Finite Group Databasebeta

← #13118959

Subgroups — #13118959

Order 1664.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88207C211yesmaximal, characteristic
2C22×C22⋊Dic13C211yesmaximal, characteristic, complemented
3C2×#88139C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#379C211yesmaximal, characteristic, complemented
6#11718622C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic, complemented
8#11718619C211yesmaximal, characteristic, complemented
9#11718619C211yesmaximal, characteristic, complemented
10#11718618C211yesmaximal, characteristic, complemented
11#11718613C211yesmaximal, characteristic, complemented
12#11718612C211yesmaximal, characteristic, complemented
13#11718608C211yesmaximal, characteristic, complemented
14#11718605C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C25×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C22×Dic26C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C13×C22⋊C4C2211yescharacteristic
29#88207—24no—
30C2×C22⋊Dic13—24no—
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C22⋊Dic13C2211yescharacteristic
37C2×C22⋊Dic13C2211yescharacteristic
38C2×#6103C2211yescharacteristic, complemented
39C2×#6103C2211yescharacteristic, complemented
40C2×#6103C2211yescharacteristic, complemented
41C2×#6103C2211yescharacteristic, complemented
42C2×C4⋊Dic13C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45C2×C4×Dic13C2211yescharacteristic, complemented
46C2×C4×Dic13C2211yescharacteristic, complemented
47#88139—24no—
48#88132—24no—
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—22no—
58C24×C13—22no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—41no—
62C24×C13C2311yescharacteristic
63C24×C13C2311yescharacteristic
64C24×C13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—22no—
73C2×C22⋊D13—22no—
74C2×C22⋊D13—22no—
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—22no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C22×Dic13C2311yescharacteristic
90C22×Dic13C2311yescharacteristic
91C22×Dic13C2311yescharacteristic
92C2×Dic26—22no—
93C2×Dic26—22no—
94C2×Dic26—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C22⋊Dic13—22no—
102C22⋊Dic13—22no—
103C22⋊Dic13—22no—
104C22⋊Dic13—22no—
105C22⋊Dic13—22no—
106C22⋊Dic13D414yes—
107C22⋊Dic13D414yescomplemented
108#6103—22no—
109#6103—22no—
110#6103—41no—
111#6103—41no—
112C4⋊Dic13—22no—
113#6101—22no—
114#6101—22no—
115C4×Dic13—22no—
116C4×Dic13—41no—
117#2472—131nomaximal, Sylow
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—28no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—44no—
136C23×C13—44no—
137C23×C13—44no—
138C23×C13—44no—
139C23×C13—44no—
140C23×C13—44no—
141C23×C13C2×D412yes—
142C23×C13C2×D412yes—
143C23×C13#4112yes—
144C23×C13#4112yes—
145C23×C13#4112yes—
146C23×C13C2411yescharacteristic
147C22×D13—21no—
148C22×D13—21no—
149C22×D13—21no—
150C22×D13—21no—
151C22×D13—21no—
152C22×D13—21no—
153C22×D13—21no—
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—
166C22⋊D13—44no—
167C22⋊D13—44no—
168C22⋊D13—44no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
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—44no—
187C2×Dic13—44no—
188C2×Dic13C2×D412yes—
189C2×Dic13C2×D412yes—
190C2×Dic13C2×D412yes—
191C2×Dic13C2×D412yes—
192Dic26—44no—
193C2×#124—131no—
194C2×C22⋊Q8—131no—
195C2×#120—131no—
196C22×C22⋊C4—131no—
197#397—131no—
198#394—131no—
199#394—131no—
200#393—131no—
201#390—131no—
202#388—131no—
203#388—131no—
204#386—131no—
205#386—131no—
206#379D1311yescharacteristic, complemented
207C4×C22⋊C4—131no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—416no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—41no—
229C22×C13#12414yescomplemented
230C22×C13C22×D411yescharacteristic
231C22×C13C22×D411yescharacteristic
232C22×C13C2×#4111yescharacteristic
233C22×C13C2×#4111yescharacteristic
234C22×C13C2×#4111yescharacteristic
235C22×C13H(5,𝔽2)11yescharacteristic
236C22×C13H(5,𝔽2)11yescharacteristic
237C2×D13—41no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13—41no—
244C4×C13—41no—
245C4×C13—41no—
246C4×C13—41no—
247C4×C13—41no—
248Dic13—22no—
249Dic13—22no—
250Dic13—22no—
