Finite Group Databasebeta

← #27198122

Subgroups — #27198122

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×#15692991C211yesmaximal, characteristic
2C2×C4×D412C211yesmaximal, characteristic, complemented
3C2×#15692983C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D103C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D103C211yesmaximal, characteristic, complemented
6#20267691C211yesmaximal, characteristic, complemented
7#20267684C211yesmaximal, characteristic, complemented
8#20267669C211yesmaximal, characteristic, complemented
9#20267669C211yesmaximal, characteristic, complemented
10#20267667C211yesmaximal, characteristic, complemented
11#20267665C211yesmaximal, characteristic, complemented
12#20267662C211yesmaximal, characteristic, complemented
13C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
14#20267638C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic, complemented
16C24×D103C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C22×D412C2211yescharacteristic
19C22×C22⋊D103C2211yescharacteristic
20C22×C4×D103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22C22×C4×D103C2211yescharacteristic
23C22×C4×D103C2211yescharacteristic
24C22×C4×D103C2211yescharacteristic, complemented
25#15692991C418yescomplemented
26C4×D412—24no—
27#15692983—24no—
28C2×C4⋊Dic103C2211yescharacteristic, complemented
29C2×Dic103⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic103C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
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, complemented
39C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D103—24no—
42C22⋊C4×D103—24no—
43C2×C4×Dic103C2211yescharacteristic, complemented
44C2×C4×Dic103C2211yescharacteristic, complemented
45C103⋊#95C2211yescharacteristic, complemented
46C103⋊#95C2211yescharacteristic, complemented
47C103⋊#95C2211yescharacteristic, complemented
48C103⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C103C2211yescharacteristic, complemented
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103C2211yescharacteristic
52C2×C22⋊C4×C103C2211yescharacteristic
53C2×C42×C103C2211yescharacteristic, complemented
54#95×C103C2211yescharacteristic, complemented
55#95×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
65C23×D103C2311yescharacteristic
66C2×D412—22no—
67C2×D412—22no—
68C2×D412—22no—
69C2×D412—22no—
70C2×D412C2×C414yescomplemented
71C2×D412C2×C414yescomplemented
72C2×C22⋊D103—41no—
73C2×C22⋊D103—41no—
74C2×C22⋊D103C2×C414yescomplemented
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—22no—
85C2×C4×D103—22no—
86C2×C4×D103—22no—
87C2×C4×D103—22no—
88C2×C4×D103—22no—
89C2×C4×D103—22no—
90C2×C4×D103—41no—
91C2×C4×D103—41no—
92C2×C4×D103—41no—
93C2×C4×D103—41no—
94C2×C4×D103—41no—
95C4⋊Dic103—22no—
96Dic103⋊C4—41no—
97C22⋊Dic103—22no—
98C22⋊Dic103—22no—
99(C2×D103)⋊C4—22no—
100(C2×D103)⋊C4—22no—
101(C2×D103)⋊C4—22no—
102(C2×D103)⋊C4—22no—
103(C2×D103)⋊C4—41no—
104(C2×D103)⋊C4C2×C414yescomplemented
105(C2×D103)⋊C4C2×C414yescomplemented
106(C2×D103)⋊C4D414yescomplemented
107(C2×D103)⋊C4D414yescomplemented
108C4×Dic103—22no—
109C4×Dic103—41no—
110C24×C103C2311yescharacteristic
111C22×C4×C103C2311yescharacteristic
112C22×C4×C103C2311yescharacteristic
113C22×C4×C103C2311yescharacteristic
114C22×C4×C103C2311yescharacteristic
115C22×C4×C103C2311yescharacteristic
116C22×C4×C103C2311yescharacteristic
117C4⋊C4×C103—22no—
118C22⋊C4×C103—22no—
119C22⋊C4×C103—22no—
120C22⋊C4×C103C2×C414yescomplemented
121C42×C103—22no—
122C23×C103—21no—
123C23×C103—21no—
124C23×C103—21no—
125C23×C103—21no—
126C23×C103—21no—
127C23×C103—21no—
128C23×C103C22×C412yes—
129C23×C103C2411yescharacteristic
130C22×D103—21no—
131C22×D103—21no—
132C22×D103—21no—
133C22×D103—21no—
134C22×D103—21no—
135C22×D103—21no—
136C22×D103—21no—
137C22×D103—21no—
138C22×D103—21no—
