Finite Group Databasebeta

← #16832557

Subgroups — #16832557

Order 3712.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271895C211yesmaximal, characteristic, complemented
2#14271887C211yesmaximal, characteristic, complemented
3#14271549C211yesmaximal, characteristic
4#14271548C211yesmaximal, characteristic, complemented
5#14271387C211yesmaximal, characteristic, complemented
6#14271387C211yesmaximal, characteristic, complemented
7#14271380C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271365C211yesmaximal, characteristic, complemented
10#14271361C211yesmaximal, characteristic, complemented
11#14271291C211yesmaximal, characteristic, complemented
12#14271276C211yesmaximal, characteristic, complemented
13#14271270C211yesmaximal, characteristic, complemented
14SD16×Dic29C211yesmaximal, characteristic, complemented
15C29×#497C211yesmaximal, characteristic, complemented
16C2×Q16×C29C2211yescharacteristic
17C2×Q16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C29×C4⋊Q8C2211yescharacteristic
21C29×#124C2211yescharacteristic
22#11745309C2211yescharacteristic
23#11745309C2211yescharacteristic
24#11745309C2211yescharacteristic
25Q8×Dic29C2211yescharacteristic
26Q8×Dic29C2211yescharacteristic
27Q8×Dic29C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90784C2211yescharacteristic
30C2×#90784C2211yescharacteristic
31#11745302C2211yescharacteristic
32D4×Dic29C2211yescharacteristic
33C2×#90782C2211yescharacteristic
34C2×D232C2211yescharacteristic
35#11745260—21no—
36#11745260—21no—
37#11745259—21no—
38#11745254—21no—
39#11745248—21no—
40#11745247—21no—
41#11745245—21no—
42#11745243—21no—
43C4×D116C2211yescharacteristic
44C4×D116C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×#97C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745183C2211yescharacteristic
49#11745183C2211yescharacteristic
50#11745180C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic
53#11745165C2211yescharacteristic
54#11745163C2211yescharacteristic
55#11745162C2211yescharacteristic
56#11745162C2211yescharacteristic
57C8×Dic29C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C22×Dic29—21no—
66C2×D116C2311yescharacteristic
67C2×D116C2311yescharacteristic
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×Dic58D411yescharacteristic
71Q16×C29—22no—
72Q16×C29—41no—
73SD16×C29—22no—
74SD16×C29—41no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C42×C29C2311yescharacteristic
82C22⋊Dic29—21no—
83#90784—41no—
84#90784—41no—
85#90784—41no—
86#90782—41no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779D411yescharacteristic
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110D232—22no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—81no—
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—21no—
138D116—21no—
139D116—21no—
140D116—21no—
141C4×D29—42no—
142C4×D29—81no—
143Dic58—41no—
144C8×C29—21no—
145C8×C29#4112yes—
146#6597—21no—
147#6597—21no—
148#3401—291nomaximal, Sylow
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C22×D411yescharacteristic
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29H(5,𝔽2)11yescharacteristic
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556—291no—
174#497D2911yescharacteristic, complemented
175#496—291no—
176#495—291no—
177#464—291no—
178#464—291no—
179#463—291no—
180#463—291no—
181#461—291no—
182#460—291no—
183#446—291no—
184#442—291no—
185#441—291no—
186C4×SD16—291no—
187C2×C29—81no—
188C2×C29#55011yescharacteristic
189C2×C29#57511yescharacteristic
190C2×C29#57711yescharacteristic
191D29—81no—
192D29—81no—
193C2×Q16C2×D2911yescharacteristic
194C2×Q16C2×D2911yescharacteristic
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16C2×D2911yescharacteristic
199C2×SD16C2×D2911yescharacteristic
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8C2×D2911yescharacteristic
203#127—291no—
204#126—581no—
205#126—581no—
206#124—291no—
207#124—291no—
208#124—291no—
209#124—581no—
210#124C2×D2911yescharacteristic
211#123—581no—
212#123—581no—
213C22⋊Q8—581no—
214C4×Q8—291no—
215C4×Q8—291no—
216C4×Q8—291no—
217C4×Q8—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—581no—
222#117—581no—
223#106—291no—
224C4⋊C8—291no—
225C4⋊C8—291no—
226C4⋊C8—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#97—291no—
234#97C2×D2911yescharacteristic
235C4×C8—291no—
236C29#340111yescharacteristic, complemented, Sylow
237C2×Q8—291no—
238C2×Q8C22×D2911yescharacteristic
239C2×Q8C22×D2911yescharacteristic
240C2×Q8C22×D2911yescharacteristic
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4C22×D2911yescharacteristic
246C22×C4—581no—
247C22×C4—581no—
248C22×C4—581no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—582no—
257D8—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—291no—
284C42—291no—
285C42—581no—
286C42—581no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—581no—
291C23—581no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—1161no—
299D4—21no—
300D4—21no—
301D4—581no—
302D4—581no—
303D4—581no—
304D4—581no—
305D4—1162no—
306D4—2321no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—1162no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4D4×D2911yescharacteristic
320C2×C4D4×D2911yescharacteristic
321C2×C4C23×D2911yescharacteristic
322C8—21no—
323C8—581no—
324C8—581no—
325C8#9080712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22C2×D4×D2911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—581no—
342C4—581no—
343C4—581no—
344C4—581no—
345C4—1161no—
346C4—1161no—
347C4C2×#9080711yescharacteristic
348C4#1174535911yescharacteristic
349C2—81no—
350C2—2321no—
351C2—2321no—
352C2#1427183311yescharacteristic
353C2#1427196211yescharacteristic
354C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#497C2
socleC22×C29C22×D4
prime radical#14271549C2
hypercenter#497D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14271895C2semidirect
2. #14271887C2semidirect
4. #14271548C2semidirect
5. #14271387C2semidirect
6. #14271387C2semidirect
7. #14271380C2semidirect
8. #14271375C2semidirect
9. #14271365C2semidirect
10. #14271361C2semidirect
11. #14271291C2semidirect
12. #14271276C2semidirect
13. #14271270C2semidirect
14. SD16×Dic29C2semidirect
15. C29×#497C2semidirect
174. #497D29semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718952
#142718872
#142715492
#142715482
#142713872
#142713802
#142713752
#142713652
#142713612
#142712912
#142712762
#142712702
SD16×Dic292
C29×#4972
#340129