Finite Group Databasebeta

← #34060544

Subgroups — #34060544

Order 19072.

536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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#23750623C212yesmaximal, complemented
2#23750618C212yesmaximal, complemented
3#23750611C211yesmaximal, characteristic, complemented
4#23750604C211yesmaximal, characteristic, complemented
5C2×#18011958C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7#18011990C2212yes—
8#18011975—24no—
9#18011974—24no—
10#18011972—21no—
11#18011971—21no—
12#18011970—21no—
13#18011969—21no—
14#18011958—24no—
15#18011958—24no—
16C2×#14558736—21no—
17C2×#14558736C2211yescharacteristic
18C2×#14558735—21no—
19C2×#14558735—21no—
20C2×#14558735C411yescharacteristic, complemented
21C2×#14558735C2211yescharacteristic
22C22×Dic298—21no—
23C22×Dic298C411yescharacteristic, complemented
24C2×Q8×D149C411yescharacteristic, complemented
25C2×Q8×D149C2211yescharacteristic
26C2×#41×C149C411yescharacteristic, complemented
27#14558746—22no—
28#14558745—22no—
29D149⋊C8—22no—
30C4⋊#10597010—22no—
31C22⋊#10597010—22no—
32C4×#10597010—22no—
33#14558736—28no—
34#14558736—22no—
35#14558736—22no—
36#14558735—28no—
37#14558735—28no—
38#14558735—22no—
39#14558735—22no—
40#14558735—22no—
41#14558735D414yes—
42C2×Dic298—28no—
43C2×Dic298—22no—
44C2×Dic298—22no—
45C2×Dic298—21no—
46C2×Dic298—21no—
47C2×Dic298—21no—
48C2×Dic298C2×C411yescharacteristic
49C2×Dic298C2×C411yescharacteristic
50C2×Dic298D411yescharacteristic
51Q8×D149—22no—
52Q8×D149—22no—
53Q8×D149—22no—
54Q8×D149D414yes—
55C2×D596D411yescharacteristic
56C2×C22⋊D149—21no—
57C2×C22⋊D149—21no—
58C2×C22⋊D149D411yescharacteristic
59C2×C22⋊D149D411yescharacteristic
60C22×Dic149—21no—
61C22×Dic149—21no—
62C22×Dic149—21no—
63C2×C4×D149—21no—
64C2×C4×D149—21no—
65C2×C4×D149C2×C411yescharacteristic
66C2×C4×D149C2311yescharacteristic
67#41×C149—22no—
68#41×C149—22no—
69C2×Q8×C149C2×C411yescharacteristic
70C2×D4×C149—21no—
71C2×D4×C149C2×C411yescharacteristic
72C22×C4×C149—21no—
73C22×C4×C149C2×C411yescharacteristic
74C2×#10597010—42no—
75#11924753—42no—
76C22×D149C22⋊C411yescharacteristic
77C22×D149C2×D411yescharacteristic
78Dic298—24no—
79Dic298—24no—
80Dic298—21no—
81Dic298—21no—
82Dic298—24no—
83Dic298—22no—
84Dic298C22⋊C412yes—
85Dic298C22⋊C412yes—
86D596—22no—
87C22⋊D149—24no—
88C22⋊D149—24no—
89C22⋊D149—22no—
90C22⋊D149—22no—
91C2×Dic149—24no—
92C2×Dic149—24no—
93C2×Dic149—21no—
94C2×Dic149—21no—
95C2×Dic149—24no—
96C2×Dic149C22⋊C411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C4×D149—24no—
99C4×D149—24no—
100C4×D149—21no—
101C4×D149—21no—
102C4×D149C2×D412yes—
103C4×D149C2×D412yes—
104C23×C149—21no—
105C23×C149C22⋊C411yescharacteristic
106Q8×C149—21no—
107Q8×C149C22⋊C412yes—
108D4×C149—24no—
109D4×C149—21no—
110D4×C149C22⋊C412yes—
111C2×C4×C149—24no—
112C2×C4×C149—21no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
115C2×C4×C149C22⋊C411yescharacteristic
116C2×C4×C149C22×C411yescharacteristic
117C22×C149—21no—
118C22×C149—22no—
119C22×C149—41no—
120C22×C149—42no—
121C22×C149C2×C22⋊C411yescharacteristic
122C2×D149—21no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149#12012yes—
126#10597010—82no—
127C4×C149—21no—
128C4×C149—22no—
129C4×C149C2×C22⋊C411yescharacteristic
130C4×C149C2×C22⋊C411yescharacteristic
131Dic149—22no—
132Dic149—22no—
