Finite Group Databasebeta

← #15880515

Subgroups — #15880515

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123490C211yesmaximal, characteristic
2C2×#11718659C211yesmaximal, characteristic
3#13115581C212yesmaximal, complemented
4#13115435C212yesmaximal, complemented
5#13115432C212yesmaximal, complemented
6#13114935C211yesmaximal, characteristic
7#13114933C211yesmaximal, characteristic
8#13114872C211yesmaximal, characteristic
9#13114716C212yesmaximal, complemented
10#13114610C211yesmaximal, characteristic
11C13×#2924C211yesmaximal, characteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C13×#433—22no—
16C13×#432—21no—
17C13×#431—21no—
18C13×#424C2212yes—
19C13×#407C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#405C2212yes—
22C4×C22⋊Dic13C2211yescharacteristic
23#11718868C2211yescharacteristic
24C2×#88062C2212yes—
25#11718763C2212yes—
26#11718762C2212yes—
27C2×C8×Dic13C2212yes—
28#11718659C411yescharacteristic, complemented
29#11718659C411yescharacteristic, complemented
30#11718659C411yescharacteristic, complemented
31#11718659C411yescharacteristic, complemented
32#11718659C2211yescharacteristic
33#11718659C2211yescharacteristic
34#11718659C2211yescharacteristic
35#11718659C2211yescharacteristic
36C2×#88048C411yescharacteristic, complemented
37C2×#88048C411yescharacteristic, complemented
38C2×#88047C411yescharacteristic, complemented
39C2×#88047C411yescharacteristic, complemented
40#11718381—22no—
41#11718380—21no—
42#11718379—21no—
43#11718150C2212yes—
44#11718147C2212yes—
45#11718147C2212yes—
46#11718142C2212yes—
47#11718124C2212yes—
48#11718124C2212yes—
49C23×C4×C13C2311yescharacteristic
50C2×C13×M16C2312yes—
51C22×C8×C13C2312yes—
52C13×#117—21no—
53C13×#117—21no—
54C13×#117C2×C411yescharacteristic
55C13×#117C2×C411yescharacteristic
56C13×#117C2311yescharacteristic
57C13×#117C2311yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64#88180—21no—
65#88180—21no—
66#88180C2×C411yescharacteristic
67#88180C2×C411yescharacteristic
68#88180C2311yescharacteristic
69#88180C2311yescharacteristic
70C2×C4⋊Dic13C2×C411yescharacteristic
71C2×C4⋊Dic13C2×C411yescharacteristic
72C2×C4×Dic13—21no—
73C2×C4×Dic13C2312yes—
74C2×#6099C2312yes—
75C22×#1055—24no—
76C22×#1055C2×C411yescharacteristic
77C22×#1055C2×C411yescharacteristic
78C22×#1055C2×C411yescharacteristic
79C22×#1055C2×C411yescharacteristic
80C22×#1055C2311yescharacteristic
81C22×#1055C2311yescharacteristic
82C13×C4⋊C8—22no—
83C13×C4⋊C8—22no—
84C13×C22⋊C8—21no—
85C13×C22⋊C8—21no—
86C13×C22⋊C8D411yescharacteristic
87C13×C22⋊C8D411yescharacteristic
88C13×C22⋊C8D412yes—
89C13×#97—22no—
90C4×C8×C13—22no—
91#88071—21no—
92C22⋊#1055—21no—
93C22⋊#1055—21no—
94#88062—24no—
95#88055—22no—
96#88054—22no—
97#88054—22no—
98C8×Dic13—22no—
99C8×Dic13—24no—
100#88048C2×C411yescharacteristic
101#88048C2×C411yescharacteristic
102#88048C2×C411yescharacteristic
103#88048C2×C411yescharacteristic
104#88048C2×C411yescharacteristic
105#88048C2×C411yescharacteristic
106#88048C2×C411yescharacteristic
107#88048C2×C411yescharacteristic
108#88047C2×C411yescharacteristic
109#88047C2×C411yescharacteristic
110#88047C2×C411yescharacteristic
111#88047C2×C411yescharacteristic
112#88047C2×C411yescharacteristic
113#88047C2×C411yescharacteristic
114#88047C2×C411yescharacteristic
115#88047C2×C411yescharacteristic
116#22606—131nomaximal, Sylow
117C24×C13#4111yescharacteristic
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C13×M16—22no—
132C13×M16—22no—
133C2×C8×C13—22no—
134C2×C8×C13—22no—
135C2×C8×C13—22no—
136C2×C8×C13C2×D412yes—
137C2×C8×C13C2×D412yes—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4C22×C411yescharacteristic
