Finite Group Databasebeta

← #34061448

Subgroups — #34061448

Order 19072.

506 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750694C211yesmaximal, characteristic, complemented
2#23750692C211yesmaximal, characteristic, complemented
3#23750666C212yesmaximal, complemented
4#23750664C212yesmaximal, complemented
5SD16×#10597010C212yesmaximal, complemented
6D8×#10597010C212yesmaximal, complemented
7#23750636C211yesmaximal, characteristic, complemented
8#23750615C211yesmaximal, characteristic, complemented
9C2×#18011973C211yesmaximal, characteristic, complemented
10#23750591C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×D149C211yesmaximal, characteristic
12C2×D149⋊C8C2211yescharacteristic
13Q8×#10597010C2212yescomplemented
14D4×#10597010—21no—
15D4×#10597010—21no—
16D4×#10597010—22no—
17D4×#10597010C2212yes—
18D4×#10597010C2212yes—
19D4×#10597010C2212yescomplemented
20#18011990—21no—
21#18011990C2211yescharacteristic
22#18011990C2211yescharacteristic
23C2×C4⋊#10597010—21no—
24C2×C4⋊#10597010C2211yescharacteristic
25C2×C22⋊#10597010—22no—
26#18011980C2212yescomplemented
27#18011979C2212yescomplemented
28#18011974C2211yescharacteristic, complemented
29#18011974C2211yescharacteristic, complemented
30#18011973C2212yes—
31#18011973C2212yes—
32#18011973C2211yescharacteristic, complemented
33#18011973C2211yescharacteristic, complemented
34#18011965C2212yescomplemented
35C8×#10597010C2212yescomplemented
36#41×D149C2211yescharacteristic
37C2×D4×D149C2211yescharacteristic
38#18011939C411yescharacteristic, complemented
39#18011938C412yescomplemented
40#18011937C411yescharacteristic, complemented
41#18011936C411yescharacteristic, complemented
42#18011935C412yescomplemented
43SD16×D149C2212yes—
44D8×D149C2212yes—
45M16×D149C2211yescharacteristic
46AGL(1,ℤ/8)×C149C411yescharacteristic, complemented
47C22×#10597010—22no—
48C22×#10597010—22no—
49C22×#10597010—22no—
50C22×#10597010—21no—
51D149⋊C8—21no—
52D149⋊C8C2311yescharacteristic
53D149⋊C8C2311yescharacteristic
54C2×#11924753—21no—
55C4⋊#10597010—22no—
56C4⋊#10597010—21no—
57C4⋊#10597010D411yescharacteristic
58C4⋊#10597010D411yescharacteristic
59C4⋊#10597010C2312yes—
60C4⋊#10597010C2311yescharacteristic
61C4⋊#10597010C2311yescharacteristic
62C22⋊#10597010—22no—
63C22⋊#10597010—22no—
64C22⋊#10597010—22no—
65C22⋊#10597010—21no—
66C22⋊#10597010D412yes—
67C4×#10597010—22no—
68C4×#10597010—21no—
69C4×#10597010C2312yes—
70C23×D149—21no—
71#14558737C2×C411yescharacteristic, complemented
72#14558736—21no—
73#14558736C2×C411yescharacteristic, complemented
74#14558735—21no—
75#14558735C2×C411yescharacteristic, complemented
76Q8×D149C2311yescharacteristic
77C2×D596C2×C411yescharacteristic, complemented
78C2×C22⋊D149—21no—
79D4×D149—21no—
80D4×D149—21no—
81D4×D149—21no—
82D4×D149C2×C412yescomplemented
83D4×D149C2311yescharacteristic
84D4×D149C2312yes—
85C2×C4×D149—21no—
86C2×C4×D149C2311yescharacteristic
87#14558725C2×C412yescomplemented
88#14558724C2×C412yescomplemented
89#14558723C2×C412yescomplemented
90D1192C2×C412yescomplemented
91#14558721C2×C412yescomplemented
92#14558721C2×C412yescomplemented
93#14558720C2×C411yescharacteristic, complemented
94#14558719C2×C412yescomplemented
95C8×D149C2312yes—
96#41×C149C2×C411yescharacteristic, complemented
97C2×D4×C149C2×C411yescharacteristic, complemented
98SD16×C149C2×C412yescomplemented
99D8×C149C2×C412yescomplemented
100M16×C149C2×C411yescharacteristic, complemented
101C2×#10597010—21no—
102C2×#10597010—21no—
103C2×#10597010—22no—
104C2×#10597010—82no—
