Finite Group Databasebeta

← #34056216

Subgroups — #34056216

Order 19072.

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×#18011935C211yesmaximal, characteristic, complemented
2#23750274C211yesmaximal, characteristic, complemented
3#23750263C211yesmaximal, characteristic, complemented
4#23750018C211yesmaximal, characteristic, complemented
5#23749880C211yesmaximal, characteristic, complemented
6#23749854C211yesmaximal, characteristic, complemented
7#23749842C211yesmaximal, characteristic, complemented
8#23749828C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749784C211yesmaximal, characteristic, complemented
11#23749774C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749737C211yesmaximal, characteristic, complemented
14#23749696C211yesmaximal, characteristic, complemented
15C2×#135×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18#18011935—24no—
19C2×#14558726C2211yescharacteristic, complemented
20C2×#14558725C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558719C2211yescharacteristic
25#18011909C2211yescharacteristic, complemented
26#18011900C2211yescharacteristic
27#18011894—21no—
28#18011894—21no—
29#18011892—21no—
30#18011890C2211yescharacteristic, complemented
31#18011887C2211yescharacteristic
32#18011887C2211yescharacteristic
33#18011885C2211yescharacteristic
34#18011883—21no—
35#18011883—21no—
36#18011879—21no—
37D4×Dic149C2211yescharacteristic
38D4×Dic149C2211yescharacteristic, complemented
39C4×C22⋊D149C2211yescharacteristic
40C2×#14558715—21no—
41C2×#14558713—21no—
42#18011843C2211yescharacteristic, complemented
43#18011840C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic, complemented
50C22⋊#11924746C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic
52#18011821C2211yescharacteristic, complemented
53C2×#41×C149C2211yescharacteristic
54C2×#41×C149C2211yescharacteristic, complemented
55#135×C149—24no—
56C2×Q16×C149C2211yescharacteristic, complemented
57C2×SD16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic, complemented
59C2×D8×C149C2211yescharacteristic
60C22×C8×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558735—22no—
63#14558735—41no—
64C2×Dic298C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149D411yescharacteristic
70D4×D149—22no—
71D4×D149—41no—
72C22×Dic149—21no—
73C22×Dic149—21no—
74C22×Dic149—21no—
75C2×C4×D149C2311yescharacteristic
76#14558726—41no—
77#14558725—22no—
78#14558724—22no—
79#14558723—41no—
80#14558721—22no—
81#14558719—22no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715D411yescharacteristic
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149D411yescharacteristic
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713D411yescharacteristic
102C4×Dic149C2311yescharacteristic
103#41×C149—22no—
104#41×C149—22no—
105#41×C149—41no—
106#41×C149—41no—
107C2×Q8×C149C2311yescharacteristic
108C2×Q8×C149C2311yescharacteristic
109C2×D4×C149—21no—
110C2×D4×C149—21no—
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116Q16×C149—22no—
117SD16×C149—22no—
118SD16×C149—22no—
119D8×C149D414yescomplemented
120C2×C8×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—42no—
125C22×D149—42no—
126C22×D149—81no—
127C22×D149C2×D411yescharacteristic
128Dic298—21no—
129Dic298—21no—
130D596—21no—
131D596—21no—
132C22⋊D149—41no—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—81no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—42no—
140C2×Dic149—42no—
141C2×Dic149—81no—
142C2×Dic149C2×D411yescharacteristic
143C2×Dic149C2×D411yescharacteristic
144C2×Dic149C2×D411yescharacteristic
145C4×D149—21no—
146C4×D149—21no—
147#11924746—21no—
148#11924746—21no—
149C23×C149—21no—
150C23×C149—21no—
151C23×C149C2×D411yescharacteristic
152Q8×C149—21no—
153Q8×C149—21no—
154Q8×C149—21no—
155Q8×C149—21no—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—42no—
159D4×C149—42no—
160D4×C149C2×D412yes—
161D4×C149C2×D412yes—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—42no—
167C2×C4×C149—42no—
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—22no—
174C22×C149—22no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149C22×D411yescharacteristic
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—21no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149C22×D411yescharacteristic
193C4×C149H(5,𝔽2)11yescharacteristic
194Dic149—21no—
195Dic149—21no—
196Dic149—21no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—42no—
201C2×C149—41no—
202C2×C149—42no—
203C2×C149D4211yescharacteristic
204C2×C149#57511yescharacteristic
205C2×C149#57711yescharacteristic
206D149—41no—
