Finite Group Databasebeta

← #34045909

Subgroups — #34045909

Order 19072.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750199C211yesmaximal, characteristic
2#23749667C211yesmaximal, characteristic, complemented
3C2×#18011837C211yesmaximal, characteristic
4#23749627C211yesmaximal, characteristic
5#23749532C211yesmaximal, characteristic, complemented
6#23749386C211yesmaximal, characteristic, complemented
7C2×#101×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011909—21no—
10#18011900—21no—
11#18011894—22no—
12#18011887—21no—
13#18011887—21no—
14#18011870C2211yescharacteristic
15C2×C4⋊Dic149C2211yescharacteristic
16C2×C4×Dic149C2211yescharacteristic
17#18011845—21no—
18#18011843—21no—
19#18011837—22no—
20#18011836—21no—
21#18011833—21no—
22#18011818—22no—
23C22×Q8×C149C2211yescharacteristic
24C2×M16×C149C2211yescharacteristic
25C2×M16×C149C2211yescharacteristic
26#101×C149—22no—
27#14558736—21no—
28#14558736—21no—
29#14558736—21no—
30#14558736—21no—
31C2×Dic298D411yescharacteristic
32C2×D596D411yescharacteristic
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C22×Dic149—21no—
36C2×C4×D149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149D411yescharacteristic
40C4⋊Dic149D411yescharacteristic
41#14558715—22no—
42#14558715—22no—
43C22⋊Dic149—21no—
44#14558713—22no—
45#14558713—22no—
46C4×Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149—21no—
49C2×Q8×C149—21no—
50C2×Q8×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C22×C4×C149D412yes—
56C22×C4×C149C2311yescharacteristic
57M16×C149—21no—
58M16×C149—21no—
59M16×C149—21no—
60M16×C149D412yes—
61C2×C8×C149—21no—
62C2×C8×C149—21no—
63C22×D149—21no—
64Dic298—21no—
65Dic298—21no—
66D596—21no—
67D596—21no—
68C22⋊D149—41no—
69C22⋊D149—41no—
70C2×Dic149—22no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—41no—
75C2×Dic149—41no—
76C2×Dic149—42no—
77C2×Dic149—41no—
78C4×D149—41no—
79C4×D149—41no—
80C23×C149C2×D411yescharacteristic
81Q8×C149—41no—
82Q8×C149—41no—
83Q8×C149—41no—
84Q8×C149—41no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149—22no—
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149#4111yescharacteristic
92C2×C4×C149#4111yescharacteristic
93C2×C4×C149#4111yescharacteristic
94C8×C149—22no—
95C8×C149—41no—
96C22×C149—21no—
97C22×C149—21no—
98C22×C149#12011yescharacteristic
99C22×C149#12111yescharacteristic
100C22×C149#12311yescharacteristic
101C2×D149—41no—
102C2×D149—41no—
103C2×D149—41no—
104C4×C149—42no—
105C4×C149#12111yescharacteristic
106C4×C149#12111yescharacteristic
107C4×C149#12311yescharacteristic
108C4×C149#12411yescharacteristic
109Dic149—42no—
110Dic149—41no—
111Dic149—41no—
112Dic149—41no—
113Dic149—81no—
114C2×C149—21no—
115C2×C149—21no—
116C2×C149#39411yescharacteristic
117C2×C149#45411yescharacteristic
118C2×C149#45611yescharacteristic
119D149—81no—
120C149#203811yescharacteristic, complemented, Sylow
121#2038—1491nomaximal, Sylow
122#536—1491no—
123#428—1491no—
124C2×#104—1491no—
125#417—1491no—
126C2×#101D14911yescharacteristic, complemented
127#391—1491no—
128#339—1491no—
129C2×#41—1491no—
130C22×Q8C2×D14911yescharacteristic
131C2×M16C2×D14911yescharacteristic
132C2×M16C2×D14911yescharacteristic
133C4⋊Q8—2981no—
134#124—2981no—
135#123—2982no—
136C22⋊Q8—2981no—
137C22⋊Q8—2981no—
138#117—1491no—
139C2×C4⋊C4—1491no—
140C2×C42—1491no—
141#107—2981no—
142#106—2981no—
143#104—2982no—
144#103—2981no—
145#102—2981no—
146#101—22no—
147#95—2982no—
148#41—2981no—
149#41—2981no—
150#41—2981no—
151#41—2981no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—1491no—
159C2×D4—2981no—
160C2×D4—1491no—
161C22×C4—2981no—
162C22×C4—2981no—
163C22×C4—2981no—
164C22×C4D59612yes—
165C22×C4C22×D14911yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16C22⋊D14912yes—
170C2×C8—21no—
171C2×C8—21no—
172C4⋊C4—2982no—
173C4⋊C4—2982no—
174C4⋊C4—2981no—
175C4⋊C4—2981no—
176C4⋊C4—1491no—
177C4⋊C4—1491no—
178C22⋊C4—2982no—
179C22⋊C4—2982no—
180C22⋊C4—2981no—
181C42—2981no—
182C42—2981no—
183C42—2981no—
184C23—2981no—
185C23C2×D59611yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—2981no—
191Q8—2981no—
192D4—2981no—
193D4—2981no—
194D4—5961no—
195D4—5961no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—2982no—
200C2×C4—2981no—
201C2×C4—2981no—
202C2×C4—2981no—
203C2×C4—5961no—
204C2×C4—5961no—
205C2×C4—5961no—
206C2×C4—5961no—
207C2×C4—5962no—
208C2×C4—5961no—
209C2×C4D4×D14911yescharacteristic
210C2×C4D4×D14911yescharacteristic
211C2×C4C2×C22⋊D14911yescharacteristic
212C2×C4#1455873511yescharacteristic
213C2×C4#1455873511yescharacteristic
214C2×C4#1455873611yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—5961no—
220C22—5961no—
221C22—5961no—
222C22#1801188111yescharacteristic
223C22#1801188511yescharacteristic
224C22#1801189511yescharacteristic
225C4—42no—
226C4—5962no—
227C4—5961no—
228C4—5961no—
229C4—5961no—
230C4—11921no—
231C4#1801188211yescharacteristic
232C4#1801188311yescharacteristic
233C4#1801189311yescharacteristic
234C4#1801189711yescharacteristic
235C2—21no—
236C2—21no—
237C2—11921no—
238C2#2374954111yescharacteristic
239C2#2374980011yescharacteristic
240C2#2374981011yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#101×C149C2
socleC22×C149#120
prime radicalC2×#14558736C22
hypercenterC2×#101D149
hypocenterC149#2038
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #23749667C2semidirect
5. #23749532C2semidirect
6. #23749386C2semidirect
7. C2×#101×C149C2semidirect
120. C149#2038semidirect
126. C2×#101D149semidirect

Maximal subgroups

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

subgroupindex
#237501992
#237496672
C2×#180118372
#237496272
#237495322
#237493862
C2×#101×C1492
#2038149