Finite Group Databasebeta

← #13118229

Subgroups — #13118229

Order 1664.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6103C211yesmaximal, characteristic, complemented
2C2×#88148C211yesmaximal, characteristic, complemented
3C2×#88136C211yesmaximal, characteristic
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#380C211yesmaximal, characteristic, complemented
6#11718874C211yesmaximal, characteristic, complemented
7#11718654C211yesmaximal, characteristic, complemented
8#11718652C211yesmaximal, characteristic, complemented
9#11718650C211yesmaximal, characteristic, complemented
10#11718619C211yesmaximal, characteristic, complemented
11#11718603C211yesmaximal, characteristic, complemented
12#11718336C211yesmaximal, characteristic, complemented
13#11718333C211yesmaximal, characteristic, complemented
14#11718326C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C22×D52C2211yescharacteristic
21C22×D52C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25C2×C13×C4⋊C4C2211yescharacteristic, complemented
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×#6103—24no—
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×#6103C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44#88148—24no—
45#88136—24no—
46C22⋊C4×D13—24no—
47C13×#95C2211yescharacteristic, complemented
48C13×#95C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C23×D13—22no—
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—41no—
61C23×D13—41no—
62C23×D13D414yes—
63C23×D13C2311yescharacteristic
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—41no—
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13—22no—
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13—41no—
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C2×D52—22no—
87C2×D52—22no—
88C2×D52—22no—
89C2×D52—22no—
90C2×D52—41no—
91C2×D52—41no—
92C2×C4×D13—22no—
93C2×C4×D13—22no—
94C2×C4×D13—22no—
95C2×C4×D13—22no—
96C2×C4×D13—41no—
97C2×C4×D13—41no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—41no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—22no—
102C22⋊Dic13—22no—
103#6103—22no—
104#6103—22no—
105#6103—22no—
106#6103—22no—
107#6103—22no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—22no—
112#6103—41no—
113#6103—41no—
114#6103D414yescomplemented
115#6101—22no—
116#6101—41no—
117#2412—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13C2×D412yes—
123C23×C13#4112yes—
124C23×C13#4112yes—
125C23×C13C2411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—28no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—28no—
138C22×D13—21no—
139C22×D13—21no—
140C22×D13—21no—
141C22×D13—21no—
142C22×D13—21no—
143C22×D13—21no—
144C22×D13—21no—
145C22×D13—44no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13—44no—
150C22×D13C2×D412yes—
151C22×D13C2×D412yes—
152C22×D13C2×D412yes—
153C22×D13#4112yes—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—44no—
172C2×C4×C13C2×D412yes—
173C22⋊D13—44no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—44no—
189C2×Dic13C2×D412yes—
190D52—44no—
191D52—44no—
192C4×D13—44no—
193C4×D13—44no—
194C2×#123—131no—
195C2×#120—131no—
196C22×C22⋊C4—131no—
197C22×C22⋊C4—131no—
198#397—131no—
199#397—131no—
200#394—131no—
201#394—131no—
202#386—131no—
203#386—131no—
204#386—131no—
205#385—131no—
206#381—131no—
207#380—131no—
208#380D1311yescharacteristic, complemented
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13#12314yescomplemented
216C22×C13C22×D411yescharacteristic
217C22×C13C22×D411yescharacteristic
218C22×C13C2×#4111yescharacteristic
219C22×C13C2×#4111yescharacteristic
220C22×C13C2×#4111yescharacteristic
221C22×C13H(5,𝔽2)11yescharacteristic
222C22×C13H(5,𝔽2)11yescharacteristic
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—22no—
228C2×D13—22no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—416no—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—41no—
237C2×D13—41no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13—41no—
244C2×D13#12114yes—
245C4×C13—22no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—41no—
250C4×C13—41no—
251Dic13—22no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255Dic13—41no—
256C25—131no—
257C22×D4—131no—
258C22×D4—131no—
259C22×D4—131no—
260C23×C4—131no—
261C23×C4—131no—
262C23×C4—131no—
263C23×C4C2×D1311yescharacteristic
264#123—264no—
265#120—264no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4C2×D1311yescharacteristic, complemented
269C2×C4⋊C4C2×D1311yescharacteristic, complemented
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4—131no—
