Finite Group Databasebeta

← #16832561

Subgroups — #16832561

Order 3712.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271898C211yesmaximal, characteristic, complemented
2#14271882C211yesmaximal, characteristic, complemented
3#14271556C211yesmaximal, characteristic, complemented
4#14271553C211yesmaximal, characteristic
5#14271544C211yesmaximal, characteristic, complemented
6#14271387C211yesmaximal, characteristic, complemented
7#14271380C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271367C211yesmaximal, characteristic, complemented
10#14271364C211yesmaximal, characteristic, complemented
11#14271292C211yesmaximal, characteristic, complemented
12#14271272C211yesmaximal, characteristic, complemented
13#14271268C211yesmaximal, characteristic, complemented
14#14271248C211yesmaximal, characteristic, complemented
15C29×#464C211yesmaximal, characteristic, complemented
16C2×Q16×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C29×#124C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20#11745309C2211yescharacteristic
21#11745309C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic
23#11745306C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25C2×#90784C2211yescharacteristic
26C2×#90784C2211yescharacteristic
27#11745298C2211yescharacteristic
28D4×Dic29C2211yescharacteristic
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32C2×#90773C2211yescharacteristic
33#11745256—21no—
34#11745256—21no—
35#11745255C2211yescharacteristic
36#11745255C2211yescharacteristic
37#11745241—21no—
38#11745241—21no—
39#11745240—21no—
40#11745239—21no—
41#11745237—21no—
42#11745236C2211yescharacteristic
43C4×D116—21no—
44C4×Dic58C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×C4⋊C8C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#102C2211yescharacteristic
49#11745183C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745163C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745162C2211yescharacteristic
55C8×Dic29C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×Dic29—21no—
63C2×D116—21no—
64C2×D116—21no—
65C2×D116C2311yescharacteristic
66C2×D116C2311yescharacteristic
67C2×C4×D29—21no—
68C2×C4×D29—21no—
69C2×Dic58D411yescharacteristic
70C2×Dic58C2311yescharacteristic
71Q16×C29—41no—
72SD16×C29—41no—
73C2×C8×C29C2311yescharacteristic
74C2×C8×C29C2311yescharacteristic
75C4⋊C4×C29—21no—
76C4⋊C4×C29C2311yescharacteristic
77C22⋊C4×C29—21no—
78C22⋊C4×C29—21no—
79C42×C29—21no—
80C42×C29C2311yescharacteristic
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84#90785—22no—
85#90784—22no—
86#90784—41no—
87#90782—22no—
88#90782—41no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29D411yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779D411yescharacteristic
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90773—41no—
110#90773—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—42no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—21no—
134D116—21no—
135D116—21no—
136D116—21no—
137D116—42no—
138D116—81no—
139C4×D29—81no—
140C4×D29—81no—
141Dic58—21no—
142Dic58—21no—
143Dic58—41no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597#4112yes—
148#3401—291nomaximal, Sylow
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C22×D411yescharacteristic
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29H(5,𝔽2)11yescharacteristic
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556—291no—
174#497—291no—
175#496—291no—
176#495—291no—
177#464—291no—
178#464D2911yescharacteristic, complemented
179#463—291no—
180#463—291no—
181#461—291no—
182#460—291no—
183#446—291no—
184#442—291no—
185#441—291no—
186C4×SD16—291no—
187C2×C29—81no—
188C2×C29#55011yescharacteristic
189C2×C29#57511yescharacteristic
190C2×C29#57711yescharacteristic
191D29—81no—
192D29—81no—
193C2×Q16—291no—
194C2×Q16C2×D2911yescharacteristic
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×SD16C2×D2911yescharacteristic
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8—291no—
203#127—291no—
204#126—581no—
205#126—581no—
206#124—291no—
207#124—291no—
208#124—291no—
209#124—581no—
210#124C2×D2911yescharacteristic
211#123—581no—
212#123—581no—
213C22⋊Q8—581no—
214C4×Q8—291no—
215C4×Q8—291no—
216C4×Q8—291no—
217C4×Q8C2×D2911yescharacteristic
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—581no—
222#117—581no—
223#106—291no—
224C4⋊C8—291no—
225C4⋊C8—291no—
226C4⋊C8C2×D2911yescharacteristic
227#103—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#102—291no—
231#102—291no—
232#102C2×D2911yescharacteristic
233#97—291no—
234#97—291no—
235C4×C8—291no—
236C29#340111yescharacteristic, complemented, Sylow
237C2×Q8—291no—
238C2×Q8—291no—
239C2×Q8C22×D2911yescharacteristic
240C2×Q8C22×D2911yescharacteristic
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4C22×D2911yescharacteristic
246C22×C4—581no—
247C22×C4—581no—
248C22×C4—581no—
249Q16—41no—
250Q16—582no—
251SD16—41no—
252SD16—582no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—582no—
257D8—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4C22×D2911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—21no—
284C42—291no—
285C42—291no—
286C42—581no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—581no—
291C23—581no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—581no—
297Q8—581no—
298Q8—1161no—
299D4—21no—
300D4—21no—
301D4—581no—
302D4—581no—
303D4—581no—
304D4—581no—
305D4—1162no—
306D4—2321no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—1162no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4D4×D2911yescharacteristic
320C2×C4D4×D2911yescharacteristic
321C2×C4C23×D2911yescharacteristic
322C8—21no—
323C8—21no—
324C8—292no—
325C8—581no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22C2×D4×D2911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—581no—
342C4—581no—
343C4—581no—
344C4—581no—
345C4—1161no—
346C4—1161no—
347C4#1174535911yescharacteristic
348C4#41×D2911yescharacteristic
349C2—81no—
350C2—2321no—
351C2—2321no—
352C2#1427183111yescharacteristic
353C2#1427196211yescharacteristic
354C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#464C2
socleC22×C29C22×D4
prime radical#14271553C2
hypercenter#464D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271882C2semidirect
3. #14271556C2semidirect
5. #14271544C2semidirect
6. #14271387C2semidirect
7. #14271380C2semidirect
8. #14271377C2semidirect
9. #14271367C2semidirect
10. #14271364C2semidirect
11. #14271292C2semidirect
12. #14271272C2semidirect
13. #14271268C2semidirect
14. #14271248C2semidirect
15. C29×#464C2semidirect
178. #464D29semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142718822
#142715562
#142715532
#142715442
#142713872
#142713802
#142713772
#142713672
#142713642
#142712922
#142712722
#142712682
#142712482
C29×#4642
#340129