Finite Group Databasebeta

← #14575181

Subgroups — #14575181

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×#10597357C211yesmaximal, characteristic, complemented
2C2×#10597358C211yesmaximal, characteristic, complemented
3#11927214C211yesmaximal, characteristic, complemented
4#11927189C211yesmaximal, characteristic, complemented
5#11926931C211yesmaximal, characteristic, complemented
6#11926789C211yesmaximal, characteristic, complemented
7#11926779C211yesmaximal, characteristic, complemented
8#11926767C211yesmaximal, characteristic, complemented
9#11926707C211yesmaximal, characteristic, complemented
10#11926690C211yesmaximal, characteristic, complemented
11#11926686C211yesmaximal, characteristic, complemented
12#11926676C211yesmaximal, characteristic, complemented
13#11926644C211yesmaximal, characteristic, complemented
14#11926614C211yesmaximal, characteristic, complemented
15C19×#459C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×#64543C2211yescharacteristic, complemented
19C2×D4×D19C2211yescharacteristic
20C2×D8×C19C2211yescharacteristic
21C2×D8×C19C2211yescharacteristic
22C19×#127C2211yescharacteristic, complemented
23C4×D4×C19C2211yescharacteristic
24#10597386—21no—
25#10597385—21no—
26#10597385—21no—
27#10597384C2211yescharacteristic
28#10597384C2211yescharacteristic, complemented
29D4×Dic19—21no—
30C2×#64526C2211yescharacteristic
31C2×#64526C2211yescharacteristic, complemented
32C2×#64526C2211yescharacteristic, complemented
33C2×#64525C2211yescharacteristic
34C2×#64525C2211yescharacteristic
35#10597376—21no—
36C2×(C2×D19)⋊C4—21no—
37#10597358—24no—
38#10597357—24no—
39C2×Dic76C2211yescharacteristic, complemented
40C2×#64516C2211yescharacteristic
41C2×#64515C2211yescharacteristic
42C2×C8×D19C2211yescharacteristic, complemented
43#10597343C2211yescharacteristic
44#10597341C2211yescharacteristic
45#10597332—21no—
46#10597328—21no—
47#10597321C2211yescharacteristic
48C4×D76C2211yescharacteristic
49C4×Dic38C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic, complemented
52C19×#102C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597264C2211yescharacteristic, complemented
60#10597260C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C22×C4×C19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77#64543—22no—
78#64543—22no—
79#64543—22no—
80#64543—41no—
81#64543—41no—
82#64543—41no—
83D4×D19—22no—
84D4×D19—41no—
85C2×D76—21no—
86C2×D76D411yescharacteristic
87C2×D76C2311yescharacteristic
88C2×C4×D19C2311yescharacteristic
89C2×C4×D19C2311yescharacteristic
90C2×Dic38C2311yescharacteristic
91C2×Dic38C2311yescharacteristic
92D8×C19—22no—
93D8×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C4⋊C4×C19C2311yescharacteristic
97C22⋊C4×C19—21no—
98C42×C19C2311yescharacteristic
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101#64526—22no—
102#64526—41no—
103#64526D414yescomplemented
104#64525—22no—
105#64525—41no—
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—
116C4×Dic19—21no—
117C2×C19⋊C8C2311yescharacteristic
118C2×C19⋊C8C2311yescharacteristic
119Dic76—22no—
120#64516—22no—
121#64515—22no—
122C8×D19—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—21no—
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19C2×D411yescharacteristic
131C22×D19C2×D411yescharacteristic
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—21no—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—42no—
138D4×C19—81no—
139D4×C19C2×D412yes—
140C2×C4×C19—21no—
141C2×C4×C19—81no—
142C2×C4×C19C2×D411yescharacteristic
143C2×C4×C19C2×D411yescharacteristic
144C2×C4×C19C2411yescharacteristic
145C22⋊D19—42no—
146C22⋊D19—42no—
147C22⋊D19—42no—
148C22⋊D19—42no—
149C22⋊D19—81no—
150C22⋊D19—81no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19C2×D411yescharacteristic
158C2×Dic19C2×D411yescharacteristic
159D76—21no—
160D76—21no—
161D76—41no—
162D76—81no—
163C4×D19—21no—
164C4×D19—21no—
165C4×D19—21no—
166C4×D19—21no—
167Dic38—21no—
168Dic38—21no—
169Dic38—21no—
170Dic38C2×D412yes—
171C8×C19—21no—
172C8×C19—21no—
173C19⋊C8—21no—
174C19⋊C8C2×D412yes—
175#3268—191nomaximal, Sylow
176C22×C19—22no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19C22×D411yescharacteristic
186C2×D19—21no—
187C2×D19—21no—
188C2×D19—21no—
189C2×D19—21no—
190C2×D19—21no—
191C2×D19—21no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—84no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19C22×D411yescharacteristic
