Finite Group Databasebeta

← #16831002

Subgroups — #16831002

Order 3712.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745277C211yesmaximal, characteristic, complemented
2Q8×C22⋊D29C211yesmaximal, characteristic, complemented
3#14271807C211yesmaximal, characteristic
4#14271554C211yesmaximal, characteristic, complemented
5#14271406C211yesmaximal, characteristic, complemented
6#14271404C211yesmaximal, characteristic, complemented
7#14271383C211yesmaximal, characteristic, complemented
8#14271366C211yesmaximal, characteristic, complemented
9#14271322C211yesmaximal, characteristic, complemented
10#14271319C211yesmaximal, characteristic, complemented
11#14271314C211yesmaximal, characteristic, complemented
12#14271300C211yesmaximal, characteristic, complemented
13#14271264C211yesmaximal, characteristic, complemented
14#14271234C211yesmaximal, characteristic, complemented
15C22×SD16×C29C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic, complemented
19C2×#90807C2211yescharacteristic
20C2×SD16×C29—24no—
21C2×SD16×C29C2211yescharacteristic
22C2×SD16×C29C2211yescharacteristic
23C2×SD16×C29C2211yescharacteristic
24C2×SD16×C29C2211yescharacteristic
25C22×C8×C29C2211yescharacteristic
26#11745315—21no—
27C2×C22⋊Dic29—21no—
28#11745308—21no—
29#11745308C2211yescharacteristic, complemented
30Q8×Dic29C2211yescharacteristic, complemented
31#11745306—21no—
32#11745306C2211yescharacteristic, complemented
33C2×#90785C2211yescharacteristic, complemented
34C2×#90785C2211yescharacteristic, complemented
35#11745301—21no—
36#11745300C2211yescharacteristic
37#11745298C2211yescharacteristic
38#11745297—21no—
39D4×Dic29C2211yescharacteristic
40C2×#90783C2211yescharacteristic
41C2×#90783C2211yescharacteristic
42C4×C22⋊D29—21no—
43C4×C22⋊D29C2211yescharacteristic
44#11745286—21no—
45#11745286C2211yescharacteristic
46#11745286C2211yescharacteristic
47#11745277—24no—
48C2×Dic116C2211yescharacteristic, complemented
49C2×#90772C2211yescharacteristic, complemented
50#11745183C2211yescharacteristic, complemented
51#11745183C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic
53#11745180C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic
55#11745168C2211yescharacteristic, complemented
56#11745166C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59#11745163C2211yescharacteristic, complemented
60#11745162C2211yescharacteristic, complemented
61C24×C29—21no—
62C2×Q8×C29—21no—
63C2×Q8×C29—22no—
64C2×Q8×C29—41no—
65C2×Q8×C29C2311yescharacteristic
66C2×Q8×C29C2311yescharacteristic
67C2×D4×C29—22no—
68C2×D4×C29—21no—
69C2×D4×C29—41no—
70C2×D4×C29C2311yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29D411yescharacteristic
77C22×Dic29—21no—
78C22×Dic29—21no—
79Q8×D29—22no—
80Q8×D29—41no—
81#90807—22no—
82#90807—41no—
83C2×C4×D29—21no—
84C2×C4×D29C2311yescharacteristic
85C2×Dic58—21no—
86C2×Dic58C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88SD16×C29—22no—
89SD16×C29—22no—
90SD16×C29—22no—
91SD16×C29D414yescomplemented
92C2×C8×C29—22no—
93C2×C8×C29C2311yescharacteristic
94C2×C8×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29D411yescharacteristic
102#90785—22no—
103#90785—41no—
104#90783—22no—
105#90783—41no—
106#90781—21no—
107#90781D411yescharacteristic
108C4⋊Dic29—21no—
109C4⋊Dic29C2311yescharacteristic
110C4⋊Dic29C2311yescharacteristic
