Finite Group Databasebeta

← #16822632

Subgroups — #16822632

Order 3712.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745244C211yesmaximal, characteristic
2#14271065C211yesmaximal, characteristic, complemented
3#14271064C211yesmaximal, characteristic, complemented
4#14271063C211yesmaximal, characteristic, complemented
5#14271056C211yesmaximal, characteristic, complemented
6#14271055C211yesmaximal, characteristic, complemented
7#14271054C211yesmaximal, characteristic, complemented
8#14271053C211yesmaximal, characteristic, complemented
9#14271052C211yesmaximal, characteristic, complemented
10#14271041C211yesmaximal, characteristic, complemented
11#14271041C211yesmaximal, characteristic, complemented
12#14271039C211yesmaximal, characteristic, complemented
13#14271018C211yesmaximal, characteristic, complemented
14#14271018C211yesmaximal, characteristic, complemented
15C29×#388C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C22×C4×D29C2211yescharacteristic, complemented
21C2×C4⋊C4×C29C2211yescharacteristic, complemented
22C2×C22⋊C4×C29C2211yescharacteristic
23C2×C22⋊C4×C29C2211yescharacteristic
24C2×C22⋊C4×C29C2211yescharacteristic
25C2×C42×C29C2211yescharacteristic, complemented
26C2×C22⋊Dic29C2211yescharacteristic
27C2×C22⋊Dic29C2211yescharacteristic
28C2×#90781C2211yescharacteristic
29C2×#90781C2211yescharacteristic
30C2×#90781C2211yescharacteristic
31C2×#90781C2211yescharacteristic
32C2×#90781C2211yescharacteristic
33C2×#90781C2211yescharacteristic
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic, complemented
39C2×#90781C2211yescharacteristic, complemented
40C2×#90781C2211yescharacteristic, complemented
41C2×C4⋊Dic29C2211yescharacteristic, complemented
42C2×#90779C2211yescharacteristic, complemented
43C2×C4×Dic29C2211yescharacteristic, complemented
44C2×C4×Dic29C2211yescharacteristic, complemented
45#11745244C418yescomplemented
46C29×#95C2211yescharacteristic, complemented
47C29×#95C2211yescharacteristic, complemented
48#11745179C2211yescharacteristic, complemented
49#11745179C2211yescharacteristic, complemented
50#11745179C2211yescharacteristic, complemented
51#11745179C2211yescharacteristic, complemented
52C24×C29C2311yescharacteristic
53C23×D29—41no—
54C23×D29—41no—
55C23×D29—41no—
56C23×D29—41no—
57C23×D29—41no—
58C23×D29—41no—
59C23×D29C2×C414yescomplemented
60C23×D29C2311yescharacteristic
61C23×D29C2311yescharacteristic
62C23×D29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C22×C4×C29C2311yescharacteristic
69C2×C22⋊D29—41no—
70C2×C22⋊D29—41no—
71C2×C22⋊D29C2×C414yes—
72C22×Dic29C2311yescharacteristic
73C22×Dic29C2311yescharacteristic
74C22×Dic29C2311yescharacteristic
75C22×Dic29C2311yescharacteristic
76C22×Dic29C2311yescharacteristic
77C2×D116—41no—
78C2×D116—41no—
79C2×D116—41no—
80C2×D116—41no—
81C2×D116C2×C414yes—
82C2×D116C2×C414yes—
83C2×C4×D29—41no—
84C2×C4×D29—41no—
85C2×C4×D29—41no—
86C4⋊C4×C29—41no—
87C22⋊C4×C29—41no—
88C22⋊C4×C29—41no—
89C22⋊C4×C29C2×C414yescomplemented
90C42×C29—41no—
91C22⋊Dic29—41no—
92C22⋊Dic29—41no—
93#90781—41no—
94#90781—41no—
95#90781—41no—
96#90781—41no—
97#90781—41no—
98#90781—41no—
99#90781—41no—
100#90781—41no—
101#90781—41no—
102#90781—41no—
103#90781—41no—
104#90781C2×C414yescomplemented
105#90781C2×C414yescomplemented
106C4⋊Dic29—41no—
107#90779—41no—
108C4×Dic29—41no—
109C4×Dic29—41no—
110C23×C29—21no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—21no—
115C23×C29—21no—
116C23×C29C22×C412yes—
117C23×C29C2411yescharacteristic
118C22×D29—21no—
119C22×D29—21no—
120C22×D29—21no—
121C22×D29—21no—
122C22×D29—21no—
123C22×D29—21no—
124C22×D29—21no—
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—21no—
130C22×D29—21no—
131C22×D29—21no—
132C22×D29—21no—
133C22×D29—21no—
