Finite Group Databasebeta

← #16831056

Subgroups — #16831056

Order 3712.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D29C211yesmaximal, characteristic, complemented
2Q8×C22⋊D29C211yesmaximal, characteristic, complemented
3#14271820C211yesmaximal, characteristic
4#14271554C211yesmaximal, characteristic, complemented
5#14271421C211yesmaximal, characteristic, complemented
6#14271389C211yesmaximal, characteristic, complemented
7#14271383C211yesmaximal, characteristic, complemented
8#14271371C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271319C211yesmaximal, characteristic, complemented
11#14271317C211yesmaximal, characteristic, complemented
12#14271300C211yesmaximal, characteristic, complemented
13#14271270C211yesmaximal, characteristic, complemented
14#14271232C211yesmaximal, characteristic, complemented
15C2×C29×#137C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C2×Q8×D29C2211yescharacteristic
20C29×#137—24no—
21C2×Q16×C29C2211yescharacteristic
22C2×Q16×C29C2211yescharacteristic
23C2×SD16×C29C2211yescharacteristic
24C2×SD16×C29C2211yescharacteristic
25C2×M16×C29C2211yescharacteristic
26#11745308—21no—
27#11745308C2211yescharacteristic
28Q8×Dic29C2211yescharacteristic
29Q8×Dic29C2211yescharacteristic
30#11745306—21no—
31#11745306C2211yescharacteristic
32C2×#90785C2211yescharacteristic
33C2×#90785C2211yescharacteristic
34C2×#90785C2211yescharacteristic
35#11745300—21no—
36#11745300C2211yescharacteristic
37#11745298—21no—
38#11745298C2211yescharacteristic
39C2×#90783C2211yescharacteristic
40C4×C22⋊D29—21no—
41C4×C22⋊D29—21no—
42C4×C22⋊D29C2211yescharacteristic
43#11745286—21no—
44#11745286—21no—
45#11745286C2211yescharacteristic
46#11745286C2211yescharacteristic
47Q16×D29—24no—
48C2×Dic116C2211yescharacteristic
49C2×C8×D29C2211yescharacteristic
50#11745183C2211yescharacteristic
51#11745183C2211yescharacteristic
52#11745183C2211yescharacteristic
53#11745180C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic
55#11745168C2211yescharacteristic
56#11745165C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59#11745163C2211yescharacteristic
60#11745162C2211yescharacteristic
61#41×C29—22no—
62#41×C29—41no—
63C2×Q8×C29—21no—
64C2×Q8×C29—22no—
65C2×Q8×C29—41no—
66C2×Q8×C29C2311yescharacteristic
67C2×Q8×C29C2311yescharacteristic
68C2×Q8×C29C2311yescharacteristic
69C2×D4×C29—21no—
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29D411yescharacteristic
76Q8×D29—22no—
77Q8×D29—22no—
78Q8×D29—41no—
79Q8×D29—41no—
80C2×C4×D29—21no—
81C2×C4×D29—21no—
82C2×C4×D29C2311yescharacteristic
83C2×Dic58—21no—
84C2×Dic58—21no—
85C2×Dic58C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87Q16×C29—22no—
88Q16×C29D414yescomplemented
89SD16×C29—22no—
90SD16×C29—22no—
91M16×C29—22no—
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C22⋊Dic29—21no—
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29D411yescharacteristic
100#90785—22no—
101#90785—22no—
102#90785—41no—
103#90783—41no—
104#90781—21no—
105#90781D411yescharacteristic
106C4⋊Dic29—21no—
107C4⋊Dic29—21no—
108C4⋊Dic29C2311yescharacteristic
109C4⋊Dic29C2311yescharacteristic
110#90779—21no—
111#90779—21no—
112#90779—21no—
113#90779—21no—
114#90779—21no—
115#90779D411yescharacteristic
116C4×Dic29—21no—
117C4×Dic29—21no—
118C4×Dic29C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121Dic116—22no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29C2×D411yescharacteristic
126Q8×C29—21no—
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—42no—
131Q8×C29C2×D412yes—
132Q8×C29C2×D412yes—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—42no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—42no—
142C2×C4×C29—42no—
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2411yescharacteristic
145C22⋊D29—22no—
146C22⋊D29—42no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—21no—
151C2×Dic29C2×D411yescharacteristic
152C2×Dic29C2×D411yescharacteristic
153C2×Dic29C2×D411yescharacteristic
154C4×D29—21no—
155C4×D29—21no—
156C4×D29—42no—
157C4×D29—42no—
158Dic58—21no—
159Dic58—21no—
160Dic58—21no—
161Dic58—21no—
162Dic58—42no—
163Dic58—42no—
164C8×C29—21no—
165C8×C29C2×D412yes—
166#6597—21no—
167#6597—21no—
168#3270—291nomaximal, Sylow
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29C22×D411yescharacteristic
176C2×D29—21no—
177C2×D29—21no—
178C2×D29#13712yescomplemented
179C4×C29—22no—
180C4×C29—22no—
181C4×C29—21no—
182C4×C29—41no—
183C4×C29C22×D411yescharacteristic
184C4×C29H(5,𝔽2)11yescharacteristic
