Finite Group Databasebeta

← #16822469

Subgroups — #16822469

Order 3712.

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×#11745299C211yesmaximal, characteristic
2C2×C4×C22⋊D29C211yesmaximal, characteristic, complemented
3C22×#90781C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
5#14271063C211yesmaximal, characteristic, complemented
6#14271054C211yesmaximal, characteristic, complemented
7#14271053C211yesmaximal, characteristic, complemented
8#14271043C211yesmaximal, characteristic, complemented
9#14271042C211yesmaximal, characteristic, complemented
10#14271039C211yesmaximal, characteristic, complemented
11#14271036C211yesmaximal, characteristic, complemented
12#14271034C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic29C211yesmaximal, characteristic, complemented
14C4×#90781C211yesmaximal, characteristic, complemented
15C2×C4×D4×C29C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C23×C4×C29C2211yescharacteristic
19C23×C4×C29C2211yescharacteristic, complemented
20C22×C22⋊D29C2211yescharacteristic
21C22×C22⋊D29C2211yescharacteristic
22C23×Dic29C2211yescharacteristic
23C22×C4×D29C2211yescharacteristic
24C22×C4×D29C2211yescharacteristic
25C4×D4×C29—24no—
26C2×C4⋊C4×C29C2211yescharacteristic, complemented
27C2×C22⋊C4×C29C2211yescharacteristic
28C2×C22⋊C4×C29C2211yescharacteristic, complemented
29C2×C42×C29C2211yescharacteristic, complemented
30C2×C22⋊Dic29C2211yescharacteristic
31C2×C22⋊Dic29C2211yescharacteristic
32C2×C22⋊Dic29C2211yescharacteristic, complemented
33C2×C22⋊Dic29C2211yescharacteristic, complemented
34#11745299C418yescomplemented
35C4×C22⋊D29—24no—
36C2×#90781—24no—
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×#90781C2211yescharacteristic
41C2×#90781C2211yescharacteristic
42C2×#90781C2211yescharacteristic
43C2×#90781C2211yescharacteristic
44C2×#90781C2211yescharacteristic
45C2×#90779C2211yescharacteristic, complemented
46C2×#90779C2211yescharacteristic, complemented
47C2×C4×Dic29C2211yescharacteristic, complemented
48C2×C4×Dic29C2211yescharacteristic, complemented
49C22⋊C4×D29—24no—
50#11745179C2211yescharacteristic, complemented
51#11745179C2211yescharacteristic, complemented
52#11745179C2211yescharacteristic, complemented
53#11745179C2211yescharacteristic, complemented
54#11745179C2211yescharacteristic, complemented
55#11745179C2211yescharacteristic, complemented
56C24×C29C2311yescharacteristic
57C24×C29C2311yescharacteristic
58C23×D29—22no—
59C23×D29—22no—
60C23×D29—22no—
61C23×D29—22no—
62C23×D29—41no—
63C23×D29—41no—
64C23×D29C2×C414yescomplemented
65C23×D29C2311yescharacteristic
66C23×D29C2311yescharacteristic
67C2×D4×C29—22no—
68C2×D4×C29—22no—
69C2×D4×C29C2×C414yescomplemented
70C22×C4×C29—22no—
71C22×C4×C29—22no—
72C22×C4×C29—22no—
73C22×C4×C29—22no—
74C22×C4×C29—41no—
75C22×C4×C29—41no—
76C22×C4×C29C2311yescharacteristic
77C22×C4×C29C2311yescharacteristic
78C22×C4×C29C2311yescharacteristic
79C22×C4×C29C2311yescharacteristic
80C22×C4×C29C2311yescharacteristic
81C2×C22⋊D29—22no—
82C2×C22⋊D29—22no—
83C2×C22⋊D29—41no—
84C2×C22⋊D29—41no—
85C2×C22⋊D29C2×C414yescomplemented
86C2×C22⋊D29C2×C414yescomplemented
87C22×Dic29—22no—
88C22×Dic29—22no—
