Finite Group Databasebeta

← #34045708

Subgroups — #34045708

Order 19072.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#18011939C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic, complemented
3C2×#18011907C211yesmaximal, characteristic, complemented
4C2×#18011837C211yesmaximal, characteristic, complemented
5#23749631C211yesmaximal, characteristic, complemented
6#23749386C211yesmaximal, characteristic, complemented
7C2×#100×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×D596C2211yescharacteristic
10C22×C22⋊D149—22no—
11#18011939—22no—
12#18011939—22no—
13C2×#14558725—21no—
14C2×D1192—21no—
15#18011907—22no—
16#18011907—22no—
17#18011907—21no—
18#18011898—21no—
19#18011882—22no—
20#18011880—22no—
21#18011870C2211yescharacteristic
22C2×C4×Dic149C2211yescharacteristic
23#18011837—22no—
24#18011833—22no—
25C22×D4×C149C2211yescharacteristic
26C2×M16×C149C2211yescharacteristic
27C2×M16×C149C2211yescharacteristic
28#100×C149—22no—
29C23×D149—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34C2×Dic298D411yescharacteristic, complemented
35C2×D596—21no—
36C2×D596—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596D411yescharacteristic, complemented
41C2×D596D412yescomplemented
42C2×C22⋊D149—28no—
43C2×C22⋊D149—24no—
44C2×C22⋊D149—21no—
45C2×C22⋊D149—48no—
46C22×Dic149—21no—
47C2×C4×D149—21no—
48#14558725—24no—
49D1192—24no—
50C4⋊Dic149D412yescomplemented
51C22⋊Dic149—24no—
52C22⋊Dic149—21no—
53C4×Dic149—21no—
54C4×Dic149—21no—
55C4×Dic149D412yescomplemented
56C24×C149D412yes—
57C2×D4×C149—21no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C22×C4×C149C2311yescharacteristic
64M16×C149—21no—
65M16×C149—21no—
66M16×C149—21no—
67M16×C149D412yescomplemented
68C2×C8×C149—21no—
69C2×C8×C149—21no—
70C22×D149—21no—
71C22×D149—22no—
72C22×D149—44no—
73C22×D149—41no—
74C22×D149—41no—
75Dic298—21no—
76Dic298—21no—
77D596—21no—
78D596—22no—
79D596—22no—
80D596—21no—
81D596—41no—
82D596—41no—
83C22⋊D149—416no—
84C22⋊D149—41no—
85C22⋊D149—41no—
86C22⋊D149—84no—
87C2×Dic149—24no—
88C2×Dic149—22no—
89C2×Dic149—21no—
90C2×Dic149—22no—
91C4×D149—41no—
92C4×D149—41no—
93C23×C149—22no—
94C23×C149—22no—
95C23×C149—22no—
96C23×C149—44no—
97C23×C149C2×D411yescharacteristic
98D4×C149—41no—
99D4×C149—41no—
100D4×C149—41no—
101D4×C149—41no—
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149#4111yescharacteristic
108C8×C149—22no—
109C8×C149—41no—
110C22×C149—22no—
111C22×C149—44no—
112C22×C149—42no—
113C22×C149—44no—
114C22×C149—82no—
115C22×C149#12011yescharacteristic
116C22×C149#12011yescharacteristic
117C22×C149#12111yescharacteristic
118C2×D149—44no—
119C2×D149—41no—
120C2×D149—42no—
121C2×D149—42no—
122C2×D149—82no—
123C2×D149—82no—
124C4×C149#12011yescharacteristic
125C4×C149#12111yescharacteristic
126C4×C149#12111yescharacteristic
127C4×C149#12711yescharacteristic
128Dic149—24no—
129Dic149—41no—
130Dic149—42no—
131C2×C149—21no—
132C2×C149—21no—
133C2×C149—82no—
134C2×C149#39211yescharacteristic
135C2×C149#45312yes—
136D149—81no—
137D149—82no—
138C149#200211yescharacteristic, complemented, Sylow
139#2002—1491nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1491no—
