Finite Group Databasebeta

← #16831055

Subgroups — #16831055

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×#11745277C211yesmaximal, characteristic, complemented
2C22×#90785C211yesmaximal, characteristic, complemented
3Q8×C22⋊D29C211yesmaximal, characteristic, complemented
4#14271819C211yesmaximal, characteristic
5#14271554C211yesmaximal, characteristic, complemented
6#14271420C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271383C211yesmaximal, characteristic, complemented
9#14271372C211yesmaximal, characteristic, complemented
10#14271322C211yesmaximal, characteristic, complemented
11#14271321C211yesmaximal, characteristic, complemented
12#14271320C211yesmaximal, characteristic, complemented
13#14271267C211yesmaximal, characteristic, complemented
14#14271231C211yesmaximal, characteristic, complemented
15C29×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×#90807C2211yescharacteristic
19C22×Dic58C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C2×SD16×C29C2211yescharacteristic
22C29×#121C2211yescharacteristic
23#11745308—21no—
24#11745308C2211yescharacteristic
25Q8×Dic29C2211yescharacteristic
26#11745306—21no—
27#11745306C2211yescharacteristic
28C2×#90785—24no—
29C2×#90785C2211yescharacteristic
30C2×#90785C2211yescharacteristic
31C2×#90785C2211yescharacteristic
32C2×#90785C2211yescharacteristic
33#11745301—21no—
34#11745298C2211yescharacteristic
35D4×Dic29—21no—
36C2×#90783C2211yescharacteristic
37C4×C22⋊D29—21no—
38C4×C22⋊D29C2211yescharacteristic
39#11745286—21no—
40#11745286C2211yescharacteristic
41C22×#6597C2211yescharacteristic
42#11745277—24no—
43C2×Dic116C2211yescharacteristic
44C2×Dic116C2211yescharacteristic
45C2×#90772C2211yescharacteristic
46#11745259C2211yescharacteristic
47#11745249C2211yescharacteristic
48#11745247—21no—
49#11745240—21no—
50C29×#103C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×C22⋊C8C2211yescharacteristic
53#11745180C2211yescharacteristic
54#11745168C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745163C2211yescharacteristic
58#11745162C2211yescharacteristic
59#11745158C2211yescharacteristic
60#11745156C2211yescharacteristic
61C2×Q8×C29—21no—
62C2×Q8×C29—22no—
63C2×Q8×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29C2311yescharacteristic
68C22×C4×C29—21no—
69C22×C4×C29C2311yescharacteristic
70C2×C22⋊D29—21no—
71C2×C22⋊D29D411yescharacteristic
72C22×Dic29—21no—
73C22×Dic29—21no—
74Q8×D29—22no—
75Q8×D29—41no—
76#90807—22no—
77#90807—41no—
78C2×C4×D29—21no—
79C2×C4×D29C2311yescharacteristic
80C2×Dic58—22no—
81C2×Dic58—21no—
82C2×Dic58—21no—
83C2×Dic58—41no—
84C2×Dic58C2311yescharacteristic
85C2×Dic58C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87SD16×C29—22no—
88SD16×C29—41no—
89C2×C8×C29C2311yescharacteristic
90C2×C8×C29C2311yescharacteristic
91C4⋊C4×C29C2311yescharacteristic
92C22⋊C4×C29—21no—
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95C22⋊Dic29—21no—
96C22⋊Dic29D411yescharacteristic
97#90785—22no—
98#90785—22no—
99#90785—22no—
100#90785D414yescomplemented
101#90783—22no—
102#90781—21no—
103#90781—21no—
104#90781D411yescharacteristic
105C4⋊Dic29—21no—
106C4⋊Dic29—21no—
107C4⋊Dic29C2311yescharacteristic
108#90779—21no—
109#90779—21no—
110#90779—21no—
111#90779—21no—
112#90779—21no—
113#90779D411yescharacteristic
114C4×Dic29—21no—
115C4×Dic29—21no—
116C4×Dic29C2311yescharacteristic
117C2×#6597—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120Dic116—22no—
121Dic116—41no—
122#90772—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29C2×D411yescharacteristic
126Q8×C29—21no—
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—42no—
130Q8×C29C2×D412yes—
131D4×C29—21no—
132D4×C29—21no—
133D4×C29—42no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—42no—
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2411yescharacteristic
142C22⋊D29—22no—
143C22⋊D29—42no—
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—42no—
149C2×Dic29—42no—
150C2×Dic29C2×D411yescharacteristic
151C2×Dic29C2×D411yescharacteristic
152C2×Dic29C2×D411yescharacteristic
153C4×D29—21no—
154C4×D29—21no—
155C4×D29—42no—
156Dic58—21no—
157Dic58—21no—
158Dic58—21no—
159Dic58—21no—
160Dic58—21no—
161Dic58—42no—
162Dic58—42no—
163Dic58C2×D412yes—
164C8×C29—21no—
165C8×C29—21no—
166#6597—21no—
167#6597C2×D412yes—
168#3270—291nomaximal, Sylow