141C13×C4⋊C4C22×C411yescharacteristic
142C13×C4⋊C4C22×C411yescharacteristic
143C13×C4⋊C4C22×C411yescharacteristic
144C13×C22⋊C4—21no—
145C13×C22⋊C4—21no—
146C13×C22⋊C4—21no—
147C13×C22⋊C4—21no—
148C42×C13—21no—
149C42×C13—21no—
150C42×C13—21no—
151C42×C13—21no—
152C22⋊Dic13—24no—
153C22⋊Dic13—21no—
154C22⋊Dic13—21no—
155C22⋊Dic13—21no—
156C22⋊Dic13—21no—
157C4⋊Dic13—21no—
158C4⋊Dic13—21no—
159C4⋊Dic13C22×C411yescharacteristic
160C4⋊Dic13C22×C411yescharacteristic
161C4⋊Dic13C22×C411yescharacteristic
162C4⋊Dic13C22×C411yescharacteristic
163C4×Dic13—21no—
164C4×Dic13—21no—
165C4×Dic13—21no—
166C4×Dic13—21no—
167C4×Dic13—22no—
168C4×Dic13—22no—
169#6099—22no—
170#6099—22no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055C22×C411yescharacteristic
178C2×#1055C22×C411yescharacteristic
179C2×#1055C22×C411yescharacteristic
180C2×#1055C22×C411yescharacteristic
181C2×#1055#4114yes—
182#2924—131no—
183#2924D1311yescharacteristic
184C2×#427—131no—
185#1945—132no—
186#1922—132no—
187#1922—132no—
188#1826—131no—
189#1826—131no—
190#1810—131no—
191#1772—132no—
192C8×C22⋊C4—131no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—41no—
196C23×C13C4×D411yescharacteristic
197C23×C13C4×D411yescharacteristic
198C23×C13C2×#4111yescharacteristic
199C2×C4×C13—22no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—42no—
211C2×C4×C13—81no—
212C2×C4×C13C4×D411yescharacteristic
213C2×C4×C13C4×D411yescharacteristic
214C2×C4×C13C23×C411yescharacteristic
215C2×C4×C13C22×D411yescharacteristic
216C2×C4×C13C2×#4112yes—
217C2×C4×C132−1+412yes—
218C2×Dic13—24no—
219C2×Dic13—21no—
220C2×Dic13—21no—
221C2×Dic13—21no—
222C2×Dic13—21no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—81no—
227C8×C13—22no—
228C8×C13—22no—
229C8×C13—42no—
230#1055—21no—
231#1055—21no—
232#1055—42no—
233#1055#11712yes—
234#1055#11712yes—
235C23×C8—131no—
236C2×#117—131no—
237C2×#117C2×D1311yescharacteristic
238#433—22no—
239#433—262no—
240#432—21no—
241#432—261no—
242#431—21no—
243#431—261no—
244C2×#108—132no—
245#427—131no—
246#427—131no—
247#427—131no—
248#427—131no—
249#427—131no—
250#427—131no—
251#427—131no—
252#427—131no—
253C2×#107—131no—
254C2×#107—131no—
255C2×#106—131no—
256C2×#106—131no—
257#424—132no—
258#424C2×D1312yes—
259#407—131no—
260#407C2×D1311yescharacteristic
261C2×C22⋊C8C2×D1311yescharacteristic
262#405—132no—
263#405C2×D1312yes—
264C2×C4×C8—132no—
265C4×C22⋊C4—131no—
266#341—132no—
267#339—132no—
268#339—132no—
269#339—132no—
270#339—132no—
271#336—132no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—44no—
280C22×C13#44312yes—
281C22×C13C2×C4×D411yescharacteristic
282C22×C13#55212yes—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—41no—
286C4×C13—41no—
287C4×C13—41no—
288C4×C13—41no—
289C4×C13C2×#11711yescharacteristic
290C4×C13#51911yescharacteristic
291C4×C13#54712yes—
292Dic13—44no—
293Dic13—41no—
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297C23×C4C22×D1311yescharacteristic
298C2×M16—132no—
299C2×M16C22×D1312yes—
300C22×C8—131no—
301C22×C8—131no—
302C22×C8—131no—
303C22×C8—131no—
304C22×C8—131no—
305C22×C8—131no—
306C22×C8—264no—
307C22×C8C22×D1312yes—
308#117—21no—
309#117—21no—
310#117—131no—
311#117—131no—
312#117—131no—
313#117—131no—
314#117—261no—
315#117—261no—
316#117C4×D1311yescharacteristic
317#117C4×D1311yescharacteristic
318#117C22×D1311yescharacteristic
319#117C22×D1311yescharacteristic
320C2×C4⋊C4—131no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4C4×D1311yescharacteristic
323C2×C4⋊C4C4×D1311yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—261no—
326C2×C22⋊C4—261no—
327C2×C42—21no—
328C2×C42—132no—
329C2×C42—261no—
330#108—264no—
331#107—131no—
332#107—131no—
