Finite Group Databasebeta

← #34045700

Subgroups — #34045700

Order 19072.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#14558726C211yesmaximal, characteristic, complemented
2C2×#18011891C211yesmaximal, characteristic
3C2×#18011887C211yesmaximal, characteristic
4C2×#18011836C211yesmaximal, characteristic, complemented
5C2×#18011823C211yesmaximal, characteristic
6#23749387C211yesmaximal, characteristic, complemented
7C2×#103×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C22×C4×D149C2211yescharacteristic
10C2×#14558726—22no—
11C2×#14558726—22no—
12C2×#14558726—22no—
13C22×#11924746C2211yescharacteristic
14#18011891—22no—
15#18011891—22no—
16#18011887—22no—
17#18011887—22no—
18C2×C4⋊Dic149—21no—
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715—21no—
21C2×#14558713—21no—
22C2×#14558713—21no—
23#18011836—22no—
24#18011823—22no—
25C22×Q8×C149C2211yescharacteristic
26C22×C8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#103×C149—22no—
29C23×D149D411yescharacteristic
30C2×Dic298—21no—
31C2×Dic298—21no—
32C2×Dic298—21no—
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×Dic298D412yes—
36C22×Dic149—21no—
37C22×Dic149—21no—
38C22×Dic149D411yescharacteristic
39C2×C4×D149—21no—
40C2×C4×D149—21no—
41C2×C4×D149—21no—
42C2×C4×D149—21no—
43C2×C4×D149—21no—
44C2×C4×D149—21no—
45#14558726—28no—
46C2×#11924746—21no—
47C2×#11924746—21no—
48C2×#11924746D412yes—
49C4⋊Dic149—24no—
50C4⋊Dic149—21no—
51C4⋊Dic149D412yes—
52#14558715—24no—
53#14558713—24no—
54#14558713—24no—
55C2×Q8×C149—21no—
56C2×Q8×C149—21no—
57C2×Q8×C149—21no—
58C2×Q8×C149—21no—
59C2×Q8×C149—21no—
60C2×Q8×C149D412yes—
61C22×C4×C149—21no—
62C22×C4×C149—21no—
63C22×C4×C149C2311yescharacteristic
64C2×C8×C149—21no—
65C2×C8×C149—21no—
66C2×C8×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149D412yes—
69C22×D149—21no—
70C22×D149—21no—
71C22×D149—21no—
72C22×D149—21no—
73C22×D149—21no—
74C22×D149—21no—
75C22×D149Q1612yescomplemented
76Dic298—22no—
77Dic298—22no—
78Dic298—41no—
79Dic298—41no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—21no—
85C2×Dic149—41no—
86C2×Dic149—41no—
87C2×Dic149—41no—
88C2×Dic149—41no—
89C4×D149—41no—
90C4×D149—41no—
91C4×D149—41no—
92C4×D149—41no—
93#11924746—22no—
94C23×C149C2×D411yescharacteristic
95Q8×C149—22no—
96Q8×C149—22no—
97Q8×C149—41no—
98Q8×C149—41no—
99C2×C4×C149—22no—
100C2×C4×C149—22no—
101C2×C4×C149—41no—
102C2×C4×C149—41no—
103C2×C4×C149—41no—
104C2×C4×C149—41no—
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149#4111yescharacteristic
111C8×C149—41no—
112C22×C149#12011yescharacteristic
113C22×C149#12011yescharacteristic
114C22×C149#12111yescharacteristic
115C22×C149C2×Q1611yescharacteristic
116C22×C149#13511yescharacteristic
117C22×C149#13711yescharacteristic
118C22×C149#13711yescharacteristic
119C2×D149—22no—
120C2×D149—22no—
121C2×D149—22no—
122C2×D149—41no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—41no—
126C4×C149—42no—
127C4×C149—42no—
128C4×C149#12011yescharacteristic
129C4×C149#12111yescharacteristic
130C4×C149#12111yescharacteristic
131C4×C149#12711yescharacteristic
132Dic149—41no—
133Dic149—42no—
134Dic149—42no—
135C2×C149#39211yescharacteristic
136C2×C149#45111yescharacteristic
137C2×C149#45111yescharacteristic
138C2×C149#45211yescharacteristic
139C2×C149#45211yescharacteristic
140C2×C149#46711yescharacteristic
141C2×C149#47011yescharacteristic
