Finite Group Databasebeta

← #16831391

Subgroups — #16831391

Order 3712.

398 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#14271825C211yesmaximal, characteristic, complemented
3#14271520C211yesmaximal, characteristic, complemented
4#14271506C211yesmaximal, characteristic, complemented
5#14271483C211yesmaximal, characteristic, complemented
6#14271400C211yesmaximal, characteristic, complemented
7#14271393C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271303C211yesmaximal, characteristic, complemented
11C4×#90784C211yesmaximal, characteristic, complemented
12#14271228C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#479C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C29×#125C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20C2×#90784C2211yescharacteristic
21C2×D232C2211yescharacteristic
22C2×#90773C2211yescharacteristic
23C2×C8×D29C2211yescharacteristic
24C2×C8×D29C2211yescharacteristic
25#11745260—21no—
26#11745259—21no—
27#11745259C2211yescharacteristic
28#11745257—21no—
29#11745257—21no—
30#11745257C2211yescharacteristic
31#11745257C2211yescharacteristic
32#11745257C2211yescharacteristic
33#11745256—21no—
34#11745255—21no—
35#11745254C2211yescharacteristic
36C4⋊C4×D29C2211yescharacteristic
37#11745237—21no—
38#11745237C2211yescharacteristic
39C4×D116—21no—
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×C4⋊C8C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×#103C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745158C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60#90809—22no—
61#90809—41no—
62Q8×D29—22no—
63Q8×D29—41no—
64C2×D116—21no—
65C2×D116—21no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116D411yescharacteristic
69C2×D116C2311yescharacteristic
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C42×C29—21no—
88C42×C29C2311yescharacteristic
89#90784—22no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781D411yescharacteristic
99#90781D411yescharacteristic
100C4⋊Dic29—21no—
101C4⋊Dic29D411yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107D232—41no—
108#90773—41no—
109C8×D29—41no—
110C8×D29—41no—
111C22×D29—21no—
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29#4112yes—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29C2×D411yescharacteristic
127C2×Dic29C2×D411yescharacteristic
128D116—22no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—21no—
133D116—42no—
134D116—42no—
135D116—42no—
136D116—81no—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—42no—
142C4×D29—42no—
143C4×D29—81no—
144C4×D29—81no—
145Dic58—21no—
146Dic58—21no—
147Dic58—42no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
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—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29#13512yes—
166C4×C29—22no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29H(5,𝔽2)11yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#548—291no—
180#488—291no—
181#485—291no—
182#481—291no—
183#479D2911yescharacteristic, complemented
184#466—291no—
185#465—291no—
186#463—291no—
187#449—291no—
188#448—291no—
189C4×SD16—291no—
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29#54611yescharacteristic
194C2×C29C2×#13511yescharacteristic
195C2×C29#57711yescharacteristic
196D29—22no—
197D29—41no—
198D29—81no—
199D29—81no—
200C2×#41—291no—
201C22×Q8—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C22×C8—291no—
206C22×C8—291no—
207#126—581no—
208#125C2×D2911yescharacteristic
209#124—291no—
210#124—581no—
211#123—581no—
212C22⋊Q8—291no—
213C22⋊Q8—581no—
214#121—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×Q8C2×D2911yescharacteristic
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223C4×D4—581no—
224#117—291no—
225C2×C4⋊C4—291no—
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#103C2×D2911yescharacteristic
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240C22⋊C8—291no—
241C22⋊C8—291no—
242C4×C8—291no—
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—291no—
247C2×Q8—581no—
248C2×Q8—582no—
249C2×Q8—1161no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C22×C4—291no—
259C22×C4—291no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264SD16—582no—
265SD16—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—291no—
277C4⋊C4—291no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4C22×D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—291no—
284C22⋊C4—291no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—21no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—291no—
297C23—291no—
298C23—581no—
299C23—581no—
300Q8—21no—
301Q8—581no—
302Q8—581no—
303Q8—1162no—
304Q8#9080912yes—
305D4—582no—
306D4—581no—
307D4—581no—
308D4—581no—
309D4—581no—
310D4—1162no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—291no—
319C2×C4—291no—
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—292no—
338C22—581no—
339C22—581no—
340C22—581no—
341C22—581no—
342C22—581no—
343C22—1161no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—581no—
357C4—581no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080911yescharacteristic
361C4#1174536411yescharacteristic
362C2—582no—
363C2—1161no—
364C2—2321no—
365C2—2321no—
366C2#1427180411yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#479C2
socleC22×C29C22×D4
hypercenter#479D29
hypocenterC29#3301
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. #14271866C2semidirect
2. #14271825C2semidirect
3. #14271520C2semidirect
4. #14271506C2semidirect
5. #14271483C2semidirect
6. #14271400C2semidirect
7. #14271393C2semidirect
8. #14271379C2semidirect
9. #14271311C2semidirect
10. #14271303C2semidirect
11. C4×#90784C2semidirect
12. #14271228C2semidirect
13. #14271158C2semidirect
14. #103×D29C2semidirect
15. C29×#479C2semidirect
183. #479D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718662
#142718252
#142715202
#142715062
#142714832
#142714002
#142713932
#142713792
#142713112
#142713032
C4×#907842
#142712282
#142711582
#103×D292
C29×#4792
#330129