200C4×C19H(5,𝔽2)11yescharacteristic
201Dic19—22no—
202Dic19—21no—
203Dic19—21no—
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#459D1911yescharacteristic, complemented
215#452—191no—
216#449—191no—
217#449—191no—
218#447—191no—
219#440—191no—
220#435—191no—
221C2×C19—42no—
222C2×C19—81no—
223C2×C19—81no—
224C2×C19D4211yescharacteristic
225C2×C19#57511yescharacteristic
226C2×C19#57611yescharacteristic
227D19—41no—
228D19—41no—
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×D8C2×D1911yescharacteristic
244C2×D8C2×D1911yescharacteristic
245C2×M16—191no—
246C22×C8—191no—
247#127—381no—
248#127C2×D1911yescharacteristic, complemented
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#102C2×D1911yescharacteristic, complemented
271#102C2×D1911yescharacteristic, complemented
272C22⋊C8—191no—
273C22⋊C8—191no—
274#97—191no—
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—21no—
286C2×D4—21no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—382no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—381no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—761no—
298C2×D4C22×D1911yescharacteristic
299C2×D4C22×D1911yescharacteristic
300C2×D4C22×D1911yescharacteristic
301C22×C4—21no—
302C22×C4—191no—
303C22×C4—191no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4—381no—
307Q16—382no—
308SD16—194no—
309SD16—382no—
310SD16—382no—
311SD16—761no—
312D8—22no—
313D8—22no—
314D8—382no—
315D8—761no—
316M16—382no—
317C2×C8—191no—
318C2×C8—191no—
319C2×C8—382no—
320C2×C8C22×D1911yescharacteristic
321C2×C8C22×D1911yescharacteristic
322C4⋊C4—191no—
323C4⋊C4—191no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4C22×D1911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—191no—
329C22⋊C4—191no—
330C22⋊C4—381no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C42—381no—
337C42C22×D1911yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—191no—
342C23—191no—
343C23—381no—
344C23—762no—
345C23—762no—
346C23—1521no—
347Q8—192no—
348Q8—381no—
349Q8—381no—
350Q8—381no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—381no—
359D4—381no—
360D4—761no—
361D4—762no—
362D4—762no—
363D4—762no—
364D4—762no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4D4×D1912yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—191no—
372C2×C4—191no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4D4×D1911yescharacteristic
384C2×C4D4×D1911yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—21no—
388C8—192no—
389C8—381no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—381no—
400C22—381no—
401C22—381no—
402C22—381no—
403C22—381no—
404C22—381no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C2×D4×D1911yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—381no—
414C4—381no—
415C4—382no—
416C4—761no—
417C4—761no—
418C4C2×D4×D1911yescharacteristic
419C4#1059743511yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—761no—
424C2—761no—
425C2—1521no—
426C2#1192717811yescharacteristic
427C2#1192734011yescharacteristic
428C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#459C2
socleC22×C19C22×D4
hypercenter#459D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#10597357C2semidirect
2. C2×#10597358C2semidirect
3. #11927214C2semidirect
4. #11927189C2semidirect
5. #11926931C2semidirect
6. #11926789C2semidirect
7. #11926779C2semidirect
8. #11926767C2semidirect
9. #11926707C2semidirect
10. #11926690C2semidirect
11. #11926686C2semidirect
12. #11926676C2semidirect
13. #11926644C2semidirect
14. #11926614C2semidirect
15. C19×#459C2semidirect
18. C2×#64543C22semidirect
22. C19×#127C22semidirect
28. #10597384C22semidirect
31. C2×#64526C22semidirect
32. C2×#64526C22semidirect
39. C2×Dic76C22semidirect
42. C2×C8×D19C22semidirect
49. C4×Dic38C22semidirect
50. C19×C4⋊C8C22semidirect
51. C19×#102C22semidirect
52. C19×#102C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597273C22semidirect
58. #10597267C22semidirect
59. #10597264C22semidirect
60. #10597260C22semidirect
103. #64526D4semidirect
214. #459D19semidirect
248. #127C2×D19semidirect
265. C4⋊C8C2×D19semidirect
270. #102C2×D19semidirect
271. #102C2×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×#105973572
C2×#105973582
#119272142
#119271892
#119269312
#119267892
#119267792
#119267672
#119267072
#119266902
#119266862
#119266762
#119266442
#119266142
C19×#4592
#326819