Finite Group Databasebeta

← #16829698

Subgroups — #16829698

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271769C211yesmaximal, characteristic, complemented
2#14271645C211yesmaximal, characteristic, complemented
3#14271483C211yesmaximal, characteristic, complemented
4#14271478C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271363C211yesmaximal, characteristic, complemented
7#14271359C211yesmaximal, characteristic, complemented
8#14271311C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271274C211yesmaximal, characteristic, complemented
11#14271266C211yesmaximal, characteristic, complemented
12#14271248C211yesmaximal, characteristic, complemented
13#14271245C211yesmaximal, characteristic, complemented
14#14271223C211yesmaximal, characteristic, complemented
15C29×#479C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C29×#125C2211yescharacteristic
18C4×Q8×C29C2211yescharacteristic
19Q8×Dic29C2211yescharacteristic
20C2×#90784C2211yescharacteristic
21C2×#90784C2211yescharacteristic
22C2×D232C2211yescharacteristic
23C2×D232C2211yescharacteristic
24#11745257—21no—
25#11745257—21no—
26#11745257C2211yescharacteristic
27#11745257C2211yescharacteristic
28#11745256—21no—
29#11745256—21no—
30#11745255—21no—
31#11745255C2211yescharacteristic
32#11745255C2211yescharacteristic
33#11745255C2211yescharacteristic
34C4⋊C4×D29—21no—
35C4⋊C4×D29C2211yescharacteristic
36#11745236C2211yescharacteristic
37C4×D116—21no—
38C4×D116C2211yescharacteristic
39#11745234—21no—
40#11745234C2211yescharacteristic
41C29×#107C2211yescharacteristic
42C29×#106C2211yescharacteristic
43C29×C4⋊C8C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745163C2211yescharacteristic
51C8×Dic29C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60#90809—22no—
61#90809—22no—
62C2×D116—21no—
63C2×D116—21no—
64C2×D116—21no—
65C2×D116—21no—
66C2×D116—21no—
67C2×D116C2311yescharacteristic
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C42×C29—21no—
86C42×C29C2311yescharacteristic
87#90784—22no—
88#90784—22no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106D232—22no—
107D232—22no—
108C22×D29—21no—
109C22×D29—21no—
110C22×D29—21no—
111C22×D29C2×D411yescharacteristic
112Q8×C29—21no—
113Q8×C29#4112yes—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2×D411yescharacteristic
120C2×C4×C29C2411yescharacteristic
121C2×Dic29—21no—
122C2×Dic29C2×D411yescharacteristic
123C2×Dic29C2×D411yescharacteristic
124C2×Dic29C2×D411yescharacteristic
125D116—24no—
126D116—21no—
127D116—21no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116—81no—
132D116—81no—
133D116—81no—
134D116—81no—
135D116#4112yes—
136C4×D29—24no—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—81no—
140C4×D29—81no—
141C4×D29—81no—
142C4×D29—81no—
143C4×D29—81no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148#3119—291nomaximal, Sylow
149C22×C29C22×D411yescharacteristic
150C2×D29—21no—
151C2×D29—22no—
152C2×D29—21no—
153C2×D29—21no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C4×C29—22no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29C2×#4111yescharacteristic
170Dic29—21no—
171Dic29—21no—
172Dic29—21no—
173Dic29—41no—
174#540—291no—
175#520—291no—
176#481—291no—
177#480—291no—
178#479D2911yescharacteristic, complemented
179#478—291no—
180#460—291no—
181#459—291no—
182#449—291no—
183#449—291no—
184#442—291no—
185#440—291no—
186C4×SD16—291no—
187C4×D8—291no—
188#433—291no—
189C2×C29#52511yescharacteristic
190C2×C29#57611yescharacteristic
191C2×C29#57711yescharacteristic
192D29—41no—
193D29—42no—
194D29—81no—
195D29—81no—
196C2×#41—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×D8—291no—
200C2×D8—291no—
201#127—291no—
202#125C2×D2911yescharacteristic
203#123—581no—
204#123—581no—
205#121—291no—
206#121—291no—
207#121—581no—
208#121—581no—
209C4×Q8—291no—
210C4×Q8C2×D2911yescharacteristic
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—581no—
216C4×D4—581no—
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
220C2×C4⋊C4—581no—
221#107—291no—
222#107C2×D2911yescharacteristic
223#106—291no—
224#106C2×D2911yescharacteristic
225C4⋊C8—291no—
226C4⋊C8C2×D2911yescharacteristic
227#103C2×D2911yescharacteristic
228#103C2×D2911yescharacteristic
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235C22⋊C8—291no—
236C22⋊C8—291no—
237#97—291no—
238C4×C8—291no—
239C29#311911yescharacteristic, complemented, Sylow
240#41—582no—
241#41—582no—
242C2×Q8C22×D2911yescharacteristic
243C2×D4—291no—
244C2×D4—291no—
245C2×D4—291no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—581no—
251C22×C4—291no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258SD16—582no—
259SD16—582no—
260D8—582no—
261D8—582no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8C22×D2911yescharacteristic
265C2×C8C22×D2911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—291no—
270C4⋊C4—291no—
271C4⋊C4—291no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4C22×D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—291no—
278C22⋊C4—291no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C42—21no—
286C42—291no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C23—291no—
290C23—581no—
291C23—581no—
292C23—581no—
293Q8—21no—
294Q8#9080912yes—
295D4—292no—
296D4—584no—
297D4—581no—
298D4—581no—
299D4—581no—
300D4—581no—
301D4—581no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305D4—2321no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—584no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4—2321no—
320C2×C4—2321no—
321C2×C4—2321no—
322C2×C4D4×D2911yescharacteristic
323C2×C4D4×D2911yescharacteristic
324C2×C4C23×D2911yescharacteristic
325C8—21no—
326C8—21no—
327C8—581no—
328C8—581no—
329C22—582no—
330C22—581no—
331C22—581no—
332C22—581no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22C2×D4×D2911yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—581no—
349C4—581no—
350C4—581no—
351C4—1161no—
352C4C2×#9080911yescharacteristic
353C4#41×D2911yescharacteristic
354C2—1161no—
355C2—1162no—
356C2—2321no—
357C2—2321no—
358C2#1427167611yescharacteristic
359C2#1427196511yescharacteristic
360C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#479C2
socleC22×C29C22×D4
hypercenter#479D29
hypocenterC29#3119
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14271769C2semidirect
2. #14271645C2semidirect
3. #14271483C2semidirect
4. #14271478C2semidirect
5. #14271460C2semidirect
6. #14271363C2semidirect
7. #14271359C2semidirect
8. #14271311C2semidirect
9. #14271311C2semidirect
10. #14271274C2semidirect
11. #14271266C2semidirect
12. #14271248C2semidirect
13. #14271245C2semidirect
14. #14271223C2semidirect
15. C29×#479C2semidirect
178. #479D29semidirect
239. C29#3119semidirect

Maximal subgroups

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

subgroupindex
#142717692
#142716452
#142714832
#142714782
#142714602
#142713632
#142713592
#142713112
#142712742
#142712662
#142712482
#142712452
#142712232
C29×#4792
#311929