Finite Group Databasebeta

← #16831471

Subgroups — #16831471

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271861C211yesmaximal, characteristic, complemented
2#14271815C211yesmaximal, characteristic, complemented
3#14271530C211yesmaximal, characteristic, complemented
4#14271507C211yesmaximal, characteristic, complemented
5#14271462C211yesmaximal, characteristic, complemented
6#14271411C211yesmaximal, characteristic, complemented
7#14271393C211yesmaximal, characteristic, complemented
8#14271367C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic, complemented
11#14271274C211yesmaximal, characteristic, complemented
12#14271237C211yesmaximal, characteristic, complemented
13#14271162C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#483C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745306C2211yescharacteristic
21C2×#90784C2211yescharacteristic
22#11745292—21no—
23#11745292C2211yescharacteristic
24C4×C22⋊D29—21no—
25C4×C22⋊D29C2211yescharacteristic
26C2×#90777C2211yescharacteristic
27C2×D232C2211yescharacteristic
28C2×#90773C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic
30#11745260—21no—
31#11745259C2211yescharacteristic
32#11745257C2211yescharacteristic
33#11745256—21no—
34#11745256—21no—
35#11745255C2211yescharacteristic
36#11745255C2211yescharacteristic
37#11745254C2211yescharacteristic
38C4⋊C4×D29—21no—
39#11745252C2211yescharacteristic
40#11745246—21no—
41#11745245—21no—
42C29×#106C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745163C2211yescharacteristic
52#11745162C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29D411yescharacteristic
65#90809—22no—
66#90809—41no—
67#90805—22no—
68#90805—41no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78C2×Dic58C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C22⋊Dic29D411yescharacteristic
88#90784—41no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105#90777—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—22no—
109#90773—41no—
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29—21no—
113C22×D29—21no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—81no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—41no—
127C22⋊D29—42no—
128C22⋊D29—42no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116—21no—
136D116—21no—
137D116—42no—
138D116—81no—
139D116#4112yes—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—42no—
143C4×D29—42no—
144C4×D29—42no—
145C4×D29—81no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3307—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—22no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#547—291no—
180#491—291no—
181#485—291no—
182#483D2911yescharacteristic, complemented
183#478—291no—
184#468—291no—
185#465—291no—
186#461—291no—
187#449—291no—
188#449—291no—
189#442—291no—
190#435—291no—
191#417—291no—
192#416—291no—
193C2×C29—41no—
194C2×C29#54611yescharacteristic
195C2×C29#57511yescharacteristic
196C2×C29#57711yescharacteristic
197D29—41no—
198D29—42no—
199D29—81no—
200C2×#41—291no—
201C2×#41—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C2×M16—291no—
206C22×C8—291no—
207C4⋊Q8—291no—
208#126—581no—
209#125—291no—
210#123—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—291no—
214C22⋊Q8C2×D2911yescharacteristic
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223#117—291no—
224C2×C4⋊C4—581no—
225C2×C4⋊C4C2×D2911yescharacteristic
226#107—291no—
227#106C2×D2911yescharacteristic
228#106C2×D2911yescharacteristic
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103C2×D2911yescharacteristic
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240C22⋊C8—291no—
241C22⋊C8C2×D2911yescharacteristic
242#97—291no—
243C29#330711yescharacteristic, complemented, Sylow
244#41—582no—
245#41—582no—
246#41—1161no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C22×C4—21no—
258C22×C4—291no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264SD16—1161no—
265SD16—1161no—
266D8—582no—
267M16—1161no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C4⋊C4C22×D2911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—291no—
287C22⋊C4—291no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—291no—
295C42—581no—
296C23—291no—
297C23—581no—
298C23—581no—
299C23D4×D2911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—581no—
303Q8—581no—
304D4—292no—
305D4—581no—
306D4—581no—
307D4—581no—
308D4—1162no—
309D4—1161no—
310D4—1162no—
311D4—1162no—
312D4—2321no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—291no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—1162no—
328C2×C4—1162no—
329C2×C4—1162no—
330C2×C4—2321no—
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—581no—
341C22—582no—
342C22—581no—
343C22—581no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—581no—
356C4—581no—
357C4—581no—
358C4—1161no—
359C4—1161no—
360C4#41×D2911yescharacteristic
361C4#1174536411yescharacteristic
362C2—41no—
363C2—1161no—
364C2—1162no—
365C2—2321no—
366C2#1427180511yescharacteristic
367C2#1427196211yescharacteristic
368C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#483C2
socleC22×C29C22×D4
hypercenter#483D29
hypocenterC29#3307
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14271861C2semidirect
2. #14271815C2semidirect
3. #14271530C2semidirect
4. #14271507C2semidirect
5. #14271462C2semidirect
6. #14271411C2semidirect
7. #14271393C2semidirect
8. #14271367C2semidirect
9. #14271311C2semidirect
10. #14271310C2semidirect
11. #14271274C2semidirect
12. #14271237C2semidirect
13. #14271162C2semidirect
14. #14271158C2semidirect
15. C29×#483C2semidirect
182. #483D29semidirect
243. C29#3307semidirect

Maximal subgroups

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

subgroupindex
#142718612
#142718152
#142715302
#142715072
#142714622
#142714112
#142713932
#142713672
#142713112
#142713102
#142712742
#142712372
#142711622
#142711582
C29×#4832
#330729