111#90779—21no—
112#90779—21no—
113#90779—21no—
114#90779—21no—
115#90779—21no—
116#90779D411yescharacteristic
117C4×Dic29—21no—
118C4×Dic29C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121Dic116—22no—
122#90772—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—42no—
126C23×C29—42no—
127C23×C29—81no—
128C23×C29C2×D411yescharacteristic
129C22×D29C2×D411yescharacteristic
130Q8×C29—21no—
131Q8×C29—21no—
132Q8×C29—21no—
133Q8×C29—42no—
134Q8×C29C2×D412yes—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—42no—
139D4×C29C2×D412yes—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—42no—
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C22⋊D29—22no—
148C22⋊D29—42no—
149C22⋊D29—81no—
150C2×Dic29—21no—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—42no—
155C2×Dic29—81no—
156C2×Dic29C2×D411yescharacteristic
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159C4×D29—21no—
160C4×D29—21no—
161C4×D29—42no—
162Dic58—21no—
163Dic58—21no—
164Dic58—21no—
165Dic58—21no—
166Dic58—42no—
167C8×C29—21no—
168C8×C29C2×D412yes—
169#6597—21no—
170#6597—21no—
171#3266—291nomaximal, Sylow
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—22no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29—41no—
180C22×C29—84no—
181C22×C29#13712yescomplemented
182C22×C29C22×D411yescharacteristic
183C2×D29—21no—
184C2×D29—21no—
185C2×D29—21no—
186C4×C29—22no—
187C4×C29—21no—
188C4×C29—41no—
189C4×C29C22×D411yescharacteristic
190C4×C29H(5,𝔽2)11yescharacteristic
191Dic29—21no—
192Dic29—21no—
193Dic29—21no—
194Dic29—41no—
195Dic29—41no—
196Dic29—41no—
197Dic29—41no—
198C2×#137—291no—
199C22×SD16D2911yescharacteristic, complemented
200D4×Q8—291no—
201#546—291no—
202#497—291no—
203#468—291no—
204#467—291no—
205#464—291no—
206#461—291no—
207#452—291no—
208#451—291no—
209#450—291no—
210#448—291no—
211#440—291no—
212#435—291no—
213C2×C29—22no—
214C2×C29—42no—
215C2×C29—81no—
216C2×C29D4211yescharacteristic
217C2×C29C2×#13711yescharacteristic
218C2×C29#57711yescharacteristic
219D29—41no—
220C2×#41—291no—
221C22×Q8—291no—
222C22×Q8C2×D2911yescharacteristic
223C22×D4C2×D2911yescharacteristic
224#137—584no—
225C2×Q16—291no—
226C2×Q16—291no—
227C2×Q16—291no—
228C2×SD16—24no—
229C2×SD16—291no—
230C2×SD16—291no—
231C2×SD16C2×D2911yescharacteristic
232C2×SD16C2×D2911yescharacteristic
233C2×SD16C2×D2911yescharacteristic
234C2×SD16C2×D2911yescharacteristic
235C2×M16—291no—
236C22×C8C2×D2911yescharacteristic
237C4⋊Q8—291no—
238C4⋊Q8—581no—
239#124—291no—
240#123—581no—
241C22⋊Q8—291no—
242C22⋊Q8—291no—
243C22⋊Q8—291no—
244C22⋊Q8—581no—
245C22⋊Q8—581no—
246#121—291no—
247#121—581no—
248#120—581no—
249C4×Q8—291no—
250C4×D4—291no—
251C4×D4—291no—
252C4×D4—581no—
253C2×C22⋊C4—581no—
254#107—291no—
255C4⋊C8—291no—
256#103—291no—
257#103—291no—
258#103—291no—
259#103—291no—
260#102—291no—
261#102—291no—
262C22⋊C8—291no—
263C22⋊C8—291no—
264#97—291no—
265C29#326611yescharacteristic, complemented, Sylow
266C24—21no—
267#41—582no—
268#41—1161no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—291no—
273C2×Q8—291no—
274C2×Q8—581no—
275C2×Q8—582no—
276C2×Q8—1161no—
277C2×Q8C22×D2911yescharacteristic
278C2×Q8C22×D2911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—291no—
283C2×D4—581no—
284C2×D4—581no—
285C2×D4C22×D2911yescharacteristic
286C2×D4C22×D2911yescharacteristic
