Finite Group Databasebeta

← #16832083

Subgroups — #16832083

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271876C211yesmaximal, characteristic, complemented
2#14271814C211yesmaximal, characteristic, complemented
3#14271560C211yesmaximal, characteristic, complemented
4#14271490C211yesmaximal, characteristic, complemented
5#14271487C211yesmaximal, characteristic, complemented
6#14271483C211yesmaximal, characteristic, complemented
7#14271481C211yesmaximal, characteristic, complemented
8#14271452C211yesmaximal, characteristic, complemented
9#14271442C211yesmaximal, characteristic, complemented
10#14271417C211yesmaximal, characteristic, complemented
11#14271416C211yesmaximal, characteristic, complemented
12#14271245C211yesmaximal, characteristic, complemented
13#14271239C211yesmaximal, characteristic, complemented
14#14271204C211yesmaximal, characteristic, complemented
15C29×#428C211yesmaximal, characteristic, complemented
16C2×#90805—21no—
17C2×M16×C29C2211yescharacteristic
18C29×#117C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745292C2211yescharacteristic
21#11745292C2211yescharacteristic
22#11745291—21no—
23C4×C22⋊D29C2211yescharacteristic
24C2×D232C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26#11745258—21no—
27#11745257C2211yescharacteristic
28#11745257C2211yescharacteristic
29#11745256—21no—
30#11745255C2211yescharacteristic
31#11745255C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34#11745250C2211yescharacteristic
35#11745250C2211yescharacteristic
36#11745247—21no—
37#11745246—21no—
38#11745237—21no—
39#11745234—21no—
40C29×#107C2211yescharacteristic
41C29×#107C2211yescharacteristic
42C29×#106C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745169C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745168C2211yescharacteristic
48#11745165C2211yescharacteristic
49#11745162C2211yescharacteristic
50C8×Dic29C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745156C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59C22×C4×C29—21no—
60C22×C4×C29C2311yescharacteristic
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29D411yescharacteristic
64#90805—44no—
65C2×D116—21no—
66C2×D116—21no—
67C2×D116C2311yescharacteristic
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29C2311yescharacteristic
73C2×Dic58—21no—
74C2×Dic58—21no—
75M16×C29—22no—
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29—21no—
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C22⋊Dic29D411yescharacteristic
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781D411yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779D411yescharacteristic
100C4×Dic29—21no—
101C4×Dic29C2311yescharacteristic
102C2×#6597C2311yescharacteristic
103C2×#6597C2311yescharacteristic
104D232—22no—
105#90772—22no—
106C23×C29C2×D411yescharacteristic
107C22×D29—21no—
108C22×D29—21no—
109C22×D29C2×D411yescharacteristic
110C2×C4×C29—21no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—42no—
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2411yescharacteristic
119C22⋊D29—22no—
120C22⋊D29—42no—
121C22⋊D29—81no—
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29C2×D411yescharacteristic
125C2×Dic29C2×D411yescharacteristic
126C2×Dic29C2×D411yescharacteristic
127D116—21no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116—42no—
132D116—81no—
133C4×D29—21no—
134C4×D29—21no—
135C4×D29—42no—
136C4×D29—42no—
137C4×D29—42no—
138Dic58—42no—
139Dic58—81no—
140C8×C29—21no—
141C8×C29#4112yescomplemented
142#6597—21no—
143#6597—21no—
144#3354—291nomaximal, Sylow
145C22×C29—21no—
146C22×C29—21no—
147C22×C29—21no—
148C22×C29C22×D411yescharacteristic
149C2×D29—21no—
150C2×D29—21no—
151C2×D29—21no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29C2×#4111yescharacteristic
164C4×C292−1+411yescharacteristic
165Dic29—21no—
166Dic29—21no—
167Dic29—41no—
168Dic29—41no—
169Dic29AGL(1,ℤ/8)12yes—
170#555—291no—
171#547—291no—
172#498—291no—
173#482—291no—