333#107—131no—
334#107—131no—
335#107—131no—
336#107—131no—
337#107—131no—
338#107—131no—
339#106—131no—
340#106—131no—
341#106—131no—
342#106—131no—
343#106—131no—
344#106—131no—
345#106—131no—
346#106—131no—
347C4⋊C8—22no—
348C4⋊C8—22no—
349C4⋊C8—262no—
350C4⋊C8—262no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—261no—
354C22⋊C8—261no—
355C22⋊C8C22⋊D1311yescharacteristic
356C22⋊C8C22⋊D1311yescharacteristic
357C22⋊C8C22⋊D1312yes—
358#97—22no—
359#97—262no—
360C4×C8—22no—
361C4×C8—264no—
362C4×C8—262no—
363#95—261no—
364C2×C13—22no—
365C2×C13—22no—
366C2×C13—41no—
367C2×C13#234411yescharacteristic
368C2×C13C2×#44311yescharacteristic
369C2×C13#295711yescharacteristic
370C24#612711yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—261no—
376C22×C4—262no—
377C22×C4—261no—
378C22×C4C2×C4×D1311yescharacteristic
379C22×C4C2×C4×D1311yescharacteristic
380C22×C4#612711yescharacteristic
381C22×C4C2×C22⋊D1311yescharacteristic
382C22×C4C2×C22⋊D1311yescharacteristic
383C22×C4C23×D1311yescharacteristic
384M16—22no—
385M16—22no—
386M16—262no—
387M16—262no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—131no—
392C2×C8—131no—
393C2×C8—134no—
394C2×C8—131no—
395C2×C8—131no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—262no—
401C2×C8—262no—
402C2×C8C2×C22⋊D1312yes—
403C2×C8C2×C22⋊D1312yes—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—131no—
407C4⋊C4—131no—
408C4⋊C4—131no—
409C4⋊C4—131no—
410C4⋊C4—261no—
411C4⋊C4—261no—
412C4⋊C4C2×C4×D1311yescharacteristic
413C4⋊C4C2×C4×D1311yescharacteristic
414C4⋊C4C2×C4×D1311yescharacteristic
415C4⋊C4C2×C4×D1311yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—264no—
421C22⋊C4—261no—
422C22⋊C4—261no—
423C22⋊C4—261no—
424C22⋊C4—261no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—261no—
430C42—261no—
431C42—261no—
432C42—261no—
433C42—262no—
434C42—262no—
435C13#2260611yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—41no—
439C23C4×C22⋊D1311yescharacteristic
440C23C4×C22⋊D1311yescharacteristic
441C23C2×#612711yescharacteristic
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—81no—
455C2×C4—264no—
456C2×C4—261no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—1041no—
464C2×C4C4×C22⋊D1311yescharacteristic
465C2×C4C4×C22⋊D1311yescharacteristic
466C2×C4C22×C4×D1311yescharacteristic
467C2×C4#41×D1312yes—
468C2×C4#8825712yes—
469C2×C4C22×C22⋊D1311yescharacteristic
470C8—22no—
471C8—22no—
472C8—42no—
473C8—132no—
474C8—132no—
475C8—261no—
476C8—261no—
477C8—522no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—44no—
486C22#1171880512yes—
487C22#1171923612yes—
488C22C2×C4×C22⋊D1311yescharacteristic
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—524no—
496C4—521no—
497C4—521no—
498C4—521no—
499C4—521no—
500C4#1171922111yescharacteristic
501C4D13×#11711yescharacteristic
502C4#1171952912yes—
503C2—22no—
504C2—22no—
505C2—41no—
506C2#1311770611yescharacteristic
507C2C2×#1171880511yescharacteristic
508C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C2×C4×D4
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#22606
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #13115581C2semidirect
4. #13115435C2semidirect
5. #13115432C2semidirect
9. #13114716C2semidirect
28. #11718659C4semidirect
29. #11718659C4semidirect
30. #11718659C4semidirect
31. #11718659C4semidirect
36. C2×#88048C4semidirect
37. C2×#88048C4semidirect
38. C2×#88047C4semidirect
39. C2×#88047C4semidirect
435. C13#22606semidirect

Maximal subgroups

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

subgroupindex
#131234902
C2×#117186592
#131155812
#131154352
#131154322
#131149352
#131149332
#131148722
#131147162
#131146102
C13×#29242
#2260613