105C2×#10597010—82no—
106C2×#10597010—82no—
107C2×#10597010—81no—
108C2×#10597010C2×D412yes—
109C2×#10597010C2×D412yes—
110#11924753—21no—
111#11924753—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—22no—
115C22×D149—22no—
116C22×D149—81no—
117C22×D149—81no—
118C22×D149C2×D411yescharacteristic
119Dic298—21no—
120Dic298C22×C411yescharacteristic
121D596—21no—
122D596—21no—
123D596C22×C411yescharacteristic
124D596C22×C412yes—
125C22⋊D149—21no—
126C22⋊D149—21no—
127C22⋊D149—22no—
128C22⋊D149—22no—
129C22⋊D149—21no—
130C2×Dic149—21no—
131C2×Dic149#4111yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—21no—
135C4×D149C22×C411yescharacteristic
136C4×D149C2×D411yescharacteristic
137C4×D149#4111yescharacteristic
138C4×D149C2411yescharacteristic
139#11924746C22×C412yes—
140C23×C149—21no—
141Q8×C149C22×C411yescharacteristic
142D4×C149—21no—
143D4×C149—21no—
144D4×C149C22×C411yescharacteristic
145D4×C149C22×C412yes—
146C2×C4×C149—21no—
147C2×C4×C149C22×C411yescharacteristic
148C8×C149C22×C412yes—
149C22×C149—21no—
150C22×C149—22no—
151C22×C149—81no—
152C22×C149C4×D411yescharacteristic
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—22no—
157C2×D149—42no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—42no—
161C2×D149—82no—
162C2×D149—81no—
163C2×D149C4×D411yescharacteristic
164C2×D149C22×D411yescharacteristic
165#10597010—22no—
166#10597010—22no—
167#10597010—41no—
168#10597010—42no—
169#10597010—41no—
170C4×C149—21no—
171C4×C149C4×D411yescharacteristic
172C4×C149C23×C411yescharacteristic
173Dic149—21no—
174Dic149C4×D411yescharacteristic
175Dic149C2×#4111yescharacteristic
176C2×C149—21no—
177C2×C149—42no—
178C2×C149—41no—
179C2×C149C2×C4×D411yescharacteristic
180D149—21no—
181D149—41no—
182D149—42no—
183D149#57611yescharacteristic
184D149#57711yescharacteristic
185C149#294611yescharacteristic, complemented, Sylow
186#2946—1491nomaximal, Sylow
187C2×AGL(1,ℤ/8)—1491no—
188#520—1491no—
189#518—1491no—
190#442—1492no—
191#440—1492no—
192C4×SD16—1492no—
193C4×D8—1492no—
194#428—1491no—
195#416—1491no—
196C2×#102—1491no—
197#405—1491no—
198C2×#41—1491no—
199C22×D4—1491no—
200AGL(1,ℤ/8)—1491no—
201AGL(1,ℤ/8)—1491no—
202AGL(1,ℤ/8)—1492no—
203AGL(1,ℤ/8)—1492no—
204AGL(1,ℤ/8)—1491no—
205AGL(1,ℤ/8)#1059701011yescharacteristic, complemented
206C2×SD16—1492no—
207C2×D8—1492no—
208C2×M16—1491no—
209C22×C8—1491no—
210C4×Q8—1492no—
211C4×D4—2981no—
212C4×D4—2981no—
213C4×D4—2982no—
214C4×D4—1492no—
215C4×D4—1492no—
216C4×D4—1492no—
217#117—2981no—
218#117—1491no—
219#117—1491no—
220C2×C4⋊C4—2981no—
221C2×C4⋊C4—1491no—
222C2×C22⋊C4—2982no—
223#107—1492no—
224#106—1492no—
225#103—1491no—
226#103—1491no—
227#102—1492no—
228#102—1492no—
229#102—1491no—
230#102—1491no—
231#97—1492no—
232C4×C8—1492no—
233C24—2981no—
234#41—2981no—
235#41—2981no—
236#41—1491no—
237#41—1491no—
238#41—1491no—
239#41C2×#1059701011yescharacteristic, complemented
240C2×Q8—1491no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—1492no—
246C2×D4—1491no—
247C2×D4—1492no—
248C2×D4—1491no—
249C2×D4C2×#1059701011yescharacteristic, complemented
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2982no—
253C22×C4—2982no—
254C22×C4—2982no—
255C22×C4—1491no—
256SD16—1492no—
257SD16—1492no—
258SD16—1492no—
259SD16C2×#1059701012yescomplemented
260D8—1492no—
261D8—1492no—
262D8—1492no—
263D8C2×#1059701012yescomplemented
264M16—1491no—
265M16—1492no—
266M16C2×#1059701011yescharacteristic, complemented
267C2×C8—2981no—
268C2×C8—2981no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8—1492no—
