Finite Group Databasebeta

← #16831397

Subgroups — #16831397

Order 3712.

398 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#14271857C211yesmaximal, characteristic, complemented
2#14271823C211yesmaximal, characteristic, complemented
3#14271519C211yesmaximal, characteristic, complemented
4#14271483C211yesmaximal, characteristic, complemented
5#14271469C211yesmaximal, characteristic, complemented
6#14271400C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271381C211yesmaximal, characteristic, complemented
9#14271310C211yesmaximal, characteristic, complemented
10#14271303C211yesmaximal, characteristic, complemented
11#14271250C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#485C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C29×#117C2211yescharacteristic
20#11745309C2211yescharacteristic
21C2×#90784C2211yescharacteristic
22#11745292C2211yescharacteristic
23C4×C22⋊D29C2211yescharacteristic
24C22×#6597C2211yescharacteristic
25C2×D232C2211yescharacteristic
26C2×#90773C2211yescharacteristic
27C2×C8×D29C2211yescharacteristic
28#11745258—21no—
29#11745257C2211yescharacteristic
30#11745257C2211yescharacteristic
31#11745255—21no—
32#11745255C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34#11745252C2211yescharacteristic
35#11745249C2211yescharacteristic
36#11745247—21no—
37#11745246—21no—
38#11745246—21no—
39#11745245—21no—
40#11745238—21no—
41C4×D116—21no—
42C29×#107C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745162C2211yescharacteristic
52C8×Dic29C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29D411yescharacteristic
64Q8×D29—22no—
65Q8×D29—41no—
66#90805—22no—
67#90805—41no—
68C2×D116—21no—
69C2×D116—21no—
70C2×D116C2311yescharacteristic
71C2×D116C2311yescharacteristic
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C42×C29—21no—
88C22⋊Dic29D411yescharacteristic
89#90784—41no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—41no—
109#90773—22no—
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×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C22⋊D29—22no—
126C22⋊D29—42no—
127C22⋊D29—81no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—21no—
134D116—21no—
135D116—21no—
136D116—21no—
137D116—42no—
138D116—42no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—42no—
142C4×D29—42no—
143C4×D29—81no—
144C4×D29—81no—
145Dic58—21no—
146Dic58—42no—
147Dic58#4112yes—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29#13512yes—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—22no—
174Dic29—21no—
175Dic29—21no—
176Dic29—21no—
177Dic29—41no—
178#553—291no—
179#548—291no—
180#488—291no—
181#485D2911yescharacteristic, complemented
182#481—291no—
183#479—291no—
184#466—291no—
185#465—291no—
186#463—291no—
187#449—291no—
188#448—291no—
189C4×SD16—291no—
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29—41no—
194C2×C29#54611yescharacteristic
195C2×C29C2×#13511yescharacteristic
196C2×C29#57711yescharacteristic
197D29—22no—
198D29—81no—
199D29—81no—
200C2×#41—291no—
201C22×Q8—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C22×C8—291no—
206C22×C8—291no—
207#126—581no—
208#125—291no—
209#124—291no—
210#124—581no—
211#123—581no—
212C22⋊Q8—581no—
213C22⋊Q8C2×D2911yescharacteristic
214#121—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×Q8—291no—
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223C4×D4—581no—
224#117C2×D2911yescharacteristic
225C2×C4⋊C4—291no—
226#107C2×D2911yescharacteristic
227#106—291no—
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
242C4×C8—291no—
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—291no—
247C2×Q8—581no—
248C2×Q8—582no—
249C2×Q8—1161no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C22×C4—291no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264SD16—582no—
265SD16—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4C22×D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—291no—
286C22⋊C4—291no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—21no—
294C42—291no—
295C42—581no—
296C23—291no—
297C23—581no—
298C23—581no—
299C23D4×D2911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—292no—
303Q8—581no—
304Q8—1162no—
305D4—582no—
306D4—581no—
307D4—581no—
308D4—581no—
309D4—581no—
310D4—1162no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
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—2321no—
330C2×C4—2321no—
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—292no—
341C22—581no—
342C22—581no—
343C22—1161no—
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—582no—
357C4—581no—
358C4—581no—
359C4—1161no—
360C4#41×D2911yescharacteristic
361C4#1174536411yescharacteristic
362C2—41no—
363C2—582no—
364C2—2321no—
365C2—2321no—
366C2#1427180511yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#485C2
socleC22×C29C22×D4
hypercenter#485D29
hypocenterC29#3301
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14271857C2semidirect
2. #14271823C2semidirect
3. #14271519C2semidirect
4. #14271483C2semidirect
5. #14271469C2semidirect
6. #14271400C2semidirect
7. #14271394C2semidirect
8. #14271381C2semidirect
9. #14271310C2semidirect
10. #14271303C2semidirect
11. #14271250C2semidirect
12. #14271226C2semidirect
13. #14271157C2semidirect
14. #103×D29C2semidirect
15. C29×#485C2semidirect
181. #485D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718572
#142718232
#142715192
#142714832
#142714692
#142714002
#142713942
#142713812
#142713102
#142713032
#142712502
#142712262
#142711572
#103×D292
C29×#4852
#330129