134C22×D29—21no—
135C22×D29—21no—
136C22×D29—44no—
137C22×D29—44no—
138C22×D29—44no—
139C22×D29—44no—
140C22×D29—44no—
141C22×D29—44no—
142C22×D29—44no—
143C22×D29C22×C412yes—
144C22×D29C22×C412yes—
145C22×D29C22×C412yes—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
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×C29C22×C412yes—
163C2×C4×C29C22×C412yes—
164C22⋊D29—44no—
165C2×Dic29—21no—
166C2×Dic29—21no—
167C2×Dic29—21no—
168C2×Dic29—21no—
169C2×Dic29—21no—
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×Dic29C22×C412yes—
180D116—44no—
181D116—44no—
182C4×D29—44no—
183#2375—291nomaximal, Sylow
184C22×C29—22no—
185C22×C29—22no—
186C22×C29—22no—
187C22×C29—41no—
188C22×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29C23×C411yescharacteristic
192C22×C29H(5,𝔽2)11yescharacteristic
193C22×C29H(5,𝔽2)11yescharacteristic
194C22×C29H(5,𝔽2)11yescharacteristic
195C22×C29H(5,𝔽2)11yescharacteristic
196C22×C29H(5,𝔽2)11yescharacteristic
197C22×C29H(5,𝔽2)11yescharacteristic
198C2×D29—22no—
199C2×D29—22no—
200C2×D29—22no—
201C2×D29—22no—
202C2×D29—22no—
203C2×D29—22no—
204C2×D29—22no—
205C2×D29—22no—
206C2×D29—22no—
207C2×D29—416no—
208C2×D29—41no—
209C2×D29—41no—
210C2×D29—41no—
211C2×D29—41no—
212C2×D29—41no—
213C2×D29—41no—
214C2×D29—41no—
215C2×D29—41no—
216C2×D29—41no—
217C2×D29—41no—
218C2×D29—41no—
219C2×D29—41no—
220C4×C29—22no—
221C4×C29—22no—
222C4×C29—41no—
223C4×C29—41no—
224C4×C29—41no—
225C4×C29—41no—
226Dic29—22no—
227Dic29—41no—
228Dic29—41no—
229Dic29—41no—
230Dic29—41no—
231C2×#120—291no—
232#390—291no—
233#390—291no—
234#390—291no—
235#388—291no—
236#388—291no—
237#388—291no—
238#388—291no—
239#388—291no—
240#388D2911yescharacteristic, complemented
241#386—291no—
242#386—291no—
243#386—291no—
244#379—291no—
245#379—291no—
246C2×C29—42no—
247C2×C29#51811yescharacteristic
248C2×C29#51811yescharacteristic
249C2×C29#51811yescharacteristic
250C2×C29#56011yescharacteristic
251C2×C29#56011yescharacteristic
252C2×C29#56011yescharacteristic
253C2×C29H(3,𝔽4)11yescharacteristic
254D29—42no—
255D29—42no—
256D29—42no—
257C25—291no—
258C22×D4—291no—
259C22×D4—291no—
260C22×D4—291no—
261C23×C4—291no—
262#120—298no—
263C2×C4⋊C4—291no—
264C2×C4⋊C4—291no—
265C2×C4⋊C4C2×D2911yescharacteristic, complemented
266C2×C22⋊C4—291no—
267C2×C22⋊C4—291no—
268C2×C22⋊C4—291no—
269C2×C22⋊C4—291no—
270C2×C22⋊C4—291no—
271C2×C22⋊C4—291no—
272C2×C22⋊C4—291no—
273C2×C22⋊C4—291no—
274C2×C22⋊C4—291no—
275C2×C22⋊C4—291no—
276C2×C22⋊C4—291no—
277C2×C22⋊C4—291no—
278C2×C22⋊C4—291no—
279C2×C22⋊C4—291no—
280C2×C22⋊C4—291no—
281C2×C22⋊C4C2×D2911yescharacteristic
282C2×C22⋊C4C2×D2911yescharacteristic
283C2×C22⋊C4C2×D2911yescharacteristic
284C2×C42—291no—
285C2×C42—291no—
286C2×C42C2×D2911yescharacteristic, complemented
287#95—291no—
288#95—291no—
289#95—291no—
290#95—291no—
291#95C2×D2911yescharacteristic, complemented
292#95C2×D2911yescharacteristic, complemented
293C29#237511yescharacteristic, complemented, Sylow
294C24—291no—
295C24—291no—
296C24—291no—
297C24—294no—
298C24—1161no—
299C24—1161no—
300C24—1161no—
301C24—1161no—
302C24—1161no—
303C24—1161no—
304C24C22×D2911yescharacteristic
305C2×D4—294no—
306C2×D4—294no—
307C2×D4—294no—
308C2×D4—1161no—
309C2×D4—1161no—
310C2×D4—1161no—
311C2×D4—1161no—
312C2×D4—1161no—
313C2×D4—1161no—
314C22×C4—291no—
315C22×C4—291no—
316C22×C4—291no—
317C22×C4—291no—
318C22×C4—291no—
319C22×C4—1161no—
320C22×C4—1161no—
321C22×C4—1161no—
322C22×C4C22×D2911yescharacteristic
323C22×C4C22×D2911yescharacteristic
324C22×C4C22×D2911yescharacteristic
325C22×C4C22×D2911yescharacteristic
326C22×C4C22×D2911yescharacteristic
327C22×C4C22×D2911yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—1161no—
330C4⋊C4—1161no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—294no—
