Finite Group Databasebeta

← #16831465

Subgroups — #16831465

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271866C211yesmaximal, characteristic, complemented
2#14271817C211yesmaximal, characteristic, complemented
3#14271533C211yesmaximal, characteristic, complemented
4#14271506C211yesmaximal, characteristic, complemented
5#14271495C211yesmaximal, characteristic, complemented
6#14271410C211yesmaximal, characteristic, complemented
7#14271393C211yesmaximal, characteristic, complemented
8#14271369C211yesmaximal, characteristic, complemented
9#14271309C211yesmaximal, characteristic, complemented
10#14271309C211yesmaximal, characteristic, complemented
11#14271273C211yesmaximal, characteristic, complemented
12#14271233C211yesmaximal, characteristic, complemented
13#14271161C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C29×#478C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C29×#125C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20C2×#90782C2211yescharacteristic
21#11745292—21no—
22C2×C4⋊Dic29—21no—
23C2×#90773C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745260—21no—
28#11745259C2211yescharacteristic
29#11745259C2211yescharacteristic
30#11745257—21no—
31#11745257C2211yescharacteristic
32#11745257C2211yescharacteristic
33#11745256—21no—
34#11745255—21no—
35#11745254C2211yescharacteristic
36C4⋊C4×D29C2211yescharacteristic
37#11745248—21no—
38#11745248—21no—
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic
41#11745231C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×C4⋊C8C2211yescharacteristic
45C29×#102C2211yescharacteristic
46C29×#102C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745158C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C22×Dic29—21no—
64C22×Dic29—21no—
65#90807—22no—
66#90807—22no—
67#90807—41no—
68#90807—41no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116D411yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×Dic58C2311yescharacteristic
78C2×Dic58C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C42×C29C2311yescharacteristic
88#90782—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⋊Dic29—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29—21no—
101C4⋊Dic29D411yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107#90773—41no—
108#90773—41no—
109#90772—41no—
110C8×D29—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115D4×C29—21no—
116D4×C29#4112yes—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—42no—
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29—42no—
125C22⋊D29—42no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—42no—
130C2×Dic29—42no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—21no—
134D116—21no—
135D116—41no—
136D116—42no—
137D116—81no—
138C4×D29—21no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—81no—
143C4×D29—81no—
144Dic58—21no—
145Dic58—21no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3307—291nomaximal, Sylow
153C22×C29—22no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#547—291no—
180#491—291no—
181#485—291no—
182#483—291no—
183#478D2911yescharacteristic, complemented
184#468—291no—
185#465—291no—
186#461—291no—
187#449—291no—
188#449—291no—
189#442—291no—
190#435—291no—
191#417—291no—
192#416—291no—
193C2×C29—42no—
194C2×C29#54611yescharacteristic
195C2×C29#57511yescharacteristic
196C2×C29#57711yescharacteristic
197D29—41no—
198D29—41no—
199D29—81no—
200C2×#41—291no—
201C2×#41—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C2×M16—291no—
206C22×C8—291no—
207C4⋊Q8—291no—
208#126—581no—
209#125C2×D2911yescharacteristic
210#123—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—291no—
214C22⋊Q8—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—581no—
222C4×D4C2×D2911yescharacteristic
223#117—291no—
224C2×C4⋊C4—291no—
225C2×C4⋊C4—581no—
226#107C2×D2911yescharacteristic
227#106—291no—
228#106C2×D2911yescharacteristic
229C4⋊C8C2×D2911yescharacteristic
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#102—291no—
237#102—291no—
238#102C2×D2911yescharacteristic
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8—291no—
242#97—291no—
243C29#330711yescharacteristic, complemented, Sylow
244#41—582no—
245#41—582no—
246#41—1161no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—291no—
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—581no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22×D2911yescharacteristic
257C22×C4—21no—
258C22×C4—291no—
259C22×C4—291no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264SD16—1161no—
265SD16—1161no—
266D8—582no—
267M16—1161no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C4⋊C4C22×D2911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—291no—
287C22⋊C4—291no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—291no—
298C23—291no—
299C23—581no—
300Q8—581no—
301Q8—581no—
302Q8—581no—
303Q8—581no—
304D4—21no—
305D4—581no—
306D4—581no—
307D4—1161no—
308D4—1162no—
309D4—1162no—
310D4—1162no—
311D4—2321no—
312D4#9080912yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—291no—
318C2×C4—291no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—1162no—
327C2×C4—1162no—
328C2×C4—2321no—
329C2×C4—2321no—
330C2×C4D4×D2911yescharacteristic
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—581no—
341C22—581no—
342C22—581no—
343C22—581no—
344C22—581no—
345C22—581no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—581no—
356C4—581no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080911yescharacteristic
361C4#1174536411yescharacteristic
362C2—42no—
363C2—1161no—
364C2—1161no—
365C2—2321no—
366C2#1427180411yescharacteristic
367C2#1427195911yescharacteristic
368C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#478C2
socleC22×C29C22×D4
hypercenter#478D29
hypocenterC29#3307
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14271866C2semidirect
2. #14271817C2semidirect
3. #14271533C2semidirect
4. #14271506C2semidirect
5. #14271495C2semidirect
6. #14271410C2semidirect
7. #14271393C2semidirect
8. #14271369C2semidirect
9. #14271309C2semidirect
10. #14271309C2semidirect
11. #14271273C2semidirect
12. #14271233C2semidirect
13. #14271161C2semidirect
14. #14271156C2semidirect
15. C29×#478C2semidirect
183. #478D29semidirect
243. C29#3307semidirect

Maximal subgroups

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

subgroupindex
#142718662
#142718172
#142715332
#142715062
#142714952
#142714102
#142713932
#142713692
#142713092
#142712732
#142712332
#142711612
#142711562
C29×#4782
#330729