139C22×D103—21no—
140C22×D103—21no—
141C22×D103—21no—
142C22×D103—21no—
143C22×D103—21no—
144C22×D103—28no—
145C22×D103—28no—
146C22×D103—44no—
147C22×D103—44no—
148C22×D103—44no—
149C22×D103—44no—
150C22×D103—44no—
151C22×D103C22×C412yes—
152C22×D103C22×C412yes—
153C22×D103C22×C412yes—
154C22×D103C2×D412yes—
155C22×D103C2×D412yes—
156C22×D103#4112yes—
157C22×D103#4112yes—
158C2×C4×C103—21no—
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—21no—
171C2×C4×C103—21no—
172C2×C4×C103C22×C412yes—
173C2×C4×C103C22×C412yes—
174C2×C4×C103C2×D412yes—
175C2×C4×C103C2×D412yes—
176C22⋊D103—44no—
177C2×Dic103—21no—
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×Dic103C22×C412yes—
190C2×Dic103C2×D412yes—
191C2×Dic103C2×D412yes—
192D412—28no—
193D412—28no—
194C4×D103—44no—
195C4×D103—44no—
196C4×D103—44no—
197C4×D103—44no—
198C4×D103—44no—
199C22×C103—22no—
200C22×C103—22no—
201C22×C103—22no—
202C22×C103—41no—
203C22×C103—41no—
204C22×C103—41no—
205C22×C103—41no—
206C22×C103C23×C411yescharacteristic
207C22×C103C22×D411yescharacteristic
208C22×C103C22×D411yescharacteristic
209C22×C103C2×#4111yescharacteristic
210C22×C103C2×#4111yescharacteristic
211C22×C103H(5,𝔽2)11yescharacteristic
212C22×C103H(5,𝔽2)11yescharacteristic
213C2×D103—22no—
214C2×D103—22no—
215C2×D103—22no—
216C2×D103—22no—
217C2×D103—22no—
218C2×D103—22no—
219C2×D103—22no—
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—416no—
229C2×D103—41no—
230C2×D103—41no—
231C2×D103—41no—
232C2×D103—41no—
233C2×D103C4×D414yescomplemented
234C2×D103C4×D414yescomplemented
235C4×C103—22no—
236C4×C103—22no—
237C4×C103—22no—
238C4×C103—22no—
239C4×C103—41no—
240C4×C103—41no—
241Dic103—22no—
242Dic103—22no—
243Dic103—22no—
244Dic103—41no—
245Dic103—41no—
246C2×C103—42no—
247C2×C103C2×C4×D411yescharacteristic
248C2×C103C2×C4×D411yescharacteristic
249C2×C103#51811yescharacteristic
250C2×C103D4211yescharacteristic
251C2×C103#54611yescharacteristic
252C2×C103#54611yescharacteristic
253C2×C103#55111yescharacteristic
254D103—24no—
255D103—24no—
256D103—42no—
257#2358—1031nomaximal, Sylow
258C103#235811yescharacteristic, complemented, Sylow
259C2×#120—1031no—
260C2×C4×D4—1031no—
261C2×C4×D4—1031no—
262C22×C22⋊C4—1031no—
263C22×C22⋊C4—1031no—
264#390—1031no—
265#388—1031no—
266#388D10311yescharacteristic, complemented
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×D4—1031no—
278C23×C4—1031no—
279C23×C4—1031no—
280C23×C4—1031no—
281C23×C4—1031no—
282C23×C4—1031no—
283#120—1038no—
284C4×D4—2064no—
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—2064no—
301C2×C22⋊C4—2064no—
302C2×C22⋊C4C2×D10311yescharacteristic
303C2×C22⋊C4C2×D10311yescharacteristic
304C2×C22⋊C4C2×D10311yescharacteristic
305C2×C42—1031no—
306C2×C42—1031no—
307C2×C42C2×D10311yescharacteristic, complemented
308#95—1031no—
309#95—1031no—
310#95—1031no—
311#95—1031no—
312#95C2×D10311yescharacteristic, complemented
313#95C2×D10311yescharacteristic, complemented
314C24—1031no—
315C24—1031no—
316C24—1034no—
317C24—1031no—
318C24—4121no—
319C24—4121no—
320C24—2062no—
321C24—2062no—
322C24—2062no—
323C24—2062no—
324C24C22×D10311yescharacteristic
325C2×D4—1034no—
326C2×D4—1034no—
327C2×D4—1034no—
328C2×D4—4121no—
329C2×D4—4121no—
330C2×D4—2062no—
331C2×D4—2062no—
332C2×D4—2062no—
333C2×D4—2062no—
334C22×C4—1031no—
335C22×C4—1031no—
336C22×C4—1031no—
337C22×C4—1031no—
338C22×C4—1031no—
339C22×C4—4121no—
340C22×C4—4121no—
341C22×C4—4121no—
342C22×C4—4121no—
343C22×C4—4121no—
344C22×C4—2062no—
345C22×C4—2062no—
346C22×C4—2062no—
347C22×C4—2062no—
348C22×C4—2062no—
349C22×C4—2062no—
350C22×C4—2062no—
351C22×C4—2062no—
352C22×C4—2062no—
353C22×C4—2062no—
354C22×C4C22×D10311yescharacteristic
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—22no—
365C22⋊C4—1034no—
366C22⋊C4—1034no—
367C22⋊C4—1034no—
368C22⋊C4—1034no—
369C22⋊C4—4121no—
