Finite Group Databasebeta

← #34044710

Subgroups — #34044710

Order 19072.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#23750093C211yesmaximal, characteristic
2#23749648C211yesmaximal, characteristic, complemented
3C2×#18011839C211yesmaximal, characteristic
4C2×#18011837C211yesmaximal, characteristic
5C4×#14558715C211yesmaximal, characteristic, complemented
6#23749384C211yesmaximal, characteristic, complemented
7#339×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10#18011876C411yescharacteristic, complemented
11#18011876C411yescharacteristic, complemented
12#18011873C411yescharacteristic, complemented
13#18011873C411yescharacteristic, complemented
14#18011871—21no—
15#18011871—21no—
16#18011868—21no—
17C2×#14558715—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4×Dic149C2211yescharacteristic
20C42×D149—21no—
21#18011840—21no—
22#18011840—21no—
23#18011839—22no—
24#18011837—22no—
25#18011818—21no—
26C2×M16×C149C2211yescharacteristic
27#117×C149C2211yescharacteristic
28C2×C42×C149C2211yescharacteristic
29#14558736—21no—
30#14558736—21no—
31#14558736D412yes—
32#14558736Q812yes—
33C2×Dic298C2×C411yescharacteristic
34C2×D596C2×C411yescharacteristic
35C2×C22⋊D149—21no—
36C22×Dic149—21no—
37C22×Dic149D411yescharacteristic
38C22×Dic149D411yescharacteristic
39C2×C4×D149—21no—
40C2×C4×D149—21no—
41C2×C4×D149—21no—
42#14558720—21no—
43#14558720—21no—
44C2×#11924746—21no—
45#14558715—24no—
46#14558715—21no—
47#14558715—21no—
48#14558713—21no—
49#14558713—21no—
50C4×Dic149—21no—
51C4×Dic149—21no—
52C4×Dic149—21no—
53C4×Dic149—21no—
54C4×Dic149C2×C411yescharacteristic
55C4×Dic149C2×C411yescharacteristic
56C4×Dic149D411yescharacteristic
57C4×Dic149D411yescharacteristic
58C22×C4×C149—21no—
59C22×C4×C149C2311yescharacteristic
60M16×C149—21no—
61M16×C149—21no—
62C2×C8×C149—21no—
63C4⋊C4×C149C2×C411yescharacteristic
64C4⋊C4×C149C2×C411yescharacteristic
65C22⋊C4×C149—21no—
66C42×C149—21no—
67C42×C149—21no—
68C42×C149—21no—
69C22×D149—21no—
70Dic298—21no—
71Dic298C4⋊C412yescomplemented
72D596—21no—
73D596C4⋊C412yescomplemented
74C22⋊D149—22no—
75C22⋊D149—22no—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C2×Dic149—22no—
79C2×Dic149—41no—
80C2×Dic149—41no—
81C2×Dic149—41no—
82C2×Dic149C22⋊C411yescharacteristic
83C2×Dic149C22⋊C411yescharacteristic
84C2×Dic149C22⋊C411yescharacteristic
85C2×Dic149C22⋊C411yescharacteristic
86C4×D149—22no—
87C4×D149—22no—
88C4×D149—42no—
89C4×D149—42no—
90#11924746—41no—
91C23×C149C2×D411yescharacteristic
92C2×C4×C149—22no—
93C2×C4×C149—21no—
94C2×C4×C149—21no—
95C2×C4×C149—41no—
96C2×C4×C149—41no—
97C2×C4×C149C22×C411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×Q811yescharacteristic
101C2×C4×C149#4111yescharacteristic
102C2×C4×C149#4111yescharacteristic
103C8×C149—41no—
104C22×C149—21no—
105C22×C149—21no—
106C22×C149C2×C22⋊C411yescharacteristic
107C22×C149#12111yescharacteristic
108C22×C149C22⋊Q811yescharacteristic
109C2×D149—22no—
110C2×D149—41no—
111C2×D149—41no—
112C4×C149—42no—
113C4×C149—41no—
114C4×C149—41no—
115C4×C149C2×C4⋊C411yescharacteristic
116C4×C149#11711yescharacteristic
117C4×C149#12111yescharacteristic
118C4×C149C22⋊Q811yescharacteristic
119Dic149—22no—
120Dic149—21no—
121Dic149—21no—
122Dic149—21no—
123Dic149—42no—
124Dic149#10412yescomplemented
125C2×C149—21no—
126C2×C149—21no—
127C2×C149#38011yescharacteristic
128C2×C149C2×#10411yescharacteristic
