Finite Group Databasebeta

← #27198121

Subgroups — #27198121

Order 13184.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692989C211yesmaximal, characteristic
2C2×C4×C22⋊D103C211yesmaximal, characteristic, complemented
3C22×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D103C211yesmaximal, characteristic, complemented
5#20267691C211yesmaximal, characteristic, complemented
6#20267682C211yesmaximal, characteristic, complemented
7#20267681C211yesmaximal, characteristic, complemented
8#20267671C211yesmaximal, characteristic, complemented
9#20267670C211yesmaximal, characteristic, complemented
10#20267667C211yesmaximal, characteristic, complemented
11#20267664C211yesmaximal, characteristic, complemented
12#20267662C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic103C211yesmaximal, characteristic, complemented
14C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C103C211yesmaximal, characteristic, complemented
16C24×D103C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C22×C22⋊D103C2211yescharacteristic
19C23×Dic103C2211yescharacteristic
20C22×C4×D103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22#15692989C418yescomplemented
23C4×C22⋊D103—24no—
24C2×Dic103⋊C4C2211yescharacteristic, complemented
25C2×Dic103⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic103C2211yescharacteristic
27C2×C22⋊Dic103C2211yescharacteristic
28C2×C22⋊Dic103C2211yescharacteristic, complemented
29C2×C22⋊Dic103C2211yescharacteristic, complemented
30C2×(C2×D103)⋊C4—24no—
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×(C2×D103)⋊C4C2211yescharacteristic
37C2×(C2×D103)⋊C4C2211yescharacteristic
38C2×(C2×D103)⋊C4C2211yescharacteristic
39C22⋊C4×D103—24no—
40C2×C4×Dic103C2211yescharacteristic, complemented
41C2×C4×Dic103C2211yescharacteristic, complemented
42C103⋊#95C2211yescharacteristic, complemented
43C103⋊#95C2211yescharacteristic, complemented
44C103⋊#95C2211yescharacteristic, complemented
45C103⋊#95C2211yescharacteristic, complemented
46C103⋊#95C2211yescharacteristic, complemented
47C103⋊#95C2211yescharacteristic, complemented
48C22×D4×C103C2211yescharacteristic
49C23×C4×C103C2211yescharacteristic
50C23×C4×C103C2211yescharacteristic, complemented
51C4×D4×C103—24no—
52C2×C4⋊C4×C103C2211yescharacteristic, complemented
53C2×C22⋊C4×C103C2211yescharacteristic
54C2×C22⋊C4×C103C2211yescharacteristic, complemented
55C2×C42×C103C2211yescharacteristic, complemented
56C23×D103—22no—
57C23×D103—22no—
58C23×D103—22no—
59C23×D103—22no—
60C23×D103—41no—
61C23×D103—41no—
62C23×D103C2×C414yescomplemented
63C23×D103C2311yescharacteristic
64C23×D103C2311yescharacteristic
65C2×C22⋊D103—22no—
66C2×C22⋊D103—22no—
67C2×C22⋊D103—41no—
68C2×C22⋊D103—41no—
69C2×C22⋊D103C2×C414yescomplemented
70C2×C22⋊D103C2×C414yescomplemented
71C22×Dic103—22no—
72C22×Dic103—22no—
73C22×Dic103—41no—
74C22×Dic103C2311yescharacteristic
75C22×Dic103C2311yescharacteristic
76C22×Dic103C2311yescharacteristic
77C22×Dic103C2311yescharacteristic
78C22×Dic103C2311yescharacteristic
79C22×Dic103C2311yescharacteristic
80C2×C4×D103—22no—
81C2×C4×D103—22no—
82C2×C4×D103—22no—
83C2×C4×D103—22no—
84C2×C4×D103—41no—
85C2×C4×D103—41no—
86Dic103⋊C4—22no—
87Dic103⋊C4—41no—
88C22⋊Dic103—22no—
89C22⋊Dic103—22no—
90C22⋊Dic103—41no—
91C22⋊Dic103C2×C414yescomplemented
92(C2×D103)⋊C4—22no—
93(C2×D103)⋊C4—22no—
94(C2×D103)⋊C4—22no—
