Finite Group Databasebeta

← #15880517

Subgroups — #15880517

Order 3328.

692 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#13123496C211yesmaximal, characteristic
2#13123494C211yesmaximal, characteristic
3C2×#11718659C211yesmaximal, characteristic
4#13115588C212yesmaximal, complemented
5#13115438C212yesmaximal, complemented
6#13115433C212yesmaximal, complemented
7#13114936C211yesmaximal, characteristic
8#13114872C211yesmaximal, characteristic
9#13114719C212yesmaximal, complemented
10#13114614C211yesmaximal, characteristic
11C13×#1826C211yesmaximal, characteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C13×#407C2211yescharacteristic
16C4×C13×C22⋊C4C2211yescharacteristic
17#11718868C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19C2×#88062C2212yes—
20#11718783C2212yes—
21#11718780C2212yes—
22#11718661—22no—
23#11718660C2212yes—
24#11718659C411yescharacteristic, complemented
25#11718659C411yescharacteristic, complemented
26#11718659C411yescharacteristic, complemented
27#11718659C411yescharacteristic, complemented
28#11718659C2211yescharacteristic
29#11718659C2211yescharacteristic
30#11718659C2211yescharacteristic
31#11718659C2211yescharacteristic
32#11718658C2212yes—
33C2×#88048C411yescharacteristic, complemented
34C2×#88048C411yescharacteristic, complemented
35C2×#88047C411yescharacteristic, complemented
36C2×#88047C411yescharacteristic, complemented
37#11718587—21no—
38#11718586—21no—
39C2×#88043C2212yes—
40#11718381—22no—
41#11718380—21no—
42#11718379—21no—
43C13×#339C2212yes—
44C13×#339C2212yes—
45#11718150C2212yes—
46#11718116C2212yes—
47#11718115C2212yes—
48#11718115C2212yes—
49C23×C4×C13C2311yescharacteristic
50C2×C13×M16C2312yes—
51C13×#117—21no—
52C13×#117—21no—
53C13×#117C2×C411yescharacteristic
54C13×#117C2×C411yescharacteristic
55C13×#117C2311yescharacteristic
56C13×#117C2311yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C42×C13C2312yes—
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×#6099C2312yes—
74C22×#1055—24no—
75C22×#1055C2×C411yescharacteristic
76C22×#1055C2×C411yescharacteristic
77C22×#1055C2×C411yescharacteristic
78C22×#1055C2×C411yescharacteristic
79C22×#1055C2311yescharacteristic
80C22×#1055C2312yes—
81C22×#1055C2311yescharacteristic
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84C13×#95—21no—
85C22⋊#1055—21no—
86C22⋊#1055—21no—
87C22⋊#1055D412yes—
88C22⋊#1055D411yescharacteristic
89C22⋊#1055D411yescharacteristic
90#88062—24no—
91#88055—22no—
92#88054—22no—
93#88054—22no—
94C8×Dic13—22no—
95#88048C2×C411yescharacteristic
96#88048C2×C411yescharacteristic
97#88048C2×C411yescharacteristic
98#88048C2×C411yescharacteristic
99#88048C2×C411yescharacteristic
100#88048C2×C411yescharacteristic
101#88048C2×C411yescharacteristic
102#88048C2×C411yescharacteristic
103#88047C2×C411yescharacteristic
104#88047C2×C411yescharacteristic
105#88047C2×C411yescharacteristic
106#88047C2×C411yescharacteristic
107#88047C2×C411yescharacteristic
108#88047C2×C411yescharacteristic
109#88047C2×C411yescharacteristic
110#88047C2×C411yescharacteristic
111C4⋊#1055—22no—
112C4⋊#1055—22no—
113#88043—22no—
114#88043—24no—
115C4×#1055—22no—
116#22607—131nomaximal, Sylow
117C24×C13#4111yescharacteristic
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13#4111yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C13×M16—22no—
132C13×M16—22no—
133C2×C8×C13—22no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4C22×C411yescharacteristic
137C13×C4⋊C4C22×C411yescharacteristic
138C13×C4⋊C4C22×C411yescharacteristic
139C13×C4⋊C4C22×C411yescharacteristic
140C13×C22⋊C4—21no—
141C13×C22⋊C4—21no—
142C13×C22⋊C4—21no—
143C13×C22⋊C4—21no—
144C13×C22⋊C4—42no—
145C42×C13—21no—
146C42×C13—21no—
147C42×C13—21no—
148C42×C13—21no—
149C42×C13—22no—
150C42×C13—22no—
151C22⋊Dic13—21no—
152C22⋊Dic13—21no—
153C22⋊Dic13—21no—
154C22⋊Dic13—21no—
155C4⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13C22×C411yescharacteristic
158C4⋊Dic13C22×C411yescharacteristic
159C4⋊Dic13C22×C411yescharacteristic
160C4⋊Dic13C22×C411yescharacteristic
161C4×Dic13—21no—
162C4×Dic13—21no—
163C4×Dic13—21no—
164C4×Dic13—21no—
165#6099—22no—
166#6099—22no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055C22×C411yescharacteristic
176C2×#1055C22×C411yescharacteristic
177C2×#1055C22×C411yescharacteristic
178C2×#1055C22×C411yescharacteristic
179C2×#1055C2×D412yes—
180C2×#1055C2×D412yes—
181C2×#1055#4114yes—
182#2924—131no—
183#2924—131no—
184C2×#427—131no—
185#1946—132no—
186#1922—132no—
187#1922—132no—
188#1826—131no—
189#1826D1311yescharacteristic
190#1810—131no—
191#1773—132no—