133Dic149—21no—
134Dic149#12012yes—
135C2×C149—21no—
136C2×C149—41no—
137C2×C149—42no—
138C2×C149#37911yescharacteristic
139D149—22no—
140D149—41no—
141C149#179611yescharacteristic, complemented, Sylow
142#1796—1491nomaximal, Sylow
143C2×2−1+4—1491no—
144#421—1492no—
145#419—1492no—
146#413—1491no—
147#410—1491no—
1482−1+4—2984no—
1492−1+4—2984no—
150C2×#41—2981no—
151C2×#41—2981no—
152C2×#41—2981no—
153C2×#41—1491no—
154C2×#41—1491no—
155C2×#41—1491no—
156C2×#41#1059701011yescharacteristic, complemented
157C22×Q8—2981no—
158C22×Q8—1491no—
159C22×Q8—1491no—
160C22×Q8—1491no—
161C2×M16—1492no—
162#117—1492no—
163#104—2984no—
164#103—2984no—
165#101—2981no—
166#100—2981no—
167#99—2981no—
168#99—2981no—
169#41—22no—
170#41—22no—
171#41—2988no—
172#41—2982no—
173#41—2982no—
174#41—2988no—
175#41—2988no—
176#41—2982no—
177#41—2982no—
178#41—2982no—
179#41—1494no—
180C2×Q8—2988no—
181C2×Q8—2982no—
182C2×Q8—2982no—
183C2×Q8—2981no—
184C2×Q8—2981no—
185C2×Q8—2982no—
186C2×Q8—2982no—
187C2×Q8—2982no—
188C2×Q8—2981no—
189C2×Q8—1494no—
190C2×Q8—1491no—
191C2×Q8—1491no—
192C2×Q8—1491no—
193C2×Q8C2×#1059701011yescharacteristic
194C2×D4—21no—
195C2×D4—2981no—
196C2×D4—2981no—
197C2×D4—1491no—
198C2×D4—1491no—
199C2×D4—1491no—
200C2×D4C2×#1059701011yescharacteristic
201C22×C4—21no—
202C22×C4—2981no—
203C22×C4—2981no—
204C22×C4—2981no—
205C22×C4—2981no—
206C22×C4—2981no—
207C22×C4—1491no—
208C22×C4—1491no—
209C22×C4C2×#1059701011yescharacteristic
210M16—2982no—
211M16—2982no—
212C2×C8—2982no—
213C4⋊C4—2982no—
214C22⋊C4—2982no—
215C42—2982no—
216C23—21no—
217C23—1491no—
218C23—1491no—
219C23C22⋊#1059701011yescharacteristic
220Q8—21no—
221Q8—2984no—
222Q8—2984no—
223Q8—2982no—
224Q8—2984no—
225Q8—2981no—
226Q8—2981no—
227Q8—1492no—
228Q8—1492no—
229Q8C22⋊#1059701012yes—
230D4—24no—
231D4—21no—
232D4—2982no—
233D4—2984no—
234D4—2984no—
235D4—2982no—
236D4—2982no—
237D4C22⋊#1059701012yes—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—2984no—
243C2×C4—2984no—
244C2×C4—2984no—
245C2×C4—2984no—
246C2×C4—2981no—
247C2×C4—2981no—
248C2×C4—2984no—
249C2×C4—2981no—
250C2×C4—2981no—
251C2×C4—5962no—
252C2×C4—1491no—
253C2×C4—1491no—
254C2×C4—1492no—
255C2×C4—1492no—
256C2×C4C22⋊#1059701011yescharacteristic
257C2×C4C22×#1059701011yescharacteristic
258C8—5962no—
259C22—21no—
260C22—22no—
261C22—41no—
262C22—42no—
263C22—2981no—
264C22—5961no—
265C22—5961no—
266C22—1492no—
267C22C2×C22⋊#1059701011yescharacteristic
268C4—21no—
269C4—22no—
270C4—2982no—
271C4—2982no—
272C4—2981no—
273C4—1492no—
274C4—11922no—
275C4C2×C22⋊#1059701011yescharacteristic
276C4C2×C22⋊#1059701011yescharacteristic
277C2—21no—
278C2—42no—
279C2—41no—
280C2—2982no—
281C2—5961no—
282C2#2375056611yescharacteristic
subgroupG/H
centerC2#23750566
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC2×C149#379
prime radicalC2×#18011958C2
cosocleC2×C4×D149C23
hypercenterC2×#41#10597010
hypocenterC149#1796
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750623C2semidirect
2. #23750618C2semidirect
3. #23750611C2semidirect
4. #23750604C2semidirect
20. C2×#14558735C4semidirect
23. C22×Dic298C4semidirect
24. C2×Q8×D149C4semidirect
26. C2×#41×C149C4semidirect
141. C149#1796semidirect
156. C2×#41#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506232
#237506182
#237506112
#237506042
C2×#180119582
#1796149