Finite Group Databasebeta

← #34060661

Subgroups — #34060661

Order 19072.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#18011999C211yesmaximal, characteristic
2C2×#18011981C211yesmaximal, characteristic, complemented
3#23750632C211yesmaximal, characteristic, complemented
4C2×#18011976C211yesmaximal, characteristic
5#23750495C211yesmaximal, characteristic, complemented
6(C2×#10597010)⋊C8C211yesmaximal, characteristic, complemented
7#23749620C211yesmaximal, characteristic
8#18011999—22no—
9#18011999—22no—
10C2×#14558746—21no—
11C2×#14558746C2211yescharacteristic
12C2×#14558746C2211yescharacteristic
13C2×D149⋊C8—21no—
14C2×D149⋊C8C2211yescharacteristic
15C2×C4×#10597010C2211yescharacteristic
16#18011981—22no—
17#18011978—21no—
18C4⋊#11924753—21no—
19#18011976—22no—
20C2×#14558737C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011869C2211yescharacteristic
23#18011835C411yescharacteristic, complemented
24#18011833C411yescharacteristic, complemented
25#18011831C411yescharacteristic, complemented
26#103×C149C411yescharacteristic, complemented
27C22×#10597010—21no—
28#14558746—24no—
29#14558746—21no—
30#14558746—21no—
31#14558746—21no—
32#14558746D412yes—
33D149⋊C8—24no—
34D149⋊C8—21no—
35D149⋊C8—21no—
36C2×#11924753—21no—
37C2×#11924753—21no—
38C2×#11924753D411yescharacteristic
39C2×#11924753D411yescharacteristic
40C4×#10597010—21no—
41C4×#10597010—21no—
42#14558737—21no—
43#14558737—21no—
44#14558737D412yes—
45#14558737Q812yes—
46C2×D596—21no—
47C2×D596C2×C411yescharacteristic
48C2×C4×D149—21no—
49C2×C4×D149C2311yescharacteristic
50C2×#11924746C2×C411yescharacteristic
51C8×D149—21no—
52C8×D149—21no—
53C4⋊Dic149C2×C411yescharacteristic
54#14558713—21no—
55C4×Dic149—21no—
56C2×Q8×C149C2×C411yescharacteristic
57C2×C8×C149C2×C411yescharacteristic
58C4⋊C4×C149C2×C411yescharacteristic
59C2×#10597010—22no—
60C2×#10597010—41no—
61C2×#10597010—41no—
62#11924753—22no—
63#11924753—21no—
64#11924753—21no—
65#11924753—41no—
66C22×D149—21no—
67C22×D149#4111yescharacteristic
68D596—22no—
69D596—22no—
70D596—21no—
71D596C4⋊C412yes—
72C2×Dic149—21no—
73C2×Dic149C2×D411yescharacteristic
74C4×D149—22no—
75C4×D149—22no—
76C4×D149C2×D411yescharacteristic
77C4×D149C2×D411yescharacteristic
78C4×D149C2×Q811yescharacteristic
79C4×D149#4111yescharacteristic
80#11924746—21no—
81Q8×C149—21no—
82Q8×C149C4⋊C412yes—
83C2×C4×C149—21no—
84C2×C4×C149—21no—
85C2×C4×C149C22×C411yescharacteristic
86C8×C149—21no—
87C22×C149C4×D411yescharacteristic
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—22no—
91C2×D149—41no—
92C2×D149—41no—
93C2×D149C22⋊Q811yescharacteristic
94C2×D149#12311yescharacteristic
95#10597010—42no—
96C4×C149—22no—
97C4×C149—41no—
98C4×C149C2×C4⋊C411yescharacteristic
99C4×C149C4×D411yescharacteristic
100Dic149—41no—
101Dic149#12011yescharacteristic
102Dic149C22⋊Q811yescharacteristic
103C2×C149#38511yescharacteristic
104C2×C149#44311yescharacteristic
105C2×C149#44411yescharacteristic
106D149—21no—
107D149—21no—
108D149—42no—
109C149#186611yescharacteristic, complemented, Sylow
110#1866—1491nomaximal, Sylow
111C2×#131—1491no—
112C2×#108—1491no—
113#424—1491no—
114C2×#104—1491no—
115#416—1491no—
116#339—1491no—
117#336—1491no—
118C2×#41—1491no—
119#131—2982no—
120#131—2982no—
121C2×M16—2981no—
122C2×M16—1491no—
123C2×M16—1491no—
124C22×C8—2981no—
125C22×C8—1491no—
126C22×C8—1491no—
127#117—1491no—
128C2×C42—1491no—
129#108—2982no—
130C4⋊C8—2981no—
131C4⋊C8—2981no—
132#104—2982no—
133#103—1491no—
134#103#1059701011yescharacteristic, complemented
135#102—1491no—
136#102—1491no—
137#41—2981no—
138#41—2981no—
139#41—1492no—
140#41—1492no—
141C2×Q8C2×#1059701011yescharacteristic
142C2×D4—2981no—
143C2×D4—1491no—
144C22×C4—2981no—
145C22×C4—2981no—
146C22×C4—1491no—
147M16—2984no—
148M16—2981no—
149M16—2981no—
150M16—2981no—
151M16—1492no—
152C2×C8—2981no—
153C2×C8—2981no—
154C2×C8—2984no—
155C2×C8—2981no—
156C2×C8—2981no—
157C2×C8—2981no—
158C2×C8—2981no—
159C2×C8—1491no—
160C2×C8—1491no—
161C2×C8—1491no—
162C2×C8C2×#1059701011yescharacteristic
163C4⋊C4—1491no—
164C4⋊C4C2×#1059701011yescharacteristic
165C22⋊C4—2981no—
166C42—2981no—
167C42—2981no—
168C42—2981no—
169C23—2981no—
170C23—1491no—
171Q8—21no—
172Q8C4⋊#1059701012yes—
173D4—2982no—
174D4—2982no—
175D4—2981no—
176D4—1492no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2981no—
183C2×C4—5961no—
184C2×C4—5961no—
185C2×C4—1491no—
186C2×C4—1491no—
187C2×C4—1491no—
188C2×C4—1491no—
189C2×C4—1491no—
190C2×C4C22×#1059701011yescharacteristic
191C8—21no—
192C8—2981no—
193C8—2982no—
194C8—2981no—
195C8—2981no—
196C8—5961no—
197C22—2981no—
198C22—2981no—
199C22—2982no—
200C22—5961no—
201C22—5961no—
202C22—1491no—
203C22—1491no—
204C22D4×#1059701011yescharacteristic
205C4—22no—
206C4—41no—
207C4—5962no—
208C4—5961no—
209C4—1491no—
210C4—1491no—
211C4C2×C4⋊#1059701011yescharacteristic
212C4D4×#1059701011yescharacteristic
213C2—2981no—
214C2—2981no—
215C2—5962no—
216C2#2375057211yescharacteristic
217C2#2375066811yescharacteristic
218C2#2375067111yescharacteristic
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#103×C149C4
socleC22×C149C4×D4
prime radicalC2×#14558737C22
cosocleC2×C4×D149C23
hypercenter#103#10597010
hypocenterC149#1866
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#18011981C2semidirect
3. #23750632C2semidirect
5. #23750495C2semidirect
6. (C2×#10597010)⋊C8C2semidirect
23. #18011835C4semidirect
24. #18011833C4semidirect
25. #18011831C4semidirect
26. #103×C149C4semidirect
109. C149#1866semidirect
134. #103#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119992
C2×#180119812
#237506322
C2×#180119762
#237504952
(C2×#10597010)⋊C82
#237496202
#1866149