Finite Group Databasebeta

← #14575180

Subgroups — #14575180

Order 2432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597354C211yesmaximal, characteristic, complemented
2C2×#10597350C211yesmaximal, characteristic, complemented
3#11927215C211yesmaximal, characteristic, complemented
4#11927190C211yesmaximal, characteristic, complemented
5#11926933C211yesmaximal, characteristic, complemented
6#11926790C211yesmaximal, characteristic, complemented
7#11926780C211yesmaximal, characteristic, complemented
8#11926767C211yesmaximal, characteristic, complemented
9#11926740C211yesmaximal, characteristic, complemented
10#11926708C211yesmaximal, characteristic, complemented
11#11926691C211yesmaximal, characteristic, complemented
12#11926691C211yesmaximal, characteristic, complemented
13#11926680C211yesmaximal, characteristic, complemented
14#11926646C211yesmaximal, characteristic, complemented
15C19×#435C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C2×#64541C2211yescharacteristic, complemented
19C22×D76C2211yescharacteristic
20C2×M16×C19C2211yescharacteristic
21C22×C8×C19C2211yescharacteristic, complemented
22C4×D4×C19C2211yescharacteristic
23#10597386—21no—
24#10597383—21no—
25#10597376C2211yescharacteristic
26#10597376C2211yescharacteristic
27#10597376C2211yescharacteristic, complemented
28#10597370C2211yescharacteristic
29#10597354—24no—
30C2×Dic76C2211yescharacteristic, complemented
31#10597350—24no—
32C2×D152C2211yescharacteristic
33C2×D152C2211yescharacteristic
34C2×D152C2211yescharacteristic
35C2×D152C2211yescharacteristic
36C2×#64516C2211yescharacteristic
37C2×#64516C2211yescharacteristic
38C2×#64516C2211yescharacteristic, complemented
39C2×#64516C2211yescharacteristic, complemented
40#10597340—21no—
41#10597339—21no—
42#10597330—21no—
43#10597330—21no—
44#10597330—21no—
45C22⋊C4×D19—21no—
46#10597321C2211yescharacteristic
47#10597320C2211yescharacteristic, complemented
48C4×D76C2211yescharacteristic
49C4×Dic38C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×C22⋊C8C2211yescharacteristic
52C19×C22⋊C8C2211yescharacteristic, complemented
53C19×#97C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic
55#10597278C2211yescharacteristic
56#10597278C2211yescharacteristic, complemented
57#10597278C2211yescharacteristic, complemented
58#10597275C2211yescharacteristic, 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—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71#64541—22no—
72#64541—22no—
73#64541—22no—
74#64541—41no—
75#64541—41no—
76#64541—41no—
77C2×D76—22no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76—41no—
82C2×D76C2311yescharacteristic
83C2×D76C2311yescharacteristic
84C2×D76C2311yescharacteristic
85C2×D76C2311yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×C4×D19—21no—
90C2×Dic38C2311yescharacteristic
91C2×Dic38C2311yescharacteristic
92M16×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C2×C8×C19C2311yescharacteristic
97C2×C8×C19C2311yescharacteristic
98C4⋊C4×C19D411yescharacteristic
99C22⋊C4×C19D411yescharacteristic
100C22⋊C4×C19D411yescharacteristic
101C42×C19C2311yescharacteristic
102C22⋊Dic19—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—
108(C2×D19)⋊C4—21no—
109C4⋊Dic19C2311yescharacteristic
110C4⋊Dic19C2311yescharacteristic
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113C4×Dic19—21no—
114Dic76—22no—
115D152—22no—
116D152—22no—
117D152—22no—
118D152—41no—
119#64516—22no—
120#64516—22no—
121#64516—41no—
122#64516D414yescomplemented
123C23×C19C2×D411yescharacteristic
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—21no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—81no—
132D4×C19—41no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2411yescharacteristic
142C22⋊D19—42no—
143C22⋊D19—42no—
144C22⋊D19—42no—
145C22⋊D19—81no—
146C22⋊D19—81no—
147C22⋊D19—81no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152D76—21no—
153D76—21no—
154D76—21no—
155D76—21no—
156D76—21no—
157D76—21no—
158D76—21no—
159D76—42no—
160D76—42no—
161D76—81no—
162D76C2×D412yes—
163C4×D19—42no—
164C4×D19—42no—
165C4×D19—42no—
166C4×D19—81no—
167Dic38—21no—
168Dic38—21no—
169Dic38—21no—
170Dic38C2×D412yes—
171C8×C19—21no—
172C8×C19—21no—
173C8×C19—21no—
174C8×C19C2×D412yes—
175#3268—191nomaximal, Sylow
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19C22×D411yescharacteristic
183C2×D19—22no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—84no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19C22×D411yescharacteristic
201C4×C19H(5,𝔽2)11yescharacteristic
202Dic19—22no—
203Dic19—41no—
204Dic19—41no—
205Dic19—41no—
206C2×AGL(1,ℤ/8)—191no—
207C2×#135—191no—
208#550—191no—
209#546—191no—
210#496—191no—
211#468—191no—
212#466—191no—
213#464—191no—
214#459—191no—
215#452—191no—
216#449—191no—
217#449—191no—
218#447—191no—
219#440—191no—
220#435D1911yescharacteristic, complemented
221C2×C19—41no—
