Finite Group Databasebeta

← #16832553

Subgroups — #16832553

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#14271899C211yesmaximal, characteristic, complemented
2#14271882C211yesmaximal, characteristic, complemented
3#14271554C211yesmaximal, characteristic, complemented
4#14271546C211yesmaximal, characteristic, complemented
5#14271383C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271376C211yesmaximal, characteristic, complemented
8#14271376C211yesmaximal, characteristic, complemented
9#14271366C211yesmaximal, characteristic, complemented
10#14271360C211yesmaximal, characteristic, complemented
11#14271291C211yesmaximal, characteristic, complemented
12#14271275C211yesmaximal, characteristic, complemented
13#14271271C211yesmaximal, characteristic, complemented
14SD16×Dic29C211yesmaximal, characteristic, complemented
15C29×#496C211yesmaximal, characteristic
16C2×SD16×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C29×#127C2211yescharacteristic
21C29×#124C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic
23#11745306C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25#11745298—21no—
26#11745298C2211yescharacteristic
27#11745298C2211yescharacteristic
28#11745298C2211yescharacteristic
29#11745297—21no—
30#11745297—21no—
31D4×Dic29—21no—
32D4×Dic29C2211yescharacteristic
33D4×Dic29C2211yescharacteristic
34D4×Dic29C2211yescharacteristic
35C2×#90783C2211yescharacteristic
36C2×#90783C2211yescharacteristic
37C2×#90783C2211yescharacteristic
38C2×Dic116C2211yescharacteristic
39#11745241—21no—
40#11745241—21no—
41#11745240—21no—
42#11745239—21no—
43C4×Dic58C2211yescharacteristic
44C4×Dic58C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×#97C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745163C2211yescharacteristic
55#11745162C2211yescharacteristic
56#11745162C2211yescharacteristic
57C8×Dic29C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×Dic29—21no—
66C22×Dic29—21no—
67C22×Dic29—21no—
68C2×Dic58D411yescharacteristic
69C2×Dic58C2311yescharacteristic
70C2×Dic58C2311yescharacteristic
71SD16×C29—22no—
72SD16×C29—41no—
73D8×C29—22no—
74D8×C29—41no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C22⋊C4×C29—21no—
78C22⋊C4×C29—21no—
79C42×C29C2311yescharacteristic
80C22⋊Dic29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89#90785—41no—
90#90783—41no—
91#90783—41no—
92#90783—41no—
93C4⋊Dic29—21no—
94C4⋊Dic29D411yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779D411yescharacteristic
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110Dic116—22no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—81no—
124C2×C4×C29—21no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—42no—
133C2×Dic29—81no—
134C2×Dic29—81no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
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×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29C22×D411yescharacteristic
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C29H(5,𝔽2)11yescharacteristic
164Dic29—21no—
165Dic29—21no—
166Dic29—21no—
167Dic29—21no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556—291no—
174#497—291no—
175#496D2911yescharacteristic
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—81no—
189C2×C29—81no—
190C2×C29#55011yescharacteristic
191C2×C29#57511yescharacteristic
192C2×C29#57711yescharacteristic
193C2×Q16—291no—
194C2×Q16—291no—
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16C2×D2911yescharacteristic
199C2×SD16C2×D2911yescharacteristic
200C2×D8C2×D2911yescharacteristic
201C2×D8C2×D2911yescharacteristic
202C4⋊Q8—291no—
203#127C2×D2911yescharacteristic
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×Q8—291no—
239C2×Q8—291no—
240C2×Q8C22×D2911yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C22×D2911yescharacteristic
244C2×D4C22×D2911yescharacteristic
245C2×D4C22×D2911yescharacteristic
246C22×C4—581no—
247C22×C4—581no—
248C22×C4—581no—
249Q16—582no—
250Q16—1161no—
251SD16—22no—
252SD16—41no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—22no—
257D8—41no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
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—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—1161no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—291no—
309C2×C4—291no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—581no—
313C2×C4—581no—
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—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D2911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—581no—
340C4—581no—
341C4—581no—
342C4—581no—
343C4—1161no—
344C4—1161no—
345C4—1161no—
346C4—1161no—
347C4C2×#9080711yescharacteristic
348C4#1174535911yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#1427183311yescharacteristic
353C2#1427195911yescharacteristic
354C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#496C2
socleC22×C29C22×D4
hypercenter#496D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14271899C2semidirect
2. #14271882C2semidirect
3. #14271554C2semidirect
4. #14271546C2semidirect
5. #14271383C2semidirect
6. #14271382C2semidirect
7. #14271376C2semidirect
8. #14271376C2semidirect
9. #14271366C2semidirect
10. #14271360C2semidirect
11. #14271291C2semidirect
12. #14271275C2semidirect
13. #14271271C2semidirect
14. SD16×Dic29C2semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718992
#142718822
#142715542
#142715462
#142713832
#142713822
#142713762
#142713662
#142713602
#142712912
#142712752
#142712712
SD16×Dic292
C29×#4962
#340129