Finite Group Databasebeta

← #16829471

Subgroups — #16829471

Order 3712.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271743C211yesmaximal, characteristic
2#14271644C211yesmaximal, characteristic, complemented
3#14271502C211yesmaximal, characteristic, complemented
4#14271501C211yesmaximal, characteristic, complemented
5#14271497C211yesmaximal, characteristic, complemented
6#14271490C211yesmaximal, characteristic, complemented
7#14271488C211yesmaximal, characteristic, complemented
8#14271478C211yesmaximal, characteristic, complemented
9#14271476C211yesmaximal, characteristic, complemented
10#14271204C211yesmaximal, characteristic, complemented
11#107×D29C211yesmaximal, characteristic, complemented
12#14271163C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14#14271128C211yesmaximal, characteristic, complemented
15C29×#484C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745308C2211yescharacteristic
21#11745292C2211yescharacteristic
22C4×C22⋊D29—21no—
23C4×C22⋊D29—21no—
24#11745288C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745258—21no—
28#11745257—21no—
29#11745257C2211yescharacteristic
30#11745255—21no—
31#11745254C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34C4⋊C4×D29C2211yescharacteristic
35C4⋊C4×D29C2211yescharacteristic
36#11745249—21no—
37#11745246—21no—
38#11745246—21no—
39C29×#107C2211yescharacteristic
40C29×#107C2211yescharacteristic
41C29×#103C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745166C2211yescharacteristic
52#11745165C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745156C2211yescharacteristic
56#11745155C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C2×C22⋊D29D411yescharacteristic
64C2×C22⋊D29D411yescharacteristic
65#90809—22no—
66#90809—22no—
67#90805—22no—
68#90805—22no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116D411yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78C2×C4×D29C2311yescharacteristic
79C2×Dic58D411yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90772—22no—
107C8×D29—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29C2×D411yescharacteristic
111C22×D29C2×D411yescharacteristic
112Q8×C29—21no—
113Q8×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—81no—
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2411yescharacteristic
123C22⋊D29—22no—
124C22⋊D29—22no—
125C22⋊D29—81no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131D116—22no—
132D116—21no—
133D116—21no—
134D116—42no—
135D116—81no—
136C4×D29—21no—
137C4×D29—21no—
138C4×D29—42no—
139C4×D29—81no—
140C4×D29—81no—
141C4×D29—81no—
142C4×D29#4112yes—
143C4×D29#4112yes—
144Dic58—22no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3098—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29C22×D411yescharacteristic
154C2×D29—21no—
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29#12312yes—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29C2×#4111yescharacteristic
170Dic29—21no—
171Dic29—41no—
172Dic29—41no—
173Dic29—41no—
174Dic29#12312yes—
175#537—291no—
176#520—291no—
177#485—291no—
178#485—291no—
179#484—291no—
180#484D2911yescharacteristic, complemented
181#482—291no—
182#482—291no—
183#480—291no—
184#480—291no—
185#428—291no—
186C2×#107—291no—
187#417—291no—
188#416—291no—
189#408—291no—
190C2×C29—41no—
191C2×C29C2×#12311yescharacteristic
192C2×C29#57611yescharacteristic
193C2×C29#57811yescharacteristic
194D29—22no—
195D29—41no—
196D29—81no—
197C2×#41—291no—
198C2×#41—291no—
199C2×M16—291no—
200C22×C8—291no—
201C22⋊Q8—291no—
202C22⋊Q8—581no—
203C22⋊Q8C2×D2911yescharacteristic
204#121—291no—
205#121—291no—
206#121—581no—
207#121—581no—
208#121—581no—
209C4×Q8—581no—
210C4×D4—581no—
211C4×D4—581no—
212C4×D4—581no—
213#117—291no—
214#117—291no—
215#117—291no—
216C2×C4⋊C4—291no—
217C2×C4⋊C4—291no—
218C2×C4⋊C4—291no—
219C2×C4⋊C4C2×D2911yescharacteristic
220#107—291no—
221#107—291no—
222#107—291no—
223#107—291no—
224#107C2×D2911yescharacteristic
225#107C2×D2911yescharacteristic
226#106—291no—
227#106—291no—
228#103—291no—
229#103—291no—
230#103C2×D2911yescharacteristic
231#103C2×D2911yescharacteristic
232#102—291no—
233#102—291no—
234#102—291no—
235#102—291no—
236C22⋊C8—291no—
237C22⋊C8—291no—
238C22⋊C8—291no—
239C22⋊C8C2×D2911yescharacteristic
240C29#309811yescharacteristic, complemented, Sylow
241#41—582no—
242#41—582no—
243#41—582no—
244#41—582no—
245C2×Q8—291no—
246C2×Q8C22×D2911yescharacteristic
247C2×D4—291no—
248C2×D4—291no—
249C2×D4—291no—
250C2×D4—291no—
251C2×D4—581no—
252C2×D4—581no—
253C2×D4—581no—
254C22×C4—21no—
255C22×C4—291no—
256C22×C4—291no—
257C22×C4—581no—
258C22×C4—581no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4C22×D2911yescharacteristic
262M16—582no—
263C2×C8—291no—
264C2×C8—291no—
265C2×C8—582no—
266C2×C8C22×D2911yescharacteristic
267C2×C8C22×D2911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—291no—
271C4⋊C4—291no—
272C4⋊C4—291no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4—581no—
277C4⋊C4C22×D2911yescharacteristic
278C4⋊C4C22×D2911yescharacteristic
279C4⋊C4C22×D2911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C42—581no—
288C42—581no—
289C42—581no—
290C23—291no—
291C23—291no—
292C23—581no—
293C23D4×D2911yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—582no—
297D4—582no—
298D4—582no—
299D4—582no—
300D4—581no—
301D4—581no—
302D4—1162no—
303D4—2321no—
304D4—2321no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—291no—
313C2×C4—292no—
314C2×C4—292no—
315C2×C4—291no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—1162no—
322C2×C4—2321no—
323C2×C4—2321no—
324C2×C4—2321no—
325C2×C4D4×D2911yescharacteristic
326C2×C4C23×D2911yescharacteristic
327C8—21no—
328C8—21no—
329C8—581no—
330C8—581no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—292no—
335C22—581no—
336C22—581no—
337C22—581no—
338C22—581no—
339C22—581no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—292no—
350C4—581no—
351C4—1161no—
352C4—1161no—
353C4—1161no—
354C4#41×D2911yescharacteristic
355C4#41×D2911yescharacteristic
356C2—41no—
357C2—582no—
358C2—1161no—
359C2—2321no—
360C2#123×D2911yescharacteristic
361C2#1427196711yescharacteristic
362C2#1427197611yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#484C2
socleC22×C29C22×D4
prime radical#14271743C2
hypercenter#484D29
hypocenterC29#3098
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #14271644C2semidirect
3. #14271502C2semidirect
4. #14271501C2semidirect
5. #14271497C2semidirect
6. #14271490C2semidirect
7. #14271488C2semidirect
8. #14271478C2semidirect
9. #14271476C2semidirect
10. #14271204C2semidirect
11. #107×D29C2semidirect
12. #14271163C2semidirect
13. #14271158C2semidirect
14. #14271128C2semidirect
15. C29×#484C2semidirect
180. #484D29semidirect
240. C29#3098semidirect

Maximal subgroups

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

subgroupindex
#142717432
#142716442
#142715022
#142715012
#142714972
#142714902
#142714882
#142714782
#142714762
#142712042
#107×D292
#142711632
#142711582
#142711282
C29×#4842
#309829