Finite Group Databasebeta

← #15875224

Subgroups — #15875224

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#13124626C211yesmaximal, characteristic
2#13123766C211yesmaximal, characteristic, complemented
3#13123481C211yesmaximal, characteristic
4#13115780C211yesmaximal, characteristic, complemented
5#13115582C212yesmaximal, complemented
6#13115538C212yesmaximal
7#13115483C212yesmaximal
8#13115434C212yesmaximal, complemented
9#13114853C211yesmaximal, characteristic
10#13114701C211yesmaximal, characteristic, complemented
11C13×#1950C211yesmaximal, characteristic, complemented
12C4×#6127C2211yescharacteristic
13#11719175C2211yescharacteristic
14C2×C13×#108C2212yes—
15C13×#423C2211yescharacteristic
16C2×C13×C4⋊C8C2211yescharacteristic
17C4×C13×M16C2211yescharacteristic
18C2×#88065C2212yes—
19#11718790C2211yescharacteristic
20#11718790C2211yescharacteristic
21#11718783C2212yes—
22#11718780C2211yescharacteristic
23#11718780C2212yes—
24#11718780C2211yescharacteristic
25#11718774C2212yes—
26#11718767C2212yes—
27C2×C8×Dic13C2212yes—
28C4×C4⋊Dic13C2211yescharacteristic
29C2×C4×#1055C2211yescharacteristic
30#11718512C411yescharacteristic, complemented
31#11718511C411yescharacteristic, complemented
32#11718508C412yescomplemented
33#11718507C411yescharacteristic, complemented
34#11718503C411yescharacteristic, complemented
35#11718492—21no—
36#11718492—21no—
37#11718491—21no—
38#11718491—21no—
39#11718490C412yescomplemented
40#11718370—21no—
41#11718370—21no—
42#11718346—21no—
43#11718346—21no—
44C13×#341C2212yes—
45#11718147C2212yes—
46#11718147C2212yes—
47#11718147C2212yes—
48#11718142C2212yes—
49C2×#6127C2311yescharacteristic
50C2×C13×M16C2311yescharacteristic
51C2×C13×M16C2311yescharacteristic
52C2×C13×M16C2312yes—
53C22×C8×C13C2312yes—
54C2×C42×C13C2311yescharacteristic
55C4×C22⋊D13—21no—
56C4×C22⋊D13—21no—
57#88180C2312yes—
58#88180C2311yescharacteristic
59C2×C4⋊Dic13—21no—
60#88178—21no—
61#88178—21no—
62C2×C4×Dic13C2312yes—
63C22×#1055C2311yescharacteristic
64C22×#1055C2311yescharacteristic
65C4×D52C2×C411yescharacteristic
66C4×D52C2×C411yescharacteristic
67#88126—21no—
68C42×D13—21no—
69#88124C2×C412yes—
70#88123C2×C411yescharacteristic
71#88123C2×C411yescharacteristic
72C4×Dic26—21no—
73C4×Dic26—21no—
74C4×Dic26C2×C411yescharacteristic
75C4×Dic26C2×C411yescharacteristic
76C13×#108—42no—
77C13×C4⋊C8—21no—
78C13×C4⋊C8—21no—
79C13×C4⋊C8C2×C412yes—
80C13×C4⋊C8C2×C411yescharacteristic
81C13×C4⋊C8C2×C411yescharacteristic
82C13×#97—21no—
83C4×C8×C13—21no—
84#88071—21no—
85#88065—42no—
86#88061C2×C412yes—
87#88061C2×C412yes—
88#88060—21no—
89#88060—21no—
90#88060—21no—
91#88060—21no—
92#88058C2×C412yes—
93#88058C2×C412yes—
94#88057C2×C412yes—
95#88057C2×C412yes—
96#88056C2×C412yes—
97#88056C2×C412yes—
98#88055—22no—
99#88054—22no—
100#88054—22no—
101#88054—21no—
102#88054—21no—
103#88054—21no—
104#88054—21no—
105C8×Dic13—22no—
106C8×Dic13—42no—
107C4×#1055D411yescharacteristic
108C4×#1055D411yescharacteristic
109C4×#1055D411yescharacteristic
110C4×#1055D411yescharacteristic
111#22130—131nomaximal, Sylow
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13C2411yescharacteristic
115C2×C22⋊D13—21no—
116C22×Dic13—22no—
117#6127—21no—
118#6127—21no—
119#6127—21no—
120#6127—21no—
121C2×D52C22×C411yescharacteristic
122C2×C4×D13—21no—
123C2×C4×D13—21no—
124C2×C4×D13—21no—
125C2×Dic26—21no—
126C2×Dic26—21no—
127C2×Dic26C22×C411yescharacteristic
128C13×M16—22no—
