Finite Group Databasebeta

← #14575347

Subgroups — #14575347

Order 2432.

504 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×#10597350C211yesmaximal, characteristic, complemented
2C22×#64516C211yesmaximal, characteristic, complemented
3#11927203C211yesmaximal, characteristic, complemented
4#11927190C211yesmaximal, characteristic, complemented
5#11926928C211yesmaximal, characteristic, complemented
6#11926773C211yesmaximal, characteristic, complemented
7#11926773C211yesmaximal, characteristic, complemented
8#11926767C211yesmaximal, characteristic, complemented
9#11926760C211yesmaximal, characteristic, complemented
10#11926708C211yesmaximal, characteristic, complemented
11#11926702C211yesmaximal, characteristic, complemented
12#11926691C211yesmaximal, characteristic, complemented
13#11926680C211yesmaximal, characteristic, complemented
14C4×#64516C211yesmaximal, characteristic, complemented
15C8×D4×C19C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C2×#64541C2211yescharacteristic, complemented
18C22×D76C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C22×C8×C19C2211yescharacteristic
21C22×C8×C19C2211yescharacteristic, complemented
22C4×D4×C19C2211yescharacteristic
23#10597385—21no—
24#10597383—21no—
25#10597376C2211yescharacteristic
26#10597376C2211yescharacteristic
27#10597370C2211yescharacteristic
28#10597370C2211yescharacteristic, complemented
29C2×Dic76C2211yescharacteristic, complemented
30C2×Dic76C2211yescharacteristic, complemented
31#10597350—24no—
32C2×D152C2211yescharacteristic
33C2×D152C2211yescharacteristic
34C2×#64516—24no—
35C2×#64516C2211yescharacteristic
36C2×#64516C2211yescharacteristic
37C2×#64516C2211yescharacteristic
38C2×#64516C2211yescharacteristic
39C2×#64516C2211yescharacteristic, complemented
40#10597342—21no—
41#10597340—21no—
42#10597331—21no—
43#10597330—21no—
44(C22⋊D19)⋊C4—21no—
45C22⋊C4×D19—21no—
46#10597321C2211yescharacteristic
47#10597321C2211yescharacteristic, complemented
48C4×D76C2211yescharacteristic
49C4×Dic38C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×C22⋊C8C2211yescharacteristic
52C19×C22⋊C8C2211yescharacteristic, complemented
53C4×C8×C19C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic
55#10597278C2211yescharacteristic
56#10597278C2211yescharacteristic, complemented
57#10597274C2211yescharacteristic, complemented
58#10597273C2211yescharacteristic, complemented
59#10597273C2211yescharacteristic, complemented
60#10597273C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×D4×C19D411yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C22×Dic19—21no—
70#64541—22no—
71#64541—22no—
72#64541—41no—
73#64541—41no—
74C2×D76—22no—
75C2×D76—21no—
76C2×D76—41no—
77C2×D76C2311yescharacteristic
78C2×D76C2311yescharacteristic
79C2×D76C2311yescharacteristic
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×Dic38—22no—
84C2×Dic38—21no—
85C2×Dic38—41no—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88C2×Dic38C2311yescharacteristic
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C2×C8×C19C2311yescharacteristic
94C2×C8×C19C2311yescharacteristic
95C4⋊C4×C19D411yescharacteristic
96C22⋊C4×C19D411yescharacteristic
97C22⋊C4×C19D411yescharacteristic
98C42×C19C2311yescharacteristic
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108C4⋊Dic19C2311yescharacteristic
109C4⋊Dic19C2311yescharacteristic
110Dic19⋊C4—21no—
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113C4×Dic19—21no—
114Dic76—22no—
115Dic76—41no—
116D152—22no—
117D152—41no—
118#64516—22no—
119#64516—22no—
120#64516—22no—
121#64516—22no—
122#64516D414yescomplemented
123C23×C19C2×D411yescharacteristic
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—81no—
131D4×C19—22no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2411yescharacteristic
141C22⋊D19—42no—
142C22⋊D19—42no—
143C22⋊D19—42no—
144C22⋊D19—81no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—42no—
151D76—21no—
152D76—21no—
153D76—21no—
154D76—21no—
155D76—21no—
156D76—42no—
157D76C2×D412yes—
158C4×D19—42no—
159C4×D19—42no—
160C4×D19—81no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—21no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C8×C19—21no—
169C8×C19—21no—
170C8×C19—21no—
171C8×C19C2×D412yes—
172#3282—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19#13512yescomplemented
179C22×C19C22×D411yescharacteristic
180C2×D19—22no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—84no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19C22×D411yescharacteristic
195C4×C19H(5,𝔽2)11yescharacteristic
196Dic19—22no—
197Dic19—41no—
198Dic19—41no—
199Dic19—41no—
200Dic19—41no—
201C2×#135—191no—
202C22×SD16—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#465—191no—
207#465—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#451—191no—
212#449—191no—
213#447—191no—
214C4×SD16—191no—
215C8×D4D1911yescharacteristic, complemented
