Finite Group Databasebeta

← #34057308

Subgroups — #34057308

Order 19072.

342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750348C211yesmaximal, characteristic
2#23750335C211yesmaximal, characteristic
3#23750023C211yesmaximal, characteristic, complemented
4#23749964C212yesmaximal, complemented
5#23749954C212yesmaximal, complemented
6#23749920C211yesmaximal, characteristic, complemented
7#23749910C211yesmaximal, characteristic, complemented
8#23749880C212yesmaximal, complemented
9#23749704C211yesmaximal, characteristic
10#23749666C212yesmaximal, complemented
11C4×Q16×C149C211yesmaximal, characteristic, complemented
12C2×#14558719C2212yes—
13#18011911C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011906—22no—
16#18011903—21no—
17#18011899—21no—
18#18011889—22no—
19#18011887C2212yes—
20#18011887C2212yes—
21C4×Dic298—21no—
22C4×D596—21no—
23C4×D596C2211yescharacteristic
24#18011869C2212yes—
25C4⋊C4×D149C2212yes—
26#18011844C2212yes—
27#18011843C2212yes—
28#18011843C2212yes—
29#18011842C2212yes—
30C4⋊#11924746C2211yescharacteristic
31#18011835C2212yes—
32#18011835C2212yes—
33#18011823C2212yes—
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2211yescharacteristic
36C4×Q8×C149C2211yescharacteristic
37#107×C149C2211yescharacteristic
38#103×C149C2211yescharacteristic
39#103×C149C2211yescharacteristic
40C4×C8×C149C2211yescharacteristic
41C2×Dic298—21no—
42C2×Dic298—21no—
43C2×D596D411yescharacteristic
44C2×C4×D149—22no—
45C2×C4×D149C2312yes—
46#14558719—24no—
47C2×#11924746C2312yes—
48C4⋊Dic149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149D411yescharacteristic
51C4⋊Dic149C2312yes—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558715—22no—
55#14558715—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59#14558713D412yes—
60C4×Dic149—22no—
61C2×Q8×C149C2311yescharacteristic
62C2×Q8×C149C2311yescharacteristic
63Q16×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2311yescharacteristic
69C4⋊C4×C149C2311yescharacteristic
70C42×C149—21no—
71C42×C149—21no—
72C42×C149C2311yescharacteristic
73C22×D149C2×D412yes—
74Dic298—42no—
75Dic298—81no—
76D596—22no—
77C2×Dic149—22no—
78C2×Dic149—22no—
79C2×Dic149C2×D412yes—
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—82no—
83#11924746—22no—
84Q8×C149—21no—
85Q8×C149—21no—
86Q8×C149—21no—
87Q8×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149—21no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2411yescharacteristic
95C8×C149—21no—
96C8×C149#4112yes—
97C22×C149C22×D411yescharacteristic
98C2×D149—22no—
99C2×D149—22no—
100C2×D149—22no—
101C4×C149—21no—
102C4×C149—41no—
103C4×C149—41no—
104C4×C149—41no—
105C4×C149—41no—
106C4×C149#13712yes—
107C4×C149C2×#4111yescharacteristic
108C4×C1492−1+411yescharacteristic
109Dic149—22no—
110Dic149—42no—
111Dic149—42no—
112C2×C149#54711yescharacteristic
113C2×C149C2×#13711yescharacteristic
114C2×C149#57711yescharacteristic
115D149—42no—
116C149#335611yescharacteristic, complemented, Sylow
117#3356—1491nomaximal, Sylow
118#556—1491no—
119#554—1491no—
120#498—1491no—
121#485—1492no—
122#483—1492no—
123#477—1491no—
124#475—1491no—
125#470—1492no—
126C4×Q16D14911yescharacteristic, complemented
127#436—1491no—
128#428—1492no—
129C2×Q16C2×D14911yescharacteristic
130C2×M16—1492no—
131C4⋊Q8—1491no—
132C4⋊Q8—1491no—
133#126—2982no—
134#125—2981no—
135#124—2981no—
136C22⋊Q8—2982no—
137C22⋊Q8—1492no—
138C22⋊Q8—1492no—
139C4×Q8—2981no—
140C4×Q8C2×D14911yescharacteristic
141C4×Q8C2×D14911yescharacteristic
142C4×D4—2981no—
143C4×D4—1491no—
144#117—1492no—
145C2×C4⋊C4—1492no—
146#107—1492no—
147#107C2×D14911yescharacteristic
148#106—1492no—
149#106—1492no—
150#106—1492no—
151C4⋊C8—1491no—
152#103—1492no—
153#103—1492no—
154#103C2×D14911yescharacteristic
155#103C2×D14911yescharacteristic
156C22⋊C8—1492no—
157C4×C8C2×D14911yescharacteristic
158C2×Q8—2981no—
159C2×Q8—2981no—
160C2×Q8C22×D14911yescharacteristic
161C2×Q8C22×D14911yescharacteristic
162C2×D4—1491no—
163C22×C4—2982no—
164C22×C4—1492no—
165Q16—22no—
166M16—2984no—
167C2×C8—1492no—
168C2×C8C22×D14911yescharacteristic
169C2×C8C22×D14911yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—2982no—
173C4⋊C4—2982no—
174C4⋊C4—2982no—
175C4⋊C4—2981no—
176C4⋊C4—2981no—
177C4⋊C4—1492no—
178C4⋊C4—1492no—
179C4⋊C4—1491no—
180C4⋊C4C22×D14911yescharacteristic
181C4⋊C4C22×D14911yescharacteristic
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—1492no—
186C42—21no—
187C42—21no—
188C42—2982no—
189C42C22×D14911yescharacteristic
190C23—1492no—
191Q8—21no—
192Q8—21no—
193Q8—21no—
194Q8—21no—
195Q8—5962no—
196Q8—11921no—
197D4—2982no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—1492no—
207C2×C4—11922no—
208C2×C4D4×D14911yescharacteristic
209C2×C4D4×D14911yescharacteristic
210C2×C4C23×D14911yescharacteristic
211C8—21no—
212C8—2982no—
213C8#1455873612yes—
214C22—2982no—
215C22—2982no—
216C22—2982no—
217C22C2×D4×D14911yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—41no—
223C4—2982no—
224C4—5962no—
225C4—5962no—
226C4#1801194312yes—
227C4C2×#1455873611yescharacteristic
228C4#1801195811yescharacteristic
229C2—5962no—
230C2#2375028011yescharacteristic
231C2C2×#1801194311yescharacteristic
232C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×Q16×C149C2
socleC22×C149C22×D4
prime radicalC2×D596D4
hypercenterC4×Q16D149
hypocenterC149#3356
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
3. #23750023C2semidirect
4. #23749964C2semidirect
5. #23749954C2semidirect
6. #23749920C2semidirect
7. #23749910C2semidirect
8. #23749880C2semidirect
10. #23749666C2semidirect
11. C4×Q16×C149C2semidirect
116. C149#3356semidirect
126. C4×Q16D149semidirect

Maximal subgroups

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

subgroupindex
#237503482
#237503352
#237500232
#237499642
#237499542
#237499202
#237499102
#237498802
#237497042
#237496662
C4×Q16×C1492
#3356149