89C22×Dic29—41no—
90C22×Dic29C2311yescharacteristic
91C22×Dic29C2311yescharacteristic
92C22×Dic29C2311yescharacteristic
93C22×Dic29C2311yescharacteristic
94C22×Dic29C2311yescharacteristic
95C22×Dic29C2311yescharacteristic
96C2×C4×D29—22no—
97C2×C4×D29—22no—
98C2×C4×D29—22no—
99C2×C4×D29—22no—
100C2×C4×D29—41no—
101C2×C4×D29—41no—
102C4⋊C4×C29—22no—
103C22⋊C4×C29—22no—
104C22⋊C4×C29D414yescomplemented
105C42×C29—22no—
106C22⋊Dic29—22no—
107C22⋊Dic29—22no—
108C22⋊Dic29—41no—
109C22⋊Dic29C2×C414yescomplemented
110#90781—22no—
111#90781—22no—
112#90781—22no—
113#90781—22no—
114#90781—22no—
115#90781C2×C414yescomplemented
116#90781C2×C414yescomplemented
117#90781D414yescomplemented
118#90779—22no—
119#90779—41no—
120C4×Dic29—22no—
121C4×Dic29—41no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—21no—
128C23×C29—21no—
129C23×C29—21no—
130C23×C29—21no—
131C23×C29—21no—
132C23×C29C22×C412yes—
133C23×C29C22×C412yes—
134C23×C29C2×D412yes—
135C23×C29#4112yes—
136C23×C29C2411yescharacteristic
137C22×D29—21no—
138C22×D29—21no—
139C22×D29—21no—
140C22×D29—21no—
141C22×D29—28no—
142C22×D29—21no—
143C22×D29—21no—
144C22×D29—21no—
145C22×D29—21no—
146C22×D29—21no—
147C22×D29—21no—
148C22×D29—28no—
149C22×D29—44no—
150C22×D29—44no—
151C22×D29—44no—
152C22×D29—44no—
153C22×D29—44no—
154C22×D29C22×C412yes—
155C22×D29C22×C412yes—
156C22×D29C2×D412yes—
157C22×D29#4112yes—
158D4×C29—28no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29—21no—
169C2×C4×C29—21no—
170C2×C4×C29—44no—
171C2×C4×C29—44no—
172C2×C4×C29C22×C412yes—
173C2×C4×C29C2×D412yes—
174C2×C4×C29C2×D412yes—
175C2×C4×C29C2×D412yes—
176C22⋊D29—28no—
177C22⋊D29—44no—
178C2×Dic29—21no—
179C2×Dic29—21no—
180C2×Dic29—21no—
181C2×Dic29—21no—
182C2×Dic29—21no—
183C2×Dic29—21no—
184C2×Dic29—21no—
185C2×Dic29—21no—
186C2×Dic29—21no—
187C2×Dic29—21no—
188C2×Dic29—21no—
189C2×Dic29—21no—
190C2×Dic29—21no—
191C2×Dic29—21no—
192C2×Dic29—21no—
193C2×Dic29—44no—
194C2×Dic29C22×C412yes—
195C2×Dic29C22×C412yes—
196C2×Dic29C2×D412yes—
197C4×D29—44no—
198C4×D29—44no—
199#2358—291nomaximal, Sylow
200C22×C29—22no—
201C22×C29—22no—
202C22×C29—22no—
203C22×C29—22no—
204C22×C29—22no—
205C22×C29—22no—
206C22×C29—22no—
207C22×C29—22no—
208C22×C29—22no—
209C22×C29—41no—
210C22×C29—41no—
211C22×C29—41no—
212C22×C29—41no—
213C22×C29C4×D414yescomplemented
214C22×C29C23×C411yescharacteristic
215C22×C29C22×D411yescharacteristic
216C22×C29C22×D411yescharacteristic
217C22×C29C2×#4111yescharacteristic
218C22×C29C2×#4111yescharacteristic
219C22×C29H(5,𝔽2)11yescharacteristic
220C22×C29H(5,𝔽2)11yescharacteristic
221C2×D29—22no—
222C2×D29—22no—
223C2×D29—22no—
224C2×D29—22no—
225C2×D29—22no—
226C2×D29—22no—
227C2×D29—22no—
228C2×D29—22no—
229C2×D29—22no—
230C2×D29—416no—
231C2×D29—41no—
232C2×D29—41no—
233C2×D29—41no—
234C2×D29—41no—
235C2×D29C4×D414yescomplemented
236C4×C29—22no—
237C4×C29—22no—
238C4×C29—22no—
239C4×C29—22no—
240C4×C29—41no—
241Dic29—22no—
242Dic29—22no—
243Dic29—22no—
244Dic29—41no—
245Dic29—41no—
246Dic29—41no—
247C2×#120—291no—
248C2×C4×D4—291no—
249C2×C4×D4D2911yescharacteristic, complemented
250C22×C22⋊C4—291no—
251C22×C22⋊C4—291no—
252#390—291no—
