Finite Group Databasebeta

← #15875222

Subgroups — #15875222

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#13124624C211yesmaximal, characteristic
2#13123766C211yesmaximal, characteristic, complemented
3#13123480C211yesmaximal, characteristic
4#13115779C211yesmaximal, characteristic, complemented
5#13115609C211yesmaximal, characteristic, complemented
6#13115583C212yesmaximal, complemented
7#13115537C212yesmaximal
8#13115487C212yesmaximal
9#13115438C212yesmaximal, complemented
10C4⋊C4×#1055C211yesmaximal, characteristic, complemented
11C13×#1806C211yesmaximal, characteristic
12C4×C13×#41C2211yescharacteristic
13#11719175C2211yescharacteristic
14C13×#423C2211yescharacteristic
15C2×C13×#104C2212yes—
16C4×C13×C4⋊C4C2211yescharacteristic
17#11718895C2211yescharacteristic
18#11718895C2211yescharacteristic
19#11718894C2212yes—
20C2×#88062C2212yes—
21#11718783C2212yes—
22#11718780C2212yes—
23#11718683C412yescomplemented
24#11718682C411yescharacteristic, complemented
25#11718681C411yescharacteristic, complemented
26#11718670C412yescomplemented
27#11718669C411yescharacteristic, complemented
28#11718668C411yescharacteristic, complemented
29#11718661—21no—
30#11718661—21no—
31#11718660C2211yescharacteristic
32#11718660C2211yescharacteristic
33#11718659C2212yes—
34#11718586—21no—
35#11718586—21no—
36C2×C4⋊#1055C2211yescharacteristic
37C4×#6099C2211yescharacteristic
38C2×C4×#1055C2212yes—
39C2×C4×#1055C2211yescharacteristic
40#11718492—21no—
41#11718492—21no—
42#11718491—21no—
43#11718491—21no—
44C13×#339C2212yes—
45#11718150C2212yes—
46#11718116C2212yes—
47#11718115C2212yes—
48#11718115C2212yes—
49C2×C13×#41C2311yescharacteristic
50C2×C13×M16C2312yes—
51C4×Q8×C13C2×C411yescharacteristic
52C4×Q8×C13C2×C411yescharacteristic
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C4×D4×C13C2×C411yescharacteristic
56C4×D4×C13C2×C411yescharacteristic
57C13×#117—21no—
58C13×#117C2311yescharacteristic
59C2×C13×C4⋊C4—21no—
60C2×C42×C13—21no—
61C2×C42×C13C2312yes—
62C2×C42×C13C2311yescharacteristic
63#88180C2312yes—
64#88178—21no—
65#88178—21no—
66C2×#6099C2311yescharacteristic
67C2×#6099C2311yescharacteristic
68C22×#1055C2312yes—
69C22×#1055C2311yescharacteristic
70C22×#1055C2311yescharacteristic
71#88124C2×C412yes—
72#88123C2×C411yescharacteristic
73#88123C2×C411yescharacteristic
74C4×Dic26—21no—
75C4×Dic26—21no—
76C13×C4⋊C8—21no—
77C13×C4⋊C8—21no—
78C13×#104—42no—
79C13×#95—21no—
80#88075C2×C412yes—
81#88075C2×C412yes—
82#88072C2×C412yes—
83#88072C2×C412yes—
84C22⋊#1055—21no—
85C22⋊#1055—21no—
86C22⋊#1055—21no—
87C22⋊#1055—21no—
88#88062—42no—
89#88055—22no—
90#88054—22no—
91#88054—22no—
92C8×Dic13—22no—
93#88048C2×C412yes—
94#88048C2×C412yes—
95#88047C2×C412yes—
96#88047C2×C412yes—
97C4⋊#1055—21no—
98C4⋊#1055—21no—
99C4⋊#1055—21no—
100C4⋊#1055—21no—
101C4⋊#1055C2×C411yescharacteristic
102C4⋊#1055C2×C411yescharacteristic
103C4⋊#1055C2×C412yes—
104#88043—21no—
105C4×#1055—21no—
106C4×#1055—42no—
107C4×#1055D411yescharacteristic
108C4×#1055D411yescharacteristic
109C4×#1055D411yescharacteristic
110C4×#1055D411yescharacteristic
111#22130—131nomaximal, Sylow
112C13×#41—21no—
113C13×#41—21no—
114C13×#41—21no—
115C13×#41—21no—
116C2×Q8×C13C22×C411yescharacteristic
117C2×D4×C13—21no—
118C2×D4×C13C22×C411yescharacteristic
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13#4111yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C22×C4×C13C2411yescharacteristic
126C2×Dic26—21no—
127C2×Dic26—21no—
128C13×M16—22no—
129C13×M16—22no—
