Finite Group Databasebeta

← #16831058

Subgroups — #16831058

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×#11745313C211yesmaximal, characteristic, complemented
2C22×#90785C211yesmaximal, characteristic, complemented
3D4×Dic58C211yesmaximal, characteristic, complemented
4#14271558C211yesmaximal, characteristic, complemented
5#14271419C211yesmaximal, characteristic, complemented
6#14271390C211yesmaximal, characteristic, complemented
7#14271382C211yesmaximal, characteristic, complemented
8#14271373C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271319C211yesmaximal, characteristic, complemented
11#14271318C211yesmaximal, characteristic, complemented
12#14271301C211yesmaximal, characteristic, complemented
13#14271268C211yesmaximal, characteristic, complemented
14#14271235C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C22×Dic58C2211yescharacteristic
19C22×Dic58C2211yescharacteristic
20C29×#124—21no—
21C29×#124C2211yescharacteristic
22C29×C22⋊Q8—21no—
23C29×C22⋊Q8C2211yescharacteristic
24C29×#121—21no—
25C29×#121C2211yescharacteristic
26C4×Q8×C29C2211yescharacteristic
27C4×D4×C29—21no—
28C4×D4×C29C2211yescharacteristic
29#11745313—24no—
30C2×#90785—24no—
31C2×#90785C2211yescharacteristic
32C2×#90785C2211yescharacteristic
33C2×#90785C2211yescharacteristic
34C2×#90785C2211yescharacteristic
35C2×#90785C2211yescharacteristic
36C2×#90785C2211yescharacteristic
37D4×Dic29—21no—
38C2×#90783C2211yescharacteristic
39C2×#90783C2211yescharacteristic
40C2×#90783C2211yescharacteristic
41#11745286C2211yescharacteristic
42#11745286C2211yescharacteristic
43C2×#90777C2211yescharacteristic
44C22×#6597C2211yescharacteristic
45#11745250—21no—
46#11745240—21no—
47#11745240—21no—
48#11745231C2211yescharacteristic
49C4×Dic58C2211yescharacteristic
50#11745183C2211yescharacteristic
51#11745183C2211yescharacteristic
52#11745180C2211yescharacteristic
53C22⋊#6597C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745156C2211yescharacteristic
59C4⋊#6597C2211yescharacteristic
60#11745151C2211yescharacteristic
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×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29D411yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29C2311yescharacteristic
75C22×C4×C29C2311yescharacteristic
76C22×Dic29—21no—
77C22×Dic29—21no—
78C2×Dic58—22no—
79C2×Dic58—22no—
80C2×Dic58—21no—
81C2×Dic58—21no—
82C2×Dic58—41no—
83C2×Dic58—41no—
84C2×Dic58C2311yescharacteristic
85C2×Dic58C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87C4⋊C4×C29—21no—
88C4⋊C4×C29—21no—
89C4⋊C4×C29D411yescharacteristic
90C4⋊C4×C29C2311yescharacteristic
91C22⋊C4×C29—21no—
92C22⋊C4×C29—21no—
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29D411yescharacteristic
96C22⋊C4×C29D411yescharacteristic
97C42×C29—21no—
98C42×C29C2311yescharacteristic
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101#90785—22no—
102#90785—22no—
103#90785—22no—
104#90785—22no—
105#90785—41no—
106#90785D414yescomplemented
107#90783—22no—
108#90783—22no—
109#90783—41no—
110C4⋊Dic29—21no—
111C4⋊Dic29—21no—
112C4⋊Dic29C2311yescharacteristic
113#90779—21no—
114#90779—21no—
115#90779—21no—
116C4×Dic29—21no—
117#90777—22no—
118C2×#6597—22no—
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C23×C29C2×D411yescharacteristic
126Q8×C29—21no—
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—42no—
130Q8×C29C2×D412yes—
131D4×C29—22no—
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—42no—
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—21no—
142C2×C4×C29—21no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2×D411yescharacteristic
148C2×C4×C29C2×D411yescharacteristic
149C2×C4×C29C2411yescharacteristic
150C2×Dic29—21no—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—42no—
155C2×Dic29—42no—
156Dic58—21no—
157Dic58—21no—
158Dic58—21no—
159Dic58—21no—
160Dic58—21no—
161Dic58—42no—
162Dic58—42no—
163Dic58C2×D412yes—
164#6597—21no—
165#6597—21no—
166#6597—21no—
167#6597C2×D412yes—
168#3270—291nomaximal, Sylow