95(C2×D103)⋊C4—22no—
96(C2×D103)⋊C4—22no—
97(C2×D103)⋊C4C2×C414yescomplemented
98(C2×D103)⋊C4C2×C414yescomplemented
99(C2×D103)⋊C4D414yescomplemented
100C4×Dic103—22no—
101C4×Dic103—41no—
102C24×C103C2311yescharacteristic
103C24×C103C2311yescharacteristic
104C2×D4×C103—22no—
105C2×D4×C103—22no—
106C2×D4×C103C2×C414yescomplemented
107C22×C4×C103—22no—
108C22×C4×C103—22no—
109C22×C4×C103—22no—
110C22×C4×C103—22no—
111C22×C4×C103—41no—
112C22×C4×C103—41no—
113C22×C4×C103C2311yescharacteristic
114C22×C4×C103C2311yescharacteristic
115C22×C4×C103C2311yescharacteristic
116C22×C4×C103C2311yescharacteristic
117C22×C4×C103C2311yescharacteristic
118C4⋊C4×C103—22no—
119C22⋊C4×C103—22no—
120C22⋊C4×C103D414yescomplemented
121C42×C103—22no—
122C23×C103—21no—
123C23×C103—21no—
124C23×C103—21no—
125C23×C103—21no—
126C23×C103—21no—
127C23×C103—21no—
128C23×C103—21no—
129C23×C103—21no—
130C23×C103—21no—
131C23×C103—21no—
132C23×C103C22×C412yes—
133C23×C103C22×C412yes—
134C23×C103C2×D412yes—
135C23×C103#4112yes—
136C23×C103C2411yescharacteristic
137C22×D103—21no—
138C22×D103—21no—
139C22×D103—21no—
140C22×D103—21no—
141C22×D103—28no—
142C22×D103—21no—
143C22×D103—21no—
144C22×D103—21no—
145C22×D103—21no—
146C22×D103—21no—
147C22×D103—21no—
148C22×D103—28no—
149C22×D103—44no—
150C22×D103—44no—
151C22×D103—44no—
152C22×D103—44no—
153C22×D103—44no—
154C22×D103C22×C412yes—
155C22×D103C22×C412yes—
156C22×D103C2×D412yes—
157C22×D103#4112yes—
158D4×C103—28no—
159C2×C4×C103—21no—
160C2×C4×C103—21no—
161C2×C4×C103—21no—
162C2×C4×C103—21no—
163C2×C4×C103—21no—
164C2×C4×C103—21no—
165C2×C4×C103—21no—
166C2×C4×C103—21no—
167C2×C4×C103—21no—
168C2×C4×C103—21no—
169C2×C4×C103—21no—
170C2×C4×C103—44no—
171C2×C4×C103—44no—
172C2×C4×C103C22×C412yes—
173C2×C4×C103C2×D412yes—
174C2×C4×C103C2×D412yes—
175C2×C4×C103C2×D412yes—
176C22⋊D103—28no—
177C22⋊D103—44no—
178C2×Dic103—21no—
179C2×Dic103—21no—
180C2×Dic103—21no—
181C2×Dic103—21no—
182C2×Dic103—21no—
183C2×Dic103—21no—
184C2×Dic103—21no—
185C2×Dic103—21no—
186C2×Dic103—21no—
187C2×Dic103—21no—
188C2×Dic103—21no—
189C2×Dic103—21no—
190C2×Dic103—21no—
191C2×Dic103—21no—
192C2×Dic103—21no—
193C2×Dic103—44no—
194C2×Dic103C22×C412yes—
195C2×Dic103C22×C412yes—
196C2×Dic103C2×D412yes—
197C4×D103—44no—
198C4×D103—44no—
199C22×C103—22no—
200C22×C103—22no—
201C22×C103—22no—
202C22×C103—22no—
203C22×C103—22no—
204C22×C103—22no—
205C22×C103—22no—
206C22×C103—22no—
207C22×C103—22no—
208C22×C103—41no—
209C22×C103—41no—
210C22×C103—41no—
211C22×C103—41no—
212C22×C103C4×D414yescomplemented
213C22×C103C23×C411yescharacteristic
214C22×C103C22×D411yescharacteristic
215C22×C103C22×D411yescharacteristic
216C22×C103C2×#4111yescharacteristic
217C22×C103C2×#4111yescharacteristic
218C22×C103H(5,𝔽2)11yescharacteristic
219C22×C103H(5,𝔽2)11yescharacteristic
220C2×D103—22no—
221C2×D103—22no—
222C2×D103—22no—
223C2×D103—22no—
224C2×D103—22no—
225C2×D103—22no—
226C2×D103—22no—
227C2×D103—22no—
228C2×D103—22no—
229C2×D103—416no—
230C2×D103—41no—
231C2×D103—41no—
232C2×D103—41no—
233C2×D103—41no—
234C2×D103C4×D414yescomplemented
235C4×C103—22no—
236C4×C103—22no—
237C4×C103—22no—
238C4×C103—22no—
239C4×C103—41no—
240Dic103—22no—
241Dic103—22no—
242Dic103—22no—
243Dic103—41no—
244Dic103—41no—
245Dic103—41no—
246C2×C103—24no—
247C2×C103—42no—
248C2×C103C2×C4×D411yescharacteristic
