Finite Group Databasebeta

← #34056322

Subgroups — #34056322

Order 19072.

498 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×#18011940C211yesmaximal, characteristic, complemented
2#23750282C211yesmaximal, characteristic, complemented
3#23750269C211yesmaximal, characteristic, complemented
4#23750008C211yesmaximal, characteristic, complemented
5#23749883C211yesmaximal, characteristic, complemented
6#23749875C211yesmaximal, characteristic, complemented
7#23749845C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749776C211yesmaximal, characteristic, complemented
11#23749767C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13SD16×Dic149C211yesmaximal, characteristic, complemented
14#23749701C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic, complemented
18#18011940—24no—
19C2×Dic596C2211yescharacteristic, complemented
20C2×#14558726C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558724C2211yescharacteristic, complemented
24C2×#14558719C2211yescharacteristic, complemented
25#18011898—21no—
26#18011898C2211yescharacteristic
27#18011898C2211yescharacteristic, complemented
28#18011892—21no—
29#18011890—21no—
30#18011890C2211yescharacteristic
31#18011890C2211yescharacteristic
32#18011883—21no—
33#18011882—21no—
34#18011882C2211yescharacteristic
35#18011882C2211yescharacteristic, complemented
36#18011880—21no—
37Q8×Dic149C2211yescharacteristic, complemented
38D4×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40C4×C22⋊D149C2211yescharacteristic
41C2×C22⋊Dic149—21no—
42#18011843C2211yescharacteristic, complemented
43#18011840C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011836C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic, complemented
50C22⋊#11924746C2211yescharacteristic
51#18011823C2211yescharacteristic, complemented
52C8×Dic149C2211yescharacteristic, complemented
53C2×#41×C149C2211yescharacteristic
54C22×D4×C149C2211yescharacteristic
55AGL(1,ℤ/8)×C149—24no—
56C2×SD16×C149C2211yescharacteristic
57C2×SD16×C149C2211yescharacteristic
58C2×D8×C149C2211yescharacteristic
59C2×D8×C149C2211yescharacteristic
60C2×M16×C149C2211yescharacteristic
61#14558735—22no—
62#14558735—41no—
63C2×Dic298—21no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66Q8×D149—22no—
67Q8×D149—41no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149D411yescharacteristic
72C22×Dic149—21no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76Dic596—22no—
77#14558726—22no—
78#14558724—22no—
79#14558724—41no—
80#14558724—41no—
81#14558719—22no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97C22⋊Dic149—21no—
98C22⋊Dic149—21no—
99C22⋊Dic149D411yescharacteristic
100#14558713D411yescharacteristic
101C4×Dic149—21no—
102C4×Dic149C2311yescharacteristic
103C24×C149—21no—
104#41×C149—22no—
105#41×C149—41no—
106C2×Q8×C149C2311yescharacteristic
107C2×D4×C149—22no—
108C2×D4×C149—21no—
109C2×D4×C149—21no—
110C2×D4×C149—41no—
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C2×D4×C149C2311yescharacteristic
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116SD16×C149—22no—
117SD16×C149D414yescomplemented
118D8×C149—22no—
119D8×C149—22no—
120M16×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149C2×D411yescharacteristic
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—42no—
129C22⋊D149—41no—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—81no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—42no—
138C2×Dic149—81no—
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C2×Dic149C2×D411yescharacteristic
142C4×D149—21no—
143C4×D149—21no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149—21no—
148C23×C149—21no—
149C23×C149—21no—
150C23×C149—42no—
151C23×C149—42no—
152C23×C149—81no—
153C23×C149C2×D411yescharacteristic
154Q8×C149—21no—
155Q8×C149C2×D412yes—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149—42no—
162D4×C149—42no—
163D4×C149C2×D412yes—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
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—21no—
175C22×C149—21no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149—84no—
185C22×C149C22×D411yescharacteristic
186C2×D149—21no—
187C2×D149—21no—
188C2×D149—21no—
189C4×C149—21no—
190C4×C149—22no—
191C4×C149C22×D411yescharacteristic
192C4×C149H(5,𝔽2)11yescharacteristic
193Dic149—21no—
194Dic149—21no—
195Dic149—21no—
196Dic149—41no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—41no—