142D149—42no—
143C149#200111yescharacteristic, complemented, Sylow
144#2001—1491nomaximal, Sylow
145C22×Q16—1491no—
146C2×C22⋊Q8—1491no—
147C2×C22⋊Q8—1491no—
148C2×#103—1491no—
149C2×#103D14911yescharacteristic, complemented
150C2×C22⋊C8—1491no—
151#340—1491no—
152C22×Q8—1491no—
153C22×Q8C2×D14911yescharacteristic
154C23×C4—1491no—
155C2×Q16—2982no—
156C2×Q16—2982no—
157C2×Q16—2982no—
158C22×C8—1491no—
159C22×C8C2×D14911yescharacteristic
160C22⋊Q8—2982no—
161C22⋊Q8—2982no—
162C22⋊Q8—2982no—
163C22⋊Q8—2982no—
164C2×C4⋊C4—2981no—
165C2×C4⋊C4—2981no—
166C2×C4⋊C4—1491no—
167C2×C4⋊C4C2×D14911yescharacteristic
168C2×C22⋊C4—2981no—
169C2×C22⋊C4—2981no—
170#103—22no—
171#103—2982no—
172C22⋊C8—2982no—
173C24—1491no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—2981no—
180C2×Q8—2981no—
181C2×Q8—2981no—
182C2×Q8—2981no—
183C2×Q8—2981no—
184C2×Q8—1492no—
185C2×Q8D59612yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—2981no—
189C22×C4—2981no—
190C22×C4—2981no—
191C22×C4—2981no—
192C22×C4—2981no—
193C22×C4—2981no—
194C22×C4—2981no—
195C22×C4—2981no—
196C22×C4—1491no—
197C22×C4C22×D14911yescharacteristic
198Q16—2988no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—2981no—
203C2×C8—2981no—
204C2×C8—1492no—
205C4⋊C4—21no—
206C4⋊C4—2984no—
207C4⋊C4—2984no—
208C4⋊C4—2981no—
209C4⋊C4—1492no—
210C4⋊C4C22⋊D14912yes—
211C22⋊C4—2984no—
212C22⋊C4—2984no—
213C23—2981no—
214C23—2981no—
215C23—2981no—
216C23—2981no—
217C23—2981no—
218C23—2981no—
219C23—1492no—
220C23D4×D14911yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—41no—
224Q8—41no—
225Q8—2982no—
226Q8—2982no—
227Q8—5961no—
228Q8—5961no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—2982no—
238C2×C4—2981no—
239C2×C4—2981no—
240C2×C4—5961no—
241C2×C4—5961no—
242C2×C4—5961no—
243C2×C4—5961no—
244C2×C4—5961no—
245C2×C4—5961no—
246C2×C4—5961no—
247C2×C4—5961no—
248C2×C4D4×D14911yescharacteristic
249C2×C4D4×D14911yescharacteristic
250C2×C4D4×D14911yescharacteristic
251C2×C4C2×C22⋊D14911yescharacteristic
252C2×C4C2×D59611yescharacteristic
253C2×C4#1455873611yescharacteristic
254C8—41no—
255C8—2982no—
256C22—2982no—
257C22—2982no—
258C22—2982no—
259C22—5961no—
260C22—5961no—
261C22—5961no—
262C22—5961no—
263C22#1801187911yescharacteristic
264C22#1801188111yescharacteristic
265C22#1801188411yescharacteristic
266C22Q16×D14911yescharacteristic
267C22#1801193211yescharacteristic
268C22#1801194011yescharacteristic
269C22#1801194311yescharacteristic
270C4—42no—
271C4—42no—
272C4—5961no—
273C4—5962no—
274C4—5962no—
275C4#1801188111yescharacteristic
276C4#1801188411yescharacteristic
277C4#1801188511yescharacteristic
278C4#1801190711yescharacteristic
279C2—5962no—
280C2#2374953411yescharacteristic
281C2#2374977911yescharacteristic
282C2#2374978211yescharacteristic
283C2#2374978411yescharacteristic
284C2#2374979011yescharacteristic
285C2#2374986511yescharacteristic
286C2#2374988211yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
hypercenterC2×#103D149
hypocenterC149#2001
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#14558726C2semidirect
4. C2×#18011836C2semidirect
6. #23749387C2semidirect
7. C2×#103×C149C2semidirect
75. C22×D149Q16semidirect
143. C149#2001semidirect
149. C2×#103D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587262
C2×#180118912
C2×#180118872
C2×#180118362
C2×#180118232
#237493872
C2×#103×C1492
#2001149