185Dic29—21no—
186Dic29—21no—
187Dic29—21no—
188Dic29—41no—
189Dic29—41no—
190Dic29—41no—
191Dic29—41no—
192C2×#137D2911yescharacteristic, complemented
193C22×Q16—291no—
194D4×Q8—291no—
195#548—291no—
196#497—291no—
197#470—291no—
198#465—291no—
199#464—291no—
200#462—291no—
201#452—291no—
202#451—291no—
203#451—291no—
204#448—291no—
205#441—291no—
206#435—291no—
207C2×C29—41no—
208C2×C29—81no—
209C2×C29D4211yescharacteristic
210C2×C29C2×#13711yescharacteristic
211C2×C29#57811yescharacteristic
212D29—22no—
213C2×#41C2×D2911yescharacteristic
214C22×Q8—291no—
215C22×Q8—291no—
216C22×Q8C2×D2911yescharacteristic
217#137—24no—
218C2×Q16—291no—
219C2×Q16—291no—
220C2×Q16—291no—
221C2×Q16—291no—
222C2×Q16—584no—
223C2×Q16C2×D2911yescharacteristic
224C2×Q16C2×D2911yescharacteristic
225C2×SD16—291no—
226C2×SD16C2×D2911yescharacteristic
227C2×SD16C2×D2911yescharacteristic
228C2×M16C2×D2911yescharacteristic
229C22×C8—291no—
230C4⋊Q8—291no—
231C4⋊Q8—581no—
232#124—291no—
233#124—581no—
234C22⋊Q8—291no—
235C22⋊Q8—291no—
236C22⋊Q8—291no—
237C22⋊Q8—581no—
238C22⋊Q8—581no—
239C22⋊Q8—581no—
240#121—291no—
241#121—581no—
242C4×Q8—291no—
243C4×Q8—291no—
244C4×D4—291no—
245C4×D4—581no—
246C4×D4—581no—
247#106—291no—
248C4⋊C8—291no—
249#103—291no—
250#103—291no—
251#103—291no—
252#103—291no—
253#103—291no—
254#102—291no—
255C22⋊C8—291no—
256C22⋊C8—291no—
257#97—291no—
258C29#327011yescharacteristic, complemented, Sylow
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—291no—
265C2×Q8—291no—
266C2×Q8—581no—
267C2×Q8—581no—
268C2×Q8—582no—
269C2×Q8—582no—
270C2×Q8—1161no—
271C2×Q8—1161no—
272C2×Q8C22×D2911yescharacteristic
273C2×Q8C22×D2911yescharacteristic
274C2×Q8C22×D2911yescharacteristic
275C2×D4—21no—
276C2×D4—291no—
277C2×D4—581no—
278C2×D4C22×D2911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—291no—
282C22×C4—581no—
283C22×C4—581no—
284C22×C4C22×D2911yescharacteristic
285Q16—22no—
286Q16—582no—
287Q16—582no—
288Q16—582no—
289Q16—1161no—
290Q16C22⋊D2914yescomplemented
291SD16—22no—
292SD16—22no—
293SD16—1161no—
294M16—22no—
295C2×C8—291no—
296C2×C8—291no—
297C2×C8—582no—
298C2×C8C22×D2911yescharacteristic
299C2×C8C22×D2911yescharacteristic
300C4⋊C4—291no—
301C4⋊C4—291no—
302C4⋊C4—291no—
303C4⋊C4—581no—
304C4⋊C4—581no—
305C4⋊C4—581no—
306C4⋊C4—581no—
307C4⋊C4—581no—
308C4⋊C4—581no—
309C4⋊C4—581no—
310C22⋊C4—291no—
311C22⋊C4—291no—
312C22⋊C4—581no—
313C22⋊C4—581no—
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4—581no—
317C22⋊C4—581no—
318C42—291no—
319C42—581no—
320C42—581no—
321C23—21no—
322C23—291no—
323C23D4×D2911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—42no—
329Q8—581no—
330Q8—581no—
331Q8—581no—
332Q8—581no—
333Q8—1162no—
334Q8—1162no—
335Q8C2×C22⋊D2912yes—
336Q8C2×C22⋊D2912yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—582no—
341D4—1162no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—291no—
350C2×C4—291no—
351C2×C4—291no—
352C2×C4—581no—
353C2×C4—581no—
354C2×C4—581no—
355C2×C4—581no—
356C2×C4—581no—
357C2×C4—581no—
358C2×C4—1162no—
359C2×C4—1162no—
360C2×C4D4×D2911yescharacteristic
361C2×C4C23×D2911yescharacteristic
362C8—21no—
363C8—581no—
364C8—581no—
365C8C2×C22⋊D2912yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—292no—
373C22—581no—
374C22—581no—
375C22C2×D4×D2911yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—581no—
381C4—581no—
382C4—581no—
383C4—1161no—
384C4—1161no—
385C4—1161no—
386C4—1161no—
387C4#1174535911yescharacteristic
388C4C22×C22⋊D2911yescharacteristic
389C2—41no—
390C2—81no—
391C2—582no—
392C2D4×C22⋊D2911yescharacteristic
393C2#137×D2911yescharacteristic
394C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#137C2
socleC22×C29C22×D4
prime radical#14271820C2
hypercenterC2×#137D29
hypocenterC29#3270
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D29C2semidirect
2. Q8×C22⋊D29C2semidirect
4. #14271554C2semidirect
5. #14271421C2semidirect
6. #14271389C2semidirect
7. #14271383C2semidirect
8. #14271371C2semidirect
9. #14271325C2semidirect
10. #14271319C2semidirect
11. #14271317C2semidirect
12. #14271300C2semidirect
13. #14271270C2semidirect
14. #14271232C2semidirect
15. C2×C29×#137C2semidirect
88. Q16×C29D4semidirect
178. C2×D29#137semidirect
192. C2×#137D29semidirect
258. C29#3270semidirect
290. Q16C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D292
Q8×C22⋊D292
#142718202
#142715542
#142714212
#142713892
#142713832
#142713712
#142713252
#142713192
#142713172
#142713002
#142712702
#142712322
C2×C29×#1372
#327029