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29#13712yescomplemented
175C22×C29C22×D411yescharacteristic
176C2×D29—21no—
177C2×D29—21no—
178C2×D29—21no—
179C4×C29—21no—
180C4×C29—22no—
181C4×C29—41no—
182C4×C29—41no—
183C4×C29C22×D411yescharacteristic
184C4×C29H(5,𝔽2)11yescharacteristic
185Dic29—22no—
186Dic29—21no—
187Dic29—21no—
188Dic29—21no—
189Dic29—41no—
190Dic29—41no—
191Dic29—41no—
192C2×#137—291no—
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#448D2911yescharacteristic, complemented
205#441—291no—
206#435—291no—
207C2×C29—22no—
208C2×C29—81no—
209C2×C29D4211yescharacteristic
210C2×C29C2×#13711yescharacteristic
211C2×C29#57811yescharacteristic
212D29—41no—
213C2×#41—291no—
214C22×Q8—291no—
215C22×Q8—291no—
216C22×Q8C2×D2911yescharacteristic
217#137—584no—
218C2×Q16—291no—
219C2×Q16—291no—
220C2×Q16—291no—
221C2×Q16—291no—
222C2×Q16—291no—
223C2×Q16—291no—
224C2×Q16—584no—
225C2×SD16—291no—
226C2×SD16C2×D2911yescharacteristic
227C2×SD16C2×D2911yescharacteristic
228C2×M16—291no—
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—581no—
241#121C2×D2911yescharacteristic
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#103C2×D2911yescharacteristic
253#103C2×D2911yescharacteristic
254#102—291no—
255C22⋊C8—291no—
256C22⋊C8C2×D2911yescharacteristic
257#97—291no—
258C29#327011yescharacteristic, complemented, Sylow
259#41—582no—
260#41—1161no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—291no—
265C2×Q8—291no—
266C2×Q8—291no—
267C2×Q8—581no—
268C2×Q8—582no—
269C2×Q8—581no—
270C2×Q8—582no—
271C2×Q8—1161no—
272C2×Q8—1161no—
273C2×Q8C22×D2911yescharacteristic
274C2×Q8C22×D2911yescharacteristic
275C2×D4—21no—
276C2×D4—291no—
277C2×D4—581no—
278C2×D4C22×D2911yescharacteristic
279C22×C4—21no—
280C22×C4—291no—
281C22×C4—581no—
282C22×C4—581no—
283C22×C4—581no—
284C22×C4C22×D2911yescharacteristic
285Q16—294no—
286Q16—582no—
287Q16—582no—
288Q16—582no—
289Q16—582no—
290Q16—1161no—
291SD16—22no—
292SD16—41no—
293SD16—582no—
294M16—582no—
295C2×C8—291no—
296C2×C8—291no—
297C2×C8—582no—
298C2×C8C22×D2911yescharacteristic
299C2×C8C22×D2911yescharacteristic
300C4⋊C4—291no—
301C4⋊C4—291no—
302C4⋊C4—581no—
303C4⋊C4—581no—
304C4⋊C4—581no—
305C4⋊C4—581no—
306C4⋊C4—581no—
307C4⋊C4—581no—
308C4⋊C4—581no—
309C4⋊C4C22×D2911yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—291no—
312C22⋊C4—291no—
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—42no—
328Q8—292no—
329Q8—581no—
330Q8—581no—
331Q8—581no—
332Q8—581no—
333Q8—581no—
334Q8—1162no—
335Q8—1162no—
336Q8D4×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—291no—
349C2×C4—291no—
350C2×C4—291no—
351C2×C4—581no—
352C2×C4—581no—
353C2×C4—581no—
354C2×C4—581no—
355C2×C4—581no—
356C2×C4—581no—
357C2×C4—1162no—
358C2×C4—1162no—
359C2×C4—1162no—
360C2×C4D4×D2911yescharacteristic
361C2×C4C23×D2911yescharacteristic
362C8—21no—
363C8—21no—
364C8—292no—
365C8—581no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—581no—
372C22—581no—
373C22—581no—
374C22#1174527712yescomplemented
375C22C2×D4×D2911yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—581no—
381C4—582no—
382C4—581no—
383C4—581no—
384C4—1161no—
385C4—1161no—
386C4—1161no—
387C4C2×D4×D2911yescharacteristic
388C4#1174535911yescharacteristic
389C2—22no—
390C2—81no—
391C2—1161no—
392C2#1427179511yescharacteristic
393C2C2×#1174527711yescharacteristic
394C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#448C2
socleC22×C29C22×D4
prime radical#14271819C2
hypercenter#448D29
hypocenterC29#3270
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#11745277C2semidirect
2. C22×#90785C2semidirect
3. Q8×C22⋊D29C2semidirect
5. #14271554C2semidirect
6. #14271420C2semidirect
7. #14271390C2semidirect
8. #14271383C2semidirect
9. #14271372C2semidirect
10. #14271322C2semidirect
11. #14271321C2semidirect
12. #14271320C2semidirect
13. #14271267C2semidirect
14. #14271231C2semidirect
15. C29×#448C2semidirect
100. #90785D4semidirect
174. C22×C29#137semidirect
204. #448D29semidirect
258. C29#3270semidirect
374. C22#11745277semidirect

Maximal subgroups

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

subgroupindex
C2×#117452772
C22×#907852
Q8×C22⋊D292
#142718192
#142715542
#142714202
#142713902
#142713832
#142713722
#142713222
#142713212
#142713202
#142712672
#142712312
C29×#4482
#327029