Finite Group Databasebeta

← #34060653

Subgroups — #34060653

Order 19072.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750704C211yesmaximal, characteristic
2#23750640C211yesmaximal, characteristic, complemented
3#23750630C211yesmaximal, characteristic, complemented
4#23750622C211yesmaximal, characteristic
5#23750508C211yesmaximal, characteristic, complemented
6#23750496C211yesmaximal, characteristic, complemented
7#104×D149C211yesmaximal, characteristic
8#18011999—21no—
9#18011998—22no—
10#18011998—21no—
11C2×#14558746—21no—
12C2×#14558746C2211yescharacteristic
13C2×#14558746C2211yescharacteristic
14D149⋊M16—21no—
15D149⋊M16C2211yescharacteristic
16#18011990C2211yescharacteristic
17#18011982—21no—
18#18011981—21no—
19#18011978—22no—
20#18011976—21no—
21#18011975—21no—
22#41×D149C2211yescharacteristic
23M16×D149C2211yescharacteristic
24C42×D149C2211yescharacteristic
25#18011839C411yescharacteristic, complemented
26#18011838C411yescharacteristic, complemented
27#18011837C411yescharacteristic, complemented
28#104×C149C411yescharacteristic, complemented
29#14558746—22no—
30#14558746—21no—
31#14558746—21no—
32#14558746—21no—
33#14558746—21no—
34#14558746D411yescharacteristic
35#14558746D411yescharacteristic
36#14558745—22no—
37#14558745—21no—
38D149⋊C8—22no—
39D149⋊C8—21no—
40C2×#11924753—22no—
41C2×#11924753—21no—
42C2×#11924753D412yes—
43C4⋊#10597010—21no—
44C22⋊#10597010—21no—
45C4×#10597010—21no—
46#14558737D411yescharacteristic
47#14558736—21no—
48#14558736C2×C411yescharacteristic
49#14558735—21no—
50#14558735D411yescharacteristic
51Q8×D149Q811yescharacteristic
52D4×D149—21no—
53D4×D149Q811yescharacteristic
54C2×C4×D149—21no—
55C2×C4×D149—21no—
56C2×C4×D149C2311yescharacteristic
57#14558720C2×C411yescharacteristic
58#14558719—21no—
59C8×D149—21no—
60C4×Dic149—21no—
61C4×Dic149C2×C411yescharacteristic
62#41×C149C2×C411yescharacteristic
63M16×C149C2×C411yescharacteristic
64C42×C149C2×C411yescharacteristic
65C2×#10597010—41no—
66#11924753—21no—
67#11924753—22no—
68#11924753—21no—
69#11924753—41no—
70C22×D149—21no—
71C22×D149#4111yescharacteristic
72Dic298—21no—
73Dic298C4⋊C411yescharacteristic
74D596—21no—
75D596C4⋊C411yescharacteristic
76C22⋊D149—21no—
77C22⋊D149—21no—
78C22⋊D149—21no—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149C2×D411yescharacteristic
82C4×D149—21no—
83C4×D149—21no—
84C4×D149—21no—
85C4×D149—42no—
86C4×D149C2×D411yescharacteristic
87C4×D149C2×D411yescharacteristic
88C4×D149C2×Q811yescharacteristic
89C4×D149#4111yescharacteristic
90#11924746—21no—
91Q8×C149C4⋊C411yescharacteristic
92D4×C149—21no—
93D4×C149C4⋊C411yescharacteristic
94C2×C4×C149—21no—
95C2×C4×C149—21no—
96C2×C4×C149C22×C411yescharacteristic
97C8×C149—21no—
98C22×C149—21no—
99C22×C149C4×D411yescharacteristic
100C2×D149—21no—
101C2×D149—41no—
102C2×D149—81no—
103C2×D149C22⋊Q811yescharacteristic
104C2×D149#12311yescharacteristic
105#10597010—81no—
106C4×C149—21no—
107C4×C149—41no—
108C4×C149C2×C4⋊C411yescharacteristic
109C4×C149C4×D411yescharacteristic
110Dic149—22no—
111Dic149—21no—
