Finite Group Databasebeta

← #34078483

Subgroups — #34078483

Order 19328.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753048C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C2×#18012764C211yesmaximal, characteristic, complemented
4#23752781C211yesmaximal, characteristic, complemented
5#23752386C214yesmaximal, complemented
6#23752381C214yesmaximal, complemented
7#23752230C211yesmaximal, characteristic, complemented
8#23752194C211yesmaximal, characteristic, complemented
9#421×C151C211yesmaximal, characteristic, complemented
10#18012787—21no—
11#18012786—21no—
12#18012786C2212yescomplemented
13#18012785—21no—
14#18012785C2212yescomplemented
15#18012784—21no—
16#18012784—22no—
17C2×#14559004—22no—
18C2×#14559004C2211yescharacteristic
19C2×#14559004C2211yescharacteristic
20#41×D151—22no—
21#41×D151—22no—
22C22×D604C2211yescharacteristic, complemented
23#18012767—22no—
24#18012767C2214yescomplemented
25#18012764—22no—
26#18012764C2214yescomplemented
27C2×#14558993—21no—
28C2×#14558991—21no—
29C2×D1208—21no—
30C2×#14558989—21no—
31C2×#14558988C2211yescharacteristic, complemented
32#18012736C2212yescomplemented
33#18012727C2212yescomplemented
34#18012714—22no—
35#18012709—22no—
36#18012667C2214yescomplemented
37#18012657C2212yescomplemented
38#18012655C2212yescomplemented
39C2×#41×C151C2211yescharacteristic
40C2×M16×C151C2211yescharacteristic, complemented
41#117×C151C2211yescharacteristic, complemented
42#104×C151C2214yescomplemented
43C23×D151—21no—
44#14559005—22no—
45#14559005—22no—
46#14559004—24no—
47#14559004—24no—
48#14559004—22no—
49#14559004—22no—
50#14559004—21no—
51#14559004—21no—
52#14559004—21no—
53#14559004—21no—
54#14559004—21no—
55#14559004—21no—
56#14559004D412yescomplemented
57#14559004C2312yes—
58#14559003—24no—
59#14559003—22no—
60#14559003—24no—
61#14559003—22no—
62C2×Dic302—22no—
63C2×Dic302D411yescharacteristic, complemented
64C2×Dic302C2311yescharacteristic
65Q8×D151—22no—
66Q8×D151—22no—
67C2×D604—22no—
68C2×D604—24no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604D411yescharacteristic, complemented
75C2×D604C2312yes—
76C2×D604C2311yescharacteristic
77C2×C22⋊D151—24no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151D412yes—
80D4×D151—24no—
81D4×D151—22no—
82D4×D151—24no—
83D4×D151—22no—
84C2×C4×D151—24no—
85C2×C4×D151—21no—
86C2×C4×D151D412yes—
87#14558993—24no—
88#14558991—24no—
89D1208—24no—
90#14558989—24no—
91#14558988—21no—
92#14558988C2312yes—
93C2×C151⋊C8—21no—
94(C2×D151)⋊C4—24no—
95#41×C151—21no—
96#41×C151—21no—
97#41×C151D412yescomplemented
98#41×C151C2312yes—
99C2×Q8×C151D411yescharacteristic, complemented
100C2×D4×C151—21no—
101C2×D4×C151D411yescharacteristic, complemented
102C22×C4×C151—21no—
103C22×C4×C151C2311yescharacteristic
104M16×C151—21no—
105M16×C151C2312yes—
106C2×C8×C151—21no—
107C4⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C42×C151C2312yes—
110C22×D151—24no—
111C22×D151—21no—
112C22×D151—22no—
113C22×D151—41no—
114C22×D151—41no—
115C22×D151—82no—
116C22×D151C2×D412yes—
117Dic302—24no—
118Dic302—21no—
119Dic302—21no—
120Dic302—21no—
121Dic302C2×D412yes—
122D604—24no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—22no—
127D604—22no—
128D604—41no—
129D604—41no—
