Finite Group Databasebeta

← #34045743

Subgroups — #34045743

Order 19072.

380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750423C211yesmaximal, characteristic, complemented
2C2×#18011936C211yesmaximal, characteristic, complemented
3#23750194C211yesmaximal, characteristic, complemented
4#23749643C211yesmaximal, characteristic, complemented
5#23749629C211yesmaximal, characteristic, complemented
6#23749395C211yesmaximal, characteristic, complemented
7#410×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×D596C2211yescharacteristic
10#18011942—21no—
11#18011941—21no—
12#18011937—21no—
13#18011936—22no—
14#18011936—21no—
15#18011936—22no—
16#18011931—22no—
17C2×#14558723—21no—
18C2×#14558721—21no—
19C2×#14558720C2211yescharacteristic
20C2×#14558720C2211yescharacteristic
21#18011908—21no—
22#18011899—21no—
23#18011886—22no—
24#18011881—22no—
25#18011839—22no—
26#18011831—22no—
27C2×#41×C149C2211yescharacteristic
28#117×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#99×C149—22no—
31C23×D149—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35#14558736—21no—
36C2×Dic298D411yescharacteristic
37C2×D596—24no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596—21no—
42C2×D596—21no—
43C2×D596D411yescharacteristic
44C2×D596D412yes—
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558726—22no—
48#14558724—22no—
49#14558723—24no—
50#14558723—22no—
51#14558721—24no—
52#14558721—22no—
53#14558720—21no—
54#14558720—21no—
55#14558720—21no—
56#14558720D412yescomplemented
57C2×#11924746—21no—
58C2×#11924746D412yescomplemented
59#14558713—24no—
60#41×C149—21no—
61#41×C149—21no—
62#41×C149—21no—
63#41×C149—21no—
64C2×Q8×C149D411yescharacteristic, complemented
65C2×D4×C149—21no—
66C2×D4×C149D411yescharacteristic, complemented
67C22×C4×C149—21no—
68C22×C4×C149C2311yescharacteristic
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C22⋊C4×C149—21no—
72C22⋊C4×C149D412yes—
73C42×C149—21no—
74C42×C149—21no—
75C22×D149—21no—
76C22×D149—22no—
77C22×D149—41no—
78C22×D149—41no—
79C22×D149—82no—
80Dic298—21no—
81Dic298—21no—
82D596—22no—
83D596—21no—
84D596—22no—
85D596—21no—
86D596—41no—
87D596—41no—
88D596—84no—
89C22⋊D149—41no—
90C22⋊D149—41no—
91C2×Dic149—21no—
92C4×D149—41no—
93C4×D149—41no—
94#11924746—22no—
95#11924746—22no—
96C23×C149—21no—
97C23×C149C2×D411yescharacteristic
98Q8×C149—21no—
99Q8×C149—21no—
100D4×C149—21no—
101D4×C149—21no—
102D4×C149—41no—
103D4×C149—41no—
104C2×C4×C149—22no—
105C2×C4×C149—21no—
106C2×C4×C149—41no—
107C2×C4×C149—41no—
108C2×C4×C149—41no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149#4111yescharacteristic
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—81no—
118C22×C149#12011yescharacteristic
119C22×C149#12111yescharacteristic
120C22×C149#12711yescharacteristic
121C2×D149—42no—
122C2×D149—44no—
123C2×D149—41no—
124C2×D149—42no—
125C2×D149—82no—
126C2×D149—82no—
127C4×C149—42no—
128C4×C149—41no—
129C4×C149—81no—
130C4×C149#12011yescharacteristic
131C4×C149#12011yescharacteristic
132C4×C149#12111yescharacteristic
133C4×C149#12111yescharacteristic
134Dic149—41no—
135C2×C149—21no—
136C2×C149—21no—
137C2×C149—21no—
138C2×C149—81no—
139C2×C149#39211yescharacteristic
140D149—81no—
141D149—82no—
142C149#200811yescharacteristic, complemented, Sylow
143#2008—1491nomaximal, Sylow
144#575—1491no—
145C2×AGL(1,ℤ/8)—1491no—
