Finite Group Databasebeta

← #27198126

Subgroups — #27198126

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×(C22⋊D103)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D103C211yesmaximal, characteristic, complemented
6#20267693C211yesmaximal, characteristic, complemented
7#20267683C211yesmaximal, characteristic, complemented
8#20267682C211yesmaximal, characteristic, complemented
9#20267670C211yesmaximal, characteristic, complemented
10#20267669C211yesmaximal, characteristic, complemented
11#20267669C211yesmaximal, characteristic, complemented
12#20267666C211yesmaximal, characteristic, complemented
13#20267665C211yesmaximal, characteristic, complemented
14C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C103C211yesmaximal, characteristic, complemented
16C24×D103C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C22×D412C2211yescharacteristic
19C22×C22⋊D103C2211yescharacteristic
20C23×Dic103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22C22×C4×D103C2211yescharacteristic
23C22×C4×D103C2211yescharacteristic, complemented
24#15692991C418yescomplemented
25C4×D412—24no—
26(C22⋊D103)⋊C4—24no—
27C2×C4⋊Dic103C2211yescharacteristic, complemented
28C2×C4⋊Dic103C2211yescharacteristic, complemented
29C2×Dic103⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic103C2211yescharacteristic
31C2×(C2×D103)⋊C4—24no—
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
39C2×(C2×D103)⋊C4C2211yescharacteristic
40C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
43C22⋊C4×D103—24no—
44C2×C4×Dic103C2211yescharacteristic, complemented
45C103⋊#95C2211yescharacteristic, complemented
46C103⋊#95C2211yescharacteristic, complemented
47C103⋊#95C2211yescharacteristic, complemented
48C103⋊#95C2211yescharacteristic, complemented
49C23×C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103C2211yescharacteristic
52C2×C42×C103C2211yescharacteristic, complemented
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—41no—
69C2×D412—41no—
70C2×D412C2×C414yescomplemented
71C2×D412C2×C414yescomplemented
72C2×C22⋊D103—22no—
73C2×C22⋊D103—22no—
74C2×C22⋊D103C2×C414yescomplemented
75C22×Dic103—22no—
76C22×Dic103—22no—
77C22×Dic103—41no—
78C22×Dic103C2311yescharacteristic
79C22×Dic103C2311yescharacteristic
80C22×Dic103C2311yescharacteristic
81C22×Dic103C2311yescharacteristic
82C22×Dic103C2311yescharacteristic
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—41no—
90C2×C4×D103—41no—
91C2×C4×D103—41no—
92C4⋊Dic103—22no—
93C4⋊Dic103—41no—
94Dic103⋊C4—22no—
95C22⋊Dic103—22no—
96(C2×D103)⋊C4—22no—
97(C2×D103)⋊C4—22no—
98(C2×D103)⋊C4—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
107C4×Dic103—22no—
108C24×C103C2311yescharacteristic
109C22×C4×C103—22no—
110C22×C4×C103—22no—
111C22×C4×C103—41no—
112C22×C4×C103C2311yescharacteristic
113C22×C4×C103C2311yescharacteristic
114C22×C4×C103C2311yescharacteristic
115C22×C4×C103C2311yescharacteristic
116C22×C4×C103C2311yescharacteristic
117C22×C4×C103C2311yescharacteristic
118C22⋊C4×C103C2×C414yescomplemented
119C22⋊C4×C103D414yescomplemented
120C42×C103—22no—
121C42×C103—41no—
122C23×C103—21no—
123C23×C103—21no—
124C23×C103—21no—
125C23×C103—21no—
126C23×C103C22×C412yes—
127C23×C103C2×D412yes—
128C23×C103#4112yes—
129C23×C103C2411yescharacteristic
130C22×D103—21no—
131C22×D103—21no—
132C22×D103—21no—
133C22×D103—21no—
134C22×D103—28no—
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—21no—
145C22×D103—21no—
146C22×D103—21no—
147C22×D103—28no—
148C22×D103—44no—
149C22×D103—44no—
150C22×D103—44no—
151C22×D103—44no—
152C22×D103—44no—
153C22×D103C22×C412yes—
154C22×D103C22×C412yes—
155C22×D103C22×C412yes—
156C22×D103C2×D412yes—
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—44no—
172C2×C4×C103C22×C412yes—
173C2×C4×C103C22×C412yes—
174C2×C4×C103C2×D412yes—
175C2×C4×C103C2×D412yes—
176C2×C4×C103C2×D412yes—
177C22⋊D103—28no—
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—44no—
192C2×Dic103C22×C412yes—
193C2×Dic103C2×D412yes—
194D412—28no—
195D412—44no—
196C4×D103—44no—
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×C103C4×D414yescomplemented
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—416no—
226C2×D103—41no—
227C2×D103—41no—
228C2×D103—41no—
229C2×D103—41no—
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—22no—
240C4×C103—41no—
241Dic103—22no—
242Dic103—22no—
243Dic103—41no—
244Dic103—41no—
245Dic103—41no—
246C2×C103—24no—
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—42no—
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#388—1031no—
267#386—1031no—
268#386—1031no—
269#386—1031no—
270#385—1031no—
271#385—1031no—
272C4×C22⋊C4—1031no—
273C4×C22⋊C4D10311yescharacteristic, complemented
274C25—1031no—
