Finite Group Databasebeta

← #16831018

Subgroups — #16831018

Order 3712.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745311C211yesmaximal, characteristic, complemented
2C2×#11745312C211yesmaximal, characteristic, complemented
3#14271809C211yesmaximal, characteristic, complemented
4#14271555C211yesmaximal, characteristic, complemented
5#14271419C211yesmaximal, characteristic, complemented
6#14271394C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271365C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271313C211yesmaximal, characteristic, complemented
12#14271308C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14#14271235C211yesmaximal, characteristic, complemented
15C29×#547C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C29×C4⋊Q8C2211yescharacteristic, complemented
21C29×#123—21no—
22C29×#123—21no—
23C29×C22⋊Q8C2211yescharacteristic
24C29×C22⋊Q8C2211yescharacteristic, complemented
25C29×#121—21no—
26C4×D4×C29C2211yescharacteristic
27C4×D4×C29C2211yescharacteristic, complemented
28C2×C4⋊C4×C29—21no—
29#11745312—24no—
30#11745311—24no—
31C2×#90785C2211yescharacteristic, complemented
32C2×#90785C2211yescharacteristic, complemented
33C2×#90784C2211yescharacteristic
34C2×#90784C2211yescharacteristic
35C2×#90784C2211yescharacteristic
36C2×#90784C2211yescharacteristic
37#11745299—21no—
38C2×#90783C2211yescharacteristic, complemented
39C2×#90782C2211yescharacteristic
40C2×#90782C2211yescharacteristic
41#11745292C2211yescharacteristic
42#11745286C2211yescharacteristic
43C2×#90777C2211yescharacteristic
44C22×#6597C2211yescharacteristic, complemented
45#11745256—21no—
46#11745246—21no—
47C22⋊C4×D29—21no—
48#11745237C2211yescharacteristic
49C4×D116C2211yescharacteristic
50#11745183C2211yescharacteristic, complemented
51#11745183C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic, complemented
59C4⋊#6597C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62#41×C29—22no—
63#41×C29—22no—
64#41×C29—41no—
65#41×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×C29—21no—
75C22×C4×C29C2311yescharacteristic
76C22×C4×C29C2311yescharacteristic
77C2×C22⋊D29—21no—
78C2×C22⋊D29—21no—
79#90805—22no—
80#90805—41no—
81C2×D116—22no—
82C2×D116—21no—
83C2×D116—41no—
84C2×D116C2311yescharacteristic
85C2×D116C2311yescharacteristic
86C2×C4×D29—21no—
87C2×C4×D29—21no—
88C2×Dic58C2311yescharacteristic
89C4⋊C4×C29—21no—
90C4⋊C4×C29—21no—
91C4⋊C4×C29—21no—
92C4⋊C4×C29—21no—
93C4⋊C4×C29D411yescharacteristic
94C4⋊C4×C29C2311yescharacteristic
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29D411yescharacteristic
99C22⋊C4×C29D411yescharacteristic
100C42×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102#90785—22no—
103#90785—41no—
104#90784—22no—
105#90784—22no—
106#90784—22no—
107#90784—41no—
108#90783—22no—
109#90782—22no—
110#90782D414yescomplemented
111#90781—21no—
112#90781—21no—
113#90781—21no—
114#90781—21no—
115C4⋊Dic29C2311yescharacteristic
116#90779—21no—
117#90777—22no—
118C2×#6597—22no—
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C23×C29C2×D411yescharacteristic
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—81no—
131Q8×C29—21no—
132Q8×C29—21no—
133Q8×C29—21no—
134Q8×C29—21no—
135D4×C29—21no—
136D4×C29—41no—
137D4×C29—42no—
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—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—42no—
148C2×C4×C29—42no—
149C2×C4×C29—42no—
150C2×C4×C29C2×D411yescharacteristic
151C2×C4×C29C2×D411yescharacteristic
152C2×C4×C29C2×D411yescharacteristic
153C2×C4×C29C2×D411yescharacteristic
154C2×C4×C29C2411yescharacteristic
155C22⋊D29—42no—
156C22⋊D29—81no—
157C2×Dic29—21no—
158C2×Dic29—21no—
159D116—21no—
160D116—21no—
161D116—21no—
162D116—42no—
163D116C2×D412yes—
164C4×D29—42no—
165C4×D29—81no—
166Dic58—21no—
167Dic58—21no—
168#6597—21no—
169#6597—21no—
170#6597—21no—
171#6597C2×D412yes—
172#3267—291nomaximal, Sylow
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—22no—
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29C22×D411yescharacteristic
183C2×D29—22no—
184C2×D29—41no—
185C2×D29—41no—
186C2×D29—41no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—84no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—21no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—41no—
197C4×C29C22×D411yescharacteristic
198C4×C29H(5,𝔽2)11yescharacteristic
199Dic29—41no—
200Dic29—41no—
201C2×AGL(1,ℤ/8)—291no—
202C2×#135—291no—
203#547D2911yescharacteristic, complemented
204#546—291no—
205#497—291no—
206#470—291no—
207#465—291no—
208#463—291no—
209#461—291no—
210#452—291no—
211#452—291no—
212#450—291no—
213#449—291no—
214#442—291no—
215#435—291no—
216C2×C29—41no—
217C2×C29—41no—
218C2×C29—42no—
219C2×C29D4211yescharacteristic