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29#13712yescomplemented
178C22×C29C22×D411yescharacteristic
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—22no—
182C4×C29—21no—
183C4×C29—21no—
184C4×C29—41no—
185C4×C29—41no—
186C4×C29C22×D411yescharacteristic
187C4×C29H(5,𝔽2)11yescharacteristic
188Dic29—22no—
189Dic29—41no—
190Dic29—41no—
191Dic29—41no—
192C2×#137—291no—
193C22×Q16—291no—
194D4×Q8—291no—
195#548D2911yescharacteristic
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—22no—
208C2×C29—41no—
209C2×C29—81no—
210C2×C29D4211yescharacteristic
211C2×C29C2×#13711yescharacteristic
212C2×C29#57811yescharacteristic
213C2×#41C2×D2911yescharacteristic
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×SD16—291no—
227C2×SD16—291no—
228C2×M16—291no—
229C22×C8—291no—
230C4⋊Q8—291no—
231C4⋊Q8—581no—
232#124—21no—
233#124C2×D2911yescharacteristic
234C22⋊Q8—21no—
235C22⋊Q8—291no—
236C22⋊Q8—291no—
237C22⋊Q8—581no—
238C22⋊Q8—581no—
239C22⋊Q8C2×D2911yescharacteristic
240#121—21no—
241#121C2×D2911yescharacteristic
242C4×Q8—291no—
243C4×Q8C2×D2911yescharacteristic
244C4×D4—21no—
245C4×D4—581no—
246C4×D4C2×D2911yescharacteristic
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—291no—
267C2×Q8—582no—
268C2×Q8—582no—
269C2×Q8—581no—
270C2×Q8—581no—
271C2×Q8—1161no—
272C2×Q8—1161no—
273C2×Q8C22×D2911yescharacteristic
274C2×Q8C22×D2911yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊D2911yescharacteristic
278C2×D4C22×D2911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—581no—
282C22×C4—581no—
283C22×C4C22×D2911yescharacteristic
284C22×C4C22×D2911yescharacteristic
285Q16—294no—
286Q16—582no—
287Q16—582no—
288Q16—582no—
289Q16—582no—
290Q16—1161no—
291SD16—582no—
292SD16—582no—
293SD16—1161no—
294M16—582no—
295C2×C8—291no—
296C2×C8—291no—
297C2×C8—291no—
298C2×C8—291no—
299C2×C8—582no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—291no—
303C4⋊C4—581no—
304C4⋊C4—581no—
305C4⋊C4—581no—
306C4⋊C4—581no—
307C4⋊C4—581no—
308C4⋊C4C22⋊D2911yescharacteristic
309C4⋊C4C22×D2911yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4C22⋊D2911yescharacteristic
317C22⋊C4C22⋊D2911yescharacteristic
318C42—21no—
319C42—581no—
320C42C22×D2911yescharacteristic
321C23—21no—
322C23C2×C22⋊D2911yescharacteristic
323C23C2×C22⋊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—22no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—581no—
352C2×C4—581no—
353C2×C4—581no—
354C2×C4—581no—
355C2×C4—1162no—
356C2×C4—1162no—
357C2×C4C2×C22⋊D2911yescharacteristic
358C2×C4C2×C22⋊D2911yescharacteristic
359C2×C4C2×C22⋊D2911yescharacteristic
360C2×C4C2×C22⋊D2911yescharacteristic
361C2×C4C23×D2911yescharacteristic
362C8—292no—
363C8—581no—
364C8—581no—
365C8—581no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22#1174531312yescomplemented
375C22C22×C22⋊D2911yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—582no—
384C4—1161no—
385C4—1161no—
386C4—1161no—
387C4C2×D4×D2911yescharacteristic
388C4#1174535911yescharacteristic
389C2—22no—
390C2—41no—
391C2—81no—
392C2D4×C22⋊D2911yescharacteristic
393C2C2×#1174531311yescharacteristic
394C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#548C2
socleC22×C29C22×D4
hypercenter#548D29
hypocenterC29#3270
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11745313C2semidirect
2. C22×#90785C2semidirect
3. D4×Dic58C2semidirect
4. #14271558C2semidirect
5. #14271419C2semidirect
6. #14271390C2semidirect
7. #14271382C2semidirect
8. #14271373C2semidirect
9. #14271325C2semidirect
10. #14271319C2semidirect
11. #14271318C2semidirect
12. #14271301C2semidirect
13. #14271268C2semidirect
14. #14271235C2semidirect
106. #90785D4semidirect
177. C22×C29#137semidirect
258. C29#3270semidirect
374. C22#11745313semidirect

Maximal subgroups

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

subgroupindex
C2×#117453132
C22×#907852
D4×Dic582
#142715582
#142714192
#142713902
#142713822
#142713732
#142713252
#142713192
#142713182
#142713012
#142712682
#142712352
C29×#5482
#327029