Finite Group Databasebeta

← #16822151

Subgroups — #16822151

Order 3712.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745299C211yesmaximal, characteristic
2C2×#11745243C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
4#14271063C211yesmaximal, characteristic, complemented
5#14271057C211yesmaximal, characteristic, complemented
6#14271057C211yesmaximal, characteristic, complemented
7#14271054C211yesmaximal, characteristic, complemented
8#14271053C211yesmaximal, characteristic, complemented
9#14271043C211yesmaximal, characteristic, complemented
10#14271040C211yesmaximal, characteristic, complemented
11#14271039C211yesmaximal, characteristic, complemented
12#14271034C211yesmaximal, characteristic, complemented
13#14271018C211yesmaximal, characteristic, complemented
14C4×#90781C211yesmaximal, characteristic, complemented
15C29×#390C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C22×C22⋊D29C2211yescharacteristic
19C22×C22⋊D29C2211yescharacteristic
20C23×Dic29C2211yescharacteristic, complemented
21C22×C4×D29C2211yescharacteristic
22C22×C4×D29C2211yescharacteristic
23C2×C4⋊C4×C29C2211yescharacteristic, complemented
24C2×C22⋊C4×C29C2211yescharacteristic
25C2×C22⋊C4×C29C2211yescharacteristic
26C2×C22⋊C4×C29C2211yescharacteristic, complemented
27C2×C22⋊C4×C29C2211yescharacteristic, complemented
28C2×C42×C29C2211yescharacteristic, complemented
29C2×C22⋊Dic29C2211yescharacteristic
30C2×C22⋊Dic29C2211yescharacteristic
31C2×C22⋊Dic29C2211yescharacteristic
32C2×C22⋊Dic29C2211yescharacteristic, complemented
33#11745299C418yescomplemented
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×#90781C2211yescharacteristic
41C2×#90781C2211yescharacteristic
42C2×#90779C2211yescharacteristic, complemented
43C2×#90779C2211yescharacteristic, complemented
44C2×C4×Dic29C2211yescharacteristic, complemented
45C2×C4×Dic29C2211yescharacteristic, complemented
46#11745243—24no—
47C22⋊C4×D29—24no—
48#11745179C2211yescharacteristic, complemented
49#11745179C2211yescharacteristic, complemented
50#11745179C2211yescharacteristic, complemented
51#11745179C2211yescharacteristic, complemented
52#11745179C2211yescharacteristic, complemented
53#11745179C2211yescharacteristic, complemented
54C24×C29C2311yescharacteristic
55C24×C29C2311yescharacteristic
56C23×D29—22no—
57C23×D29—22no—
58C23×D29—41no—
59C23×D29—41no—
60C23×D29—41no—
61C23×D29—41no—
62C23×D29C2×C414yescomplemented
63C23×D29C2311yescharacteristic
64C23×D29C2311yescharacteristic
65C2×D4×C29—41no—
66C2×D4×C29—41no—
67C2×D4×C29C2×C414yescomplemented
68C22×C4×C29C2311yescharacteristic
69C22×C4×C29C2311yescharacteristic
70C22×C4×C29C2311yescharacteristic
71C22×C4×C29C2311yescharacteristic
72C22×C4×C29C2311yescharacteristic
73C2×C22⋊D29—22no—
74C2×C22⋊D29—22no—
75C2×C22⋊D29—41no—
76C2×C22⋊D29—41no—
77C2×C22⋊D29C2×C414yes—
78C2×C22⋊D29C2×C414yescomplemented
79C22×Dic29—22no—
80C22×Dic29—41no—
81C22×Dic29—41no—
82C22×Dic29C2311yescharacteristic
83C22×Dic29C2311yescharacteristic
