Finite Group Databasebeta

← #16832202

Subgroups — #16832202

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271869C211yesmaximal, characteristic, complemented
2#14271834C211yesmaximal, characteristic, complemented
3#14271529C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271508C211yesmaximal, characteristic, complemented
6#14271466C211yesmaximal, characteristic, complemented
7#14271452C211yesmaximal, characteristic, complemented
8#14271359C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271357C211yesmaximal, characteristic, complemented
11#14271292C211yesmaximal, characteristic, complemented
12#14271274C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14#14271245C211yesmaximal, characteristic, complemented
15C29×#478C211yesmaximal, characteristic, complemented
16C2×#90805—21no—
17C29×#125C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19#11745302C2211yescharacteristic
20#11745302C2211yescharacteristic
21C2×#90782C2211yescharacteristic
22#11745292—21no—
23C2×D232C2211yescharacteristic
24C2×D232C2211yescharacteristic
25#11745259—21no—
26#11745258—21no—
27#11745258—21no—
28#11745255C2211yescharacteristic
29#11745255C2211yescharacteristic
30#11745255C2211yescharacteristic
31#11745255C2211yescharacteristic
32C4⋊C4×D29—21no—
33#11745252C2211yescharacteristic
34#11745250C2211yescharacteristic
35#11745246—21no—
36#11745246—21no—
37#11745236C2211yescharacteristic
38C4×D116C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C29×#107C2211yescharacteristic
41C29×#106C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745163C2211yescharacteristic
49#11745162C2211yescharacteristic
50#11745162C2211yescharacteristic
51C8×Dic29C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65#90805—44no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×Dic58—21no—
77C2×Dic58D411yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C42×C29C2311yescharacteristic
87#90782—22no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29D411yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779D411yescharacteristic
99#90779D411yescharacteristic
100C4×Dic29C2311yescharacteristic
101C4×Dic29C2311yescharacteristic
102C2×#6597C2311yescharacteristic
103C2×#6597C2311yescharacteristic
104D232—22no—
105D232—22no—
106C23×C29—21no—
107C22×D29—21no—
108C22×D29—21no—
109C22×D29—21no—
110D4×C29—21no—
111D4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—42no—
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2411yescharacteristic
119C22⋊D29—42no—
120C22⋊D29—42no—
121C22⋊D29—81no—
122C22⋊D29—81no—
123C2×Dic29—21no—
124C2×Dic29C2×D411yescharacteristic
125C2×Dic29C2×D411yescharacteristic
126C2×Dic29C2×D411yescharacteristic
127C2×Dic29C2×D411yescharacteristic
128D116—21no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—21no—
133D116—42no—
134D116—81no—
135D116#4112yescomplemented
136C4×D29—42no—
137C4×D29—42no—
138C4×D29—42no—
139C4×D29—81no—
140C4×D29—81no—
141Dic58—22no—
142Dic58—81no—
143C8×C29—21no—
144C8×C29—21no—
145#6597—21no—
146#6597—21no—
147#3366—291nomaximal, Sylow
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29C22×D411yescharacteristic
152C2×D29—22no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29C2×#4111yescharacteristic
167C4×C292−1+411yescharacteristic
168Dic29—21no—
169Dic29—21no—
170Dic29—21no—
171Dic29—41no—
172Dic29AGL(1,ℤ/8)12yes—
173#554—291no—
174#550—291no—
175#490—291no—
176#490—291no—
177#486—291no—
178#478—291no—
179#478D2911yescharacteristic, complemented
180#476—291no—
181#459—291no—
182#459—291no—
183#459—291no—
184#446—291no—
185#442—291no—
186#442—291no—
187C4×D8—291no—
188C2×C29—81no—
189C2×C29#54811yescharacteristic
190C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C29#57611yescharacteristic
192D29—42no—
193D29—81no—
194D29—81no—
195C2×#41—581no—
196C2×D8—291no—
197C2×D8—291no—
198C2×D8—291no—
199C4⋊Q8—291no—
200#127—291no—
201#127—291no—
202#127—291no—
203#125—291no—
204#125C2×D2911yescharacteristic
205C22⋊Q8—581no—
206C22⋊Q8—581no—
207C22⋊Q8—581no—
208#121—581no—
209#121—581no—
210#121—581no—
211C4×Q8—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4—291no—
217C4×D4C2×D2911yescharacteristic
218C2×C4⋊C4—581no—
219#107C2×D2911yescharacteristic
220#106—291no—
221#106C2×D2911yescharacteristic
222C4⋊C8—291no—
223C4⋊C8—291no—
224C4⋊C8C2×D2911yescharacteristic
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102C2×D2911yescharacteristic
234#102C2×D2911yescharacteristic
235#97—291no—
236#97—291no—
237C4×C8—291no—
238C29#336611yescharacteristic, complemented, Sylow
239#41—1164no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×D4—291no—
243C2×D4—291no—
244C2×D4—291no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—581no—
251C2×D4C22×D2911yescharacteristic
252C22×C4—21no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258D8—582no—
259D8—582no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—291no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4C22×D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—291no—
284C42—291no—
285C42C22×D2911yescharacteristic
286C23—21no—
287C23—581no—
288C23—581no—
289C23—581no—
290Q8—582no—
291Q8—2321no—
292D4—21no—
293D4—21no—
294D4—292no—
295D4—581no—
296D4—581no—
297D4—581no—
298D4—581no—
299D4—581no—
300D4—1162no—
301D4—1162no—
302D4—1162no—
303D4—2321no—
304D4—2321no—
305D4—2321no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—1162no—
316C2×C4—1162no—
317C2×C4—1162no—
318C2×C4—2321no—
319C2×C4—2321no—
320C2×C4D4×D2911yescharacteristic
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—21no—
324C8—21no—
325C8—581no—
326C8—581no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—582no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22C2×D4×D2911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—292no—
346C4—581no—
347C4—581no—
348C4—581no—
349C4—1161no—
350C4#1174536211yescharacteristic
351C4#41×D2911yescharacteristic
352C2—81no—
353C2—1162no—
354C2—2321no—
355C2—2321no—
356C2#1427182311yescharacteristic
357C2AGL(1,ℤ/8)×D2911yescharacteristic
358C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#478C2
socleC22×C29C22×D4
hypercenter#478D29
hypocenterC29#3366
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14271869C2semidirect
2. #14271834C2semidirect
3. #14271529C2semidirect
4. #14271526C2semidirect
5. #14271508C2semidirect
6. #14271466C2semidirect
7. #14271452C2semidirect
8. #14271359C2semidirect
9. #14271357C2semidirect
10. #14271357C2semidirect
11. #14271292C2semidirect
12. #14271274C2semidirect
13. #14271273C2semidirect
14. #14271245C2semidirect
15. C29×#478C2semidirect
135. D116#41semidirect
179. #478D29semidirect
238. C29#3366semidirect

Maximal subgroups

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

subgroupindex
#142718692
#142718342
#142715292
#142715262
#142715082
#142714662
#142714522
#142713592
#142713572
#142712922
#142712742
#142712732
#142712452
C29×#4782
#336629