334C22⋊C4—294no—
335C22⋊C4—1161no—
336C22⋊C4—1161no—
337C22⋊C4—1161no—
338C22⋊C4—1161no—
339C22⋊C4—1161no—
340C22⋊C4—1161no—
341C22⋊C4—1161no—
342C22⋊C4—1161no—
343C22⋊C4—1161no—
344C22⋊C4—1161no—
345C22⋊C4—1161no—
346C22⋊C4—1161no—
347C22⋊C4—1161no—
348C22⋊C4C4×D2914yescomplemented
349C42—41no—
350C42—1161no—
351C42—1161no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—292no—
359C23—292no—
360C23—292no—
361C23—581no—
362C23—581no—
363C23—581no—
364C23—581no—
365C23—581no—
366C23—581no—
367C23—581no—
368C23—581no—
369C23—581no—
370C23—581no—
371C23—581no—
372C23—581no—
373C23—581no—
374C23—581no—
375C23—581no—
376C23—581no—
377C23—581no—
378C23—581no—
379C23—1164no—
380C23—1164no—
381C23—1164no—
382C23—1164no—
383C23—1164no—
384C23—1164no—
385C23—1164no—
386C23C2×C4×D2912yes—
387C23C23×D2911yescharacteristic
388D4—1164no—
389D4—1164no—
390D4—1164no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—292no—
408C2×C4—581no—
409C2×C4—581no—
410C2×C4—581no—
411C2×C4—581no—
412C2×C4—581no—
413C2×C4—581no—
414C2×C4—581no—
415C2×C4—581no—
416C2×C4—581no—
417C2×C4—581no—
418C2×C4—581no—
419C2×C4—581no—
420C2×C4—581no—
421C2×C4—581no—
422C2×C4—1164no—
423C2×C4C2×C4×D2912yes—
424C2×C4C2×C4×D2912yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—582no—
433C22—582no—
434C22—582no—
435C22—582no—
436C22—582no—
437C22—582no—
438C22—582no—
439C22—582no—
440C22—582no—
441C22—11616no—
442C22—1161no—
443C22—1161no—
444C22—1161no—
445C22—1161no—
446C22—1161no—
447C22—1161no—
448C22—1161no—
449C22—1161no—
450C22—1161no—
451C22—1161no—
452C22—1161no—
453C22—1161no—
454C22C22×C4×D2911yescharacteristic
455C22#1174535911yescharacteristic
456C22#1174535911yescharacteristic
457C22#1174536411yescharacteristic
458C22#1174536411yescharacteristic
459C22#1174536411yescharacteristic
460C22#1174536411yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—582no—
468C4—1161no—
469C4—1161no—
470C4—1161no—
471C4—1161no—
472C2—42no—
473C2—1162no—
474C2—1162no—
475C2—1162no—
476C2#1427163511yescharacteristic
477C2#1427163511yescharacteristic
478C2#1427163711yescharacteristic
479C2#1427190111yescharacteristic
480C2#1427190311yescharacteristic
481C2#1427190411yescharacteristic
482C2#1427190511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#388C2
socle, cosocleC23×C29C24
prime radicalC2×#11745244C2
hypercenter#388D29
hypocenterC29#2375
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14271065C2semidirect
3. #14271064C2semidirect
4. #14271063C2semidirect
5. #14271056C2semidirect
6. #14271055C2semidirect
7. #14271054C2semidirect
8. #14271053C2semidirect
9. #14271052C2semidirect
10. #14271041C2semidirect
11. #14271041C2semidirect
12. #14271039C2semidirect
13. #14271018C2semidirect
14. #14271018C2semidirect
15. C29×#388C2semidirect
20. C22×C4×D29C22semidirect
21. C2×C4⋊C4×C29C22semidirect
25. C2×C42×C29C22semidirect
38. C2×#90781C22semidirect
39. C2×#90781C22semidirect
40. C2×#90781C22semidirect
41. C2×C4⋊Dic29C22semidirect
42. C2×#90779C22semidirect
43. C2×C4×Dic29C22semidirect
44. C2×C4×Dic29C22semidirect
45. #11745244C4semidirect
46. C29×#95C22semidirect
47. C29×#95C22semidirect
48. #11745179C22semidirect
49. #11745179C22semidirect
50. #11745179C22semidirect
51. #11745179C22semidirect
59. C23×D29C2×C4semidirect
89. C22⋊C4×C29C2×C4semidirect
104. #90781C2×C4semidirect
105. #90781C2×C4semidirect
240. #388D29semidirect
265. C2×C4⋊C4C2×D29semidirect
286. C2×C42C2×D29semidirect
291. #95C2×D29semidirect
292. #95C2×D29semidirect
293. C29#2375semidirect
348. C22⋊C4C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452442
#142710652
#142710642
#142710632
#142710562
#142710552
#142710542
#142710532
#142710522
#142710412
#142710392
#142710182
C29×#3882
#237529