Finite Group Databasebeta

← #14575166

Subgroups — #14575166

Order 2432.

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×#10597360C211yesmaximal, characteristic, complemented
2C2×#10597362C211yesmaximal, characteristic, complemented
3#11927197C211yesmaximal, characteristic, complemented
4#11927189C211yesmaximal, characteristic, complemented
5#11926936C211yesmaximal, characteristic, complemented
6#11926801C211yesmaximal, characteristic, complemented
7#11926776C211yesmaximal, characteristic, complemented
8#11926760C211yesmaximal, characteristic, complemented
9#11926709C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926692C211yesmaximal, characteristic, complemented
13#11926654C211yesmaximal, characteristic, complemented
14#11926614C211yesmaximal, characteristic, complemented
15C19×#461C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64545C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C2×SD16×C19C2211yescharacteristic
22C19×C4⋊Q8C2211yescharacteristic, complemented
23C4×D4×C19C2211yescharacteristic
24#10597392C2211yescharacteristic
25#10597392C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27C2×#64528C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic
29C2×#64527C2211yescharacteristic
30C2×#64525C2211yescharacteristic
31#10597376—21no—
32C2×(C2×D19)⋊C4—21no—
33#10597362—24no—
34#10597360—24no—
35C2×D152C2211yescharacteristic
36C2×#64516C2211yescharacteristic, complemented
37C2×#64515C2211yescharacteristic
38C2×C8×D19C2211yescharacteristic, complemented
39#10597343C2211yescharacteristic
40#10597341—21no—
41#10597341C2211yescharacteristic
42#10597340—21no—
43#10597340—21no—
44C4⋊C4×D19—21no—
45#10597332—21no—
46#10597328—21no—
47#10597321C2211yescharacteristic
48C4×D76C2211yescharacteristic
49C4×D76C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#103C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic, complemented
59#10597265C2211yescharacteristic, complemented
60#10597260C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69#64545—22no—
70#64545—22no—
71#64545—41no—
72#64545—41no—
73#64543—22no—
74#64543—41no—
75D4×D19—22no—
76D4×D19—41no—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76D411yescharacteristic
81C2×D76C2311yescharacteristic
82C2×D76C2311yescharacteristic
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×C4×D19C2311yescharacteristic
87C2×C4×D19C2311yescharacteristic
88C2×Dic38C2311yescharacteristic
89SD16×C19—22no—
90SD16×C19—22no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19C2311yescharacteristic
96C22⋊C4×C19—21no—
97C42×C19C2311yescharacteristic
98#64528—22no—
99#64528—41no—
100#64527—22no—
101#64527—41no—
102#64525D414yescomplemented
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—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4D411yescharacteristic
111(C2×D19)⋊C4D411yescharacteristic
112C4⋊Dic19—21no—
113C4⋊Dic19D411yescharacteristic
114C4⋊Dic19C2311yescharacteristic
115Dic19⋊C4—21no—
116Dic19⋊C4—21no—
117C2×C19⋊C8C2311yescharacteristic
118C2×C19⋊C8C2311yescharacteristic
119D152—22no—
120#64516—22no—
121#64515—22no—
122C8×D19—22no—
123C23×C19—21no—
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—81no—
129C22×D19C2×D411yescharacteristic
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135D4×C19—21no—
136D4×C19C2×D412yes—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—81no—
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2×D411yescharacteristic
143C2×C4×C19C2411yescharacteristic
144C22⋊D19—42no—
145C22⋊D19—42no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—42no—
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—21no—
152D76—21no—
153D76—21no—
154D76—41no—
155D76—42no—
156D76—42no—
157D76—81no—
158D76C2×D412yes—
159C4×D19—21no—
160C4×D19—21no—
161C4×D19—21no—
162C4×D19—21no—
163C4×D19—42no—
164C4×D19—42no—
165C4×D19—42no—
166Dic38—21no—
167Dic38—21no—
168C8×C19—21no—
169C8×C19—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3267—191nomaximal, Sylow
173C22×C19—22no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19C22×D411yescharacteristic
177C2×D19—21no—
178C2×D19—21no—
179C2×D19—22no—
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—21no—
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—41no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19C22×D411yescharacteristic
196C4×C19H(5,𝔽2)11yescharacteristic
197Dic19—21no—
198Dic19—21no—
199Dic19—41no—
200Dic19—41no—
201C2×AGL(1,ℤ/8)—191no—
202C2×#135—191no—
203#547—191no—
204#546—191no—
205#497—191no—
206#470—191no—
207#465—191no—
208#463—191no—
209#461D1911yescharacteristic, complemented
