Finite Group Databasebeta

← #27198123

Subgroups — #27198123

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×#15692990C211yesmaximal, characteristic
2C2×C4×C22⋊D103C211yesmaximal, characteristic, complemented
3C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic103C211yesmaximal, characteristic, complemented
5#20267691C211yesmaximal, characteristic, complemented
6#20267685C211yesmaximal, characteristic, complemented
7#20267679C211yesmaximal, characteristic, complemented
8#20267670C211yesmaximal, characteristic, complemented
9#20267668C211yesmaximal, characteristic, complemented
10#20267667C211yesmaximal, characteristic, complemented
11#20267664C211yesmaximal, characteristic, complemented
12#20267663C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic103C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C22×C22⋊D103C2211yescharacteristic
19C23×Dic103C2211yescharacteristic
20C23×Dic103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic, complemented
22#15692990C418yescomplemented
23C4×C22⋊D103—24no—
24(C22⋊D103)⋊C4—24no—
25C2×Dic103⋊C4C2211yescharacteristic, complemented
26C2×Dic103⋊C4C2211yescharacteristic, complemented
27C2×Dic103⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic103—24no—
29C2×C22⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
32C2×C22⋊Dic103C2211yescharacteristic
33C2×C22⋊Dic103C2211yescharacteristic
34C2×C22⋊Dic103C2211yescharacteristic
35C2×C22⋊Dic103C2211yescharacteristic
36C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D103)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic103C2211yescharacteristic, complemented
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
48C25×C103C2211yescharacteristic
49C23×C4×C103C2211yescharacteristic
50C23×C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103—24no—
52C2×C22⋊C4×C103C2211yescharacteristic
53C2×C22⋊C4×C103C2211yescharacteristic
54C2×C22⋊C4×C103C2211yescharacteristic
55C2×C22⋊C4×C103C2211yescharacteristic
56C23×D103C2311yescharacteristic
57C2×C22⋊D103—22no—
58C2×C22⋊D103—22no—
59C2×C22⋊D103—22no—
60C2×C22⋊D103—22no—
61C2×C22⋊D103—41no—
62C2×C22⋊D103—41no—
63C2×C22⋊D103C2×C414yescomplemented
64C2×C22⋊D103C2×C414yescomplemented
65C2×C22⋊D103C2×C414yescomplemented
66C22×Dic103—22no—
67C22×Dic103—22no—
68C22×Dic103—22no—
69C22×Dic103—22no—
70C22×Dic103—41no—
71C22×Dic103—41no—
72C22×Dic103C2311yescharacteristic
73C22×Dic103C2311yescharacteristic
74C22×Dic103C2311yescharacteristic
75C22×Dic103C2311yescharacteristic
76C22×Dic103C2311yescharacteristic
77C22×Dic103C2311yescharacteristic
78C22×Dic103C2311yescharacteristic
79C2×C4×D103—22no—
80C2×C4×D103—22no—
81C2×C4×D103—41no—
82Dic103⋊C4—22no—
83Dic103⋊C4—22no—
84Dic103⋊C4—41no—
85C22⋊Dic103—22no—
86C22⋊Dic103—22no—
87C22⋊Dic103—22no—
88C22⋊Dic103C2×C414yescomplemented
89C22⋊Dic103C2×C414yescomplemented
90C22⋊Dic103C2×C414yescomplemented
91C22⋊Dic103D414yescomplemented
92(C2×D103)⋊C4—22no—
93(C2×D103)⋊C4—22no—
94(C2×D103)⋊C4—41no—
95C4×Dic103—22no—
96C4×Dic103—22no—
97C4×Dic103—41no—
98C24×C103—22no—
99C24×C103—22no—
100C24×C103—22no—
101C24×C103—22no—
102C24×C103—41no—
103C24×C103—41no—
104C24×C103C2×C414yescomplemented
105C24×C103C2311yescharacteristic
106C24×C103C2311yescharacteristic
107C24×C103C2311yescharacteristic
108C22×C4×C103—22no—
109C22×C4×C103—22no—
110C22×C4×C103—22no—
111C22×C4×C103—22no—
112C22×C4×C103—41no—
113C22×C4×C103—41no—
114C22×C4×C103C2311yescharacteristic
115C22×C4×C103C2311yescharacteristic
116C22×C4×C103C2311yescharacteristic
117C22×C4×C103C2311yescharacteristic
118C22⋊C4×C103—22no—
119C22⋊C4×C103—22no—
120C22⋊C4×C103—22no—