222C2×C19—41no—
223C2×C19D4211yescharacteristic
224C2×C19#57511yescharacteristic
225C2×C19#57611yescharacteristic
226D19—42no—
227D19—81no—
228D19—81no—
229D19—81no—
230C2×#41—191no—
231C2×#41—191no—
232C2×#41—191no—
233C22×D4—191no—
234AGL(1,ℤ/8)—384no—
235#135—384no—
236C2×Q16—191no—
237C2×SD16—191no—
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16—191no—
241C2×D8—191no—
242C2×D8—191no—
243C2×D8—191no—
244C2×D8—191no—
245C2×M16C2×D1911yescharacteristic
246C22×C8C2×D1911yescharacteristic, complemented
247#127—191no—
248#127—381no—
249#124—191no—
250#123—381no—
251C22⋊Q8—191no—
252#121—191no—
253#121—191no—
254#121—191no—
255#121—381no—
256#121—381no—
257#121—381no—
258#120—381no—
259C4×Q8—191no—
260C4×D4—191no—
261C4×D4—381no—
262C4×D4C2×D1911yescharacteristic
263C2×C22⋊C4—381no—
264#107—191no—
265C4⋊C8C2×D1911yescharacteristic, complemented
266#103—191no—
267#103—191no—
268#102—191no—
269#102—191no—
270#102—191no—
271#102—191no—
272C22⋊C8C2×D1911yescharacteristic
273C22⋊C8C2×D1911yescharacteristic, complemented
274#97C2×D1911yescharacteristic, complemented
275C19#326811yescharacteristic, complemented, Sylow
276C24—381no—
277#41—382no—
278#41—382no—
279#41—382no—
280#41—761no—
281#41—761no—
282#41—761no—
283C2×Q8—191no—
284C2×Q8—191no—
285C2×D4—191no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—382no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—381no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—381no—
298C2×D4—381no—
299C2×D4—761no—
300C2×D4D7611yescharacteristic
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4C22×D1911yescharacteristic
306C22×C4C22×D1911yescharacteristic
307Q16—382no—
308SD16—194no—
309SD16—382no—
310SD16—382no—
311SD16—761no—
312D8—382no—
313D8—382no—
314D8—382no—
315D8—761no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D1911yescharacteristic
319C2×C8C22×D1911yescharacteristic
320C2×C8C22×D1911yescharacteristic
321C2×C8C22×D1911yescharacteristic
322C4⋊C4—191no—
323C4⋊C4—191no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4D7611yescharacteristic
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C22⋊C4—381no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4D7611yescharacteristic
335C22⋊C4D7611yescharacteristic
336C42—381no—
337C42C22×D1911yescharacteristic
338C23—381no—
339C23—381no—
340C23—381no—
341C23—381no—
342C23—762no—
343C23—762no—
344C23—1521no—
345C23C2×D7611yescharacteristic
346C23C2×D7611yescharacteristic
347Q8—192no—
348Q8—381no—
349Q8—381no—
350Q8—381no—
351D4—41no—
352D4—192no—
353D4—381no—
354D4—381no—
355D4—381no—
356D4—381no—
357D4—381no—
358D4—381no—
359D4—381no—
360D4—762no—
361D4—762no—
362D4—762no—
363D4—762no—
364D4—762no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4—1521no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—762no—
378C2×C4—762no—
379C2×C4—762no—
380C2×C4—1521no—
381C2×C4C2×D7611yescharacteristic
382C2×C4C2×D7611yescharacteristic
383C2×C4C2×D7611yescharacteristic
384C2×C4C2×D7611yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D1912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—382no—
397C22—761no—
398C22—761no—
399C22—761no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C22×D7611yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—382no—
415C4—761no—
416C4—761no—
417C4—761no—
418C4C2×D4×D1911yescharacteristic
419C4#1059743511yescharacteristic
420C2—41no—
421C2—41no—
422C2—762no—
423C2—1521no—
424C2—1521no—
425C2—1521no—
426C2D4×D7611yescharacteristic
427C2#1192734411yescharacteristic
428C2#1192734911yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#435C2
socleC22×C19C22×D4
hypercenter#435D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#10597354C2semidirect
2. C2×#10597350C2semidirect
3. #11927215C2semidirect
4. #11927190C2semidirect
5. #11926933C2semidirect
6. #11926790C2semidirect
7. #11926780C2semidirect
8. #11926767C2semidirect
9. #11926740C2semidirect
10. #11926708C2semidirect
11. #11926691C2semidirect
12. #11926691C2semidirect
13. #11926680C2semidirect
14. #11926646C2semidirect
15. C19×#435C2semidirect
18. C2×#64541C22semidirect
21. C22×C8×C19C22semidirect
27. #10597376C22semidirect
30. C2×Dic76C22semidirect
38. C2×#64516C22semidirect
39. C2×#64516C22semidirect
47. #10597320C22semidirect
49. C4×Dic38C22semidirect
50. C19×C4⋊C8C22semidirect
52. C19×C22⋊C8C22semidirect
53. C19×#97C22semidirect
56. #10597278C22semidirect
57. #10597278C22semidirect
58. #10597275C22semidirect
59. #10597273C22semidirect
60. #10597273C22semidirect
122. #64516D4semidirect
220. #435D19semidirect
246. C22×C8C2×D19semidirect
265. C4⋊C8C2×D19semidirect
273. C22⋊C8C2×D19semidirect
274. #97C2×D19semidirect
275. C19#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#105973542
C2×#105973502
#119272152
#119271902
#119269332
#119267902
#119267802
#119267672
#119267402
#119267082
#119266912
#119266802
#119266462
C19×#4352
#326819