272C4⋊C4—2981no—
273C4⋊C4—2982no—
274C4⋊C4—1492no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C22⋊C4—2981no—
280C22⋊C4—2982no—
281C22⋊C4—2982no—
282C22⋊C4—2982no—
283C22⋊C4—1492no—
284C42—2982no—
285C42—2981no—
286C42—1492no—
287C23—21no—
288C23—2981no—
289C23—2982no—
290C23—2982no—
291C23—2981no—
292C23—1491no—
293C23—11921no—
294C23—11921no—
295Q8—2981no—
296Q8—1491no—
297Q8C22×#1059701011yescharacteristic
298D4—21no—
299D4—21no—
300D4—2981no—
301D4—2981no—
302D4—2981no—
303D4—2982no—
304D4—2982no—
305D4—2981no—
306D4—2981no—
307D4—1491no—
308D4—1492no—
309D4C22×#1059701011yescharacteristic
310D4C22×#1059701012yes—
311C2×C4—21no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2982no—
319C2×C4—1492no—
320C2×C4—1492no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1491no—
325C2×C4—1491no—
326C2×C4—11922no—
327C2×C4—11922no—
328C2×C4—11922no—
329C2×C4—11921no—
330C2×C4C22×#1059701011yescharacteristic
331C8—2981no—
332C8—2981no—
333C8—1492no—
334C8C22×#1059701012yes—
335C22—21no—
336C22—22no—
337C22—81no—
338C22—2981no—
339C22—2981no—
340C22—2981no—
341C22—2982no—
342C22—5961no—
343C22—5962no—
344C22—5962no—
345C22—5961no—
346C22—1491no—
347C22—1491no—
348C22—11921no—
349C22—11922no—
350C22D4×#1059701011yescharacteristic
351C4—21no—
352C4—2982no—
353C4—2982no—
354C4—2981no—
355C4—5961no—
356C4—5962no—
357C4—5961no—
358C4—1491no—
359C4—1491no—
360C4D4×#1059701011yescharacteristic
361C4C23×#1059701011yescharacteristic
362C2—21no—
363C2—42no—
364C2—41no—
365C2—2981no—
366C2—5962no—
367C2—5961no—
368C2—1491no—
369C2—1491no—
370C2C2×D4×#1059701011yescharacteristic
subgroupG/H
centerC2C2×D4×#10597010
commutatorC4×C149C23×C4
FrattiniC4C23×#10597010
FittingAGL(1,ℤ/8)×C149C4
socleC2×C149C2×C4×D4
prime radicalAGL(1,ℤ/8)×D149C2
cosocleC4×D149C24
hypercenterAGL(1,ℤ/8)#10597010
hypocenterC149#2946
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #23750694C2semidirect
2. #23750692C2semidirect
3. #23750666C2semidirect
4. #23750664C2semidirect
5. SD16×#10597010C2semidirect
6. D8×#10597010C2semidirect
7. #23750636C2semidirect
8. #23750615C2semidirect
9. C2×#18011973C2semidirect
10. #23750591C2semidirect
13. Q8×#10597010C22semidirect
19. D4×#10597010C22semidirect
26. #18011980C22semidirect
27. #18011979C22semidirect
28. #18011974C22semidirect
29. #18011974C22semidirect
32. #18011973C22semidirect
33. #18011973C22semidirect
34. #18011965C22semidirect
35. C8×#10597010C22semidirect
38. #18011939C4semidirect
39. #18011938C4semidirect
40. #18011937C4semidirect
41. #18011936C4semidirect
42. #18011935C4semidirect
46. AGL(1,ℤ/8)×C149C4semidirect
71. #14558737C2×C4semidirect
73. #14558736C2×C4semidirect
75. #14558735C2×C4semidirect
77. C2×D596C2×C4semidirect
82. D4×D149C2×C4semidirect
87. #14558725C2×C4semidirect
88. #14558724C2×C4semidirect
89. #14558723C2×C4semidirect
90. D1192C2×C4semidirect
91. #14558721C2×C4semidirect
92. #14558721C2×C4semidirect
93. #14558720C2×C4semidirect
94. #14558719C2×C4semidirect
96. #41×C149C2×C4semidirect
97. C2×D4×C149C2×C4semidirect
98. SD16×C149C2×C4semidirect
99. D8×C149C2×C4semidirect
100. M16×C149C2×C4semidirect
185. C149#2946semidirect
205. AGL(1,ℤ/8)#10597010semidirect
239. #41C2×#10597010semidirect
249. C2×D4C2×#10597010semidirect
259. SD16C2×#10597010semidirect
263. D8C2×#10597010semidirect
266. M16C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506942
#237506922
#237506662
#237506642
SD16×#105970102
D8×#105970102
#237506362
#237506152
C2×#180119732
#237505912
AGL(1,ℤ/8)×D1492
#2946149