220C2×C29#57511yescharacteristic
221C2×C29#57711yescharacteristic
222D29—42no—
223D29—81no—
224C2×#41—291no—
225C2×#41C2×D2911yescharacteristic
226C2×#41C2×D2911yescharacteristic, complemented
227C22×D4—291no—
228AGL(1,ℤ/8)—584no—
229#135—584no—
230C2×Q16—291no—
231C2×Q16—291no—
232C2×SD16—291no—
233C2×SD16—291no—
234C2×SD16—291no—
235C2×SD16—291no—
236C2×SD16—291no—
237C2×D8—291no—
238C2×D8—291no—
239C2×M16—291no—
240C22×C8—291no—
241C4⋊Q8C2×D2911yescharacteristic, complemented
242#124—291no—
243#123—21no—
244#123—21no—
245#123—581no—
246C22⋊Q8—291no—
247C22⋊Q8C2×D2911yescharacteristic
248C22⋊Q8C2×D2911yescharacteristic, complemented
249#121—21no—
250#121—291no—
251#121—581no—
252#120—581no—
253C4×D4—291no—
254C4×D4C2×D2911yescharacteristic
255C4×D4C2×D2911yescharacteristic, complemented
256C2×C4⋊C4—21no—
257C2×C22⋊C4—581no—
258#106—291no—
259C4⋊C8—291no—
260#103—291no—
261#103—291no—
262#103—291no—
263#102—291no—
264#102—291no—
265#102—291no—
266C22⋊C8—291no—
267C22⋊C8—291no—
268#97—291no—
269C29#326711yescharacteristic, complemented, Sylow
270C24—581no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—582no—
276#41—1161no—
277C2×Q8—291no—
278C2×Q8C22×D2911yescharacteristic
279C2×Q8C22×D2911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—291no—
283C2×D4—291no—
284C2×D4—582no—
285C2×D4—581no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—1161no—
289C2×D4C22⋊D2911yescharacteristic
290C2×D4C22×D2911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—581no—
295C22×C4—581no—
296C22×C4C22×D2911yescharacteristic
297C22×C4C22×D2911yescharacteristic
298Q16—582no—
299Q16—1161no—
300SD16—582no—
301SD16—582no—
302SD16—582no—
303SD16—582no—
304SD16—1161no—
305D8—294no—
306D8—582no—
307M16—582no—
308C2×C8—291no—
309C2×C8—291no—
310C2×C8—291no—
311C2×C8—291no—
312C2×C8—582no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—291no—
318C4⋊C4—581no—
319C4⋊C4C22⋊D2911yescharacteristic
320C4⋊C4C22×D2911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—581no—
325C22⋊C4—581no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C22⋊C4C22⋊D2911yescharacteristic
330C22⋊C4C22⋊D2911yescharacteristic
331C42C22×D2911yescharacteristic
332C23—21no—
333C23—581no—
334C23—581no—
335C23—1162no—
336C23—1162no—
337C23—2321no—
338C23C2×C22⋊D2911yescharacteristic
339C23C2×C22⋊D2911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—581no—
345Q8—581no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—292no—
351D4—581no—
352D4—581no—
353D4—581no—
354D4—1162no—
355D4—1162no—
356D4—2321no—
357D4D4×D2912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—581no—
369C2×C4—581no—
370C2×C4—1162no—
371C2×C4—2321no—
372C2×C4C2×C22⋊D2911yescharacteristic
373C2×C4C2×C22⋊D2911yescharacteristic
374C2×C4C2×C22⋊D2911yescharacteristic
375C2×C4C2×C22⋊D2911yescharacteristic
376C2×C4C23×D2911yescharacteristic
377C8—292no—
378C8—581no—
379C8—581no—
380C8—581no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—582no—
391C22—1161no—
392C22—1161no—
393C22—1161no—
394C22—1161no—
395C22—1161no—
396C22—2324no—
397C22C22×C22⋊D2911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—1161no—
406C4—1161no—
407C4C2×D4×D2911yescharacteristic
408C4#1174535911yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—1162no—
413C2—2321no—
414C2D4×C22⋊D2911yescharacteristic
415C2#1427196111yescharacteristic
416C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#547C2
socleC22×C29C22×D4
hypercenter#547D29
hypocenterC29#3267
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#11745311C2semidirect
2. C2×#11745312C2semidirect
3. #14271809C2semidirect
4. #14271555C2semidirect
5. #14271419C2semidirect
6. #14271394C2semidirect
7. #14271378C2semidirect
8. #14271365C2semidirect
9. #14271325C2semidirect
10. #14271323C2semidirect
11. #14271313C2semidirect
12. #14271308C2semidirect
13. #14271273C2semidirect
14. #14271235C2semidirect
15. C29×#547C2semidirect
17. C2×#41×C29C22semidirect
20. C29×C4⋊Q8C22semidirect
24. C29×C22⋊Q8C22semidirect
27. C4×D4×C29C22semidirect
31. C2×#90785C22semidirect
32. C2×#90785C22semidirect
38. C2×#90783C22semidirect
44. C22×#6597C22semidirect
50. #11745183C22semidirect
51. #11745183C22semidirect
52. #11745180C22semidirect
54. C22⋊#6597C22semidirect
55. #11745158C22semidirect
58. #11745156C22semidirect
59. C4⋊#6597C22semidirect
60. #11745151C22semidirect
110. #90782D4semidirect
203. #547D29semidirect
226. C2×#41C2×D29semidirect
241. C4⋊Q8C2×D29semidirect
248. C22⋊Q8C2×D29semidirect
255. C4×D4C2×D29semidirect
269. C29#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#117453112
C2×#117453122
#142718092
#142715552
#142714192
#142713942
#142713782
#142713652
#142713252
#142713232
#142713132
#142713082
#142712732
#142712352
C29×#5472
#326729