121C22⋊C4×C103D414yescomplemented
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—28no—
131C23×C103—28no—
132C23×C103—21no—
133C23×C103—21no—
134C23×C103—21no—
135C23×C103—21no—
136C23×C103—21no—
137C23×C103—21no—
138C23×C103—44no—
139C23×C103—44no—
140C23×C103—44no—
141C23×C103—44no—
142C23×C103—44no—
143C23×C103C22×C412yes—
144C23×C103C22×C412yes—
145C23×C103C22×C412yes—
146C23×C103C2×D412yes—
147C23×C103C2×D412yes—
148C23×C103#4112yes—
149C23×C103#4112yes—
150C23×C103C2411yescharacteristic
151C22×D103—21no—
152C22×D103—21no—
153C22×D103—21no—
154C22×D103—21no—
155C22×D103—21no—
156C22×D103—21no—
157C22×D103C22×C412yes—
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—44no—
169C2×C4×C103—44no—
170C2×C4×C103C2×D412yes—
171C2×C4×C103C2×D412yes—
172C22⋊D103—28no—
173C22⋊D103—28no—
174C22⋊D103—44no—
175C2×Dic103—21no—
176C2×Dic103—21no—
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×Dic103—21no—
190C2×Dic103—21no—
191C2×Dic103—44no—
192C2×Dic103—44no—
193C2×Dic103C22×C412yes—
194C2×Dic103C22×C412yes—
195C2×Dic103C22×C412yes—
196C2×Dic103C2×D412yes—
197C2×Dic103C2×D412yes—
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—22no—
209C22×C103—22no—
210C22×C103—22no—
211C22×C103—22no—
212C22×C103—22no—
213C22×C103—22no—
214C22×C103—416no—
215C22×C103—41no—
216C22×C103—41no—
217C22×C103—41no—
218C22×C103—41no—
219C22×C103C4×D414yescomplemented
220C22×C103C4×D414yescomplemented
221C22×C103C23×C411yescharacteristic
222C22×C103C22×D411yescharacteristic
223C22×C103C22×D411yescharacteristic
224C22×C103C2×#4111yescharacteristic
225C22×C103C2×#4111yescharacteristic
226C22×C103H(5,𝔽2)11yescharacteristic
227C22×C103H(5,𝔽2)11yescharacteristic
228C2×D103—22no—
229C2×D103—22no—
230C2×D103—22no—
231C2×D103—41no—
232C2×D103—41no—
233C2×D103—41no—
234C2×D103—41no—
235C4×C103—22no—
236C4×C103—22no—
237C4×C103—41no—
238C4×C103—41no—
239Dic103—22no—
240Dic103—22no—
241Dic103—22no—
242Dic103—22no—
243Dic103—22no—
244Dic103—41no—
245Dic103—41no—
246C2×C103—24no—
247C2×C103—24no—
248C2×C103—42no—
249C2×C103C2×C4×D411yescharacteristic
250C2×C103C2×C4×D411yescharacteristic
251C2×C103#51811yescharacteristic
252C2×C103D4211yescharacteristic
253C2×C103#54611yescharacteristic
254C2×C103#54611yescharacteristic
255C2×C103#55111yescharacteristic
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⋊C4D10311yescharacteristic, complemented
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—
274C25C2×D10311yescharacteristic
275C22×D4—1031no—
276C22×D4—1031no—
277C22×D4—1031no—
278C23×C4—1031no—
279C23×C4—1031no—
280C23×C4—1031no—
281C23×C4C2×D10311yescharacteristic
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—24no—
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⋊C4C2×D10311yescharacteristic
302C2×C22⋊C4C2×D10311yescharacteristic
303C2×C22⋊C4C2×D10311yescharacteristic
304C2×C22⋊C4C2×D10311yescharacteristic
305C2×C42—1031no—
306C2×C42—1031no—
307C2×C42—1031no—
308#95—1031no—
309#95—1031no—
310#95—1031no—
311#95—1031no—
312#95—1031no—
313#95—1031no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—1031no—
321C24C4×D10314yescomplemented
322C24C22×D10311yescharacteristic
323C24C22×D10311yescharacteristic
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—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—1031no—
347C22×C4—4121no—
348C22×C4—4121no—
349C22×C4—4121no—
350C22×C4—2062no—
351C22×C4—2062no—
352C22×C4—2062no—
353C22×C4—2062no—
354C22×C4—2062no—
355C22×C4—2062no—
356C22×C4C22×D10311yescharacteristic
357C22×C4C22×D10311yescharacteristic
358C22×C4C22×D10311yescharacteristic
359C22×C4C22×D10311yescharacteristic