146#535—1491no—
147#421—1491no—
148#418—1491no—
149#410D14911yescharacteristic, complemented
150#344—1491no—
151C2×#41—1491no—
152C2×#41C2×D14911yescharacteristic
153C22×D4—1491no—
154#137—2981no—
155#137—2981no—
156AGL(1,ℤ/8)—2982no—
157AGL(1,ℤ/8)—2981no—
158AGL(1,ℤ/8)—2981no—
159AGL(1,ℤ/8)—2982no—
160#135—2982no—
161C2×SD16—2981no—
162C2×D8—2981no—
163C2×M16—1491no—
164C2×M16—1491no—
165#127—2981no—
166#124—2981no—
167#121—2982no—
168#120—2982no—
169#117C2×D14911yescharacteristic
170#117C2×D14911yescharacteristic
171#104—2982no—
172#102—2982no—
173#99—22no—
174C24—2981no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—2981no—
180#41—2981no—
181#41—2981no—
182#41—2981no—
183C2×Q8—1491no—
184C2×Q8D59611yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—2984no—
187C2×D4—2981no—
188C2×D4—2981no—
189C2×D4—2981no—
190C2×D4—2981no—
191C2×D4—2981no—
192C2×D4—2981no—
193C2×D4—1492no—
194C2×D4—1491no—
195C2×D4D59611yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—2981no—
198C22×C4C22×D14911yescharacteristic
199Q16—2982no—
200SD16—2982no—
201SD16—2984no—
202SD16—2982no—
203D8—2984no—
204D8—2982no—
205M16—2981no—
206M16—2981no—
207M16—2981no—
208M16—1492no—
209C2×C8—2981no—
210C2×C8—1492no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—2984no—
215C22⋊C4C22⋊D14912yes—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—2982no—
220C23—2981no—
221C23—5961no—
222C23—5961no—
223C23—11922no—
224C23C2×C22⋊D14911yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—2981no—
228Q8—2981no—
229D4—21no—
230D4—21no—
231D4—41no—
232D4—41no—
233D4—2982no—
234D4—2981no—
235D4—2982no—
236D4—2981no—
237D4—5961no—
238D4—5961no—
239D4—5961no—
240D4—5961no—
241D4—11924no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—2981no—
248C2×C4—5961no—
249C2×C4—5961no—
250C2×C4D4×D14911yescharacteristic
251C2×C4D4×D14911yescharacteristic
252C2×C4D4×D14911yescharacteristic
253C2×C4D4×D14911yescharacteristic
254C2×C4C2×D59611yescharacteristic
255C2×C4#1455873611yescharacteristic
256C8—2982no—
257C8—2982no—
258C22—41no—
259C22—41no—
260C22—81no—
261C22—5962no—
262C22—5964no—
263C22—5961no—
264C22—5962no—
265C22—11922no—
266C22—11922no—
267C22#1801187911yescharacteristic
268C22#1801188511yescharacteristic
269C22#1801190711yescharacteristic
270C4—42no—
271C4—41no—
272C4—81no—
273C4—5961no—
274C4#1801188111yescharacteristic
275C4#1801188111yescharacteristic
276C4#1801188411yescharacteristic
277C4#1801188411yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—11922no—
283C2—11921no—
284C2#2374953411yescharacteristic
subgroupG/H
centerC2#23749534
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#410×C149C2
socleC2×C149#392
hypercenter#410D149
hypocenterC149#2008
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23750423C2semidirect
2. C2×#18011936C2semidirect
3. #23750194C2semidirect
4. #23749643C2semidirect
5. #23749629C2semidirect
6. #23749395C2semidirect
7. #410×C149C2semidirect
56. #14558720D4semidirect
58. C2×#11924746D4semidirect
64. C2×Q8×C149D4semidirect
66. C2×D4×C149D4semidirect
142. C149#2008semidirect
149. #410D149semidirect
184. C2×Q8D596semidirect
195. C2×D4D596semidirect

Maximal subgroups

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

subgroupindex
#237504232
C2×#180119362
#237501942
#237496432
#237496292
#237493952
#410×C1492
#2008149