Finite Group Databasebeta

← #34054189

Subgroups — #34054189

Order 19072.

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×#18011935C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750188C211yesmaximal, characteristic, complemented
4#23750097C211yesmaximal, characteristic, complemented
5#23749841C211yesmaximal, characteristic, complemented
6#23749840C211yesmaximal, characteristic, complemented
7#23749839C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749819C211yesmaximal, characteristic, complemented
10#23749818C211yesmaximal, characteristic, complemented
11#23749817C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic, complemented
14#23749618C211yesmaximal, characteristic, complemented
15#459×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic
19#18011935—24no—
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic, complemented
22C2×D1192C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25C2×#14558721C2211yescharacteristic, complemented
26D8×D149—24no—
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011907C2211yescharacteristic, complemented
30#18011899C2211yescharacteristic, complemented
31#18011898C2211yescharacteristic, complemented
32#18011883—21no—
33#18011883—21no—
34#18011879—21no—
35#18011879—21no—
36C4×D596C2211yescharacteristic, complemented
37D4×Dic149C2211yescharacteristic, complemented
38#18011873C2211yescharacteristic, complemented
39C4×C22⋊D149—21no—
40#18011871—21no—
41#18011869C2211yescharacteristic
42#18011868C2211yescharacteristic
43C2×#14558713—21no—
44C22⋊C4×D149—21no—
45C4⋊#11924746C2211yescharacteristic, complemented
46#18011840C2211yescharacteristic, complemented
47#18011840C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011834C2211yescharacteristic, complemented
50#18011833C2211yescharacteristic, complemented
51#18011832C2211yescharacteristic, complemented
52#18011832C2211yescharacteristic, complemented
53#18011831C2211yescharacteristic, complemented
54C2×D8×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic, complemented
56#127×C149C2211yescharacteristic, complemented
57C4×D4×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#102×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62C23×D149—21no—
63#14558735—22no—
64#14558735—22no—
65C2×Dic298C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73D4×D149—22no—
74D4×D149—22no—
75D4×D149—22no—
76D4×D149D414yescomplemented
77C22×Dic149—21no—
78C22×Dic149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82#14558725—22no—
83#14558724—22no—
84D1192—22no—
85#14558721—22no—
86#14558721—22no—
87#14558721—22no—
88#14558719—22no—
89C2×#11924746C2311yescharacteristic
90C2×#11924746C2311yescharacteristic
91C8×D149—22no—
92C4⋊Dic149C2311yescharacteristic
93#14558715D411yescharacteristic
94#14558715D411yescharacteristic
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97C22⋊Dic149—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713—21no—
103#14558713D411yescharacteristic
104#14558713D411yescharacteristic
105C4×Dic149—21no—
106C4×Dic149C2311yescharacteristic
107C2×D4×C149—21no—
108C2×D4×C149—21no—
109C2×D4×C149C2311yescharacteristic
110C2×D4×C149C2311yescharacteristic
111C2×D4×C149C2311yescharacteristic
112C22×C4×C149—21no—
113D8×C149—22no—
114D8×C149—22no—
115C2×C8×C149C2311yescharacteristic
116C2×C8×C149C2311yescharacteristic
117C4⋊C4×C149C2311yescharacteristic
118C22⋊C4×C149—21no—
119C42×C149C2311yescharacteristic
120C22×D149—21no—
121C22×D149—24no—
122C22×D149—21no—
123C22×D149—42no—
124C22×D149—81no—
125C22×D149—81no—
126C22×D149—81no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—21no—
131D596—21no—
132D596—21no—
133D596—21no—
134D596C2×D412yes—
135C22⋊D149—24no—
136C22⋊D149—42no—
137C22⋊D149—42no—
138C22⋊D149—81no—
139C22⋊D149—81no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—42no—
143C2×Dic149—81no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C4×D149—81no—
148C4×D149—81no—
149C4×D149C2×D412yes—
150C4×D149#4112yes—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149—81no—
162D4×C149—81no—
163D4×C149C2×D412yes—
164C2×C4×C149—21no—
165C2×C4×C149—81no—
166C2×C4×C149C2×D411yescharacteristic
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C8×C149—21no—
170C8×C149—21no—
171C22×C149—22no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149C22×D411yescharacteristic
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—22no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—41no—
189C2×D149—84no—
190C2×D149—84no—
191C2×D149#12112yes—
192C4×C149—21no—
193C4×C149—21no—
194C4×C149—41no—
195C4×C149C22×D411yescharacteristic
196C4×C149C2×#4111yescharacteristic
197Dic149—21no—
198Dic149—21no—
199Dic149—41no—
200Dic149—41no—
201Dic149#12112yes—
202C2×C149—42no—
203C2×C149—81no—
204C2×C149—81no—
205C2×C149C2×#12111yescharacteristic
206C2×C149#57611yescharacteristic
207C2×C149#57611yescharacteristic
208D149—22no—
209D149—42no—
210D149—81no—
211C149#304111yescharacteristic, complemented, Sylow
212#3041—1491nomaximal, Sylow
213C2×AGL(1,ℤ/8)—1491no—
214C22×D8—1491no—
215#535—1491no—
216#518—1491no—