360C4⋊C4—4121no—
361C4⋊C4—2062no—
362C4⋊C4—2062no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—1034no—
367C22⋊C4—1034no—
368C22⋊C4—1034no—
369C22⋊C4—1034no—
370C22⋊C4—4121no—
371C22⋊C4—2062no—
372C22⋊C4—2062no—
373C22⋊C4—2062no—
374C22⋊C4—2062no—
375C22⋊C4—2062no—
376C22⋊C4C22⋊D10314yescomplemented
377C42—4121no—
378C42—2062no—
379C42—2062no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—28no—
395C23—28no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—1032no—
402C23—2061no—
403C23—2061no—
404C23—2061no—
405C23—2061no—
406C23—2061no—
407C23—2061no—
408C23C2×C4×D10312yes—
409C23C2×C4×D10312yes—
410C23C2×C4×D10312yes—
411C23D4×D10312yes—
412C23C2×C22⋊D10312yes—
413C23#1311010412yes—
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—44no—
430C2×C4—44no—
431C2×C4—1032no—
432C2×C4—1032no—
433C2×C4—1032no—
434C2×C4—1032no—
435C2×C4—1032no—
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×C4—2061no—
453C2×C4—2061no—
454C2×C4—2061no—
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—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—4121no—
478C22—4121no—
479C22—4121no—
480C22—4121no—
481C22—2062no—
482C22—2062no—
483C22—2062no—
484C22(C22⋊D103)⋊C414yescomplemented
485C22C4×C22⋊D10314yescomplemented
486C22C22×C4×D10311yescharacteristic
487C22C2×D4×D10311yescharacteristic
488C22C22×C22⋊D10311yescharacteristic
489C22C2×#1311010411yescharacteristic
490C22C2×#1311010511yescharacteristic
491C22#1569306611yescharacteristic
492C22#1569306611yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—4121no—
498C4—4121no—
499C4—2062no—
500C4—2062no—
501C4—2062no—
502C4—2062no—
503C4—2062no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—4122no—
508C2C2×(C22⋊D103)⋊C411yescharacteristic
509C2C2×C4×C22⋊D10311yescharacteristic
510C2#2026826411yescharacteristic
511C2D4×C22⋊D10311yescharacteristic
512C2#2026843111yescharacteristic
513C2#2026843511yescharacteristic
514C2#2026846711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC22×C22⋊C4×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692990C2
hypercenterC22×C22⋊C4D103
hypocenterC103#2358
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D103C2semidirect
3. C2×(C22⋊D103)⋊C4C2semidirect
4. C22×C22⋊Dic103C2semidirect
5. #20267691C2semidirect
6. #20267685C2semidirect
7. #20267679C2semidirect
8. #20267670C2semidirect
9. #20267668C2semidirect
10. #20267667C2semidirect
11. #20267664C2semidirect
12. #20267663C2semidirect
13. C22⋊C4×Dic103C2semidirect
14. C4×C22⋊Dic103C2semidirect
15. C22×C22⋊C4×C103C2semidirect
21. C22×C4×D103C22semidirect
22. #15692990C4semidirect
25. C2×Dic103⋊C4C22semidirect
26. C2×Dic103⋊C4C22semidirect
27. C2×Dic103⋊C4C22semidirect
36. C2×(C2×D103)⋊C4C22semidirect
37. C2×(C2×D103)⋊C4C22semidirect
38. C2×(C2×D103)⋊C4C22semidirect
39. C2×C4×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
63. C2×C22⋊D103C2×C4semidirect
64. C2×C22⋊D103C2×C4semidirect
65. C2×C22⋊D103C2×C4semidirect
88. C22⋊Dic103C2×C4semidirect
89. C22⋊Dic103C2×C4semidirect
90. C22⋊Dic103C2×C4semidirect
91. C22⋊Dic103D4semidirect
104. C24×C103C2×C4semidirect
121. C22⋊C4×C103D4semidirect
219. C22×C103C4×D4semidirect
220. C22×C103C4×D4semidirect
258. C103#2358semidirect
263. C22×C22⋊C4D103semidirect
321. C24C4×D103semidirect
376. C22⋊C4C22⋊D103semidirect
484. C22(C22⋊D103)⋊C4semidirect
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×#156929902
C2×C4×C22⋊D1032
C2×(C22⋊D103)⋊C42
C22×C22⋊Dic1032
#202676912
#202676852
#202676792
#202676702
#202676682
#202676672
#202676642
#202676632
C22⋊C4×Dic1032
C4×C22⋊Dic1032
C22×C22⋊C4×C1032
#2358103