207D149—81no—
208C149#326711yescharacteristic, complemented, Sylow
209#3267—1491nomaximal, Sylow
210C2×AGL(1,ℤ/8)—1491no—
211C2×#135D14911yescharacteristic, complemented
212#547—1491no—
213#546—1491no—
214#497—1491no—
215#470—1491no—
216#465—1491no—
217#463—1491no—
218#461—1491no—
219#452—1491no—
220#452—1491no—
221#450—1491no—
222#449—1491no—
223#442—1491no—
224#435—1491no—
225C2×#41—1491no—
226C2×#41C2×D14911yescharacteristic
227C2×#41C2×D14911yescharacteristic, complemented
228C22×D4—1491no—
229AGL(1,ℤ/8)—2984no—
230#135—24no—
231C2×Q16—1491no—
232C2×Q16C2×D14911yescharacteristic, complemented
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16C2×D14911yescharacteristic
237C2×SD16C2×D14911yescharacteristic, complemented
238C2×D8—1491no—
239C2×D8C2×D14911yescharacteristic
240C2×M16—1491no—
241C22×C8C2×D14911yescharacteristic, complemented
242C4⋊Q8—1491no—
243#124—1491no—
244#123—2981no—
245#123—2981no—
246#123—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8—1491no—
249C22⋊Q8—1491no—
250#121—2981no—
251#121—2981no—
252#121—1491no—
253#120—2981no—
254C4×D4—1491no—
255C4×D4—1491no—
256C4×D4—1491no—
257C2×C4⋊C4—2981no—
258C2×C22⋊C4—2981no—
259#106—1491no—
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103—1491no—
264#102—1491no—
265#102—1491no—
266#102—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269#97—1491no—
270C24—2981no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—2982no—
276#41—5961no—
277C2×Q8—1491no—
278C2×Q8C22×D14911yescharacteristic
279C2×Q8C22×D14911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—2982no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—5961no—
287C2×D4—1491no—
288C2×D4—1491no—
289C2×D4C22×D14911yescharacteristic
290C2×D4C22×D14911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4C22×D14911yescharacteristic
298Q16—22no—
299Q16—5961no—
300SD16—22no—
301SD16—22no—
302SD16—2982no—
303SD16—2982no—
304SD16—5961no—
305D8—2982no—
306D8C22⋊D14914yescomplemented
307M16—2982no—
308C2×C8—22no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—2981no—
318C4⋊C4—1491no—
319C4⋊C4—1491no—
320C4⋊C4—1491no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—2981no—
329C22⋊C4—1491no—
330C22⋊C4—1491no—
331C42—1491no—
332C23—21no—
333C23—21no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—11921no—
339C23D4×D14911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2981no—
345Q8—2981no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—42no—
350D4—2981no—
351D4—2981no—
352D4—5961no—
353D4—5962no—
354D4—5962no—
355D4—11921no—
356D4C2×C22⋊D14912yes—
357D4C2×C22⋊D14912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4—1491no—
372C2×C4—1491no—
373C2×C4—1491no—
374C2×C4—11921no—
375C2×C4D4×D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—21no—
378C8—2981no—
379C8—2981no—
380C8C2×C22⋊D14912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—2981no—
391C22—2981no—
392C22—2981no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—2981no—
402C4—2981no—
403C4—2981no—
404C4—5961no—
405C4—5961no—
406C4—5961no—
407C4C22×C22⋊D14911yescharacteristic
408C4#1801195611yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—5961no—
413C2—11921no—
414C2D4×C22⋊D14911yescharacteristic
415C2#2375042211yescharacteristic
416C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3267
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. #23750274C2semidirect
3. #23750263C2semidirect
4. #23750018C2semidirect
5. #23749880C2semidirect
6. #23749854C2semidirect
7. #23749842C2semidirect
8. #23749828C2semidirect
9. #23749787C2semidirect
10. #23749784C2semidirect
11. #23749774C2semidirect
12. #23749770C2semidirect
13. #23749737C2semidirect
14. #23749696C2semidirect
15. C2×#135×C149C2semidirect
19. C2×#14558726C22semidirect
25. #18011909C22semidirect
30. #18011890C22semidirect
38. D4×Dic149C22semidirect
42. #18011843C22semidirect
43. #18011840C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
49. #18011832C22semidirect
50. C22⋊#11924746C22semidirect
52. #18011821C22semidirect
54. C2×#41×C149C22semidirect
56. C2×Q16×C149C22semidirect
58. C2×SD16×C149C22semidirect
60. C22×C8×C149C22semidirect
119. D8×C149D4semidirect
208. C149#3267semidirect
211. C2×#135D149semidirect
227. C2×#41C2×D149semidirect
232. C2×Q16C2×D149semidirect
237. C2×SD16C2×D149semidirect
241. C22×C8C2×D149semidirect
306. D8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
#237502742
#237502632
#237500182
#237498802
#237498542
#237498422
#237498282
#237497872
#237497842
#237497742
#237497702
#237497372
#237496962
C2×#135×C1492
#3267149