—
249#423—131no—
250C2×C4⋊C8—131no—
251C2×#104—132no—
252#416—132no—
253#408—131no—
254#408—131no—
255#405—132no—
256C4×M16C2×D1311yescharacteristic
257C2×C4×C8—131no—
258C2×C4×C8—132no—
259C4×C4⋊C4C2×D1311yescharacteristic
260#341—132no—
261#339—132no—
262#339C2×D1312yes—
263#339C2×D1312yes—
264#336—132no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13C2×C4×D411yescharacteristic
268C22×C13#54111yescharacteristic
269C22×C13#54211yescharacteristic
270C2×D13—41no—
271C2×D13—41no—
272C2×D13—41no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—44no—
277C4×C13—42no—
278C4×C13—42no—
279C4×C13#44312yes—
280C4×C13#51911yescharacteristic
281C4×C13#52011yescharacteristic
282C4×C13#53611yescharacteristic
283C4×C13#53711yescharacteristic
284Dic13—41no—
285Dic13—41no—
286Dic13—41no—
287C2×#41—131no—
288C2×M16—132no—
289C2×M16C22×D1311yescharacteristic
290C2×M16C22×D1311yescharacteristic
291C22×C8—131no—
292C22×C8—132no—
293C22×C8—131no—
294C4⋊Q8C4×D1311yescharacteristic
295C4⋊Q8C4×D1311yescharacteristic
296#125C4×D1312yes—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—131no—
302C4×Q8—131no—
303C4×D4—131no—
304C4×D4—131no—
305C4×D4—261no—
306C4×D4—261no—
307#117—131no—
308#117—261no—
309#117C22×D1312yes—
310C2×C4⋊C4—21no—
311C2×C42—261no—
312C2×C42C22×D1312yes—
313C2×C42C22×D1311yescharacteristic
314#108—522no—
315#107—132no—
316#107—132no—
317#106—132no—
318#106—132no—
319C4⋊C8—131no—
320C4⋊C8—131no—
321C4⋊C8—132no—
322C4⋊C8—262no—
323C4⋊C8—262no—
324C4⋊C8—261no—
325C4⋊C8—261no—
326C4⋊C8—261no—
327C4⋊C8—261no—
328C4⋊C8—261no—
329C4⋊C8—261no—
330#104—522no—
331#103—132no—
332#103—132no—
333#102—132no—
334#102—132no—
335C22⋊C8—261no—
336C22⋊C8—261no—
337C22⋊C8—261no—
338C22⋊C8—261no—
339#97—21no—
340#97—262no—
341C4×C8—21no—
342C4×C8—131no—
343C4×C8—131no—
344C4×C8—131no—
345C4×C8—131no—
346C4×C8—262no—
347C4×C8—522no—
348#95—21no—
349C2×C13—21no—
350C2×C13—21no—
351C2×C13#232311yescharacteristic
352C2×C13C2×#44311yescharacteristic
353C2×C13#295511yescharacteristic
354D13—81no—
355#41—261no—
356#41—261no—
357#41—261no—
358#41—261no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—131no—
362C2×D4—131no—
363C2×D4—261no—
364C22×C4—22no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4#612911yescharacteristic
369C22×C4#612911yescharacteristic
370C22×C4C23×D1311yescharacteristic
371M16—21no—
372M16—21no—
373M16—21no—
374M16—21no—
375M16—262no—
376M16—262no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—132no—
380C2×C8—132no—
381C2×C8—131no—
382C2×C8—131no—
383C2×C8—131no—
384C2×C8—131no—
385C2×C8—262no—
386C2×C8—261no—
387C2×C8—261no—
388C2×C8—261no—
389C2×C8—262no—
390C2×C8—261no—
391C2×C8—262no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—131no—
398C4⋊C4—131no—
399C4⋊C4—261no—
400C4⋊C4—261no—
401C4⋊C4C2×C4×D1312yes—
402C4⋊C4C2×C4×D1312yes—
403C22⋊C4—22no—
404C22⋊C4—261no—
405C22⋊C4—261no—
406C22⋊C4—261no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42—261no—
411C42—261no—
412C42—261no—
413C42C2×C4×D1311yescharacteristic
414C42C2×C4×D1311yescharacteristic
415C42D4×D1311yescharacteristic
416C42D4×D1311yescharacteristic
417C13#2213011yescharacteristic, complemented, Sylow
418C23—261no—
419C23C2×#612911yescharacteristic
420Q8—42no—
421Q8—42no—
422Q8—261no—
423Q8—261no—
424D4—261no—
425D4—261no—
426D4—521no—
427D4—521no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4#8813511yescharacteristic
443C2×C4#8813511yescharacteristic
444C2×C4#8813511yescharacteristic
445C2×C4#8813511yescharacteristic
446C2×C4C22×C4×D1311yescharacteristic
447C2×C4C2×D4×D1311yescharacteristic
448C2×C4#8825411yescharacteristic
449C2×C4#8825411yescharacteristic
450C2×C4#8825611yescharacteristic
451C2×C4#8825711yescharacteristic
452C8—41no—
453C8—41no—
454C8—262no—
455C8—262no—
456C8—261no—
457C8—261no—
458C8—261no—
459C8—261no—
460C8—522no—
461C22—21no—
462C22—21no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22C2×#8813511yescharacteristic
467C22#1171938711yescharacteristic
468C22#1171943611yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—44no—
473C4—42no—
474C4—42no—
475C4—521no—
476C4—521no—
477C4—521no—
478C4#1171848512yes—
479C4#1171927711yescharacteristic
480C4#1171927911yescharacteristic
481C4#1171933311yescharacteristic
482C4#1171933411yescharacteristic
483C2—21no—
484C2—21no—
485C2—1041no—
486C2#1311752111yescharacteristic
487C2C2×#1171848511yescharacteristic
488C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1986C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1986D13
hypocenterC13#22130
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13123771C2semidirect
4. #13115611C2semidirect
5. #13115583C2semidirect
8. #13115433C2semidirect
10. C4⋊C4×#1055C2semidirect
11. C13×#1986C2semidirect
21. #11718755C4semidirect
22. #11718752C4semidirect
23. #11718748C4semidirect
24. #11718745C4semidirect
25. #11718727C4semidirect
26. #11718724C4semidirect
177. #1986D13semidirect
417. C13#22130semidirect

Maximal subgroups

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

subgroupindex
#131246182
#131237712
#131234812
#131156112
#131155832
#131155412
#131154822
#131154332
#131148572
C4⋊C4×#10552
C13×#19862
#2213013