Finite Group Databasebeta

← #16829733

Subgroups — #16829733

Order 3712.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271767C211yesmaximal, characteristic, complemented
2#14271635C211yesmaximal, characteristic, complemented
3#14271486C211yesmaximal, characteristic, complemented
4#14271485C211yesmaximal, characteristic, complemented
5#14271464C211yesmaximal, characteristic, complemented
6#14271463C211yesmaximal, characteristic, complemented
7#14271355C211yesmaximal, characteristic, complemented
8#14271295C211yesmaximal, characteristic, complemented
9#14271295C211yesmaximal, characteristic, complemented
10#14271275C211yesmaximal, characteristic, complemented
11#14271272C211yesmaximal, characteristic, complemented
12D8×Dic29C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14#14271223C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×D8×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#127C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745301—21no—
22#11745301—21no—
23#11745300C2211yescharacteristic
24#11745300C2211yescharacteristic
25#11745297—21no—
26#11745297—21no—
27D4×Dic29C2211yescharacteristic
28D4×Dic29C2211yescharacteristic, complemented
29D4×Dic29C2211yescharacteristic, complemented
30C2×#90782C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29—21no—
33C2×#90781—21no—
34#11745255C2211yescharacteristic
35#11745254C2211yescharacteristic
36#11745243—21no—
37C22⋊C4×D29—21no—
38C4×D116C2211yescharacteristic
39#11745234C2211yescharacteristic
40#11745232C2211yescharacteristic, complemented
41C29×C4⋊C8C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic, complemented
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745166C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745163C2211yescharacteristic, complemented
55C8×Dic29C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4⋊#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C22×Dic29—21no—
70C22×Dic29—21no—
71C22×Dic29—21no—
72D4×D29—22no—
73D4×D29—22no—
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78D8×C29—22no—
79D8×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C42×C29C2311yescharacteristic
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90782—22no—
91#90782—22no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96#90781D411yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29—21no—
110C23×C29—21no—
111C22×D29—21no—
112C22×D29—24no—
113C22×D29—81no—
114C22×D29—81no—
115C22×D29C2×D411yescharacteristic
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—81no—
122D4×C29—81no—
123D4×C29#4112yes—
124C2×C4×C29—21no—
125C2×C4×C29—81no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—24no—
130C22⋊D29—81no—
131C22⋊D29—81no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—81no—
136C2×Dic29—81no—
137C2×Dic29—81no—
138C2×Dic29C2×D411yescharacteristic
139C2×Dic29C2×D411yescharacteristic
140C2×Dic29C2×D411yescharacteristic
141D116—21no—
142D116#4112yes—
143C4×D29—21no—
144C4×D29—21no—
145C4×D29—81no—
146C4×D29—81no—
147C8×C29—21no—
148C8×C29—21no—
149#6597—21no—
150#6597—21no—
151#3122—291nomaximal, Sylow
152C22×C29—22no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29C22×D411yescharacteristic
162C2×D29—21no—
163C2×D29—22no—
164C2×D29—21no—
165C2×D29—21no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—84no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29C2×#4111yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—21no—
177Dic29—41no—
178Dic29—41no—
179Dic29—41no—
180#540—291no—
181#518—291no—
182#482—291no—
183#482—291no—
184#478—291no—
185#478—291no—
186#459—291no—
187#459D2911yescharacteristic, complemented
188#447—291no—
189#447—291no—
190#442—291no—
191#442—291no—
192C4×D8—291no—
193C4×D8—291no—
194#433—291no—
195C2×C29—42no—
196C2×C29—81no—
197C2×C29—81no—
198C2×C29#52511yescharacteristic
199C2×C29#57611yescharacteristic
200C2×C29#57611yescharacteristic
201D29—41no—
202D29—42no—
203C22×D4—291no—
204C2×D8—291no—