174#482—291no—
175#481—291no—
176#481—291no—
177#476—291no—
178#474—291no—
179#469—291no—
180#469—291no—
181C4×D8—291no—
182#436—291no—
183#428—291no—
184#428D2911yescharacteristic, complemented
185C2×C29—41no—
186C2×C29#54711yescharacteristic
187C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C29#57711yescharacteristic
189D29—41no—
190D29—81no—
191D29—81no—
192C2×#41—581no—
193C2×D8—291no—
194C2×M16—291no—
195C2×M16C2×D2911yescharacteristic
196C4⋊Q8—291no—
197C4⋊Q8—291no—
198#124—581no—
199#124—581no—
200#123—581no—
201#123—581no—
202C22⋊Q8—581no—
203#121—291no—
204#121—291no—
205#121—291no—
206#121—291no—
207#121—581no—
208C4×D4—291no—
209C4×D4—291no—
210C4×D4—291no—
211#117—291no—
212#117—581no—
213#117C2×D2911yescharacteristic
214C2×C4⋊C4—291no—
215C2×C4⋊C4C2×D2911yescharacteristic
216#107—291no—
217#107C2×D2911yescharacteristic
218#107C2×D2911yescharacteristic
219#106—291no—
220#106—291no—
221#106—291no—
222#106—291no—
223#106C2×D2911yescharacteristic
224#106C2×D2911yescharacteristic
225C4⋊C8—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232C22⋊C8—291no—
233C22⋊C8—291no—
234C4×C8—291no—
235C29#335411yescharacteristic, complemented, Sylow
236#41—1164no—
237C2×Q8—581no—
238C2×Q8—581no—
239C2×D4—291no—
240C2×D4—291no—
241C2×D4—291no—
242C2×D4—581no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4—581no—
246C22×C4—21no—
247C22×C4—291no—
248C22×C4—581no—
249C22×C4—581no—
250C22×C4—581no—
251C22×C4C22×D2911yescharacteristic
252D8—582no—
253M16—22no—
254M16—582no—
255C2×C8—291no—
256C2×C8—291no—
257C2×C8C22×D2911yescharacteristic
258C2×C8C22×D2911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—291no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4C22×D2911yescharacteristic
267C4⋊C4C22×D2911yescharacteristic
268C4⋊C4C22×D2911yescharacteristic
269C4⋊C4C22×D2911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—291no—
272C22⋊C4—291no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C42—21no—
281C42—291no—
282C42—581no—
283C23—291no—
284C23—581no—
285C23—581no—
286C23D4×D2911yescharacteristic
287Q8—1162no—
288Q8—2321no—
289D4—582no—
290D4—581no—
291D4—581no—
292D4—581no—
293D4—581no—
294D4—1162no—
295D4—1162no—
296D4—2321no—
297D4—2321no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—291no—
306C2×C4—291no—
307C2×C4—291no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—1162no—
313C2×C4—1162no—
314C2×C4—1162no—
315C2×C4D4×D2911yescharacteristic
316C2×C4C23×D2911yescharacteristic
317C8—21no—
318C8—581no—
319C8—581no—
320C8#9080512yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—581no—
325C22—581no—
326C22—581no—
327C22—1161no—
328C22—1161no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22C2×D4×D2911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—292no—
340C4—581no—
341C4—581no—
342C4—1161no—
343C4—1161no—
344C4C2×#9080511yescharacteristic
345C4#1174536211yescharacteristic
346C2—41no—
347C2—1161no—
348C2—2321no—
349C2—2321no—
350C2#1427181411yescharacteristic
351C2AGL(1,ℤ/8)×D2911yescharacteristic
352C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#428C2
socleC22×C29C22×D4
hypercenter#428D29
hypocenterC29#3354
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #14271876C2semidirect
2. #14271814C2semidirect
3. #14271560C2semidirect
4. #14271490C2semidirect
5. #14271487C2semidirect
6. #14271483C2semidirect
7. #14271481C2semidirect
8. #14271452C2semidirect
9. #14271442C2semidirect
10. #14271417C2semidirect
11. #14271416C2semidirect
12. #14271245C2semidirect
13. #14271239C2semidirect
14. #14271204C2semidirect
15. C29×#428C2semidirect
141. C8×C29#41semidirect
184. #428D29semidirect
235. C29#3354semidirect
320. C8#90805semidirect

Maximal subgroups

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

subgroupindex
#142718762
#142718142
#142715602
#142714902
#142714872
#142714832
#142714812
#142714522
#142714422
#142714172
#142714162
#142712452
#142712392
#142712042
C29×#4282
#335429