112Dic149#12011yescharacteristic
113Dic149C22⋊Q811yescharacteristic
114C2×C149—21no—
115C2×C149—41no—
116C2×C149#38511yescharacteristic
117D149—21no—
118D149—21no—
119D149—41no—
120C149#186111yescharacteristic, complemented, Sylow
121#1861—1491nomaximal, Sylow
122#568—1491no—
123#430—1491no—
124#423—1491no—
125#421—1491no—
126C2×#104—1491no—
127#344—1491no—
128#339—1491no—
129C2×#41—1491no—
130#131—2981no—
131#131—2981no—
132#131—2982no—
133C2×M16—2981no—
134C2×M16—2981no—
135C2×M16—1491no—
136C2×M16—1491no—
137C2×M16—1491no—
138C2×M16—1491no—
139#117—1491no—
140C2×C42—1491no—
141#108—2981no—
142#108—2981no—
143C4⋊C8—2982no—
144#104—2981no—
145#104—2981no—
146#104—1491no—
147#104—1491no—
148#104—1491no—
149#104#1059701011yescharacteristic, complemented
150#41—2981no—
151#41—2981no—
152#41—1491no—
153#41—1491no—
154#41—1491no—
155#41C2×#1059701011yescharacteristic
156C2×Q8—1491no—
157C2×D4—2981no—
158C2×D4—1491no—
159C22×C4—2981no—
160C22×C4—2981no—
161C22×C4—1491no—
162M16—2981no—
163M16—2982no—
164M16—2982no—
165M16—2981no—
166M16—2981no—
167M16—2981no—
168M16—2981no—
169M16—2981no—
170M16—1491no—
171M16—1491no—
172M16—1491no—
173M16C2×#1059701011yescharacteristic
174C2×C8—2981no—
175C2×C8—2982no—
176C2×C8—2982no—
177C2×C8—2981no—
178C2×C8—2981no—
179C2×C8—1492no—
180C4⋊C4—2981no—
181C22⋊C4—2981no—
182C42—2981no—
183C42—2981no—
184C42—1491no—
185C42C2×#1059701011yescharacteristic
186C23—2981no—
187C23—1491no—
188Q8—2981no—
189Q8—1491no—
190Q8C4⋊#1059701011yescharacteristic
191D4—21no—
192D4—2981no—
193D4—2981no—
194D4—2981no—
195D4—2981no—
196D4—1491no—
197D4C4⋊#1059701011yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—2981no—
201C2×C4—2981no—
202C2×C4—2981no—
203C2×C4—2981no—
204C2×C4—2981no—
205C2×C4—5962no—
206C2×C4—5961no—
207C2×C4—1491no—
208C2×C4—1491no—
209C2×C4—1491no—
210C2×C4—1491no—
211C2×C4—1491no—
212C2×C4C22×#1059701011yescharacteristic
213C8—21no—
214C8—2981no—
215C8—2981no—
216C8—2982no—
217C8—2981no—
218C8—5961no—
219C22—21no—
220C22—2981no—
221C22—5961no—
222C22—1491no—
223C22—1491no—
224C22—11921no—
225C22D4×#1059701011yescharacteristic
226C4—21no—
227C4—41no—
228C4—2982no—
229C4—2981no—
230C4—1491no—
231C4—1491no—
232C4—11921no—
233C4C2×C4⋊#1059701011yescharacteristic
234C4D4×#1059701011yescharacteristic
235C2—21no—
236C2—41no—
237C2—2981no—
238C2—2981no—
239C2—5961no—
240C2#2375057211yescharacteristic
subgroupG/H
centerC2#23750572
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#104×C149C4
socleC2×C149#385
prime radical#41×D149C22
cosocleC2×C4×D149C23
hypercenter#104#10597010
hypocenterC149#1861
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #23750640C2semidirect
3. #23750630C2semidirect
5. #23750508C2semidirect
6. #23750496C2semidirect
25. #18011839C4semidirect
26. #18011838C4semidirect
27. #18011837C4semidirect
28. #104×C149C4semidirect
120. C149#1861semidirect
149. #104#10597010semidirect

Maximal subgroups

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

subgroupindex
#237507042
#237506402
#237506302
#237506222
#237505082
#237504962
#104×D1492
#1861149