Finite Group Databasebeta

← #16831467

Subgroups — #16831467

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#14271816C211yesmaximal, characteristic, complemented
3#14271502C211yesmaximal, characteristic, complemented
4#14271492C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271412C211yesmaximal, characteristic, complemented
7#14271395C211yesmaximal, characteristic, complemented
8#14271365C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271276C211yesmaximal, characteristic, complemented
12#14271236C211yesmaximal, characteristic, complemented
13#14271163C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#491C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C29×C4⋊Q8C2211yescharacteristic
19C29×#125C2211yescharacteristic
20#11745308C2211yescharacteristic
21#11745308C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23C2×#90784C2211yescharacteristic
24C2×D232C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745260—21no—
28#11745257—21no—
29#11745257—21no—
30#11745257C2211yescharacteristic
31#11745257C2211yescharacteristic
32#11745256—21no—
33#11745256—21no—
34#11745256—21no—
35#11745255—21no—
36#11745254C2211yescharacteristic
37C4⋊C4×D29—21no—
38C4⋊C4×D29C2211yescharacteristic
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×#97C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745183C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745165C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61#90809—22no—
62#90809—22no—
63#90809—41no—
64#90809—41no—
65C2×D116—21no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116—21no—
69C2×D116D411yescharacteristic
70C2×D116C2311yescharacteristic
71C2×D116C2311yescharacteristic
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78C2×C4×D29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C42×C29C2311yescharacteristic
88#90784—41no—
89#90784—41no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781D411yescharacteristic
98#90781D411yescharacteristic
99C4⋊Dic29D411yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779—21no—
105C4×Dic29—21no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—22no—
109#90772—41no—
110C8×D29—41no—
111C22×D29—21no—
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130D116—21no—
131D116—21no—
132D116—21no—
133D116—41no—
134D116—42no—
135D116—42no—
136D116—42no—
137D116—81no—
138D116#4112yes—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—42no—
145C4×D29—42no—
146C4×D29—81no—
147C4×D29—81no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3307—291nomaximal, Sylow
153C22×C29C22×D411yescharacteristic
154C2×D29—21no—
155C2×D29—21no—
156C2×D29—22no—
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—41no—
162C2×D29—41no—
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×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29H(5,𝔽2)11yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#547—291no—
180#491D2911yescharacteristic, complemented
181#485—291no—
182#483—291no—
183#478—291no—
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#54611yescharacteristic
194C2×C29#57511yescharacteristic
195C2×C29#57711yescharacteristic
196D29—41no—
197D29—41no—
198D29—42no—
199D29—81no—
200C2×#41—291no—
201C2×#41—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C2×M16—291no—
206C22×C8—291no—
207C4⋊Q8C2×D2911yescharacteristic
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—291no—
222C4×D4—581no—
223#117—291no—
224C2×C4⋊C4—291no—
225C2×C4⋊C4—581no—
226#107—291no—
227#106—291no—
228#106—291no—
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103C2×D2911yescharacteristic
233#103C2×D2911yescharacteristic
234#103C2×D2911yescharacteristic
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240C22⋊C8—291no—
241C22⋊C8—291no—
242#97C2×D2911yescharacteristic
243C29#330711yescharacteristic, complemented, Sylow
244#41—582no—
245#41—582no—
246#41—1161no—
247#41—1161no—
248C2×Q8C22×D2911yescharacteristic
249C2×Q8C22×D2911yescharacteristic
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C22×C4—291no—
258C22×C4—291no—
259C22×C4—581no—
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—21no—
276C4⋊C4—21no—
277C4⋊C4—291no—
278C4⋊C4—291no—
279C4⋊C4—291no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4—581no—
283C4⋊C4C22×D2911yescharacteristic
284C4⋊C4C22×D2911yescharacteristic
285C22⋊C4—291no—
286C22⋊C4—291no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—291no—
297C23—291no—
298C23—581no—
299C23—581no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—292no—
305D4—581no—
306D4—581no—
307D4—581no—
308D4—1161no—
309D4—1162no—
310D4—1162no—
311D4—1162no—
312D4—2321no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
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—1162no—
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—581no—
338C22—581no—
339C22—582no—
340C22—581no—
341C22—581no—
342C22—581no—
343C22—581no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—581no—
357C4—581no—
358C4—1161no—
359C4—1161no—
360C4#41×D2911yescharacteristic
361C4#1174536411yescharacteristic
362C2—1161no—
363C2—1161no—
364C2—1162no—
365C2—2321no—
366C2#1427180611yescharacteristic
367C2#1427196211yescharacteristic
368C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#491C2
socleC22×C29C22×D4
hypercenter#491D29
hypocenterC29#3307
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14271866C2semidirect
2. #14271816C2semidirect
3. #14271502C2semidirect
4. #14271492C2semidirect
5. #14271460C2semidirect
6. #14271412C2semidirect
7. #14271395C2semidirect
8. #14271365C2semidirect
9. #14271311C2semidirect
10. #14271311C2semidirect
11. #14271276C2semidirect
12. #14271236C2semidirect
13. #14271163C2semidirect
14. #14271158C2semidirect
15. C29×#491C2semidirect
180. #491D29semidirect
243. C29#3307semidirect

Maximal subgroups

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

subgroupindex
#142718662
#142718162
#142715022
#142714922
#142714602
#142714122
#142713952
#142713652
#142713112
#142712762
#142712362
#142711632
#142711582
C29×#4912
#330729