130C2×C8×C13—22no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4C22×C411yescharacteristic
135C13×C4⋊C4C22×C411yescharacteristic
136C13×C22⋊C4—21no—
137C13×C22⋊C4—21no—
138C13×C22⋊C4—21no—
139C42×C13—21no—
140C42×C13—21no—
141C42×C13—21no—
142C42×C13—22no—
143C42×C13—22no—
144C42×C13C22×C411yescharacteristic
145C42×C13C22×C411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13C2×D411yescharacteristic
148C22⋊Dic13—22no—
149C4⋊Dic13—21no—
150C4⋊Dic13—21no—
151C4⋊Dic13C22×C412yes—
152C4⋊Dic13C22×C412yes—
153#6101—22no—
154#6101—22no—
155C4×Dic13—22no—
156#6099—21no—
157#6099—21no—
158#6099—21no—
159#6099—21no—
160C2×#1055—21no—
161C2×#1055—22no—
162C2×#1055—22no—
163C2×#1055—21no—
164C2×#1055—21no—
165C2×#1055—21no—
166C2×#1055—21no—
167C2×#1055—21no—
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#1986—131no—
178#1950—131no—
179#1945—132no—
180#1937—132no—
181#1929—132no—
182#1922—132no—
183#1806D1311yescharacteristic
184C8×C4⋊C4—131no—
185C23×C13—21no—
186C23×C13C2×#4111yescharacteristic
187Q8×C13—21no—
188Q8×C13—21no—
189D4×C13—21no—
190D4×C13—21no—
191D4×C13—41no—
192D4×C13—41no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—41no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13C4×D411yescharacteristic
206C2×C4×C13C4×D411yescharacteristic
207C2×C4×C13C4×D411yescharacteristic
208C2×C4×C13C4×D411yescharacteristic
209C2×C4×C13C23×C411yescharacteristic
210C2×C4×C13C22×D411yescharacteristic
211C2×C4×C13H(5,𝔽2)11yescharacteristic
212C2×C4×C132−1+411yescharacteristic
213C2×C4×C132−1+411yescharacteristic
214C2×C4×C132−1+411yescharacteristic
215C2×Dic13—22no—
216C2×Dic13—22no—
217Dic26—42no—
218Dic26—42no—
219C8×C13—42no—
220#1055—22no—
221#1055—22no—
222#1055—21no—
223#1055—21no—
224#1055—21no—
225#1055—21no—
226#1055—41no—
227#1055—41no—
228#533—131no—
229C4×#41C2×D1311yescharacteristic
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—132no—
247#424—131no—
248#424—131no—
249#423C2×D1311yescharacteristic
250C2×C4⋊C8—131no—
251C2×#104C2×D1312yes—
252#416—132no—
253#408—131no—
254#408—131no—
255#405—132no—
256C4×M16—131no—
257C2×C4×C8—131no—
258C2×C4×C8—132no—
259C4×C4⋊C4C2×D1311yescharacteristic
260#341—132no—
261#339—132no—
262#339—132no—
263#339C2×D1312yes—
264#336—132no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—41no—
270C22×C13C2×C4×D411yescharacteristic
271C22×C13#54111yescharacteristic
272C22×C13#54211yescharacteristic
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—44no—
277C4×C13—41no—
278C4×C13—41no—
279C4×C13—41no—
280C4×C13#44312yes—
281C4×C13#51911yescharacteristic
282C4×C13#52011yescharacteristic
283C4×C13#53611yescharacteristic
284C4×C13#53711yescharacteristic
285Dic13—42no—
286Dic13—42no—
287C2×#41C22×D1311yescharacteristic
288C2×M16—131no—
289C2×M16—131no—
290C2×M16C22×D1312yes—
291C22×C8—131no—
292C22×C8—132no—
293C22×C8—131no—
294C4⋊Q8—131no—
295C4⋊Q8—131no—
296#125—132no—
297C22⋊Q8—261no—
298C22⋊Q8—261no—
299C4×Q8—261no—
300C4×Q8—261no—
301C4×Q8C4×D1311yescharacteristic
302C4×Q8C4×D1311yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4C4×D1311yescharacteristic
306C4×D4C4×D1311yescharacteristic
307#117—21no—
308#117—132no—
309#117C22×D1311yescharacteristic
310C2×C4⋊C4—21no—
311C2×C42—21no—
312C2×C42C22×D1312yes—
313C2×C42C22×D1311yescharacteristic
314#108—522no—
315#107—132no—
316#107—132no—
317#106—132no—
318#106—132no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—131no—
322C4⋊C8—131no—
323C4⋊C8—132no—
324C4⋊C8—261no—
325C4⋊C8—261no—
326C4⋊C8—261no—
327C4⋊C8—261no—
328C4⋊C8—262no—
329C4⋊C8—262no—
330#104—42no—