129C13×M16—21no—
130C13×M16—21no—
131C13×M16—21no—
132C13×M16—21no—
133C13×M16—22no—
134C2×C8×C13—22no—
135C2×C8×C13—22no—
136C2×C8×C13—21no—
137C2×C8×C13—21no—
138C2×C8×C13—22no—
139C2×C8×C13C22×C412yes—
140C2×C8×C13C22×C412yes—
141C42×C13C22×C411yescharacteristic
142C42×C13C22×C411yescharacteristic
143C42×C13C2×D411yescharacteristic
144C42×C13C2×D411yescharacteristic
145C22⋊Dic13—22no—
146C22⋊Dic13—21no—
147#6103—21no—
148#6103—21no—
149C4⋊Dic13—24no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13C22×C411yescharacteristic
153C4⋊Dic13C22×C411yescharacteristic
154C4⋊Dic13C22×C412yes—
155C4⋊Dic13C22×C412yes—
156#6101—22no—
157#6101—22no—
158#6101—21no—
159#6101—21no—
160C4×Dic13—21no—
161C4×Dic13—21no—
162C4×Dic13—22no—
163C4×Dic13—21no—
164C4×Dic13—22no—
165C4×Dic13—22no—
166C2×#1055—21no—
167C2×#1055—21no—
168C2×#1055—21no—
169C2×#1055—21no—
170C2×#1055C2×D411yescharacteristic
171C2×#1055C2×D411yescharacteristic
172C2×#1055C2×D411yescharacteristic
173C2×#1055C2×D411yescharacteristic
174#3076—131no—
175#2960—131no—
176#2922—131no—
177#1986—131no—
178#1950D1311yescharacteristic, complemented
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—
187C2×C4×C13—22no—
188C2×C4×C13—41no—
189C2×C4×C13C4×D411yescharacteristic
190C2×C4×C13C4×D411yescharacteristic
191C2×C4×C13C4×D411yescharacteristic
192C2×C4×C13C4×D411yescharacteristic
193C2×C4×C13C23×C411yescharacteristic
194C2×C4×C13C22×D411yescharacteristic
195C2×C4×C13H(5,𝔽2)11yescharacteristic
196C2×C4×C132−1+411yescharacteristic
197C2×C4×C132−1+411yescharacteristic
198C2×C4×C132−1+411yescharacteristic
199C22⋊D13—41no—
200C22⋊D13—41no—
201C2×Dic13—24no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—22no—
206C2×Dic13—22no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209D52—21no—
210D52—21no—
211C4×D13—42no—
212C4×D13—41no—
213C4×D13—41no—
214C4×D13—42no—
215Dic26—21no—
216Dic26—21no—
217Dic26—42no—
218Dic26—42no—
219C8×C13—22no—
220C8×C13—22no—
221C8×C13—41no—
222C8×C13—41no—
223C8×C13—42no—
224#1055—21no—
225#1055—21no—
226#1055—21no—
227#1055—21no—
228#533—131no—
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×#108C2×D1312yes—
245#427—132no—
246#424—131no—
247#424—131no—
248#424—132no—
249#423C2×D1311yescharacteristic
250C2×C4⋊C8C2×D1311yescharacteristic
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⋊C4—131no—
260#341C2×D1312yes—
261#339—132no—
262#339—132no—
263#339—132no—
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#44312yes—
277C4×C13#51911yescharacteristic
278C4×C13#52011yescharacteristic
279C4×C13#53611yescharacteristic
280C4×C13#53711yescharacteristic
281Dic13—44no—
282Dic13—41no—
283Dic13—42no—
284Dic13—41no—
285Dic13—42no—
286Dic13—41no—
287C2×#41—131no—
288C2×M16C22×D1311yescharacteristic
289C2×M16C22×D1311yescharacteristic
290C2×M16C22×D1312yes—
291C22×C8—131no—
292C22×C8—131no—
293C22×C8C22×D1312yes—
294C4⋊Q8—131no—
295C4⋊Q8—131no—
296#125—132no—
297C22⋊Q8—261no—
298C22⋊Q8—261no—
299C4×Q8—131no—
300C4×Q8—131no—
301C4×Q8—261no—
302C4×Q8—261no—
303C4×D4—131no—
304C4×D4—131no—
305C4×D4—261no—
306C4×D4—261no—
307#117—131no—
308#117—132no—
309#117—261no—
310C2×C4⋊C4—261no—
311C2×C42—132no—
312C2×C42—261no—
313C2×C42C22×D1311yescharacteristic
314#108—42no—
315#107—132no—
316#107—132no—
317#106—132no—
318#106—132no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—261no—
322C4⋊C8—261no—
323C4⋊C8—261no—
324C4⋊C8—261no—
325C4⋊C8—262no—
326C4⋊C8—262no—
327C4⋊C8C4×D1311yescharacteristic