130D604—84no—
131D604C2×D412yes—
132C22⋊D151—24no—
133C22⋊D151—24no—
134C22⋊D151—22no—
135C22⋊D151—22no—
136C22⋊D151—22no—
137C22⋊D151—22no—
138C2×Dic151—24no—
139C2×Dic151—21no—
140C2×Dic151C2×D412yes—
141C4×D151—24no—
142C4×D151—24no—
143C4×D151—22no—
144C4×D151—22no—
145C4×D151—22no—
146C4×D151—22no—
147C151⋊C8—22no—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151C2×D412yes—
152D4×C151—22no—
153D4×C151—22no—
154D4×C151—21no—
155D4×C151C2×D412yes—
156C2×C4×C151—21no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—22no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2×D411yescharacteristic
162C2×C4×C151C2×D411yescharacteristic
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2411yescharacteristic
166C8×C151—22no—
167C22×C151—22no—
168C22×C151—41no—
169C22×C151—81no—
170C22×C151#12011yescharacteristic
171C22×C151#12011yescharacteristic
172C22×C151C22×D411yescharacteristic
173C2×D151—22no—
174C2×D151—22no—
175C2×D151—42no—
176C2×D151—44no—
177C2×D151—42no—
178C2×D151—81no—
179C2×D151—84no—
180C2×D151—82no—
181C2×D151—82no—
182C4×C151—22no—
183C4×C151—42no—
184C4×C151#12011yescharacteristic
185C4×C151#12011yescharacteristic
186C4×C151C22×D411yescharacteristic
187C4×C151C22×D411yescharacteristic
188Dic151—22no—
189Dic151—22no—
190C2×C151—21no—
191C2×C151—21no—
192C2×C151—21no—
193C2×C151—42no—
194C2×C151C2×#12011yescharacteristic
195D151—42no—
196D151—42no—
197D151—82no—
198C151#302111yescharacteristic, complemented, Sylow
199#3021—1511nomaximal, Sylow
200#585—1511no—
201C2×AGL(1,ℤ/8)—1511no—
202C2×AGL(1,ℤ/8)—1511no—
203#535—1511no—
204#454—1514no—
205#453—1514no—
206#421—1511no—
207#421D15111yescharacteristic, complemented
208#413—1511no—
2092−1+4—3021no—
2102−1+4—3021no—
2112−1+4—1512no—
212H(5,𝔽2)—3022no—
213H(5,𝔽2)—3021no—
214H(5,𝔽2)—3021no—
215H(5,𝔽2)—1512no—
216C2×#41—3022no—
217C2×#41—3022no—
218C2×#41—3022no—
219C2×#41—1511no—
220C2×#41—1511no—
221C2×#41C2×D15111yescharacteristic
222C22×D4—1511no—
223AGL(1,ℤ/8)—3022no—
224AGL(1,ℤ/8)—3022no—
225AGL(1,ℤ/8)—1514no—
226AGL(1,ℤ/8)—1514no—
227C2×SD16—3021no—
228C2×SD16—3021no—
229C2×D8—3021no—
230C2×D8—3021no—
231C2×M16—1511no—
232C2×M16C2×D15111yescharacteristic, complemented
233#127—1512no—
234#124—1512no—
235#121—3022no—
236#120—3022no—
237#117C2×D15111yescharacteristic, complemented
238#104—1514no—
239#104C2×D15114yescomplemented
240#101—1512no—
241#100—1512no—
242C24—3021no—
243#41—21no—
244#41—21no—
245#41—3024no—
246#41—3024no—
247#41—3022no—
248#41—3022no—
249#41—3024no—
250#41—3022no—
251#41—3022no—
252#41—3022no—
253#41—3022no—
254#41—3024no—
255#41—3021no—
256#41—3021no—
257#41—3021no—
258#41—3021no—
259#41—3021no—
260#41—3021no—
261#41—1512no—
262#41—1512no—
263#41D60412yescomplemented
264#41C22×D15112yes—
265C2×Q8—3022no—
266C2×Q8—3022no—
267C2×Q8—3022no—
268C2×Q8—1511no—
269C2×Q8—1511no—
270C2×Q8D60411yescharacteristic, complemented
271C2×D4—21no—
272C2×D4—3022no—
273C2×D4—3024no—
274C2×D4—3024no—
275C2×D4—3022no—
276C2×D4—3024no—
277C2×D4—3024no—
278C2×D4—3021no—
279C2×D4—3022no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—1512no—
286C2×D4—1511no—
287C2×D4—1512no—
288C2×D4—1511no—
289C2×D4D60411yescharacteristic, complemented
290C22×C4—21no—
291C22×C4—3024no—