216C2×C19—22no—
217C2×C19—41no—
218C2×C19D4211yescharacteristic
219C2×C19C2×#13511yescharacteristic
220C2×C19#57711yescharacteristic
221D19—42no—
222D19—81no—
223D19—81no—
224C2×#41—191no—
225C2×#41—191no—
226C22×Q8—191no—
227C22×D4—191no—
228#135—384no—
229C2×Q16—191no—
230C2×Q16—191no—
231C2×SD16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—191no—
236C2×SD16—384no—
237C2×D8—191no—
238C2×D8—191no—
239C22×C8C2×D1911yescharacteristic
240C22×C8C2×D1911yescharacteristic, complemented
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—191no—
247C22⋊Q8—381no—
248#121—191no—
249#121—191no—
250#121—381no—
251#121—381no—
252#120—381no—
253C4×Q8—191no—
254C4×D4—191no—
255C4×D4—381no—
256C4×D4C2×D1911yescharacteristic
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8C2×D1911yescharacteristic, complemented
260#103—191no—
261#103—191no—
262#103—191no—
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8C2×D1911yescharacteristic
267C22⋊C8C2×D1911yescharacteristic, complemented
268C4×C8C2×D1911yescharacteristic, complemented
269C19#328211yescharacteristic, complemented, Sylow
270C24—381no—
271#41—382no—
272#41—382no—
273#41—761no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—191no—
277C2×Q8—191no—
278C2×Q8—382no—
279C2×Q8—381no—
280C2×Q8—761no—
281C2×D4—191no—
282C2×D4—191no—
283C2×D4—191no—
284C2×D4—382no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—761no—
291C2×D4D7611yescharacteristic
292C22×C4—381no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4C22×D1911yescharacteristic
297C22×C4C22×D1911yescharacteristic
298Q16—382no—
299Q16—761no—
300SD16—194no—
301SD16—382no—
302SD16—382no—
303SD16—382no—
304SD16—382no—
305D8—382no—
306D8—761no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C22×D1911yescharacteristic
310C2×C8C22×D1911yescharacteristic
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—191no—
314C4⋊C4—191no—
315C4⋊C4—381no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4D7611yescharacteristic
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4D7611yescharacteristic
329C22⋊C4D7611yescharacteristic
330C42—381no—
331C42C22×D1911yescharacteristic
332C23—381no—
333C23—381no—
334C23—381no—
335C23—762no—
336C23—762no—
337C23—1521no—
338C23C2×D7611yescharacteristic
339C23C2×D7611yescharacteristic
340Q8—192no—
341Q8—381no—
342Q8—381no—
343Q8—381no—
344Q8—381no—
345Q8—381no—
346Q8—762no—
347D4—22no—
348D4—192no—
349D4—381no—
350D4—381no—
351D4—381no—
352D4—381no—
353D4—381no—
354D4—762no—
355D4—762no—
356D4—762no—
357D4—762no—
358D4—1521no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—762no—
369C2×C4—762no—
370C2×C4—762no—
371C2×C4—1521no—
372C2×C4C2×D7611yescharacteristic
373C2×C4C2×D7611yescharacteristic
374C2×C4C2×D7611yescharacteristic
375C2×C4C2×D7611yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D1912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—382no—
387C22—761no—
388C22—761no—
389C22—761no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—1524no—
396C22#1059735012yescomplemented
397C22C22×D7611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—382no—
403C4—761no—
404C4—761no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743511yescharacteristic
409C2—22no—
410C2—41no—
411C2—762no—
412C2—1521no—
413C2—1521no—
414C2D4×D7611yescharacteristic
415C2C2×#1059735011yescharacteristic
416C2#1192735611yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC8×D4×C19C2
socleC22×C19C22×D4
hypercenterC8×D4D19
hypocenterC19#3282
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10597350C2semidirect
2. C22×#64516C2semidirect
3. #11927203C2semidirect
4. #11927190C2semidirect
5. #11926928C2semidirect
6. #11926773C2semidirect
7. #11926773C2semidirect
8. #11926767C2semidirect
9. #11926760C2semidirect
10. #11926708C2semidirect
11. #11926702C2semidirect
12. #11926691C2semidirect
13. #11926680C2semidirect
14. C4×#64516C2semidirect
15. C8×D4×C19C2semidirect
17. C2×#64541C22semidirect
21. C22×C8×C19C22semidirect
28. #10597370C22semidirect
29. C2×Dic76C22semidirect
30. C2×Dic76C22semidirect
39. C2×#64516C22semidirect
47. #10597321C22semidirect
49. C4×Dic38C22semidirect
50. C19×C4⋊C8C22semidirect
52. C19×C22⋊C8C22semidirect
53. C4×C8×C19C22semidirect
56. #10597278C22semidirect
57. #10597274C22semidirect
58. #10597273C22semidirect
59. #10597273C22semidirect
60. #10597273C22semidirect
122. #64516D4semidirect
178. C22×C19#135semidirect
215. C8×D4D19semidirect
240. C22×C8C2×D19semidirect
259. C4⋊C8C2×D19semidirect
267. C22⋊C8C2×D19semidirect
268. C4×C8C2×D19semidirect
269. C19#3282semidirect
396. C22#10597350semidirect

Maximal subgroups

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

subgroupindex
C2×#105973502
C22×#645162
#119272032
#119271902
#119269282
#119267732
#119267672
#119267602
#119267082
#119267022
#119266912
#119266802
C4×#645162
C8×D4×C192
#328219