205C2×D8—291no—
206C2×D8C2×D2911yescharacteristic
207C2×D8C2×D2911yescharacteristic
208#127C2×D2911yescharacteristic, complemented
209#125—291no—
210#123—581no—
211#123—581no—
212#121—291no—
213#121—291no—
214#121—581no—
215#121—581no—
216C4×D4—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—581no—
222C4×D4—581no—
223C4×D4C2×D2911yescharacteristic
224#117—291no—
225#117—291no—
226C2×C22⋊C4—581no—
227C2×C22⋊C4—581no—
228#107—291no—
229#107—291no—
230#106—291no—
231#106—291no—
232C4⋊C8—291no—
233C4⋊C8C2×D2911yescharacteristic, complemented
234#102—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102C2×D2911yescharacteristic, complemented
241#102C2×D2911yescharacteristic, complemented
242C22⋊C8—291no—
243C22⋊C8—291no—
244#97—291no—
245C4×C8—291no—
246C29#312211yescharacteristic, complemented, Sylow
247C24—581no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—291no—
251C2×D4—581no—
252C2×D4—582no—
253C2×D4—582no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22×D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C2×D4C22×D2911yescharacteristic
259C22×C4—21no—
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264C22×C4—581no—
265C22×C4—581no—
266D8—22no—
267D8—22no—
268D8—582no—
269D8—582no—
270C2×C8—291no—
271C2×C8—291no—
272C2×C8C22×D2911yescharacteristic
273C2×C8C22×D2911yescharacteristic
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—291no—
278C4⋊C4—291no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—291no—
284C22⋊C4—291no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—291no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—291no—
300C23—584no—
301C23—581no—
302C23—2321no—
303C23—2321no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—292no—
312D4—584no—
313D4—581no—
314D4—2321no—
315D4—2321no—
316D4#9080712yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—291no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—2321no—
328C2×C4—2321no—
329C2×C4—2321no—
330C2×C4—2321no—
331C2×C4—2321no—
332C2×C4D4×D2911yescharacteristic
333C2×C4D4×D2911yescharacteristic
334C2×C4C23×D2911yescharacteristic
335C8—21no—
336C8—21no—
337C8—581no—
338C8—581no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—581no—
349C22—582no—
350C22—581no—
351C22—581no—
352C22—1161no—
353C22—1161no—
354C22—2324no—
355C22C2×D4×D2911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—581no—
360C4—581no—
361C4—581no—
362C4—1161no—
363C4—1161no—
364C4—1161no—
365C4C2×#9080711yescharacteristic
366C4#41×D2911yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—1161no—
371C2—1162no—
372C2#1427167311yescharacteristic
373C2#1427196411yescharacteristic
374C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3122
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14271767C2semidirect
2. #14271635C2semidirect
3. #14271486C2semidirect
4. #14271485C2semidirect
5. #14271464C2semidirect
6. #14271463C2semidirect
7. #14271355C2semidirect
8. #14271295C2semidirect
9. #14271295C2semidirect
10. #14271275C2semidirect
11. #14271272C2semidirect
12. D8×Dic29C2semidirect
13. #14271243C2semidirect
14. #14271223C2semidirect
15. C29×#459C2semidirect
19. C29×#127C22semidirect
28. D4×Dic29C22semidirect
29. D4×Dic29C22semidirect
40. #11745232C22semidirect
41. C29×C4⋊C8C22semidirect
42. C29×#102C22semidirect
43. C29×#102C22semidirect
46. #11745180C22semidirect
47. #11745180C22semidirect
52. #11745166C22semidirect
53. #11745165C22semidirect
54. #11745163C22semidirect
55. C8×Dic29C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. C4⋊#6597C22semidirect
187. #459D29semidirect
208. #127C2×D29semidirect
233. C4⋊C8C2×D29semidirect
240. #102C2×D29semidirect
241. #102C2×D29semidirect
246. C29#3122semidirect

Maximal subgroups

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

subgroupindex
#142717672
#142716352
#142714862
#142714852
#142714642
#142714632
#142713552
#142712952
#142712752
#142712722
D8×Dic292
#142712432
#142712232
C29×#4592
#312229