84C22×Dic29C2311yescharacteristic
85C22×Dic29C2311yescharacteristic
86C22×Dic29C2311yescharacteristic
87C22×Dic29C2311yescharacteristic
88C2×C4×D29—22no—
89C2×C4×D29—41no—
90C2×C4×D29—41no—
91C2×C4×D29—41no—
92C2×C4×D29—41no—
93C2×C4×D29D414yescomplemented
94C4⋊C4×C29—41no—
95C22⋊C4×C29—22no—
96C22⋊C4×C29—22no—
97C22⋊C4×C29—41no—
98C22⋊C4×C29—41no—
99C42×C29—41no—
100C22⋊Dic29—22no—
101C22⋊Dic29—41no—
102C22⋊Dic29—41no—
103C22⋊Dic29C2×C414yescomplemented
104#90781—22no—
105#90781—22no—
106#90781—22no—
107#90781—22no—
108#90781—41no—
109#90781—41no—
110#90781C2×C414yescomplemented
111#90781C2×C414yescomplemented
112#90779—22no—
113#90779—41no—
114C4×Dic29—22no—
115C4×Dic29—41no—
116C23×C29—21no—
117C23×C29—21no—
118C23×C29—21no—
119C23×C29—21no—
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—21no—
128C23×C29C22×C412yes—
129C23×C29C22×C412yes—
130C23×C29C2411yescharacteristic
131C22×D29—21no—
132C22×D29—21no—
133C22×D29—21no—
134C22×D29—21no—
135C22×D29—21no—
136C22×D29—21no—
137C22×D29—21no—
138C22×D29—21no—
139C22×D29—21no—
140C22×D29—21no—
141C22×D29—28no—
142C22×D29—44no—
143C22×D29—44no—
144C22×D29—44no—
145C22×D29—44no—
146C22×D29—44no—
147C22×D29—44no—
148C22×D29C22×C412yes—
149C22×D29C22×C412yes—
150C22×D29C2×D412yes—
151C22×D29#4112yes—
152D4×C29—44no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
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×C29C22×C412yes—
167C2×C4×C29C2×D412yes—
168C22⋊D29—28no—
169C22⋊D29—44no—
170C2×Dic29—21no—
171C2×Dic29—21no—
172C2×Dic29—21no—
173C2×Dic29—21no—
174C2×Dic29—21no—
175C2×Dic29—21no—
176C2×Dic29—21no—
177C2×Dic29—21no—
178C2×Dic29—21no—
179C2×Dic29—21no—
180C2×Dic29—21no—
181C2×Dic29—21no—
182C2×Dic29—21no—
183C2×Dic29—21no—
184C2×Dic29—21no—
185C2×Dic29—44no—
186C2×Dic29C22×C412yes—
187C2×Dic29C22×C412yes—
188C2×Dic29C2×D412yes—
189C4×D29—44no—
190C4×D29—44no—
191#2321—291nomaximal, Sylow
192C22×C29—22no—
193C22×C29—22no—
194C22×C29—22no—
195C22×C29—22no—
196C22×C29—22no—
197C22×C29—22no—
198C22×C29—41no—
199C22×C29—41no—
200C22×C29—41no—
201C22×C29—41no—
202C22×C29—41no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—41no—
206C22×C29C23×C411yescharacteristic
207C22×C29C22×D411yescharacteristic
208C22×C29C2×#4111yescharacteristic
209C22×C29H(5,𝔽2)11yescharacteristic
210C22×C29H(5,𝔽2)11yescharacteristic
211C22×C29H(5,𝔽2)11yescharacteristic
212C22×C29H(5,𝔽2)11yescharacteristic
213C2×D29—22no—
214C2×D29—22no—
215C2×D29—22no—
216C2×D29—22no—
217C2×D29—22no—
218C2×D29—22no—
219C2×D29—22no—
220C2×D29—22no—
221C2×D29—22no—
222C2×D29—416no—
223C2×D29—41no—
224C2×D29—41no—
225C2×D29—41no—
226C2×D29—41no—
227C2×D29C4×D414yes—
228C4×C29—22no—
229C4×C29—22no—
230C4×C29—41no—
231C4×C29—41no—
232C4×C29—41no—
233Dic29—22no—
234Dic29—22no—
235Dic29—22no—
236Dic29—41no—
237Dic29—41no—
238Dic29—41no—
239C2×#120—291no—
240C2×C4×D4—291no—
241C22×C22⋊C4—291no—
242#390—291no—
243#390D2911yescharacteristic, complemented
244#388—291no—