253#388—291no—
254#388—291no—
255#386—291no—
256#386—291no—
257#386—291no—
258#385—291no—
259#385—291no—
260C4×C22⋊C4—291no—
261C4×C22⋊C4—291no—
262C2×C29—24no—
263C2×C29—42no—
264C2×C29C2×C4×D411yescharacteristic
265C2×C29C2×C4×D411yescharacteristic
266C2×C29#51811yescharacteristic
267C2×C29D4211yescharacteristic
268C2×C29#54611yescharacteristic
269C2×C29#54611yescharacteristic
270C2×C29#55111yescharacteristic
271D29—24no—
272D29—42no—
273C25—291no—
274C22×D4—291no—
275C22×D4—291no—
276C22×D4C2×D2911yescharacteristic
277C23×C4—291no—
278C23×C4—291no—
279C23×C4—291no—
280C23×C4C2×D2911yescharacteristic
281C23×C4C2×D2911yescharacteristic, complemented
282#120—298no—
283C4×D4—24no—
284C4×D4—584no—
285C2×C4⋊C4—291no—
286C2×C4⋊C4—291no—
287C2×C4⋊C4C2×D2911yescharacteristic, complemented
288C2×C22⋊C4—291no—
289C2×C22⋊C4—291no—
290C2×C22⋊C4—291no—
291C2×C22⋊C4—291no—
292C2×C22⋊C4—291no—
293C2×C22⋊C4—291no—
294C2×C22⋊C4—291no—
295C2×C22⋊C4—291no—
296C2×C22⋊C4—291no—
297C2×C22⋊C4—291no—
298C2×C22⋊C4—291no—
299C2×C22⋊C4—291no—
300C2×C22⋊C4—584no—
301C2×C22⋊C4—584no—
302C2×C22⋊C4C2×D2911yescharacteristic
303C2×C22⋊C4C2×D2911yescharacteristic, complemented
304C2×C42—291no—
305C2×C42—291no—
306C2×C42C2×D2911yescharacteristic, complemented
307#95—291no—
308#95—291no—
309#95—291no—
310#95—291no—
311#95—291no—
312#95—291no—
313C29#235811yescharacteristic, complemented, Sylow
314C24—291no—
315C24—291no—
316C24—294no—
317C24—582no—
318C24—582no—
319C24—582no—
320C24—582no—
321C24—1161no—
322C24—1161no—
323C24C22×D2911yescharacteristic
324C24C22×D2911yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—294no—
328C2×D4—294no—
329C2×D4—582no—
330C2×D4—582no—
331C2×D4—1161no—
332C2×D4—1161no—
333C2×D4C4×D2914yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—291no—
341C22×C4—291no—
342C22×C4—291no—
343C22×C4—291no—
344C22×C4—291no—
345C22×C4—291no—
346C22×C4—582no—
347C22×C4—582no—
348C22×C4—582no—
349C22×C4—582no—
350C22×C4—582no—
351C22×C4—582no—
352C22×C4—1161no—
353C22×C4—1161no—
354C22×C4—1161no—
355C22×C4C22×D2911yescharacteristic
356C22×C4C22×D2911yescharacteristic
357C22×C4C22×D2911yescharacteristic
358C22×C4C22×D2911yescharacteristic
359C22×C4C22×D2911yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—582no—
362C4⋊C4—1161no—
363C22⋊C4—22no—
364C22⋊C4—294no—
365C22⋊C4—294no—
366C22⋊C4—294no—
367C22⋊C4—294no—
368C22⋊C4—582no—
369C22⋊C4—582no—
370C22⋊C4—582no—
371C22⋊C4—582no—
372C22⋊C4—582no—
373C22⋊C4—582no—
374C22⋊C4—582no—
375C22⋊C4—1161no—
376C22⋊C4C22⋊D2914yescomplemented
377C42—22no—
378C42—582no—
379C42—1161no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—292no—
391C23—292no—
392C23—292no—
393C23—292no—
394C23—588no—
395C23—581no—
396C23—581no—
397C23—581no—
398C23—581no—
399C23—588no—
400C23—581no—
401C23—581no—
402C23—581no—
403C23—581no—
404C23—581no—
405C23—581no—
406C23—1164no—
407C23—1164no—
408C23—1164no—
409C23—1164no—
410C23—1164no—
411C23C2×C4×D2912yes—
412C23C2×C4×D2912yes—
413C23#9080512yes—
414C23C2×C22⋊D2912yes—
415C23C23×D2911yescharacteristic
416D4—28no—
417D4—588no—
418D4—1164no—
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—292no—
433C2×C4—292no—
434C2×C4—292no—