251Dic13—22no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255C25C2×D1311yescharacteristic
256C22×Q8—131no—
257C22×D4—131no—
258C22×D4—131no—
259C22×D4—131no—
260C23×C4—131no—
261C23×C4—131no—
262#124—264no—
263C22⋊Q8—264no—
264#120—264no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C22⋊C4—131no—
269C2×C22⋊C4—131no—
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—264no—
280C2×C22⋊C4C2×D1311yescharacteristic
281C2×C22⋊C4C2×D1311yescharacteristic
282C2×C22⋊C4C2×D1311yescharacteristic
283C2×C22⋊C4C2×D1311yescharacteristic
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic
286C2×C42—131no—
287C2×C42—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95—131no—
294C2×C13—24no—
295C2×C13—42no—
296C2×C13—42no—
297C2×C13#52511yescharacteristic
298C2×C13C2×#12411yescharacteristic
299C2×C13#53811yescharacteristic
300C2×C13D4211yescharacteristic
301C2×C13#54611yescharacteristic
302C2×C13#54611yescharacteristic
303C2×C13#55111yescharacteristic
304D13—81no—
305C24—22no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—41no—
311C24—41no—
312C24—131no—
313C24C22×D1311yescharacteristic
314C24C22×D1311yescharacteristic
315C24C22×D1311yescharacteristic
316C2×Q8—262no—
317C2×Q8—262no—
318C2×Q8—521no—
319C2×D4—262no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—262no—
325C2×D4—262no—
326C2×D4—521no—
327C2×D4—521no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—521no—
340C22×C4—521no—
341C22×C4C22×D1311yescharacteristic
342C22×C4C22×D1311yescharacteristic
343C22×C4C22×D1311yescharacteristic
344C22×C4C22×D1311yescharacteristic
345C4⋊C4—262no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—134no—
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—521no—
364C22⋊C4—521no—
365C42—262no—
366C42—521no—
367C13#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23#612712yes—
399C23D4×D1312yes—
400C23D4×D1312yes—
401C23#612912yes—
402C23#612912yes—
403C23C23×D1311yescharacteristic
404Q8—524no—
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—132no—
421C2×C4—132no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—261no—
425C2×C4—261no—
426C2×C4—261no—
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—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—521no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22—521no—
470C22—521no—
471C22#8813914yescomplemented
472C22C2×#612711yescharacteristic
473C22C2×D4×D1311yescharacteristic
474C22C2×D4×D1311yescharacteristic
475C22C2×#612911yescharacteristic
476C22C2×#612911yescharacteristic
477C22#8825111yescharacteristic
478C22#8825111yescharacteristic
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—262no—
484C4—262no—
485C4—262no—
486C4—262no—
487C4—521no—
488C4—521no—
489C4—521no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—1041no—
494C2#1171919511yescharacteristic
495C2C2×#8813911yescharacteristic
496C2#1171920011yescharacteristic
497C2#1171929111yescharacteristic
498C2#1171929511yescharacteristic
499C2#1171929611yescharacteristic
500C2#1171929811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#379C2
prime radicalC2×#88207C2
hypercenter#379D13
hypocenterC13#2472
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic13C2semidirect
3. C2×#88139C2semidirect
4. C2×#88132C2semidirect
5. C13×#379C2semidirect
6. #11718622C2semidirect
7. #11718620C2semidirect
8. #11718619C2semidirect
9. #11718619C2semidirect
10. #11718618C2semidirect
11. #11718613C2semidirect
12. #11718612C2semidirect
13. #11718608C2semidirect
14. #11718605C2semidirect
15. C22⋊C4×Dic13C2semidirect
22. C22×Dic26C22semidirect
38. C2×#6103C22semidirect
39. C2×#6103C22semidirect
40. C2×#6103C22semidirect
41. C2×#6103C22semidirect
42. C2×C4⋊Dic13C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
45. C2×C4×Dic13C22semidirect
46. C2×C4×Dic13C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
107. C22⋊Dic13D4semidirect
206. #379D13semidirect
229. C22×C13#124semidirect
367. C13#2472semidirect
471. C22#88139semidirect

Maximal subgroups

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

subgroupindex
C2×#882072
C22×C22⋊Dic132
C2×#881392
C2×#881322
C13×#3792
#117186222
#117186202
#117186192
#117186182
#117186132
#117186122
#117186082
#117186052
C22⋊C4×Dic132
#247213