328C4⋊C8C4×D1311yescharacteristic
329C4⋊C8C4×D1312yes—
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—261no—
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—131no—
360C2×Q8—261no—
361C2×Q8—261no—
362C2×D4—131no—
363C2×D4—261no—
364C22×C4—262no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4#613111yescharacteristic
369C22×C4#613111yescharacteristic
370C22×C4C23×D1311yescharacteristic
371M16—22no—
372M16—21no—
373M16—21no—
374M16—21no—
375M16—22no—
376M16—21no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—131no—
383C2×C8—131no—
384C2×C8—131no—
385C2×C8—131no—
386C2×C8—261no—
387C2×C8—261no—
388C2×C8—261no—
389C2×C8—261no—
390C2×C8C2×C4×D1312yes—
391C2×C8C2×C4×D1312yes—
392C4⋊C4—132no—
393C4⋊C4—132no—
394C4⋊C4—131no—
395C4⋊C4—131no—
396C4⋊C4—264no—
397C4⋊C4—261no—
398C4⋊C4—261no—
399C4⋊C4—262no—
400C4⋊C4—262no—
401C4⋊C4—261no—
402C4⋊C4—261no—
403C22⋊C4—261no—
404C22⋊C4—262no—
405C22⋊C4—261no—
406C22⋊C4—261no—
407C42—261no—
408C42—261no—
409C42—262no—
410C42—261no—
411C42—262no—
412C42—262no—
413C42C2×C4×D1311yescharacteristic
414C42C2×C4×D1311yescharacteristic
415C42D4×D1311yescharacteristic
416C42D4×D1311yescharacteristic
417C13#2213011yescharacteristic, complemented, Sylow
418C23—261no—
419C23C2×#613111yescharacteristic
420Q8—261no—
421Q8—261no—
422Q8—522no—
423Q8—522no—
424D4—261no—
425D4—261no—
426D4—521no—
427D4—521no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—264no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—262no—
435C2×C4—262no—
436C2×C4—522no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—521no—
440C2×C4—522no—
441C2×C4—521no—
442C2×C4#8814711yescharacteristic
443C2×C4#8814711yescharacteristic
444C2×C4#8814711yescharacteristic
445C2×C4#8814711yescharacteristic
446C2×C4C22×C4×D1311yescharacteristic
447C2×C4C2×D4×D1311yescharacteristic
448C2×C4#8825111yescharacteristic
449C2×C4#8825411yescharacteristic
450C2×C4#8825711yescharacteristic
451C2×C4#8825711yescharacteristic
452C8—22no—
453C8—22no—
454C8—41no—
455C8—42no—
456C8—41no—
457C8—261no—
458C8—261no—
459C8—261no—
460C8—261no—
461C22—21no—
462C22—21no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22C2×#8814711yescharacteristic
467C22#1171940211yescharacteristic
468C22#1171943811yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—524no—
473C4—521no—
474C4—521no—
475C4—522no—
476C4—521no—
477C4—522no—
478C4#1171855612yes—
479C4#1171925111yescharacteristic
480C4#1171927711yescharacteristic
481C4#1171931311yescharacteristic
482C4#1171933311yescharacteristic
483C2—21no—
484C2—21no—
485C2—1041no—
486C2#1311751611yescharacteristic
487C2C2×#1171855611yescharacteristic
488C2#1312373811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1950C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1950D13
hypocenterC13#22130
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #13123766C2semidirect
4. #13115780C2semidirect
5. #13115582C2semidirect
8. #13115434C2semidirect
10. #13114701C2semidirect
11. C13×#1950C2semidirect
30. #11718512C4semidirect
31. #11718511C4semidirect
32. #11718508C4semidirect
33. #11718507C4semidirect
34. #11718503C4semidirect
39. #11718490C4semidirect
178. #1950D13semidirect
417. C13#22130semidirect

Maximal subgroups

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

subgroupindex
#131246262
#131237662
#131234812
#131157802
#131155822
#131155382
#131154832
#131154342
#131148532
#131147012
C13×#19502
#2213013