435C2×C4—581no—
436C2×C4—581no—
437C2×C4—581no—
438C2×C4—581no—
439C2×C4—581no—
440C2×C4—581no—
441C2×C4—581no—
442C2×C4—581no—
443C2×C4—581no—
444C2×C4—581no—
445C2×C4—581no—
446C2×C4—581no—
447C2×C4—581no—
448C2×C4—581no—
449C2×C4—581no—
450C2×C4—1164no—
451C2×C4—1164no—
452C2×C4—1164no—
453C2×C4C2×C4×D2912yes—
454C2×C4D4×D2912yes—
455C2×C4C2×C22⋊D2912yes—
456C2×C4C2×C22⋊D2912yes—
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—294no—
471C22—582no—
472C22—582no—
473C22—582no—
474C22—582no—
475C22—582no—
476C22—582no—
477C22—582no—
478C22—582no—
479C22—582no—
480C22—11616no—
481C22—1161no—
482C22—1161no—
483C22—1161no—
484C22—1161no—
485C22C4×C22⋊D2914yescomplemented
486C22C22×C4×D2911yescharacteristic
487C22C2×#9080511yescharacteristic
488C22C2×D4×D2911yescharacteristic
489C22#1174535911yescharacteristic
490C22#41×D2911yescharacteristic
491C22#1174536411yescharacteristic
492C22C22×C22⋊D2911yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—582no—
499C4—582no—
500C4—582no—
501C4—1161no—
502C4—1161no—
503C4—1161no—
504C2—24no—
505C2—42no—
506C2—584no—
507C2—1162no—
508C2C4×D4×D2911yescharacteristic
509C2C2×C4×C22⋊D2911yescharacteristic
510C2#1427163511yescharacteristic
511C2D4×C22⋊D2911yescharacteristic
512C2#1427180111yescharacteristic
513C2#1427180911yescharacteristic
514C2#1427184211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC2×C4×D4×C29C2
socle, cosocleC23×C29C24
prime radicalC2×#11745299C2
hypercenterC2×C4×D4D29
hypocenterC29#2358
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D29C2semidirect
3. C22×#90781C2semidirect
4. C2×C22⋊C4×D29C2semidirect
5. #14271063C2semidirect
6. #14271054C2semidirect
7. #14271053C2semidirect
8. #14271043C2semidirect
9. #14271042C2semidirect
10. #14271039C2semidirect
11. #14271036C2semidirect
12. #14271034C2semidirect
13. C22⋊C4×Dic29C2semidirect
14. C4×#90781C2semidirect
15. C2×C4×D4×C29C2semidirect
19. C23×C4×C29C22semidirect
26. C2×C4⋊C4×C29C22semidirect
28. C2×C22⋊C4×C29C22semidirect
29. C2×C42×C29C22semidirect
32. C2×C22⋊Dic29C22semidirect
33. C2×C22⋊Dic29C22semidirect
34. #11745299C4semidirect
45. C2×#90779C22semidirect
46. C2×#90779C22semidirect
47. C2×C4×Dic29C22semidirect
48. C2×C4×Dic29C22semidirect
50. #11745179C22semidirect
51. #11745179C22semidirect
52. #11745179C22semidirect
53. #11745179C22semidirect
54. #11745179C22semidirect
55. #11745179C22semidirect
64. C23×D29C2×C4semidirect
69. C2×D4×C29C2×C4semidirect
85. C2×C22⋊D29C2×C4semidirect
86. C2×C22⋊D29C2×C4semidirect
104. C22⋊C4×C29D4semidirect
109. C22⋊Dic29C2×C4semidirect
115. #90781C2×C4semidirect
116. #90781C2×C4semidirect
117. #90781D4semidirect
213. C22×C29C4×D4semidirect
235. C2×D29C4×D4semidirect
249. C2×C4×D4D29semidirect
281. C23×C4C2×D29semidirect
287. C2×C4⋊C4C2×D29semidirect
303. C2×C22⋊C4C2×D29semidirect
306. C2×C42C2×D29semidirect
313. C29#2358semidirect
333. C2×D4C4×D29semidirect
376. C22⋊C4C22⋊D29semidirect
485. C22C4×C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452992
C2×C4×C22⋊D292
C22×#907812
C2×C22⋊C4×D292
#142710632
#142710542
#142710532
#142710432
#142710422
#142710392
#142710362
#142710342
C22⋊C4×Dic292
C4×#907812
C2×C4×D4×C292
#235829