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—262no—
340#97—261no—
341C4×C8—131no—
342C4×C8—131no—
343C4×C8—131no—
344C4×C8—131no—
345C4×C8—262no—
346C4×C8—261no—
347C4×C8—522no—
348#95—21no—
349C2×C13—21no—
350C2×C13—21no—
351C2×C13—81no—
352C2×C13#232311yescharacteristic
353C2×C13C2×#44311yescharacteristic
354C2×C13#295511yescharacteristic
355#41—21no—
356#41—21no—
357#41—21no—
358#41—21no—
359C2×Q8—261no—
360C2×Q8—261no—
361C2×Q8C2×C4×D1311yescharacteristic
362C2×D4—21no—
363C2×D4C2×C4×D1311yescharacteristic
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4#612911yescharacteristic
369C22×C4#612911yescharacteristic
370C22×C4C23×D1311yescharacteristic
371M16—22no—
372M16—22no—
373M16—261no—
374M16—261no—
375M16—261no—
376M16—261no—
377C2×C8—22no—
378C2×C8—132no—
379C2×C8—132no—
380C2×C8—131no—
381C2×C8—131no—
382C2×C8—131no—
383C2×C8—131no—
384C2×C8—261no—
385C2×C8—262no—
386C2×C8—262no—
387C2×C8—261no—
388C2×C8—261no—
389C2×C8—261no—
390C2×C8—261no—
391C2×C8—261no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—132no—
396C4⋊C4—132no—
397C4⋊C4—262no—
398C4⋊C4—262no—
399C4⋊C4—261no—
400C4⋊C4—261no—
401C4⋊C4C2×C4×D1311yescharacteristic
402C4⋊C4C2×C4×D1311yescharacteristic
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—262no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—22no—
411C42—22no—
412C42—262no—
413C42C2×C4×D1311yescharacteristic
414C42C2×C4×D1311yescharacteristic
415C42D4×D1311yescharacteristic
416C42D4×D1311yescharacteristic
417C13#2213011yescharacteristic, complemented, Sylow
418C23—21no—
419C23C2×#612911yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—522no—
423Q8—522no—
424D4—21no—
425D4—21no—
426D4—41no—
427D4—41no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—262no—
441C2×C4—262no—
442C2×C4#8813511yescharacteristic
443C2×C4#8813511yescharacteristic
444C2×C4#8813511yescharacteristic
445C2×C4#8813511yescharacteristic
446C2×C4C22×C4×D1311yescharacteristic
447C2×C4C2×D4×D1311yescharacteristic
448C2×C4#8825111yescharacteristic
449C2×C4#8825411yescharacteristic
450C2×C4#8825711yescharacteristic
451C2×C4#8825711yescharacteristic
452C8—42no—
453C8—262no—
454C8—262no—
455C8—261no—
456C8—261no—
457C8—261no—
458C8—261no—
459C8—521no—
460C8—521no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22C2×#8813511yescharacteristic
467C22#1171930811yescharacteristic
468C22#1171933011yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—44no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—522no—
477C4—522no—
478C4#1171848512yes—
479C4#1171920911yescharacteristic
480C4#1171922111yescharacteristic
481C4#1171931311yescharacteristic
482C4#1171933311yescharacteristic
483C2—21no—
484C2—21no—
485C2—81no—
486C2#1311751411yescharacteristic
487C2C2×#1171848511yescharacteristic
488C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1806C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C23
cosocleC22×C4×C13C24
hypercenter#1806D13
hypocenterC13#22130
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #13123766C2semidirect
4. #13115779C2semidirect
5. #13115609C2semidirect
6. #13115583C2semidirect
9. #13115438C2semidirect
10. C4⋊C4×#1055C2semidirect
23. #11718683C4semidirect
24. #11718682C4semidirect
25. #11718681C4semidirect
26. #11718670C4semidirect
27. #11718669C4semidirect
28. #11718668C4semidirect
417. C13#22130semidirect

Maximal subgroups

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

subgroupindex
#131246242
#131237662
#131234802
#131157792
#131156092
#131155832
#131155372
#131154872
#131154382
C4⋊C4×#10552
C13×#18062
#2213013