141#535—1491no—
142C2×#127—1491no—
143C2×#104—1491no—
144#418—1491no—
145C2×#100D14911yescharacteristic, complemented
146#339—1491no—
147C2×#41—1491no—
148C22×D4—2982no—
149C22×D4—1491no—
150C22×D4C2×D14911yescharacteristic
151AGL(1,ℤ/8)—2982no—
152AGL(1,ℤ/8)—2982no—
153C2×SD16—2981no—
154C2×D8—2981no—
155C2×M16C2×D14911yescharacteristic
156C2×M16C2×D14911yescharacteristic
157#127—2982no—
158#127—2981no—
159#127—2982no—
160#124—2981no—
161#121—2982no—
162#120—2982no—
163#117—1491no—
164C2×C42—1491no—
165#104—2982no—
166#102—2982no—
167#100—22no—
168C24—2981no—
169C24D59612yes—
170#41—2981no—
171#41—2981no—
172#41—2981no—
173#41—2981no—
174C2×Q8—1491no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—2988no—
182C2×D4—2981no—
183C2×D4—2984no—
184C2×D4—2981no—
185C2×D4—2981no—
186C2×D4—2981no—
187C2×D4—2981no—
188C2×D4—2981no—
189C2×D4—5968no—
190C2×D4—1491no—
191C2×D4—1492no—
192C22×C4—2981no—
193C22×C4—2981no—
194C22×C4C22×D14911yescharacteristic
195SD16—2984no—
196D8—2984no—
197M16—21no—
198M16—21no—
199M16—21no—
200M16C22⋊D14912yescomplemented
201C2×C8—21no—
202C2×C8—21no—
203C4⋊C4—1492no—
204C22⋊C4—2984no—
205C22⋊C4—2981no—
206C42—2981no—
207C42—2981no—
208C42—1492no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—44no—
213C23—2982no—
214C23—2981no—
215C23—5964no—
216C23—5961no—
217C23—5961no—
218C23C2×D59611yescharacteristic
219Q8—2981no—
220Q8—2981no—
221D4—41no—
222D4—41no—
223D4—41no—
224D4—41no—
225D4—2981no—
226D4—2982no—
227D4—2982no—
228D4—2981no—
229D4—59616no—
230D4—5961no—
231D4—5961no—
232D4—5961no—
233D4—5961no—
234D4—11924no—
235C2×C4—2984no—
236C2×C4—2982no—
237C2×C4—2982no—
238C2×C4—2981no—
239C2×C4—5961no—
240C2×C4—5961no—
241C2×C4D4×D14911yescharacteristic
242C2×C4D4×D14911yescharacteristic
243C2×C4D4×D14911yescharacteristic
244C2×C4D4×D14911yescharacteristic
245C2×C4C2×C22⋊D14911yescharacteristic
246C2×C4#1455873611yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—5964no—
255C22—5961no—
256C22—5962no—
257C22—5962no—
258C22—11922no—
259C22—11922no—
260C22#1801188111yescharacteristic
261C22#1801188111yescharacteristic
262C22#1801188511yescharacteristic
263C4—2984no—
264C4—5961no—
265C4—5962no—
266C4#1801187911yescharacteristic
267C4#1801188411yescharacteristic
268C4#1801188411yescharacteristic
269C4#1801190711yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—11922no—
274C2—11921no—
275C2#2374953411yescharacteristic
276C2#2374979512yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#100×C149C2
socleC22×C149#120
hypercenterC2×#100D149
hypocenterC149#2002
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. #23750192C2semidirect
3. C2×#18011907C2semidirect
4. C2×#18011837C2semidirect
5. #23749631C2semidirect
6. #23749386C2semidirect
7. C2×#100×C149C2semidirect
34. C2×Dic298D4semidirect
40. C2×D596D4semidirect
41. C2×D596D4semidirect
50. C4⋊Dic149D4semidirect
55. C4×Dic149D4semidirect
67. M16×C149D4semidirect
138. C149#2002semidirect
145. C2×#100D149semidirect
200. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
#237501922
C2×#180119072
C2×#180118372
#237496312
#237493862
C2×#100×C1492
#2002149