Finite Group Databasebeta

← #16828990

Subgroups — #16828990

Order 3712.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745273C211yesmaximal, characteristic, complemented
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271726C211yesmaximal, characteristic, complemented
4#14271635C211yesmaximal, characteristic, complemented
5#14271379C211yesmaximal, characteristic, complemented
6#14271378C211yesmaximal, characteristic, complemented
7#14271377C211yesmaximal, characteristic, complemented
8#14271376C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271356C211yesmaximal, characteristic, complemented
11#14271355C211yesmaximal, characteristic, complemented
12#14271188C211yesmaximal, characteristic, complemented
13#14271166C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic, complemented
21C29×#127C2211yescharacteristic, complemented
22C4×D4×C29C2211yescharacteristic, complemented
23#11745302C2211yescharacteristic, complemented
24#11745301—21no—
25#11745301—21no—
26#11745299—21no—
27#11745299—21no—
28#11745298C2211yescharacteristic, complemented
29D4×Dic29C2211yescharacteristic, complemented
30C2×#90783C2211yescharacteristic, complemented
31C2×#90782C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33C2×#90782C2211yescharacteristic, complemented
34C4×C22⋊D29—21no—
35C2×#90781—21no—
36#11745273—24no—
37D8×D29—24no—
38C2×D232C2211yescharacteristic
39C2×#90773C2211yescharacteristic, complemented
40C2×#90772C2211yescharacteristic
41C2×C8×D29C2211yescharacteristic
42#11745255C2211yescharacteristic, complemented
43#11745254C2211yescharacteristic
44#11745243—21no—
45C22⋊C4×D29—21no—
46#11745237C2211yescharacteristic, complemented
47C4×D116C2211yescharacteristic, complemented
48#11745234C2211yescharacteristic
49C29×C4⋊C8C2211yescharacteristic, complemented
50C29×#102C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745164C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58#11745158C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60C4⋊#6597C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C2×D4×C29C2311yescharacteristic
68C22×C4×C29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C22×Dic29—21no—
75C22×Dic29—21no—
76#90807—22no—
77#90807—22no—
78D4×D29—22no—
79D4×D29—22no—
80D4×D29—22no—
81D4×D29D414yescomplemented
82C2×D116C2311yescharacteristic
83C2×D116C2311yescharacteristic
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×C4×D29C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88D8×C29—22no—
89D8×C29—22no—
90C2×C8×C29C2311yescharacteristic
91C2×C8×C29C2311yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C22⋊C4×C29—21no—
94C42×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29—21no—
98#90783—22no—
99#90782—22no—
100#90782—22no—
101#90782—22no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781D411yescharacteristic
108#90781D411yescharacteristic
109C4⋊Dic29C2311yescharacteristic
110#90779D411yescharacteristic
111#90779D411yescharacteristic
112C4×Dic29—21no—
113C4×Dic29C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116D232—22no—
117#90773—22no—
118#90772—22no—
119C8×D29—22no—
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C22×D29—21no—
124C22×D29—24no—
125C22×D29—21no—
126C22×D29—42no—
127C22×D29—81no—
128C22×D29—81no—
129C22×D29—81no—
130C22×D29—81no—