287C22×C4—21no—
288C22×C4—291no—
289C22×C4—581no—
290C22×C4—581no—
291C22×C4—581no—
292C22×C4C22×D2911yescharacteristic
293Q16—582no—
294Q16—582no—
295Q16—1161no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—582no—
300SD16—1161no—
301SD16C22⋊D2914yescomplemented
302M16—582no—
303C2×C8—22no—
304C2×C8—291no—
305C2×C8—291no—
306C2×C8C22×D2911yescharacteristic
307C2×C8C22×D2911yescharacteristic
308C4⋊C4—291no—
309C4⋊C4—291no—
310C4⋊C4—291no—
311C4⋊C4—581no—
312C4⋊C4—581no—
313C4⋊C4—581no—
314C4⋊C4—581no—
315C4⋊C4—581no—
316C4⋊C4—581no—
317C22⋊C4—291no—
318C22⋊C4—291no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C22⋊C4—581no—
322C22⋊C4—581no—
323C22⋊C4—581no—
324C22⋊C4—581no—
325C22⋊C4—581no—
326C42—291no—
327C42—581no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—291no—
334C23D4×D2911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—581no—
340Q8—581no—
341Q8—581no—
342Q8—581no—
343Q8—1162no—
344Q8C2×C22⋊D2912yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—582no—
350D4—1162no—
351D4—2321no—
352D4C2×C22⋊D2912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—291no—
359C2×C4—291no—
360C2×C4—291no—
361C2×C4—581no—
362C2×C4—581no—
363C2×C4—581no—
364C2×C4—581no—
365C2×C4—581no—
366C2×C4—581no—
367C2×C4—1162no—
368C2×C4—1162no—
369C2×C4—2321no—
370C2×C4D4×D2911yescharacteristic
371C2×C4C23×D2911yescharacteristic
372C8—21no—
373C8—581no—
374C8—581no—
375C8C2×C22⋊D2912yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—581no—
386C22—581no—
387C22—581no—
388C22#1174527712yescomplemented
389C22C2×D4×D2911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—581no—
394C4—581no—
395C4—581no—
396C4—1161no—
397C4—1161no—
398C4—1161no—
399C4—1161no—
400C4#1174535911yescharacteristic
401C4C22×C22⋊D2911yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—1161no—
406C2D4×C22⋊D2911yescharacteristic
407C2C2×#1174527711yescharacteristic
408C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×SD16×C29C2
socleC22×C29C22×D4
prime radical#14271807C2
hypercenterC22×SD16D29
hypocenterC29#3266
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11745277C2semidirect
2. Q8×C22⋊D29C2semidirect
4. #14271554C2semidirect
5. #14271406C2semidirect
6. #14271404C2semidirect
7. #14271383C2semidirect
8. #14271366C2semidirect
9. #14271322C2semidirect
10. #14271319C2semidirect
11. #14271314C2semidirect
12. #14271300C2semidirect
13. #14271264C2semidirect
14. #14271234C2semidirect
15. C22×SD16×C29C2semidirect
18. C2×Q8×D29C22semidirect
29. #11745308C22semidirect
30. Q8×Dic29C22semidirect
32. #11745306C22semidirect
33. C2×#90785C22semidirect
34. C2×#90785C22semidirect
48. C2×Dic116C22semidirect
49. C2×#90772C22semidirect
50. #11745183C22semidirect
51. #11745183C22semidirect
55. #11745168C22semidirect
56. #11745166C22semidirect
57. #11745164C22semidirect
58. #11745164C22semidirect
59. #11745163C22semidirect
60. #11745162C22semidirect
91. SD16×C29D4semidirect
181. C22×C29#137semidirect
199. C22×SD16D29semidirect
265. C29#3266semidirect
301. SD16C22⋊D29semidirect
388. C22#11745277semidirect

Maximal subgroups

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

subgroupindex
C2×#117452772
Q8×C22⋊D292
#142718072
#142715542
#142714062
#142714042
#142713832
#142713662
#142713222
#142713192
#142713142
#142713002
#142712642
#142712342
C22×SD16×C292
#326629