275C22×D4—1031no—
276C22×D4—1031no—
277C22×D4—1031no—
278C23×C4—1031no—
279C23×C4—1031no—
280C23×C4—1031no—
281C23×C4—1031no—
282C23×C4C2×D10311yescharacteristic
283#120—1038no—
284C4×D4—2064no—
285C4×D4—2064no—
286C2×C4⋊C4—1031no—
287C2×C4⋊C4—1031no—
288C2×C4⋊C4—1031no—
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
305C2×C42—1031no—
306C2×C42C2×D10311yescharacteristic, complemented
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—1034no—
316C24—1031no—
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—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—1031no—
338C22×C4—1031no—
339C22×C4—1031no—
340C22×C4—1031no—
341C22×C4—1031no—
342C22×C4—4121no—
343C22×C4—4121no—
344C22×C4—4121no—
345C22×C4—4121no—
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—4121no—
361C4⋊C4—2062no—
362C4⋊C4—2062no—
363C22⋊C4—1034no—
364C22⋊C4—1034no—
365C22⋊C4—1034no—
366C22⋊C4—4121no—
367C22⋊C4—2062no—
368C22⋊C4—2062no—
369C22⋊C4—2062no—
370C22⋊C4—2062no—
371C22⋊C4—2062no—
372C22⋊C4—2062no—
373C22⋊C4—2062no—
374C22⋊C4—2062no—
375C22⋊C4C4×D10314yescomplemented
376C22⋊C4D41214yescomplemented
377C42—22no—
378C42—41no—
379C42—2062no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—1032no—
385C23—1032no—
386C23—1032no—
387C23—1032no—
388C23—1032no—
389C23—4124no—
390C23—4124no—
391C23—4124no—
392C23—4124no—
393C23—4124no—
394C23—2068no—
395C23—2061no—
396C23—2061no—
397C23—2061no—
398C23—2061no—
399C23—2061no—
400C23—2061no—
401C23—2061no—
402C23—2061no—
403C23—2061no—
404C23—2061no—
405C23—2061no—
406C23—2061no—
407C23—2068no—
408C23—2061no—
409C23—2061no—
410C23—2061no—
411C23—2061no—
412C23C2×C4×D10312yes—
413C23C2×D41212yes—
414C23#1311010512yes—
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—44no—
433C2×C4—1032no—
434C2×C4—1032no—
435C2×C4—4124no—
436C2×C4—4124no—
437C2×C4—4124no—
438C2×C4—4124no—
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×C4C2×C4×D10312yes—
453C2×C4C2×C4×D10312yes—
454C2×C4D4×D10312yes—
455C2×C4C2×D41212yes—
456C2×C4C2×D41212yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—1034no—
464C22—41216no—
465C22—4121no—
466C22—4121no—
467C22—4121no—
468C22—4121no—
469C22—4121no—
470C22—4121no—
471C22—4121no—
472C22—4121no—
473C22—2062no—
474C22—2062no—
475C22—2062no—
476C22—2062no—
477C22—2062no—
478C22—2062no—
479C22—2062no—
480C22—2062no—
481C22—2062no—
482C22—2062no—
483C22—2062no—
484C22—2062no—
485C22C4×D41214yescomplemented
486C22C22×C4×D10311yescharacteristic
487C22C2×D4×D10311yescharacteristic
488C22C22×D41211yescharacteristic
489C22#41×D10311yescharacteristic
490C22C2×#1311010511yescharacteristic
491C22#1569306611yescharacteristic
492C22#1569306711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—4121no—
500C4—4121no—
501C4—4121no—
502C4—2062no—
503C4—2062no—
504C2—24no—
505C2—4122no—
506C2—4122no—
507C2—2064no—
508C2C4×D4×D10311yescharacteristic
509C2C2×C4×D41211yescharacteristic
510C2#2026826311yescharacteristic
511C2D4×D41211yescharacteristic
512C2#2026843111yescharacteristic
513C2#2026843611yescharacteristic
514C2#2026846511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC4×C22⋊C4×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692991C2
hypercenterC4×C22⋊C4D103
hypocenterC103#2358
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D412C2semidirect
3. C2×(C22⋊D103)⋊C4C2semidirect
4. C22×(C2×D103)⋊C4C2semidirect
5. C2×C22⋊C4×D103C2semidirect
6. #20267693C2semidirect
7. #20267683C2semidirect
8. #20267682C2semidirect
9. #20267670C2semidirect
10. #20267669C2semidirect
11. #20267669C2semidirect
12. #20267666C2semidirect
13. #20267665C2semidirect
14. C4×(C2×D103)⋊C4C2semidirect
15. C4×C22⋊C4×C103C2semidirect
23. C22×C4×D103C22semidirect
24. #15692991C4semidirect
27. C2×C4⋊Dic103C22semidirect
28. C2×C4⋊Dic103C22semidirect
29. C2×Dic103⋊C4C22semidirect
40. C2×(C2×D103)⋊C4C22semidirect
41. C2×(C2×D103)⋊C4C22semidirect
42. C2×(C2×D103)⋊C4C22semidirect
44. C2×C4×Dic103C22semidirect
45. C103⋊#95C22semidirect
46. C103⋊#95C22semidirect
47. C103⋊#95C22semidirect
48. C103⋊#95C22semidirect
52. C2×C42×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
118. C22⋊C4×C103C2×C4semidirect
119. C22⋊C4×C103D4semidirect
205. C22×C103C4×D4semidirect
234. C2×D103C4×D4semidirect
258. C103#2358semidirect
273. C4×C22⋊C4D103semidirect
306. C2×C42C2×D103semidirect
307. C2×C42C2×D103semidirect
312. #95C2×D103semidirect
313. #95C2×D103semidirect
375. C22⋊C4C4×D103semidirect
376. C22⋊C4D412semidirect
485. C22C4×D412semidirect

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×(C22⋊D103)⋊C42
C22×(C2×D103)⋊C42
C2×C22⋊C4×D1032
#202676932
#202676832
#202676822
#202676702
#202676692
#202676662
#202676652
C4×(C2×D103)⋊C42
C4×C22⋊C4×C1032
#2358103