249C2×C103C2×C4×D411yescharacteristic
250C2×C103#51811yescharacteristic
251C2×C103D4211yescharacteristic
252C2×C103#54611yescharacteristic
253C2×C103#54611yescharacteristic
254C2×C103#55111yescharacteristic
255D103—24no—
256D103—42no—
257#2358—1031nomaximal, Sylow
258C103#235811yescharacteristic, complemented, Sylow
259C2×#120—1031no—
260C2×C4×D4—1031no—
261C2×C4×D4D10311yescharacteristic, complemented
262C22×C22⋊C4—1031no—
263C22×C22⋊C4—1031no—
264#390—1031no—
265#388—1031no—
266#388—1031no—
267#386—1031no—
268#386—1031no—
269#386—1031no—
270#385—1031no—
271#385—1031no—
272C4×C22⋊C4—1031no—
273C4×C22⋊C4—1031no—
274C25—1031no—
275C22×D4—1031no—
276C22×D4—1031no—
277C22×D4C2×D10311yescharacteristic
278C23×C4—1031no—
279C23×C4—1031no—
280C23×C4—1031no—
281C23×C4C2×D10311yescharacteristic
282C23×C4C2×D10311yescharacteristic, complemented
283#120—1038no—
284C4×D4—24no—
285C4×D4—2064no—
286C2×C4⋊C4—1031no—
287C2×C4⋊C4—1031no—
288C2×C4⋊C4C2×D10311yescharacteristic, complemented
289C2×C22⋊C4—1031no—
290C2×C22⋊C4—1031no—
291C2×C22⋊C4—1031no—
292C2×C22⋊C4—1031no—
293C2×C22⋊C4—1031no—
294C2×C22⋊C4—1031no—
295C2×C22⋊C4—1031no—
296C2×C22⋊C4—1031no—
297C2×C22⋊C4—1031no—
298C2×C22⋊C4—1031no—
299C2×C22⋊C4—1031no—
300C2×C22⋊C4—1031no—
301C2×C22⋊C4—2064no—
302C2×C22⋊C4—2064no—
303C2×C22⋊C4C2×D10311yescharacteristic
304C2×C22⋊C4C2×D10311yescharacteristic, complemented
305C2×C42—1031no—
306C2×C42—1031no—
307C2×C42C2×D10311yescharacteristic, complemented
308#95—1031no—
309#95—1031no—
310#95—1031no—
311#95—1031no—
312#95—1031no—
313#95—1031no—
314C24—1031no—
315C24—1034no—
316C24—1031no—
317C24—4121no—
318C24—4121no—
319C24—2062no—
320C24—2062no—
321C24—2062no—
322C24—2062no—
323C24C22×D10311yescharacteristic
324C24C22×D10311yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—1034no—
328C2×D4—1034no—
329C2×D4—4121no—
330C2×D4—4121no—
331C2×D4—2062no—
332C2×D4—2062no—
333C2×D4C4×D10314yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—1031no—
341C22×C4—1031no—
342C22×C4—1031no—
343C22×C4—1031no—
344C22×C4—1031no—
345C22×C4—1031no—
346C22×C4—4121no—
347C22×C4—4121no—
348C22×C4—4121no—
349C22×C4—2062no—
350C22×C4—2062no—
351C22×C4—2062no—
352C22×C4—2062no—
353C22×C4—2062no—
354C22×C4—2062no—
355C22×C4C22×D10311yescharacteristic
356C22×C4C22×D10311yescharacteristic
357C22×C4C22×D10311yescharacteristic
358C22×C4C22×D10311yescharacteristic
359C22×C4C22×D10311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—4121no—
362C4⋊C4—2062no—
363C22⋊C4—22no—
364C22⋊C4—1034no—
365C22⋊C4—1034no—
366C22⋊C4—1034no—
367C22⋊C4—1034no—
368C22⋊C4—4121no—
369C22⋊C4—2062no—
370C22⋊C4—2062no—
371C22⋊C4—2062no—
372C22⋊C4—2062no—
373C22⋊C4—2062no—
374C22⋊C4—2062no—
375C22⋊C4—2062no—
376C22⋊C4C22⋊D10314yescomplemented
377C42—22no—
378C42—4121no—
379C42—2062no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—1032no—
391C23—1032no—
392C23—1032no—
393C23—1032no—
394C23—4124no—
395C23—4124no—
396C23—4124no—
397C23—4124no—
398C23—4124no—
399C23—2068no—
400C23—2061no—
401C23—2061no—
402C23—2061no—
403C23—2061no—
404C23—2061no—
405C23—2061no—
406C23—2068no—
407C23—2061no—
408C23—2061no—
409C23—2061no—
410C23—2061no—
411C23C2×C4×D10312yes—
412C23C2×C4×D10312yes—
413C23C2×C22⋊D10312yes—
414C23#1311010512yes—
415C23C23×D10311yescharacteristic
416D4—28no—
417D4—4124no—
418D4—2068no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—1032no—