292C22×C4—3021no—
293C22×C4—1512no—
294C22×C4C22×D15111yescharacteristic
295SD16—3024no—
296SD16—3024no—
297D8—3024no—
298D8—3024no—
299M16—21no—
300M16—3021no—
301M16—1512no—
302M16C22×D15112yes—
303C2×C8—21no—
304C2×C8—3021no—
305C4⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—3024no—
308C42C22×D15112yes—
309C23—21no—
310C23—3024no—
311C23—3021no—
312C23—3022no—
313C23—6041no—
314C23—6041no—
315C23—1512no—
316C23—12082no—
317C23D4×D15111yescharacteristic
318Q8—21no—
319Q8—3024no—
320Q8—3021no—
321Q8—3021no—
322Q8—3021no—
323Q8—1512no—
324Q8C2×D60412yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—3024no—
329D4—3024no—
330D4—3024no—
331D4—3022no—
332D4—3022no—
333D4—3022no—
334D4—3022no—
335D4—3021no—
336D4—3021no—
337D4—3022no—
338D4—3021no—
339D4—3022no—
340D4—6041no—
341D4—6041no—
342D4—1512no—
343D4—12084no—
344D4C2×D60412yes—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—3024no—
350C2×C4—3024no—
351C2×C4—3024no—
352C2×C4—3021no—
353C2×C4—3022no—
354C2×C4—3022no—
355C2×C4—3022no—
356C2×C4—3022no—
357C2×C4—1512no—
358C2×C4D4×D15111yescharacteristic
359C2×C4D4×D15111yescharacteristic
360C2×C4D4×D15111yescharacteristic
361C2×C4C2×D60411yescharacteristic
362C2×C4C2×D60411yescharacteristic
363C2×C4C23×D15111yescharacteristic
364C8—22no—
365C8—3022no—
366C22—22no—
367C22—41no—
368C22—81no—
369C22—3022no—
370C22—3022no—
371C22—6042no—
372C22—6044no—
373C22—6042no—
374C22—12081no—
375C22—12082no—
376C22—12082no—
377C22—12084no—
378C22#1801270911yescharacteristic
379C22#1801270911yescharacteristic
380C22C2×D4×D15111yescharacteristic
381C4—22no—
382C4—42no—
383C4—3022no—
384C4—3022no—
385C4#1801270911yescharacteristic
386C4#1801270911yescharacteristic
387C4C2×D4×D15111yescharacteristic
388C4C22×D60411yescharacteristic
389C2—21no—
390C2—21no—
391C2—21no—
392C2—42no—
393C2—6042no—
394C2—6042no—
395C2—12082no—
396C2C2×#1801270911yescharacteristic
subgroupG/H
centerC2C2×#18012709
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#421×C151C2
socleC2×C151C2×#120
hypercenter#421D151
hypocenterC151#3021
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012764C2semidirect
4. #23752781C2semidirect
5. #23752386C2semidirect
6. #23752381C2semidirect
7. #23752230C2semidirect
8. #23752194C2semidirect
9. #421×C151C2semidirect
12. #18012786C22semidirect
14. #18012785C22semidirect
22. C22×D604C22semidirect
24. #18012767C22semidirect
26. #18012764C22semidirect
31. C2×#14558988C22semidirect
32. #18012736C22semidirect
33. #18012727C22semidirect
36. #18012667C22semidirect
37. #18012657C22semidirect
38. #18012655C22semidirect
40. C2×M16×C151C22semidirect
41. #117×C151C22semidirect
42. #104×C151C22semidirect
56. #14559004D4semidirect
63. C2×Dic302D4semidirect
74. C2×D604D4semidirect
97. #41×C151D4semidirect
99. C2×Q8×C151D4semidirect
101. C2×D4×C151D4semidirect
198. C151#3021semidirect
207. #421D151semidirect
232. C2×M16C2×D151semidirect
237. #117C2×D151semidirect
239. #104C2×D151semidirect
263. #41D604semidirect
270. C2×Q8D604semidirect
289. C2×D4D604semidirect

Maximal subgroups

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

subgroupindex
#237530482
C2×#180127672
C2×#180127642
#237527812
#237523862
#237523812
#237522302
#237521942
#421×C1512
#3021151