129C2×C149#42111yescharacteristic
130D149—42no—
131C149#180611yescharacteristic, complemented, Sylow
132#1806—1491nomaximal, Sylow
133C4×#41—1491no—
134#423—1491no—
135C2×#104—1491no—
136C2×#104—1491no—
137C4×C4⋊C4—1491no—
138#339—1491no—
139#339D14911yescharacteristic, complemented
140C2×#41—1491no—
141C2×M16—1491no—
142C2×M16C2×D14911yescharacteristic
143C4×Q8—1491no—
144C4×Q8—1491no—
145C4×D4—2981no—
146C4×D4—2981no—
147C4×D4—1491no—
148C4×D4—1491no—
149#117—2981no—
150#117C2×D14911yescharacteristic
151C2×C4⋊C4—2981no—
152C2×C42—2981no—
153C2×C42—1491no—
154C2×C42—1491no—
155C2×C42C2×D14911yescharacteristic
156C4⋊C8—2981no—
157C4⋊C8—2981no—
158#104—2982no—
159#104—2982no—
160#95—2981no—
161#41—2981no—
162#41—2981no—
163#41—1492no—
164#41—1492no—
165C2×Q8—1491no—
166C2×D4—2981no—
167C2×D4—1491no—
168C22×C4—21no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—2981no—
172C22×C4—2981no—
173C22×C4—1491no—
174C22×C4—1491no—
175C22×C4C22×D14911yescharacteristic
176M16—21no—
177M16—21no—
178M16—2981no—
179M16—2981no—
180C2×C8—21no—
181C2×C8—2981no—
182C4⋊C4—2984no—
183C4⋊C4—2981no—
184C4⋊C4—2981no—
185C4⋊C4C4×D14911yescharacteristic
186C4⋊C4C4×D14911yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—2981no—
189C22⋊C4—2981no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—2981no—
194C42—2981no—
195C42—2981no—
196C42—2981no—
197C42—1491no—
198C42—1491no—
199C42—1491no—
200C42—1491no—
201C23—2981no—
202C23D4×D14911yescharacteristic
203Q8—2981no—
204Q8—1492no—
205D4—2982no—
206D4—2982no—
207D4—2981no—
208D4—1492no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2981no—
215C2×C4—2982no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—5962no—
220C2×C4—5962no—
221C2×C4—5961no—
222C2×C4—5961no—
223C2×C4—5961no—
224C2×C4—1491no—
225C2×C4—1491no—
226C2×C4—1491no—
227C2×C4—1491no—
228C2×C4C2×C4×D14911yescharacteristic
229C2×C4D4×D14911yescharacteristic
230C2×C4D4×D14911yescharacteristic
231C2×C4Q8×D14911yescharacteristic
232C2×C4#1455873611yescharacteristic
233C2×C4#1455873611yescharacteristic
234C8—41no—
235C8—5961no—
236C22—21no—
237C22—21no—
238C22—2982no—
239C22—5961no—
240C22—5961no—
241C22C22⋊C4×D14911yescharacteristic
242C22#1801188411yescharacteristic
243C22#1801188911yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—2981no—
248C4—2981no—
249C4—2981no—
250C4—2982no—
251C4—5962no—
252C4—1492no—
253C4C4⋊C4×D14911yescharacteristic
254C4#1801186811yescharacteristic
255C4#1801188411yescharacteristic
256C4#1801188911yescharacteristic
257C2—21no—
258C2—21no—
259C2—5962no—
260C2#2374948411yescharacteristic
261C2#104×D14911yescharacteristic
262C2#2374964011yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#339×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558736C22
cosocleC22×C4×C149C23
hypercenter#339D149
hypocenterC149#1806
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #23749648C2semidirect
5. C4×#14558715C2semidirect
6. #23749384C2semidirect
7. #339×C149C2semidirect
10. #18011876C4semidirect
11. #18011876C4semidirect
12. #18011873C4semidirect
13. #18011873C4semidirect
71. Dic298C4⋊C4semidirect
73. D596C4⋊C4semidirect
124. Dic149#104semidirect
131. C149#1806semidirect
139. #339D149semidirect

Maximal subgroups

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

subgroupindex
#237500932
#237496482
C2×#180118392
C2×#180118372
C4×#145587152
#237493842
#339×C1492
#1806149