217#463—1491no—
218#463—1491no—
219#463—1491no—
220#463—1491no—
221#459—1491no—
222#459—1491no—
223#459—1491no—
224#459D14911yescharacteristic, complemented
225#424—1491no—
226#418—1491no—
227#416—1491no—
228C2×#41—1491no—
229C22×D4—1491no—
230C22×D4—1491no—
231AGL(1,ℤ/8)—2984no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×D8—2984no—
235C2×D8—1491no—
236C2×D8—1491no—
237C2×D8—1491no—
238C2×D8—1491no—
239C2×D8C2×D14911yescharacteristic
240C2×D8C2×D14911yescharacteristic, complemented
241C2×M16—1491no—
242C22×C8—1491no—
243#127—1491no—
244#127C2×D14911yescharacteristic, complemented
245#124—1491no—
246#124—1491no—
247#121—2981no—
248#121—2981no—
249#120—2981no—
250#120—2981no—
251C4×D4—2981no—
252C4×D4—2981no—
253C4×D4—1491no—
254C4×D4—1491no—
255C4×D4—1491no—
256C4×D4C2×D14911yescharacteristic, complemented
257#117—1491no—
258#117—1491no—
259C2×C22⋊C4—2981no—
260C2×C22⋊C4—2981no—
261C4⋊C8—1491no—
262C4⋊C8—1491no—
263C4⋊C8—1491no—
264C4⋊C8C2×D14911yescharacteristic, complemented
265#103—1491no—
266#103—1491no—
267#102—1491no—
268#102—1491no—
269#102—1491no—
270#102—1491no—
271#102C2×D14911yescharacteristic, complemented
272#102C2×D14911yescharacteristic, complemented
273C24—2981no—
274C24—2981no—
275#41—2982no—
276#41—2982no—
277C2×Q8—1491no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—2981no—
281C2×D4—2982no—
282C2×D4—2982no—
283C2×D4—2982no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2981no—
288C2×D4—1494no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4C22×D14911yescharacteristic
292C2×D4C22×D14911yescharacteristic
293C2×D4C22×D14911yescharacteristic
294C22×C4—21no—
295C22×C4—2981no—
296C22×C4—2981no—
297C22×C4—2981no—
298C22×C4—2981no—
299C22×C4—1491no—
300SD16—2982no—
301SD16—2982no—
302D8—22no—
303D8—22no—
304D8—2982no—
305D8—2982no—
306D8—2982no—
307D8—2982no—
308M16—2982no—
309C2×C8—2982no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8C22×D14911yescharacteristic
313C2×C8C22×D14911yescharacteristic
314C4⋊C4—1491no—
315C4⋊C4—1491no—
316C4⋊C4—1491no—
317C4⋊C4C22×D14911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—1491no—
328C22⋊C4—1491no—
329C42—2981no—
330C42—1491no—
331C42C22×D14911yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—2984no—
336C23—2981no—
337C23—2981no—
338C23—5962no—
339C23—1491no—
340C23—11921no—
341C23—11921no—
342C23—11921no—
343C23—11921no—
344Q8—2981no—
345Q8—2981no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—2984no—
354D4—2981no—
355D4—2981no—
356D4—2981no—
357D4—5962no—
358D4—5962no—
359D4—1492no—
360D4—11921no—
361D4—11921no—
362D4D4×D14912yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—5962no—
368C2×C4—1491no—
369C2×C4—1491no—
370C2×C4—1491no—
371C2×C4—1492no—
372C2×C4—1492no—
373C2×C4—11921no—
374C2×C4—11921no—
375C2×C4—11921no—
376C2×C4D4×D14911yescharacteristic
377C2×C4D4×D14911yescharacteristic
378C2×C4C23×D14911yescharacteristic
379C8—21no—
380C8—21no—
381C8—2981no—
382C8—2981no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2981no—
393C22—2981no—
394C22—2982no—
395C22—5961no—
396C22—5961no—
397C22—5961no—
398C22—5961no—
399C22—5961no—
400C22—1492no—
401C22—11924no—
402C22—11924no—
403C22C2×D4×D14911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—2981no—
408C4—2981no—
409C4—5961no—
410C4—5961no—
411C4—1492no—
412C4C2×D4×D14911yescharacteristic
413C4#41×D14911yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—2982no—
418C2—5962no—
419C2—11921no—
420C2#121×D14911yescharacteristic
421C2#2375042611yescharacteristic
422C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3041
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. C2×D8×D149C2semidirect
3. #23750188C2semidirect
4. #23750097C2semidirect
5. #23749841C2semidirect
6. #23749840C2semidirect
7. #23749839C2semidirect
8. #23749838C2semidirect
9. #23749819C2semidirect
10. #23749818C2semidirect
11. #23749817C2semidirect
12. #23749650C2semidirect
13. #23749628C2semidirect
14. #23749618C2semidirect
15. #459×C149C2semidirect
20. C2×#14558725C22semidirect
21. C2×#14558724C22semidirect
25. C2×#14558721C22semidirect
29. #18011907C22semidirect
30. #18011899C22semidirect
31. #18011898C22semidirect
36. C4×D596C22semidirect
37. D4×Dic149C22semidirect
38. #18011873C22semidirect
45. C4⋊#11924746C22semidirect
46. #18011840C22semidirect
47. #18011840C22semidirect
48. #18011836C22semidirect
49. #18011834C22semidirect
50. #18011833C22semidirect
51. #18011832C22semidirect
52. #18011832C22semidirect
53. #18011831C22semidirect
55. C2×D8×C149C22semidirect
56. #127×C149C22semidirect
57. C4×D4×C149C22semidirect
58. C4⋊C8×C149C22semidirect
59. #102×C149C22semidirect
60. #102×C149C22semidirect
76. D4×D149D4semidirect
211. C149#3041semidirect
224. #459D149semidirect
240. C2×D8C2×D149semidirect
244. #127C2×D149semidirect
256. C4×D4C2×D149semidirect
264. C4⋊C8C2×D149semidirect
271. #102C2×D149semidirect
272. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
C2×D8×D1492
#237501882
#237500972
#237498412
#237498402
#237498392
#237498382
#237498192
#237498182
#237498172
#237496502
#237496282
#237496182
#459×C1492
#3041149