Finite Group Databasebeta

← #34057061

Subgroups — #34057061

Order 19072.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750316C212yesmaximal
2#23750027C211yesmaximal, characteristic, complemented
3#23749964C212yesmaximal, complemented
4#23749954C212yesmaximal, complemented
5#23749932C212yesmaximal, complemented
6#23749863C211yesmaximal, characteristic, complemented
7#23749863C211yesmaximal, characteristic, complemented
8C8×D596C211yesmaximal, characteristic
9#23749662C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11C4×Q16×C149C211yesmaximal, characteristic, complemented
12C2×C8×D149C2211yescharacteristic
13C2×C8×D149C2211yescharacteristic
14#18011905—22no—
15#18011903C2212yes—
16#18011901—22no—
17#18011896—22no—
18#18011887C2212yes—
19#18011887C2212yes—
20C4×D596C2211yescharacteristic
21#18011869C2212yes—
22#18011868—22no—
23C4⋊C4×D149C2212yes—
24#18011845C2211yescharacteristic
25#18011845C2211yescharacteristic
26#18011844C2212yes—
27#18011843C2212yes—
28#18011842C2212yes—
29C4⋊#11924746C2211yescharacteristic
30#18011835C2212yes—
31#18011835C2212yes—
32#18011823C2211yescharacteristic
33#18011823C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2212yes—
36#107×C149C2211yescharacteristic
37#103×C149C2212yes—
38C4×C8×C149C2211yescharacteristic
39C2×D596D411yescharacteristic
40C2×C4×D149—22no—
41C2×C4×D149C2311yescharacteristic
42C2×C4×D149C2311yescharacteristic
43C2×#11924746C2311yescharacteristic
44C2×#11924746C2311yescharacteristic
45C8×D149—22no—
46C8×D149—22no—
47C4⋊Dic149D411yescharacteristic
48C4⋊Dic149C2312yes—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713D411yescharacteristic
59#14558713D411yescharacteristic
60C4×Dic149—22no—
61C2×Q8×C149C2312yes—
62Q16×C149—22no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C42×C149—22no—
68C42×C149C2311yescharacteristic
69C22×D149C2×D411yescharacteristic
70C22×D149C2×D411yescharacteristic
71D596—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C4×D149—21no—
77C4×D149—21no—
78C4×D149—21no—
79C4×D149—21no—
80C4×D149—44no—
81#11924746—21no—
82#11924746—21no—
83Q8×C149—22no—
84Q8×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C8×C149—21no—
91C8×C149#4112yes—
92C22×C149C22×D411yescharacteristic
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149—21no—
97C2×D149—21no—
98C2×D149#13512yes—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149—42no—
103C4×C149C2×#4111yescharacteristic
104C4×C1492−1+411yescharacteristic
105Dic149—21no—
106Dic149—21no—
107Dic149—42no—
108Dic149—42no—
109C2×C149#54711yescharacteristic
110C2×C149C2×#13511yescharacteristic
111C2×C149#57811yescharacteristic
112D149—22no—
113D149—41no—
114C149#333611yescharacteristic, complemented, Sylow
115#3336—1491nomaximal, Sylow
116#552—1492no—
117#499—1491no—
118#485—1492no—
119#483—1492no—
120#479—1492no—
121#467—1491no—
122#467—1491no—
123C4×Q16D14911yescharacteristic, complemented
124C8×D4—1491no—
125#427—1491no—
126C2×#107—1491no—
127C2×Q16C2×D14911yescharacteristic
128C22×C8—1491no—
129C22×C8—1491no—
130#126—2982no—
131#125—2982no—
132#125—1492no—
133#123—2982no—
134C22⋊Q8—1492no—
135C22⋊Q8—1492no—
136C4×Q8C2×D14912yes—
137C4×D4—1491no—
138#117—2982no—
139#117—1492no—
140C2×C4⋊C4—1492no—
141#107—1491no—
142#107—1491no—
143#107—1492no—
144#107C2×D14911yescharacteristic
145#106—1492no—
146#106—1492no—
147C4⋊C8—1491no—
148#103—1492no—
149#103—1492no—
150#103C2×D14912yes—
151C22⋊C8—1491no—
152C22⋊C8—1491no—
153C4×C8C2×D14911yescharacteristic
154C2×Q8C22×D14912yes—
155C2×D4—1491no—
156C22×C4—2982no—
157C22×C4—1491no—
158C22×C4—1491no—
159Q16—22no—
160C2×C8—2982no—
161C2×C8—2982no—
162C2×C8—1491no—
163C2×C8—1491no—
164C2×C8C22×D14911yescharacteristic
165C2×C8C22×D14911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—1492no—
173C4⋊C4—1492no—
174C4⋊C4—1491no—
175C4⋊C4C22×D14912yes—
176C22⋊C4—2982no—
177C22⋊C4—2982no—
178C22⋊C4—2982no—
179C22⋊C4—1491no—
180C22⋊C4—1491no—
181C42—22no—
182C42—2982no—
183C42C22×D14911yescharacteristic
184C23—1491no—
185C23—1491no—
186Q8—22no—
187Q8—22no—
188D4—2982no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—2981no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—5964no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4D4×D14911yescharacteristic
201C2×C4D4×D14911yescharacteristic
202C2×C4C23×D14911yescharacteristic
203C8—21no—
204C8—2981no—
205C8—2981no—
206C8#1455873612yes—
207C22—2981no—
208C22—2981no—
209C22—2981no—
210C22—2981no—
211C22—2981no—
212C22—1492no—
213C22C2×D4×D14911yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—2981no—
219C4—2981no—
220C4—5962no—
221C4—5962no—
222C4C2×#1455873611yescharacteristic
223C4#1801195811yescharacteristic
224C2—2982no—
225C2—5961no—
226C2#2375028011yescharacteristic
227C2#135×D14911yescharacteristic
228C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×Q16×C149C2
socleC22×C149C22×D4
prime radicalC2×D596D4
hypercenterC4×Q16D149
hypocenterC149#3336
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #23750027C2semidirect
3. #23749964C2semidirect
4. #23749954C2semidirect
5. #23749932C2semidirect
6. #23749863C2semidirect
7. #23749863C2semidirect
9. #23749662C2semidirect
10. #107×D149C2semidirect
11. C4×Q16×C149C2semidirect
114. C149#3336semidirect
123. C4×Q16D149semidirect

Maximal subgroups

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

subgroupindex
#237503162
#237500272
#237499642
#237499542
#237499322
#237498632
C8×D5962
#237496622
#107×D1492
C4×Q16×C1492
#3336149