433C2×C4—1032no—
434C2×C4—1032no—
435C2×C4—4124no—
436C2×C4—4124no—
437C2×C4—4124no—
438C2×C4—2061no—
439C2×C4—2061no—
440C2×C4—2061no—
441C2×C4—2061no—
442C2×C4—2061no—
443C2×C4—2061no—
444C2×C4—2061no—
445C2×C4—2061no—
446C2×C4—2061no—
447C2×C4—2061no—
448C2×C4—2061no—
449C2×C4—2061no—
450C2×C4—2061no—
451C2×C4—2061no—
452C2×C4—2061no—
453C2×C4C2×C4×D10312yes—
454C2×C4D4×D10312yes—
455C2×C4C2×C22⋊D10312yes—
456C2×C4C2×C22⋊D10312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—1034no—
471C22—41216no—
472C22—4121no—
473C22—4121no—
474C22—4121no—
475C22—4121no—
476C22—2062no—
477C22—2062no—
478C22—2062no—
479C22—2062no—
480C22—2062no—
481C22—2062no—
482C22—2062no—
483C22—2062no—
484C22—2062no—
485C22C4×C22⋊D10314yescomplemented
486C22C22×C4×D10311yescharacteristic
487C22C2×D4×D10311yescharacteristic
488C22C22×C22⋊D10311yescharacteristic
489C22#41×D10311yescharacteristic
490C22C2×#1311010511yescharacteristic
491C22#1569306611yescharacteristic
492C22#1569306711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—4121no—
499C4—4121no—
500C4—4121no—
501C4—2062no—
502C4—2062no—
503C4—2062no—
504C2—24no—
505C2—42no—
506C2—4122no—
507C2—2064no—
508C2C4×D4×D10311yescharacteristic
509C2C2×C4×C22⋊D10311yescharacteristic
510C2#2026826311yescharacteristic
511C2D4×C22⋊D10311yescharacteristic
512C2#2026842911yescharacteristic
513C2#2026843711yescharacteristic
514C2#2026847011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC2×C4×D4×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692989C2
hypercenterC2×C4×D4D103
hypocenterC103#2358
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D103C2semidirect
3. C22×(C2×D103)⋊C4C2semidirect
4. C2×C22⋊C4×D103C2semidirect
5. #20267691C2semidirect
6. #20267682C2semidirect
7. #20267681C2semidirect
8. #20267671C2semidirect
9. #20267670C2semidirect
10. #20267667C2semidirect
11. #20267664C2semidirect
12. #20267662C2semidirect
13. C22⋊C4×Dic103C2semidirect
14. C4×(C2×D103)⋊C4C2semidirect
15. C2×C4×D4×C103C2semidirect
22. #15692989C4semidirect
24. C2×Dic103⋊C4C22semidirect
25. C2×Dic103⋊C4C22semidirect
28. C2×C22⋊Dic103C22semidirect
29. C2×C22⋊Dic103C22semidirect
40. C2×C4×Dic103C22semidirect
41. C2×C4×Dic103C22semidirect
42. C103⋊#95C22semidirect
43. C103⋊#95C22semidirect
44. C103⋊#95C22semidirect
45. C103⋊#95C22semidirect
46. C103⋊#95C22semidirect
47. C103⋊#95C22semidirect
50. C23×C4×C103C22semidirect
52. C2×C4⋊C4×C103C22semidirect
54. C2×C22⋊C4×C103C22semidirect
55. C2×C42×C103C22semidirect
62. C23×D103C2×C4semidirect
69. C2×C22⋊D103C2×C4semidirect
70. C2×C22⋊D103C2×C4semidirect
91. C22⋊Dic103C2×C4semidirect
97. (C2×D103)⋊C4C2×C4semidirect
98. (C2×D103)⋊C4C2×C4semidirect
99. (C2×D103)⋊C4D4semidirect
106. C2×D4×C103C2×C4semidirect
120. C22⋊C4×C103D4semidirect
212. C22×C103C4×D4semidirect
234. C2×D103C4×D4semidirect
258. C103#2358semidirect
261. C2×C4×D4D103semidirect
282. C23×C4C2×D103semidirect
288. C2×C4⋊C4C2×D103semidirect
304. C2×C22⋊C4C2×D103semidirect
307. C2×C42C2×D103semidirect
333. C2×D4C4×D103semidirect
376. C22⋊C4C22⋊D103semidirect
485. C22C4×C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929892
C2×C4×C22⋊D1032
C22×(C2×D103)⋊C42
C2×C22⋊C4×D1032
#202676912
#202676822
#202676812
#202676712
#202676702
#202676672
#202676642
#202676622
C22⋊C4×Dic1032
C4×(C2×D103)⋊C42
C2×C4×D4×C1032
#2358103