Finite Group Databasebeta

← #16831383

Subgroups — #16831383

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#14271855C211yesmaximal, characteristic, complemented
2#14271824C211yesmaximal, characteristic
3#14271519C211yesmaximal, characteristic, complemented
4#14271503C211yesmaximal, characteristic, complemented
5#14271477C211yesmaximal, characteristic, complemented
6#14271472C211yesmaximal, characteristic, complemented
7#14271401C211yesmaximal, characteristic, complemented
8#14271394C211yesmaximal, characteristic, complemented
9#14271387C211yesmaximal, characteristic, complemented
10#14271324C211yesmaximal, characteristic, complemented
11Q16×Dic29C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14C2×#11745183C211yesmaximal, characteristic, complemented
15C29×#451C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic
19C2×Q16×C29C2211yescharacteristic
20C29×C22⋊Q8C2211yescharacteristic
21#11745309—21no—
22#11745309C2211yescharacteristic
23#11745308—21no—
24#11745308C2211yescharacteristic
25#11745308C2211yescharacteristic
26Q8×Dic29C2211yescharacteristic
27Q8×Dic29C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29#11745292—21no—
30#11745292C2211yescharacteristic
31C4×C22⋊D29—21no—
32C4×C22⋊D29C2211yescharacteristic
33C2×C4⋊Dic29C2211yescharacteristic
34C22×#6597C2211yescharacteristic
35C2×C8×D29C2211yescharacteristic
36#11745260—21no—
37#11745254C2211yescharacteristic
38#11745252—21no—
39#11745252C2211yescharacteristic
40#11745248—21no—
41#11745239—21no—
42C29×#103C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745183C2211yescharacteristic
49#11745183C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745162C2211yescharacteristic
56C8×Dic29C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic
59C2×Q8×C29—21no—
60C2×Q8×C29—22no—
61C2×Q8×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×Q8×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29D411yescharacteristic
69C22×Dic29—21no—
70#90809—22no—
71#90809—41no—
72C2×D116—21no—
73C2×D116C2311yescharacteristic
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76Q16×C29—22no—
77Q16×C29—41no—
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊Dic29D411yescharacteristic
84#90784—41no—
85#90781—21no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781D411yescharacteristic
92C4⋊Dic29—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—42no—
120Q8×C29#4112yes—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—42no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—22no—
131C22⋊D29—42no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—42no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139D116—21no—
140D116—21no—
141D116—42no—
142C4×D29—21no—
143C4×D29—21no—
144C4×D29—42no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3300—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29#13512yes—
153C22×C29C22×D411yescharacteristic
154C2×D29—21no—
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—22no—
161C4×C29—21no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C29H(5,𝔽2)11yescharacteristic
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173#552—291no—
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#451D2911yescharacteristic, complemented
184C4×Q16—291no—
185C8×D4—291no—
186#416—291no—
187C2×#103—291no—
188C2×C29—22no—
189C2×C29#54611yescharacteristic
190C2×C29C2×#13511yescharacteristic
191C2×C29#57811yescharacteristic
192D29—41no—
193D29—81no—
194C2×#41—291no—
195C22×Q8C2×D2911yescharacteristic
196C2×Q16C2×D2911yescharacteristic
197C2×Q16C2×D2911yescharacteristic
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201#126—581no—
202#125—291no—
203#125—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—291no—
209C22⋊Q8—581no—
210C22⋊Q8C2×D2911yescharacteristic
211#121—291no—
212#121—581no—
213C4×Q8—291no—
214C4×Q8—291no—
215C4×D4—291no—
216C4×D4—581no—
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
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#103C2×D2911yescharacteristic
230#103C2×D2911yescharacteristic
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8—291no—
235C22⋊C8C2×D2911yescharacteristic
236C4×C8—291no—
237C29#330011yescharacteristic, complemented, Sylow
238#41—582no—
239#41—1161no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D2911yescharacteristic
244C2×Q8C22×D2911yescharacteristic
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4—581no—
250C22×C4—21no—
251C22×C4—291no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4C22×D2911yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—1161no—
261C2×C8—1161no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—291no—
279C22⋊C4—291no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—291no—
287C42—581no—
288C42—581no—
289C42—581no—
290C23—291no—
291C23—581no—
292C23D4×D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#9080712yes—
300D4—582no—
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—42no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—291no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—1162no—
321C2×C4—1162no—
322C2×C4D4×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—21no—
330C22—581no—
331C22—581no—
332C22—581no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22#1174528112yes—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—581no—
344C4—581no—
345C4—581no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4C2×#9080711yescharacteristic
350C4#1174535911yescharacteristic
351C2—22no—
352C2—1161no—
353C2—2321no—
354C2#1427180011yescharacteristic
355C2C2×#1174528111yescharacteristic
356C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#451C2
socleC22×C29C22×D4
prime radical#14271824C2
hypercenter#451D29
hypocenterC29#3300
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #14271855C2semidirect
3. #14271519C2semidirect
4. #14271503C2semidirect
5. #14271477C2semidirect
6. #14271472C2semidirect
7. #14271401C2semidirect
8. #14271394C2semidirect
9. #14271387C2semidirect
10. #14271324C2semidirect
11. Q16×Dic29C2semidirect
12. #14271226C2semidirect
13. #14271158C2semidirect
14. C2×#11745183C2semidirect
15. C29×#451C2semidirect
183. #451D29semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718552
#142718242
#142715192
#142715032
#142714772
#142714722
#142714012
#142713942
#142713872
#142713242
Q16×Dic292
#142712262
#142711582
C2×#117451832
C29×#4512
#330029