Finite Group Databasebeta

← #34060776

Subgroups — #34060776

Order 19072.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750636C211yesmaximal, characteristic
2#23750618C211yesmaximal, characteristic
3C2×#18011974C211yesmaximal, characteristic
4#23750591C211yesmaximal, characteristic
5#23750504C211yesmaximal, characteristic
6#23750500C211yesmaximal, characteristic
7#101×D149C211yesmaximal, characteristic
8D149⋊M16C2211yescharacteristic
9C2×D149⋊C8C2211yescharacteristic
10#18011990C2211yescharacteristic
11C2×C4⋊#10597010C2211yescharacteristic
12#18011980—21no—
13#18011979—21no—
14#18011974—21no—
15#18011974—21no—
16#18011974—21no—
17#18011974—21no—
18#18011965—21no—
19C8×#10597010—21no—
20C2×Q8×D149C2211yescharacteristic
21M16×D149C2211yescharacteristic
22M16×D149C2211yescharacteristic
23#18011830C411yescharacteristic, complemented
24#18011829C411yescharacteristic, complemented
25#18011829C411yescharacteristic, complemented
26#101×C149C411yescharacteristic, complemented
27C22×#10597010—21no—
28#14558746—21no—
29#14558745—21no—
30D149⋊C8—21no—
31D149⋊C8—21no—
32D149⋊C8D411yescharacteristic
33D149⋊C8D411yescharacteristic
34C2×#11924753—21no—
35C4⋊#10597010—21no—
36C4⋊#10597010—21no—
37C4⋊#10597010D411yescharacteristic
38C4⋊#10597010D411yescharacteristic
39C22⋊#10597010—21no—
40C4×#10597010—21no—
41C2×Dic298—21no—
42C2×Dic298C2×C411yescharacteristic
43Q8×D149—21no—
44Q8×D149—21no—
45Q8×D149—21no—
46Q8×D149—21no—
47C2×C4×D149—21no—
48C2×C4×D149C2311yescharacteristic
49#14558720C2×C411yescharacteristic
50#14558720C2×C411yescharacteristic
51#14558719—21no—
52#14558719—21no—
53C8×D149—21no—
54C8×D149—21no—
55C2×Q8×C149C2×C411yescharacteristic
56M16×C149C2×C411yescharacteristic
57M16×C149C2×C411yescharacteristic
58C2×#10597010—21no—
59C2×#10597010—21no—
60C2×#10597010—41no—
61C2×#10597010—81no—
62#11924753—21no—
63#11924753—21no—
64#11924753—41no—
65C22×D149#4111yescharacteristic
66Dic298—21no—
67Dic298—21no—
68Dic298—41no—
69Dic298—41no—
70C2×Dic149—21no—
71C2×Dic149#4111yescharacteristic
72C4×D149—41no—
73C4×D149—41no—
74C4×D149C2×D411yescharacteristic
75C4×D149C2×D411yescharacteristic
76C4×D149#4111yescharacteristic
77C4×D149#4111yescharacteristic
78#11924746—21no—
79#11924746—21no—
80Q8×C149—21no—
81Q8×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149C22×C411yescharacteristic
84C8×C149—21no—
85C8×C149—21no—
86C22×C149#11711yescharacteristic
87C2×D149—21no—
88C2×D149—21no—
89C2×D149#12111yescharacteristic
90C2×D149#12611yescharacteristic
91#10597010—41no—
92#10597010—41no—
93#10597010—81no—
94C4×C149—41no—
95C4×C149C4×D411yescharacteristic
96C4×C149C4×D411yescharacteristic
97Dic149—41no—
98Dic149#12311yescharacteristic
99Dic149#12411yescharacteristic
100C2×C149—21no—
101C2×C149#38811yescharacteristic
102D149—21no—
103D149#47111yescharacteristic
104D149#47311yescharacteristic
105C149#193011yescharacteristic, complemented, Sylow
106#1930—1491nomaximal, Sylow
107#428—1491no—
108#419—1491no—
109C2×#103—1491no—
110C2×#101—1491no—
111#405—1491no—
112#343—1491no—
113#341—1491no—
114C22×Q8—1491no—
115C2×M16—1491no—
116C2×M16—1491no—
117C2×M16—1491no—
118C22×C8—1491no—
119#117—1491no—
120C2×C4⋊C4—1491no—
121#107—2981no—
122#106—2981no—
123#103—2981no—
124#103—2981no—
125#103—2981no—
126#103—2981no—
127#101—1491no—
128#101—1491no—
129#101—1491no—
130#101#1059701011yescharacteristic, complemented
131#97—2981no—
132C4×C8—2981no—
133C2×Q8—2981no—
134C2×Q8—2981no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—1491no—
139C2×Q8C2×#1059701011yescharacteristic
140C22×C4—2981no—
141C22×C4—2981no—
142C22×C4—1491no—
143M16—2981no—
144M16—2981no—
145M16—2981no—
146M16—2981no—
147M16—1491no—
148M16—1491no—
149M16C2×#1059701011yescharacteristic
150M16C2×#1059701011yescharacteristic
151C2×C8—2981no—
152C2×C8—2981no—
153C2×C8—2981no—
154C2×C8—2981no—
155C2×C8—2981no—
156C2×C8—1491no—
157C2×C8—1491no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—1491no—
161C4⋊C4—1491no—
162C22⋊C4—2981no—
163C42—2981no—
164C23—1491no—
165Q8—21no—
166Q8—21no—
167Q8—2981no—
168Q8—2981no—
169Q8—5961no—
170Q8—5961no—
171C2×C4—21no—
172C2×C4—2981no—
173C2×C4—2981no—
174C2×C4—2981no—
175C2×C4—5961no—
176C2×C4—5961no—
177C2×C4—5961no—
178C2×C4—1491no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4—1491no—
182C2×C4—1491no—
183C2×C4—11921no—
184C2×C4C22×#1059701011yescharacteristic
185C8—21no—
186C8—21no—
187C8—2981no—
188C8—2981no—
189C8—2981no—
190C8—2981no—
191C8—5961no—
192C22—2981no—
193C22—2981no—
194C22—1491no—
195C22—1491no—
196C22#1801199011yescharacteristic
197C4—41no—
198C4—5961no—
199C4—5961no—
200C4—5961no—
201C4—1491no—
202C4—1491no—
203C4—11921no—
204C4D4×#1059701011yescharacteristic
205C4D4×#1059701011yescharacteristic
206C2—21no—
207C2—2981no—
208C2—1491no—
209C2—1491no—
210C2#2375057511yescharacteristic
subgroupG/H
centerC2#23750575
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#101×C149C4
socleC2×C149#388
prime radicalC22×D149#41
cosocleC2×C4×D149C23
hypercenter#101#10597010
hypocenterC149#1930
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #18011830C4semidirect
24. #18011829C4semidirect
25. #18011829C4semidirect
26. #101×C149C4semidirect
105. C149#1930semidirect
130. #101#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506362
#237506182
C2×#180119742
#237505912
#237505042
#237505002
#101×D1492
#1930149