210#452—191no—
211#452—191no—
212#450—191no—
213#449—191no—
214#442—191no—
215#435—191no—
216C2×C19—42no—
217C2×C19D4211yescharacteristic
218C2×C19#57511yescharacteristic
219C2×C19#57711yescharacteristic
220D19—41no—
221D19—41no—
222D19—42no—
223D19—81no—
224C2×#41—191no—
225C2×#41—191no—
226C2×#41—191no—
227C22×D4—191no—
228AGL(1,ℤ/8)—384no—
229#135—384no—
230C2×Q16—191no—
231C2×Q16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16C2×D1911yescharacteristic
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8—191no—
239C2×M16—191no—
240C22×C8—191no—
241C4⋊Q8C2×D1911yescharacteristic, complemented
242#124—191no—
243#123—381no—
244#123—381no—
245#123—381no—
246C22⋊Q8—191no—
247C22⋊Q8—191no—
248C22⋊Q8—191no—
249#121—191no—
250#121—381no—
251#121—381no—
252#120—381no—
253C4×D4—191no—
254C4×D4—191no—
255C4×D4C2×D1911yescharacteristic
256C2×C4⋊C4—381no—
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8C2×D1911yescharacteristic, complemented
260#103—191no—
261#103C2×D1911yescharacteristic, complemented
262#103C2×D1911yescharacteristic, complemented
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8—191no—
267C22⋊C8—191no—
268#97—191no—
269C19#326711yescharacteristic, complemented, Sylow
270C24—381no—
271#41—382no—
272#41—382no—
273#41—382no—
274#41—761no—
275#41—761no—
276#41—761no—
277C2×Q8—191no—
278C2×Q8C22×D1911yescharacteristic
279C2×Q8C22×D1911yescharacteristic
280C2×D4—191no—
281C2×D4—191no—
282C2×D4—191no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—382no—
288C2×D4—381no—
289C2×D4—761no—
290C2×D4C22×D1911yescharacteristic
291C22×C4—21no—
292C22×C4—191no—
293C22×C4—191no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298Q16—382no—
299Q16—761no—
300SD16—22no—
301SD16—22no—
302SD16—382no—
303SD16—382no—
304SD16—761no—
305D8—194no—
306D8—382no—
307M16—382no—
308C2×C8—191no—
309C2×C8—191no—
310C2×C8—382no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—191no—
316C4⋊C4—191no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C4⋊C4C22×D1911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—191no—
323C22⋊C4—191no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C22⋊C4—381no—
331C42C22×D1911yescharacteristic
332C23—21no—
333C23—191no—
334C23—191no—
335C23—381no—
336C23—381no—
337C23—762no—
338C23—762no—
339C23—1521no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—381no—
345Q8—381no—
346D4—21no—
347D4—192no—
348D4—381no—
349D4—381no—
350D4—381no—
351D4—761no—
352D4—762no—
353D4—762no—
354D4—762no—
355D4—762no—
356D4—1521no—
357D4D4×D1912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—191no—
363C2×C4—191no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—762no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4D4×D1911yescharacteristic
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—21no—
379C8—192no—
380C8—381no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—381no—
385C22—381no—
386C22—381no—
387C22—381no—
388C22—381no—
389C22—381no—
390C22—382no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—381no—
404C4—381no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743511yescharacteristic
409C2—42no—
410C2—761no—
411C2—761no—
412C2—762no—
413C2—1521no—
414C2#1192717811yescharacteristic
415C2#1192734311yescharacteristic
416C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#461C2
socleC22×C19C22×D4
hypercenter#461D19
hypocenterC19#3267
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597362C2semidirect
3. #11927197C2semidirect
4. #11927189C2semidirect
5. #11926936C2semidirect
6. #11926801C2semidirect
7. #11926776C2semidirect
8. #11926760C2semidirect
9. #11926709C2semidirect
10. #11926703C2semidirect
11. #11926693C2semidirect
12. #11926692C2semidirect
13. #11926654C2semidirect
14. #11926614C2semidirect
15. C19×#461C2semidirect
17. C2×#64545C22semidirect
22. C19×C4⋊Q8C22semidirect
25. #10597392C22semidirect
26. C2×#64528C22semidirect
27. C2×#64528C22semidirect
36. C2×#64516C22semidirect
38. C2×C8×D19C22semidirect
49. C4×D76C22semidirect
50. C19×C4⋊C8C22semidirect
51. C19×#103C22semidirect
52. C19×#103C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597273C22semidirect
58. #10597266C22semidirect
59. #10597265C22semidirect
60. #10597260C22semidirect
102. #64525D4semidirect
209. #461D19semidirect
241. C4⋊Q8C2×D19semidirect
259. C4⋊C8C2×D19semidirect
261. #103C2×D19semidirect
262. #103C2×D19semidirect
269. C19#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
C2×#105973622
#119271972
#119271892
#119269362
#119268012
#119267762
#119267602
#119267092
#119267032
#119266932
#119266922
#119266542
#119266142
C19×#4612
#326719