274C2×C22⋊C4—131no—
275C2×C22⋊C4—131no—
276C2×C22⋊C4—131no—
277C2×C22⋊C4—131no—
278C2×C22⋊C4—131no—
279C2×C22⋊C4—131no—
280C2×C22⋊C4—131no—
281C2×C22⋊C4—131no—
282C2×C22⋊C4—131no—
283C2×C22⋊C4—264no—
284C2×C22⋊C4—264no—
285C2×C22⋊C4C2×D1311yescharacteristic
286C2×C22⋊C4C2×D1311yescharacteristic
287#95—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95C2×D1311yescharacteristic, complemented
294#95C2×D1311yescharacteristic, complemented
295C2×C13—24no—
296C2×C13C2×#12111yescharacteristic
297C2×C13C2×#12311yescharacteristic
298C2×C13#53411yescharacteristic
299C2×C13#54611yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#55111yescharacteristic
302C2×C13#55111yescharacteristic
303D13—24no—
304D13—42no—
305D13—81no—
306C24—131no—
307C24—131no—
308C24—134no—
309C24—131no—
310C24—262no—
311C24—262no—
312C24—262no—
313C24—262no—
314C24—521no—
315C24—521no—
316C24C22×D1311yescharacteristic
317C2×D4—262no—
318C2×D4—262no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—521no—
325C2×D4—521no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—262no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—262no—
340C22×C4—521no—
341C22×C4—521no—
342C22×C4—521no—
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C22×C4C22×D1311yescharacteristic
346C22×C4C22×D1311yescharacteristic
347C22×C4C22×D1311yescharacteristic
348C22×C4C22×D1311yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—262no—
352C4⋊C4—521no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—134no—
356C22⋊C4—262no—
357C22⋊C4—262no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—262no—
362C22⋊C4—262no—
363C22⋊C4—262no—
364C22⋊C4—262no—
365C22⋊C4—262no—
366C22⋊C4—521no—
367C22⋊C4—521no—
368C13#241211yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—132no—
374C23—132no—
375C23—132no—
376C23—132no—
377C23—268no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23—268no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23—261no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23—261no—
396C23—524no—
397C23—524no—
398C23—524no—
399C23—524no—
400C23—524no—
401C23#612712yes—
402C23D4×D1312yes—
403C23#613112yes—
404C23C23×D1311yescharacteristic
405D4—524no—
406D4—524no—
407D4—524no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—44no—
426C2×C4—132no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—524no—
442C2×C4—524no—
443C2×C4—524no—
444C2×C4D4×D1312yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—134no—
452C22—262no—
453C22—262no—
454C22—262no—
455C22—262no—
456C22—262no—
457C22—262no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—5216no—
462C22—521no—
463C22—521no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22—521no—
472C22—521no—
473C22#8814814yescomplemented
474C22C2×#612711yescharacteristic
475C22C2×D4×D1311yescharacteristic
476C22C2×D4×D1311yescharacteristic
477C22#8825111yescharacteristic
478C22C2×#613111yescharacteristic
479C22#41×D1311yescharacteristic
480C22#8825611yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—262no—
488C4—521no—
489C4—521no—
490C4—521no—
491C4—521no—
492C2—24no—
493C2—264no—
494C2—522no—
495C2—1041no—
496C2#1171919511yescharacteristic
497C2C2×#8814811yescharacteristic
498C2#1171923211yescharacteristic
499C2D13×#12111yescharacteristic
500C2#1171931011yescharacteristic
501C2#1171933511yescharacteristic
502C2#1171934211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC2×#88136C2
hypercenter#380D13
hypocenterC13#2412
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#6103C2semidirect
2. C2×#88148C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#380C2semidirect
6. #11718874C2semidirect
7. #11718654C2semidirect
8. #11718652C2semidirect
9. #11718650C2semidirect
10. #11718619C2semidirect
11. #11718603C2semidirect
12. #11718336C2semidirect
13. #11718333C2semidirect
14. #11718326C2semidirect
15. #11718325C2semidirect
24. C2×C13×C4⋊C4C22semidirect
25. C2×C13×C4⋊C4C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
47. C13×#95C22semidirect
48. C13×#95C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
114. #6103D4semidirect
208. #380D13semidirect
215. C22×C13#123semidirect
268. C2×C4⋊C4C2×D13semidirect
269. C2×C4⋊C4C2×D13semidirect
293. #95C2×D13semidirect
294. #95C2×D13semidirect
368. C13#2412semidirect
473. C22#88148semidirect

Maximal subgroups

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

subgroupindex
C22×#61032
C2×#881482
C2×#881362
C2×C22⋊C4×D132
C13×#3802
#117188742
#117186542
#117186522
#117186502
#117186192
#117186032
#117183362
#117183332
#117183262
#117183252
#241213