245#388—291no—
246#388—291no—
247#388—291no—
248#386—291no—
249#386—291no—
250#386—291no—
251#385—291no—
252#379—291no—
253C4×C22⋊C4—291no—
254C2×C29—42no—
255C2×C29—42no—
256C2×C29C2×C4×D411yescharacteristic
257C2×C29#51811yescharacteristic
258C2×C29#51811yescharacteristic
259C2×C29#53411yescharacteristic
260C2×C29#53511yescharacteristic
261C2×C29#53811yescharacteristic
262C2×C29#53811yescharacteristic
263D29—24no—
264D29—42no—
265C25—291no—
266C22×D4—291no—
267C22×D4—291no—
268C22×D4C2×D2911yescharacteristic
269C23×C4—291no—
270C23×C4—291no—
271C23×C4—291no—
272#120—298no—
273C4×D4—584no—
274C2×C4⋊C4—291no—
275C2×C4⋊C4—291no—
276C2×C4⋊C4C2×D2911yescharacteristic, complemented
277C2×C22⋊C4—291no—
278C2×C22⋊C4—291no—
279C2×C22⋊C4—291no—
280C2×C22⋊C4—291no—
281C2×C22⋊C4—291no—
282C2×C22⋊C4—291no—
283C2×C22⋊C4—291no—
284C2×C22⋊C4—291no—
285C2×C22⋊C4—291no—
286C2×C22⋊C4—291no—
287C2×C22⋊C4—291no—
288C2×C22⋊C4—291no—
289C2×C22⋊C4—584no—
290C2×C22⋊C4C2×D2911yescharacteristic
291C2×C22⋊C4C2×D2911yescharacteristic
292C2×C22⋊C4C2×D2911yescharacteristic, complemented
293C2×C22⋊C4C2×D2911yescharacteristic, complemented
294C2×C42—291no—
295C2×C42—291no—
296C2×C42C2×D2911yescharacteristic, complemented
297#95—291no—
298#95—291no—
299#95—291no—
300#95—291no—
301#95—291no—
302#95—291no—
303C29#232111yescharacteristic, complemented, Sylow
304C24—291no—
305C24—291no—
306C24—294no—
307C24—582no—
308C24—582no—
309C24—1161no—
310C24—1161no—
311C24—1161no—
312C24—1161no—
313C24C22×D2911yescharacteristic
314C24C22×D2911yescharacteristic
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—294no—
318C2×D4—294no—
319C2×D4—582no—
320C2×D4—582no—
321C2×D4—1161no—
322C2×D4—1161no—
323C2×D4C4×D2914yescomplemented
324C22×C4—291no—
325C22×C4—291no—
326C22×C4—291no—
327C22×C4—294no—
328C22×C4—291no—
329C22×C4—291no—
330C22×C4—291no—
331C22×C4—582no—
332C22×C4—582no—
333C22×C4—1161no—
334C22×C4—1161no—
335C22×C4—1161no—
336C22×C4—1161no—
337C22×C4—1161no—
338C22×C4—1161no—
339C22×C4C22×D2911yescharacteristic
340C22×C4C22×D2911yescharacteristic
341C22×C4C22×D2911yescharacteristic
342C22×C4C22×D2911yescharacteristic
343C22×C4C22×D2911yescharacteristic
344C4⋊C4—41no—
345C4⋊C4—582no—
346C4⋊C4—1161no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—294no—
352C22⋊C4—294no—
353C22⋊C4—294no—
354C22⋊C4—582no—
355C22⋊C4—582no—
356C22⋊C4—582no—
357C22⋊C4—582no—
358C22⋊C4—582no—
359C22⋊C4—1161no—
360C22⋊C4—1161no—
361C22⋊C4—1161no—
362C22⋊C4—1161no—
363C42—41no—
364C42—582no—
365C42—1161no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—292no—
379C23—292no—
380C23—292no—
381C23—292no—
382C23—588no—
383C23—581no—
384C23—581no—
385C23—581no—
386C23—581no—
387C23—581no—
388C23—581no—
389C23—581no—
390C23—581no—
391C23—581no—
392C23—581no—
393C23—1164no—
394C23—1164no—
395C23—1164no—
396C23—1164no—
397C23—1164no—
398C23—1164no—
399C23C2×C4×D2912yes—
400C23C2×C4×D2912yes—
401C23C23×D2911yescharacteristic
402D4—44no—
403D4—588no—