370C22⋊C4—2062no—
371C22⋊C4—2062no—
372C22⋊C4—2062no—
373C22⋊C4—2062no—
374C22⋊C4—2062no—
375C22⋊C4—2062no—
376C22⋊C4C4×D10314yescomplemented
377C42—22no—
378C42—4121no—
379C42—2062no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—1032no—
387C23—1032no—
388C23—1032no—
389C23—1032no—
390C23—1032no—
391C23—1032no—
392C23—1032no—
393C23—4124no—
394C23—4124no—
395C23—4124no—
396C23—4124no—
397C23—4124no—
398C23—2068no—
399C23—2068no—
400C23—2061no—
401C23—2061no—
402C23—2061no—
403C23—2061no—
404C23—2061no—
405C23—2061no—
406C23—2061no—
407C23—2061no—
408C23—2061no—
409C23—2061no—
410C23—2061no—
411C23—2061no—
412C23—2061no—
413C23—2061no—
414C23C2×C4×D10312yes—
415C23C23×D10311yescharacteristic
416D4—4124no—
417D4—2068no—
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—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—1032no—
434C2×C4—1032no—
435C2×C4—1032no—
436C2×C4—4124no—
437C2×C4—4124no—
438C2×C4—4124no—
439C2×C4—4124no—
440C2×C4—4124no—
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×C4C2×C4×D10312yes—
455C2×C4D4×D10312yes—
456C2×C4D4×D10312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—1034no—
465C22—1034no—
466C22—41216no—
467C22—4121no—
468C22—4121no—
469C22—4121no—
470C22—4121no—
471C22—2062no—
472C22—2062no—
473C22—2062no—
474C22—2062no—
475C22—2062no—
476C22—2062no—
477C22—2062no—
478C22—2062no—
479C22—2062no—
480C22—2062no—
481C22—2062no—
482C22—2062no—
483C22—2062no—
484C22—2062no—
485C22—2062no—
486C22C22×C4×D10311yescharacteristic
487C22C2×D4×D10311yescharacteristic
488C22C2×D4×D10311yescharacteristic
489C22#41×D10311yescharacteristic
490C22#41×D10311yescharacteristic
491C22#1569306711yescharacteristic
492C22#1569306711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—4121no—
500C4—4121no—
501C4—2062no—
502C4—2062no—
503C4—2062no—
504C2—42no—
505C2—4122no—
506C2—2064no—
507C2—2064no—
508C2C4×D4×D10311yescharacteristic
509C2C4×D4×D10311yescharacteristic
510C2#2026826511yescharacteristic
511C2#2026842511yescharacteristic
512C2#2026843311yescharacteristic
513C2#2026843411yescharacteristic
514C2#2026846611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692991C2
hypercenter#388D103
hypocenterC103#2358
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D412C2semidirect
3. C2×#15692983C2semidirect
4. C2×C22⋊C4×D103C2semidirect
5. C2×C22⋊C4×D103C2semidirect
6. #20267691C2semidirect
7. #20267684C2semidirect
8. #20267669C2semidirect
9. #20267669C2semidirect
10. #20267667C2semidirect
11. #20267665C2semidirect
12. #20267662C2semidirect
13. C4×(C2×D103)⋊C4C2semidirect
14. #20267638C2semidirect
15. #388×C103C2semidirect
24. C22×C4×D103C22semidirect
25. #15692991C4semidirect
28. C2×C4⋊Dic103C22semidirect
29. C2×Dic103⋊C4C22semidirect
38. C2×(C2×D103)⋊C4C22semidirect
39. C2×(C2×D103)⋊C4C22semidirect
40. C2×(C2×D103)⋊C4C22semidirect
43. C2×C4×Dic103C22semidirect
44. C2×C4×Dic103C22semidirect
45. C103⋊#95C22semidirect
46. C103⋊#95C22semidirect
47. C103⋊#95C22semidirect
48. C103⋊#95C22semidirect
49. C2×C4⋊C4×C103C22semidirect
53. C2×C42×C103C22semidirect
54. #95×C103C22semidirect
55. #95×C103C22semidirect
62. C23×D103C2×C4semidirect
70. C2×D412C2×C4semidirect
71. C2×D412C2×C4semidirect
74. C2×C22⋊D103C2×C4semidirect
104. (C2×D103)⋊C4C2×C4semidirect
105. (C2×D103)⋊C4C2×C4semidirect
106. (C2×D103)⋊C4D4semidirect
107. (C2×D103)⋊C4D4semidirect
120. C22⋊C4×C103C2×C4semidirect
233. C2×D103C4×D4semidirect
234. C2×D103C4×D4semidirect
258. C103#2358semidirect
266. #388D103semidirect
288. C2×C4⋊C4C2×D103semidirect
307. C2×C42C2×D103semidirect
312. #95C2×D103semidirect
313. #95C2×D103semidirect
376. C22⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929912
C2×C4×D4122
C2×#156929832
C2×C22⋊C4×D1032
#202676912
#202676842
#202676692
#202676672
#202676652
#202676622
C4×(C2×D103)⋊C42
#202676382
#388×C1032
#2358103