192#1752—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—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—81no—
215C2×C4×C13C4×D411yescharacteristic
216C2×C4×C13C4×D411yescharacteristic
217C2×C4×C13C23×C411yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C2×C4×C13C2×#4112yes—
220C2×C4×C132−1+412yes—
221C2×Dic13—21no—
222C2×Dic13—21no—
223C2×Dic13—21no—
224C2×Dic13—21no—
225C2×Dic13—42no—
226C2×Dic13—81no—
227C8×C13—42no—
228#1055—21no—
229#1055—21no—
230#1055—22no—
231#1055—22no—
232#1055—42no—
233#1055#11712yes—
234#1055#11712yes—
235C23×C8—131no—
236C2×#117—131no—
237C2×#117C2×D1311yescharacteristic
238#433—262no—
239#433—262no—
240#432—261no—
241#432—261no—
242#431—261no—
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#424—132no—
259#407—131no—
260#407C2×D1311yescharacteristic
261C2×C22⋊C8—131no—
262#405—132no—
263#405—132no—
264C2×#97—132no—
265C4×C22⋊C4C2×D1311yescharacteristic
266#341—132no—
267#339—132no—
268#339—132no—
269#339C2×D1312yes—
270#339C2×D1312yes—
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#44412yes—
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×C13—82no—
290C4×C13C2×#11711yescharacteristic
291C4×C13#51911yescharacteristic
292C4×C13#54712yes—
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—132no—
307C22×C8—264no—
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—21no—
326C2×C22⋊C4—261no—
327C2×C42—21no—
328C2×C42—261no—
329C2×C42C22×D1312yes—
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—262no—
348C4⋊C8—262no—
349C4⋊C8—262no—
350C4⋊C8—262no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—131no—
354C22⋊C8—131no—
355C22⋊C8—132no—
356C22⋊C8—261no—
357C22⋊C8—261no—
358#97—264no—
359#97—262no—
360#97—262no—
361C4×C8—262no—
362C4×C8—262no—
363#95—21no—
364C2×C13—22no—
365C2×C13—22no—
366C2×C13—41no—
367C2×C13#234411yescharacteristic
368C2×C13C2×#44411yescharacteristic
369C2×C13#295711yescharacteristic
370C24#612911yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—261no—
377C22×C4—261no—
378C22×C4C2×C4×D1311yescharacteristic
379C22×C4C2×C4×D1311yescharacteristic
380C22×C4D4×D1311yescharacteristic
381C22×C4D4×D1311yescharacteristic
382C22×C4#612911yescharacteristic
383C22×C4C23×D1311yescharacteristic
384M16—22no—
385M16—22no—
386M16—262no—
387M16—262no—
388C2×C8—22no—
389C2×C8—131no—
390C2×C8—131no—
391C2×C8—134no—
392C2×C8—131no—
393C2×C8—131no—
394C2×C8—132no—
395C2×C8—132no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—262no—
401C2×C8—262no—
402C2×C8—262no—
403C2×C8—262no—
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—42no—
421C22⋊C4—261no—
422C22⋊C4—261no—
423C22⋊C4—261no—
424C22⋊C4—261no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—22no—
430C42—22no—
431C42—261no—
432C42—261no—
433C42—261no—
434C42—261no—
435C13#2260711yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—41no—
439C23#8813511yescharacteristic
440C23#8813511yescharacteristic
441C23C2×#612911yescharacteristic
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—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—261no—
461C2×C4—261no—
462C2×C4—522no—
463C2×C4—1041no—
464C2×C4#8813511yescharacteristic
465C2×C4#8813511yescharacteristic
466C2×C4C22×C4×D1311yescharacteristic
467C2×C4C2×D4×D1311yescharacteristic
468C2×C4#41×D1312yes—
469C2×C4#8825712yes—
470C8—42no—
471C8—132no—
472C8—132no—
473C8—261no—
474C8—261no—
475C8—262no—
476C8—262no—
477C8—522no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—44no—
486C22#1171848412yes—
487C22C2×#8813511yescharacteristic
488C22#1171935512yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—82no—
496C4—521no—
497C4—521no—
498C4—521no—
499C4—521no—
500C4#1171922111yescharacteristic
501C4D13×#11711yescharacteristic
502C4#1171936012yes—
503C2—22no—
504C2—22no—
505C2—41no—
506C2#1311770011yescharacteristic
507C2C2×#1171848411yescharacteristic
508C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1826C2
socleC22×C13C2×C4×D4
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenter#1826D13
hypocenterC13#22607
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #13115588C2semidirect
5. #13115438C2semidirect
6. #13115433C2semidirect
9. #13114719C2semidirect
24. #11718659C4semidirect
25. #11718659C4semidirect
26. #11718659C4semidirect
27. #11718659C4semidirect
33. C2×#88048C4semidirect
34. C2×#88048C4semidirect
35. C2×#88047C4semidirect
36. C2×#88047C4semidirect
435. C13#22607semidirect

Maximal subgroups

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

subgroupindex
#131234962
#131234942
C2×#117186592
#131155882
#131154382
#131154332
#131149362
#131148722
#131147192
#131146142
C13×#18262
#2260713