131C22×D29C2×D411yescharacteristic
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—81no—
138D4×C29—81no—
139D4×C29C2×D412yes—
140C2×C4×C29—21no—
141C2×C4×C29—81no—
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2411yescharacteristic
145C22⋊D29—24no—
146C22⋊D29—42no—
147C22⋊D29—42no—
148C22⋊D29—81no—
149C22⋊D29—81no—
150C2×Dic29—21no—
151C2×Dic29—21no—
152C2×Dic29—42no—
153C2×Dic29—81no—
154C2×Dic29C2×D411yescharacteristic
155C2×Dic29C2×D411yescharacteristic
156C2×Dic29C2×D411yescharacteristic
157D116—21no—
158D116—21no—
159D116—21no—
160D116C2×D412yes—
161C4×D29—81no—
162C4×D29—81no—
163C4×D29C2×D412yes—
164C4×D29#4112yes—
165Dic58—21no—
166Dic58—21no—
167C8×C29—21no—
168C8×C29—21no—
169#6597—21no—
170#6597—21no—
171#3041—291nomaximal, Sylow
172C22×C29—22no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29C22×D411yescharacteristic
182C2×D29—21no—
183C2×D29—21no—
184C2×D29—22no—
185C2×D29—41no—
186C2×D29—41no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—41no—
190C2×D29—84no—
191C2×D29—84no—
192C2×D29#12112yes—
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—41no—
196C4×C29C22×D411yescharacteristic
197C4×C29C2×#4111yescharacteristic
198Dic29—21no—
199Dic29—21no—
200Dic29—41no—
201Dic29—41no—
202Dic29#12112yes—
203C2×AGL(1,ℤ/8)—291no—
204C22×D8—291no—
205#535—291no—
206#518—291no—
207#463—291no—
208#463—291no—
209#463—291no—
210#463—291no—
211#459—291no—
212#459—291no—
213#459—291no—
214#459D2911yescharacteristic, complemented
215#424—291no—
216#418—291no—
217#416—291no—
218C2×C29—42no—
219C2×C29—81no—
220C2×C29—81no—
221C2×C29C2×#12111yescharacteristic
222C2×C29#57611yescharacteristic
223C2×C29#57611yescharacteristic
224D29—22no—
225D29—42no—
226D29—81no—
227C2×#41—291no—
228C22×D4—291no—
229C22×D4—291no—
230AGL(1,ℤ/8)—584no—
231C2×SD16—291no—
232C2×SD16—291no—
233C2×D8—291no—
234C2×D8—291no—
235C2×D8—291no—
236C2×D8—291no—
237C2×D8—584no—
238C2×D8C2×D2911yescharacteristic
239C2×D8C2×D2911yescharacteristic, complemented
240C2×M16—291no—
241C22×C8—291no—
242#127—291no—
243#127C2×D2911yescharacteristic, complemented
244#124—291no—
245#124—291no—
246#121—581no—
247#121—581no—
248#120—581no—
249#120—581no—
250C4×D4—291no—
251C4×D4—291no—
252C4×D4—291no—
253C4×D4—581no—
254C4×D4—581no—
255C4×D4C2×D2911yescharacteristic, complemented
256#117—291no—
257#117—291no—
258C2×C22⋊C4—581no—
259C2×C22⋊C4—581no—
260C4⋊C8—291no—
261C4⋊C8—291no—
262C4⋊C8—291no—
263C4⋊C8C2×D2911yescharacteristic, complemented
264#103—291no—
265#103—291no—
266#102—291no—
267#102—291no—
268#102—291no—
269#102—291no—
270#102C2×D2911yescharacteristic, complemented
271#102C2×D2911yescharacteristic, complemented
272C29#304111yescharacteristic, complemented, Sylow
273C24—581no—
274C24—581no—
275#41—582no—
276#41—582no—
277C2×Q8—291no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—294no—
281C2×D4—291no—
282C2×D4—291no—
283C2×D4—582no—
284C2×D4—582no—
285C2×D4—582no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—581no—
289C2×D4—581no—
290C2×D4—581no—
291C2×D4C22×D2911yescharacteristic
292C2×D4C22×D2911yescharacteristic
293C2×D4C22×D2911yescharacteristic
294C22×C4—21no—
295C22×C4—291no—
296C22×C4—581no—
297C22×C4—581no—
298C22×C4—581no—
299C22×C4—581no—
300SD16—582no—
301SD16—582no—
302D8—22no—
303D8—22no—
304D8—582no—
305D8—582no—
306D8—582no—