404D4—1164no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—292no—
419C2×C4—292no—
420C2×C4—292no—
421C2×C4—581no—
422C2×C4—581no—
423C2×C4—581no—
424C2×C4—581no—
425C2×C4—581no—
426C2×C4—581no—
427C2×C4—581no—
428C2×C4—581no—
429C2×C4—581no—
430C2×C4—581no—
431C2×C4—581no—
432C2×C4—581no—
433C2×C4—581no—
434C2×C4—581no—
435C2×C4—581no—
436C2×C4—1164no—
437C2×C4—1164no—
438C2×C4—1164no—
439C2×C4C2×C4×D2912yes—
440C2×C4D4×D2912yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—294no—
456C22—582no—
457C22—582no—
458C22—582no—
459C22—582no—
460C22—582no—
461C22—582no—
462C22—582no—
463C22—582no—
464C22—582no—
465C22—11616no—
466C22—1161no—
467C22—1161no—
468C22—1161no—
469C22—1161no—
470C22C22×C4×D2911yescharacteristic
471C22C2×D4×D2911yescharacteristic
472C22#1174535911yescharacteristic
473C22#1174535911yescharacteristic
474C22#1174535911yescharacteristic
475C22#41×D2911yescharacteristic
476C22#1174536411yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—582no—
483C4—582no—
484C4—582no—
485C4—1161no—
486C4—1161no—
487C4—1161no—
488C2—42no—
489C2—42no—
490C2—584no—
491C2—1162no—
492C2C4×D4×D2911yescharacteristic
493C2#1427163511yescharacteristic
494C2#1427163611yescharacteristic
495C2#1427172111yescharacteristic
496C2#1427172611yescharacteristic
497C2#1427174511yescharacteristic
498C2#1427174711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#390C2
socle, cosocleC23×C29C24
prime radicalC2×#11745299C2
hypercenter#390D29
hypocenterC29#2321
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#11745243C2semidirect
3. C2×C22⋊C4×D29C2semidirect
4. #14271063C2semidirect
5. #14271057C2semidirect
6. #14271057C2semidirect
7. #14271054C2semidirect
8. #14271053C2semidirect
9. #14271043C2semidirect
10. #14271040C2semidirect
11. #14271039C2semidirect
12. #14271034C2semidirect
13. #14271018C2semidirect
14. C4×#90781C2semidirect
15. C29×#390C2semidirect
20. C23×Dic29C22semidirect
23. C2×C4⋊C4×C29C22semidirect
26. C2×C22⋊C4×C29C22semidirect
27. C2×C22⋊C4×C29C22semidirect
28. C2×C42×C29C22semidirect
32. C2×C22⋊Dic29C22semidirect
33. #11745299C4semidirect
42. C2×#90779C22semidirect
43. C2×#90779C22semidirect
44. C2×C4×Dic29C22semidirect
45. C2×C4×Dic29C22semidirect
48. #11745179C22semidirect
49. #11745179C22semidirect
50. #11745179C22semidirect
51. #11745179C22semidirect
52. #11745179C22semidirect
53. #11745179C22semidirect
62. C23×D29C2×C4semidirect
67. C2×D4×C29C2×C4semidirect
78. C2×C22⋊D29C2×C4semidirect
93. C2×C4×D29D4semidirect
103. C22⋊Dic29C2×C4semidirect
110. #90781C2×C4semidirect
111. #90781C2×C4semidirect
243. #390D29semidirect
276. C2×C4⋊C4C2×D29semidirect
292. C2×C22⋊C4C2×D29semidirect
293. C2×C22⋊C4C2×D29semidirect
296. C2×C42C2×D29semidirect
303. C29#2321semidirect
323. C2×D4C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452992
C2×#117452432
C2×C22⋊C4×D292
#142710632
#142710572
#142710542
#142710532
#142710432
#142710402
#142710392
#142710342
#142710182
C4×#907812
C29×#3902
#232129