201C2×C149—42no—
202C2×C149—81no—
203C2×C149—81no—
204C2×C149D4211yescharacteristic
205C2×C149#57511yescharacteristic
206C2×C149#57711yescharacteristic
207D149—41no—
208C149#327511yescharacteristic, complemented, Sylow
209#3275—1491nomaximal, Sylow
210C2×#137—1491no—
211C2×AGL(1,ℤ/8)D14911yescharacteristic, complemented
212#548—1491no—
213#546—1491no—
214#495—1491no—
215#470—1491no—
216#469—1491no—
217#464—1491no—
218#463—1491no—
219#452—1491no—
220#450—1491no—
221#449—1491no—
222#448—1491no—
223C4×SD16—1491no—
224#436—1491no—
225C2×#41—1491no—
226C2×#41C2×D14911yescharacteristic
227C22×Q8—1491no—
228C22×D4C2×D14911yescharacteristic
229#137—2984no—
230AGL(1,ℤ/8)—24no—
231C2×Q16—1491no—
232C2×Q16—1491no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16C2×D14911yescharacteristic
237C2×SD16C2×D14911yescharacteristic
238C2×D8C2×D14911yescharacteristic
239C2×D8C2×D14911yescharacteristic
240C2×M16—1491no—
241C2×M16C2×D14911yescharacteristic
242#124—2981no—
243#124—1491no—
244#124—1491no—
245#123—2981no—
246C22⋊Q8—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8—1491no—
249#121—2981no—
250#121—2981no—
251#121—1491no—
252#121—1491no—
253#120—2981no—
254C4×Q8—1491no—
255C4×D4—2981no—
256C4×D4—1491no—
257C4×D4—1491no—
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—
269C4×C8—1491no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—2982no—
274#41—5961no—
275C2×Q8—2981no—
276C2×Q8—2982no—
277C2×Q8—5961no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×Q8C22×D14911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—2981no—
288C2×D4—1491no—
289C2×D4C22×D14911yescharacteristic
290C2×D4C22×D14911yescharacteristic
291C2×D4C22×D14911yescharacteristic
292C22×C4—21no—
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4C22×D14911yescharacteristic
298Q16—2982no—
299Q16—2982no—
300SD16—22no—
301SD16—2982no—
302SD16—5961no—
303SD16—5961no—
304SD16C22⋊D14914yescomplemented
305D8—22no—
306D8—22no—
307M16—22no—
308M16—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4—1491no—
318C4⋊C4—1491no—
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—2981no—
328C22⋊C4—1491no—
329C22⋊C4—1491no—
330C42—2981no—
331C42—1491no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—1491no—
339C23D4×D14911yescharacteristic
340Q8—21no—
341Q8—2981no—
342Q8—2981no—
343Q8—2981no—
344Q8—2981no—
345Q8—5962no—
346Q8C2×C22⋊D14912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—5961no—
355D4—5962no—
356D4—5962no—
357D4—11921no—
358D4C2×C22⋊D14912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—2981no—
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—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—2981no—
395C22—2981no—
396C22—2981no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—22no—
400C4—2981no—
401C4—2981no—
402C4—2981no—
403C4—5961no—
404C4—5961no—
405C4—5961no—
406C4—5961no—
407C4C22×C22⋊D14911yescharacteristic
408C4#1801195611yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—5961no—
414C2D4×C22⋊D14911yescharacteristic
415C2#2375042111yescharacteristic
416C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×AGL(1,ℤ/8)×C149C2
socleC22×C149C22×D4
hypercenterC2×AGL(1,ℤ/8)D149
hypocenterC149#3275
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. #23750282C2semidirect
3. #23750269C2semidirect
4. #23750008C2semidirect
5. #23749883C2semidirect
6. #23749875C2semidirect
7. #23749845C2semidirect
8. #23749838C2semidirect
9. #23749787C2semidirect
10. #23749776C2semidirect
11. #23749767C2semidirect
12. #23749762C2semidirect
13. SD16×Dic149C2semidirect
14. #23749701C2semidirect
15. C2×AGL(1,ℤ/8)×C149C2semidirect
17. C2×Q8×D149C22semidirect
19. C2×Dic596C22semidirect
20. C2×#14558726C22semidirect
23. C2×#14558724C22semidirect
24. C2×#14558719C22semidirect
27. #18011898C22semidirect
35. #18011882C22semidirect
37. Q8×Dic149C22semidirect
42. #18011843C22semidirect
43. #18011840C22semidirect
44. #18011836C22semidirect
45. #18011836C22semidirect
46. #18011835C22semidirect
49. #18011832C22semidirect
51. #18011823C22semidirect
52. C8×Dic149C22semidirect
117. SD16×C149D4semidirect
208. C149#3275semidirect
211. C2×AGL(1,ℤ/8)D149semidirect
304. SD16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
#237502822
#237502692
#237500082
#237498832
#237498752
#237498452
#237498382
#237497872
#237497762
#237497672
#237497622
SD16×Dic1492
#237497012
C2×AGL(1,ℤ/8)×C1492
#3275149