307D8—582no—
308M16—582no—
309C2×C8—291no—
310C2×C8—291no—
311C2×C8—582no—
312C2×C8C22×D2911yescharacteristic
313C2×C8C22×D2911yescharacteristic
314C4⋊C4—291no—
315C4⋊C4—291no—
316C4⋊C4—291no—
317C4⋊C4C22×D2911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—291no—
320C22⋊C4—291no—
321C22⋊C4—581no—
322C22⋊C4—581no—
323C22⋊C4—581no—
324C22⋊C4—581no—
325C22⋊C4—581no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C42—291no—
330C42—581no—
331C42C22×D2911yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—291no—
336C23—584no—
337C23—581no—
338C23—581no—
339C23—1162no—
340C23—2321no—
341C23—2321no—
342C23—2321no—
343C23—2321no—
344Q8—581no—
345Q8—581no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—292no—
354D4—584no—
355D4—581no—
356D4—581no—
357D4—581no—
358D4—1162no—
359D4—1162no—
360D4—2321no—
361D4—2321no—
362D4D4×D2912yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—291no—
366C2×C4—292no—
367C2×C4—292no—
368C2×C4—291no—
369C2×C4—291no—
370C2×C4—581no—
371C2×C4—581no—
372C2×C4—1162no—
373C2×C4—2321no—
374C2×C4—2321no—
375C2×C4—2321no—
376C2×C4D4×D2911yescharacteristic
377C2×C4D4×D2911yescharacteristic
378C2×C4C23×D2911yescharacteristic
379C8—21no—
380C8—21no—
381C8—581no—
382C8—581no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—292no—
393C22—581no—
394C22—581no—
395C22—582no—
396C22—1161no—
397C22—1161no—
398C22—1161no—
399C22—1161no—
400C22—1161no—
401C22—2324no—
402C22—2324no—
403C22C2×D4×D2911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—292no—
408C4—581no—
409C4—581no—
410C4—1161no—
411C4—1161no—
412C4C2×D4×D2911yescharacteristic
413C4#41×D2911yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—582no—
418C2—1162no—
419C2—2321no—
420C2#121×D2911yescharacteristic
421C2#1427196411yescharacteristic
422C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3041
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C2×D8×D29C2semidirect
3. #14271726C2semidirect
4. #14271635C2semidirect
5. #14271379C2semidirect
6. #14271378C2semidirect
7. #14271377C2semidirect
8. #14271376C2semidirect
9. #14271357C2semidirect
10. #14271356C2semidirect
11. #14271355C2semidirect
12. #14271188C2semidirect
13. #14271166C2semidirect
14. #14271156C2semidirect
15. C29×#459C2semidirect
20. C2×D8×C29C22semidirect
21. C29×#127C22semidirect
22. C4×D4×C29C22semidirect
23. #11745302C22semidirect
28. #11745298C22semidirect
29. D4×Dic29C22semidirect
30. C2×#90783C22semidirect
33. C2×#90782C22semidirect
39. C2×#90773C22semidirect
42. #11745255C22semidirect
46. #11745237C22semidirect
47. C4×D116C22semidirect
49. C29×C4⋊C8C22semidirect
50. C29×#102C22semidirect
51. C29×#102C22semidirect
52. #11745180C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745164C22semidirect
56. #11745162C22semidirect
57. #11745162C22semidirect
58. #11745158C22semidirect
59. #11745157C22semidirect
60. C4⋊#6597C22semidirect
81. D4×D29D4semidirect
214. #459D29semidirect
239. C2×D8C2×D29semidirect
243. #127C2×D29semidirect
255. C4×D4C2×D29semidirect
263. C4⋊C8C2×D29semidirect
270. #102C2×D29semidirect
271. #102C2×D29semidirect
272. C29#3041semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
C2×D8×D292
#142717262
#142716352
#142713792
#142713782
#142713772
#142713762
#142713572
#142713562
#142713552
#142711882
#142711662
#142711562
C29×#4592
#304129