Finite Group Databasebeta

← #16832558

Subgroups — #16832558

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#14271898C211yesmaximal, characteristic, complemented
2#14271555C211yesmaximal, characteristic, complemented
3#14271553C211yesmaximal, characteristic
4#14271545C211yesmaximal, characteristic, complemented
5#14271385C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271365C211yesmaximal, characteristic, complemented
10#14271363C211yesmaximal, characteristic, complemented
11#14271294C211yesmaximal, characteristic, complemented
12#14271273C211yesmaximal, characteristic, complemented
13#14271268C211yesmaximal, characteristic, complemented
14C4×#90784C211yesmaximal, characteristic, complemented
15C29×#556C211yesmaximal, characteristic, complemented
16C29×C4⋊Q8C2211yescharacteristic
17C29×#126—21no—
18C29×#126—21no—
19C29×#124C2211yescharacteristic
20C29×#124C2211yescharacteristic
21C29×C22⋊Q8—21no—
22C4×Q8×C29C2211yescharacteristic
23C4×Q8×C29C2211yescharacteristic
24C4×Q8×C29C2211yescharacteristic
25C4×D4×C29C2211yescharacteristic
26C29×#117—21no—
27#11745309—21no—
28C2×#90785C2211yescharacteristic
29C2×#90785C2211yescharacteristic
30C2×#90784C2211yescharacteristic
31C2×#90784C2211yescharacteristic
32C2×#90784C2211yescharacteristic
33C2×#90784C2211yescharacteristic
34C2×#90783C2211yescharacteristic
35C2×#90782C2211yescharacteristic
36C2×#90782C2211yescharacteristic
37#11745256—21no—
38#11745256—21no—
39#11745255—21no—
40#11745237C2211yescharacteristic
41#11745237C2211yescharacteristic
42#11745236C2211yescharacteristic
43C4×D116C2211yescharacteristic
44C4×D116C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745158C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745156C2211yescharacteristic
53C4⋊#6597C2211yescharacteristic
54C4⋊#6597C2211yescharacteristic
55C4⋊#6597C2211yescharacteristic
56#11745151C2211yescharacteristic
57#11745151C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29D411yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C2×D116—21no—
65C2×D116—21no—
66C2×D116C2311yescharacteristic
67C2×D116C2311yescharacteristic
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×Dic58C2311yescharacteristic
71C4⋊C4×C29—21no—
72C4⋊C4×C29—21no—
73C4⋊C4×C29—21no—
74C4⋊C4×C29—21no—
75C4⋊C4×C29D411yescharacteristic
76C4⋊C4×C29D411yescharacteristic
77C4⋊C4×C29D411yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C42×C29—21no—
86C42×C29C2311yescharacteristic
87C42×C29C2311yescharacteristic
88C42×C29C2311yescharacteristic
89#90785—22no—
90#90785—41no—
91#90784—22no—
92#90784—41no—
93#90784—41no—
94#90784—41no—
95#90783—41no—
96#90782—22no—
97#90782—41no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104C4⋊Dic29C2311yescharacteristic
105#90779—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—41no—
119D4×C29—21no—
120D4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—42no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2411yescharacteristic
132C2×Dic29—21no—
133C2×Dic29—21no—
134D116—21no—
135D116—21no—
136D116—21no—
137D116—21no—
138D116—42no—
139D116—81no—
140C4×D29—81no—
141C4×D29—81no—
142Dic58—21no—
143Dic58—21no—
144#6597—21no—
145#6597—21no—
146#6597—21no—
147#6597#4112yes—
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—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29H(5,𝔽2)11yescharacteristic
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556D2911yescharacteristic, complemented
174#497—291no—
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×Q16—291no—
194C2×Q16—291no—
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8C2×D2911yescharacteristic
203#127—291no—
204#126—21no—
205#126—21no—
206#124—291no—
207#124—291no—
208#124—581no—
209#124C2×D2911yescharacteristic
210#124C2×D2911yescharacteristic
211#123—581no—
212#123—581no—
213C22⋊Q8—21no—
214C4×Q8—291no—
215C4×Q8C2×D2911yescharacteristic
216C4×Q8C2×D2911yescharacteristic
217C4×Q8C2×D2911yescharacteristic
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—581no—
221C4×D4C2×D2911yescharacteristic
222#117—21no—
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#97—291no—
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—21no—
247C22×C4—581no—
248C22×C4—581no—
249Q16—582no—
250Q16—1161no—
251SD16—582no—
252SD16—1161no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—582no—
257D8—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—291no—
261C2×C8—291no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4C22⋊D2911yescharacteristic
269C4⋊C4C22⋊D2911yescharacteristic
270C4⋊C4C22⋊D2911yescharacteristic
271C4⋊C4C22×D2911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—21no—
284C42—21no—
285C42—581no—
286C42C22×D2911yescharacteristic
287C42C22×D2911yescharacteristic
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—581no—
291C23—581no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—581no—
298Q8—581no—
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—42no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—2321no—
314C2×C4—2321no—
315C2×C4C2×C22⋊D2911yescharacteristic
316C2×C4C2×C22⋊D2911yescharacteristic
317C2×C4C2×C22⋊D2911yescharacteristic
318C2×C4C2×C22⋊D2911yescharacteristic
319C2×C4C2×C22⋊D2911yescharacteristic
320C2×C4C2×C22⋊D2911yescharacteristic
321C2×C4C23×D2911yescharacteristic
322C8—292no—
323C8—581no—
324C8—581no—
325C8—581no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22C22×C22⋊D2911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—1161no—
346C4—1161no—
347C4#41×D2911yescharacteristic
348C4#1174536411yescharacteristic
349C2—81no—
350C2—2321no—
351C2—2321no—
352C2#1427183211yescharacteristic
353C2#1427196111yescharacteristic
354C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#556C2
socleC22×C29C22×D4
prime radical#14271553C2
hypercenter#556D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271555C2semidirect
4. #14271545C2semidirect
5. #14271385C2semidirect
6. #14271382C2semidirect
7. #14271378C2semidirect
8. #14271375C2semidirect
9. #14271365C2semidirect
10. #14271363C2semidirect
11. #14271294C2semidirect
12. #14271273C2semidirect
13. #14271268C2semidirect
14. C4×#90784C2semidirect
15. C29×#556C2semidirect
173. #556D29semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142715552
#142715532
#142715452
#142713852
#142713822
#142713782
#142713752
#142713652
#142713632
#142712942
#142712732
#142712682
C4×#907842
C29×#5562
#340129