Finite Group Databasebeta

← #16831373

Subgroups — #16831373

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271822C211yesmaximal, characteristic
2#14271520C211yesmaximal, characteristic, complemented
3#14271504C211yesmaximal, characteristic, complemented
4#14271476C211yesmaximal, characteristic, complemented
5#14271467C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271385C211yesmaximal, characteristic, complemented
9#14271323C211yesmaximal, characteristic, complemented
10#14271318C211yesmaximal, characteristic, complemented
11C4×#90785C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14C2×#11745158C211yesmaximal, characteristic, complemented
15C29×#552C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C29×#126—21no—
19C29×#125—21no—
20C29×#125C2211yescharacteristic
21C29×#123—21no—
22C29×C22⋊Q8C2211yescharacteristic
23C29×C22⋊Q8C2211yescharacteristic
24C4×Q8×C29C2211yescharacteristic
25C4×D4×C29C2211yescharacteristic
26C29×#117—21no—
27C29×#117C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic
29C2×#90785C2211yescharacteristic
30C2×#90785C2211yescharacteristic
31C2×#90784C2211yescharacteristic
32#11745301—21no—
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745258—21no—
38#11745247—21no—
39#11745243—21no—
40#11745237C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42#11745183C2211yescharacteristic
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745158C2211yescharacteristic
46#11745158C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745158C2211yescharacteristic
50#11745158C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29D411yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C22×Dic29—21no—
67#90805—22no—
68#90805—41no—
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×Dic58—22no—
72C2×Dic58—21no—
73C2×Dic58—41no—
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29D411yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29D411yescharacteristic
90C22⋊C4×C29D411yescharacteristic
91C42×C29—21no—
92C42×C29—21no—
93C42×C29C2311yescharacteristic
94C22⋊Dic29—21no—
95#90785—22no—
96#90785—41no—
97#90784—41no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116D4×C29—22no—
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—21no—
124C2×C4×C29—21no—
125C2×C4×C29—42no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—42no—
132C22⋊D29—42no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—42no—
137D116—21no—
138D116—21no—
139C4×D29—42no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—42no—
144Dic58#4112yes—
145#6597—21no—
146#6597—21no—
147#6597—21no—
148#6597—21no—
149#3300—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—21no—
155C22×C29#13512yes—
156C22×C29C22×D411yescharacteristic
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29H(5,𝔽2)11yescharacteristic
170Dic29—22no—
171Dic29—41no—
172Dic29—41no—
173#552D2911yescharacteristic, complemented
174#548—291no—
175#488—291no—
176#485—291no—
177#480—291no—
178#479—291no—
179#467—291no—
180#465—291no—
181#464—291no—
182#452—291no—
183#451—291no—
184C4×Q16—291no—
185C8×D4—291no—
186#416—291no—
187C2×#103—291no—
188C2×C29—22no—
189C2×C29—41no—
190C2×C29#54611yescharacteristic
191C2×C29C2×#13511yescharacteristic
192C2×C29#57811yescharacteristic
193D29—81no—
194C2×#41—291no—
195C22×Q8—291no—
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201#126—21no—
202#125—21no—
203#125C2×D2911yescharacteristic
204#124—291no—
205#124—581no—
206#123—21no—
207C22⋊Q8—291no—
208C22⋊Q8—581no—
209C22⋊Q8C2×D2911yescharacteristic
210C22⋊Q8C2×D2911yescharacteristic
211#121—291no—
212#121—581no—
213C4×Q8—291no—
214C4×Q8C2×D2911yescharacteristic
215C4×D4—581no—
216C4×D4C2×D2911yescharacteristic
217#117—21no—
218#117C2×D2911yescharacteristic
219C2×C4⋊C4C2×D2911yescharacteristic
220#107—291no—
221#107—291no—
222#106—291no—
223C4⋊C8—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8—291no—
235C22⋊C8—291no—
236C4×C8—291no—
237C29#330011yescharacteristic, complemented, Sylow
238#41—582no—
239#41—1161no—
240C2×Q8—291no—
241C2×Q8—291no—
242C2×Q8—582no—
243C2×Q8—581no—
244C2×Q8—1161no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4C22⋊D2911yescharacteristic
250C22×C4—21no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4C22×D2911yescharacteristic
254C22×C4C22×D2911yescharacteristic
255Q16—582no—
256Q16—1161no—
257SD16—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—291no—
261C2×C8—291no—
262C2×C8—1161no—
263C2×C8—1161no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—291no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4C22⋊D2911yescharacteristic
274C4⋊C4C22×D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4C22⋊D2911yescharacteristic
285C22⋊C4C22⋊D2911yescharacteristic
286C42—21no—
287C42—21no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—581no—
291C23C2×C22⋊D2911yescharacteristic
292C23C2×C22⋊D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—292no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299Q8—1162no—
300D4—22no—
301D4—581no—
302D4—581no—
303D4—1162no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—1162no—
318C2×C4—1162no—
319C2×C4C2×C22⋊D2911yescharacteristic
320C2×C4C2×C22⋊D2911yescharacteristic
321C2×C4C2×C22⋊D2911yescharacteristic
322C2×C4C2×C22⋊D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—581no—
325C8—581no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22#1174531212yes—
337C22C22×C22⋊D2911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—582no—
347C4—1161no—
348C4—1161no—
349C4#41×D2911yescharacteristic
350C4#1174536411yescharacteristic
351C2—22no—
352C2—41no—
353C2—2321no—
354C2#1427180111yescharacteristic
355C2C2×#1174531211yescharacteristic
356C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#552C2
socleC22×C29C22×D4
prime radical#14271822C2
hypercenter#552D29
hypocenterC29#3300
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14271520C2semidirect
3. #14271504C2semidirect
4. #14271476C2semidirect
5. #14271467C2semidirect
6. #14271402C2semidirect
7. #14271394C2semidirect
8. #14271385C2semidirect
9. #14271323C2semidirect
10. #14271318C2semidirect
11. C4×#90785C2semidirect
12. D4×#6597C2semidirect
13. #14271157C2semidirect
14. C2×#11745158C2semidirect
15. C29×#552C2semidirect
173. #552D29semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718222
#142715202
#142715042
#142714762
#142714672
#142714022
#142713942
#142713852
#142713232
#142713182
C4×#907852
D4×#65972
#142711572
C2×#117451582
C29×#5522
#330029