Finite Group Databasebeta

← #34060836

Subgroups — #34060836

Order 19072.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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×#18011979C211yesmaximal, characteristic, complemented
2C2×#18011974C211yesmaximal, characteristic, complemented
3C2×#18011973C211yesmaximal, characteristic
4C2×C8×#10597010C211yesmaximal, characteristic, complemented
5(C2×#10597010)⋊Q8C211yesmaximal, characteristic, complemented
6#23750577C211yesmaximal, characteristic
7C2×SD16×D149C211yesmaximal, characteristic
8C2×D149⋊C8C2211yescharacteristic
9C2×C4⋊#10597010C2211yescharacteristic
10C2×C4⋊#10597010C2211yescharacteristic
11C2×C22⋊#10597010—22no—
12C2×C4×#10597010C2211yescharacteristic
13#18011979—22no—
14#18011974—22no—
15#18011973—22no—
16C8×#10597010—22no—
17(C2×#10597010)⋊C4—22no—
18C2×Q8×D149C2211yescharacteristic
19C2×D4×D149C2211yescharacteristic
20C2×#14558725C411yescharacteristic, complemented
21C2×#14558724C411yescharacteristic, complemented
22C2×#14558723C411yescharacteristic, complemented
23SD16×D149—22no—
24SD16×D149—22no—
25C2×C8×D149C2211yescharacteristic
26C2×SD16×C149C411yescharacteristic, complemented
27C22×#10597010—21no—
28C22×#10597010—21no—
29C22×#10597010D412yes—
30D149⋊C8—21no—
31D149⋊C8D412yes—
32C2×#11924753—21no—
33C4⋊#10597010—21no—
34C4⋊#10597010—21no—
35C4⋊#10597010—21no—
36C4⋊#10597010—21no—
37C22⋊#10597010—44no—
38C4×#10597010—21no—
39C4×#10597010—21no—
40C23×D149—21no—
41C2×Dic298—21no—
42C2×Dic298C2×C411yescharacteristic
43Q8×D149—21no—
44Q8×D149—21no—
45Q8×D149—21no—
46Q8×D149—21no—
47C2×D596C2×C411yescharacteristic
48C2×C22⋊D149—21no—
49D4×D149—21no—
50D4×D149—21no—
51D4×D149—21no—
52D4×D149—21no—
53C2×C4×D149—21no—
54C2×C4×D149C2311yescharacteristic
55#14558725—22no—
56#14558724—22no—
57#14558723—22no—
58C2×#11924746C2×C411yescharacteristic
59C8×D149D412yes—
60C8×D149D412yes—
61C2×Q8×C149C2×C411yescharacteristic
62C2×D4×C149C2×C411yescharacteristic
63SD16×C149—22no—
64C2×C8×C149C2×C411yescharacteristic
65C2×#10597010—22no—
66C2×#10597010—22no—
67C2×#10597010—41no—
68C2×#10597010—41no—
69C2×#10597010—42no—
70C2×#10597010—42no—
71C2×#10597010SD1614yescomplemented
72#11924753—22no—
73C22×D149—21no—
74C22×D149—41no—
75C22×D149—41no—
76C22×D149—42no—
77C22×D149—42no—
78C22×D149C2×D411yescharacteristic
79Dic298—21no—
80Dic298—21no—
81Dic298—41no—
82Dic298—41no—
83D596—21no—
84D596—21no—
85C22⋊D149—41no—
86C22⋊D149—41no—
87C2×Dic149—21no—
88C2×Dic149#4111yescharacteristic
89C4×D149—41no—
90C4×D149—41no—
91C4×D149C2×D411yescharacteristic
92C4×D149C2×D411yescharacteristic
93C4×D149C2×D411yescharacteristic
94C4×D149#4111yescharacteristic
95#11924746C22⋊C412yescomplemented
96C23×C149—21no—
97Q8×C149—21no—
98Q8×C149—21no—
99D4×C149—21no—
100D4×C149—21no—
101C2×C4×C149—21no—
102C2×C4×C149C22×C411yescharacteristic
103C8×C149C22⋊C412yescomplemented
104C22×C149—41no—
105C22×C149—42no—
106C22×C149C4×D411yescharacteristic
107C2×D149—41no—
108C2×D149—42no—
109C2×D149—82no—
110C2×D149—81no—
111C2×D149—81no—
112C2×D149#12111yescharacteristic
113C2×D149#12711yescharacteristic
114C2×D149C2×SD1612yes—
115C2×D149#13512yes—
116#10597010—24no—
117#10597010—81no—
118#10597010—81no—
119C4×C149—41no—
120C4×C149C2×C22⋊C411yescharacteristic
121C4×C149C4×D411yescharacteristic
122Dic149—41no—
123Dic149#12111yescharacteristic
124Dic149#12411yescharacteristic
125C2×C149—81no—
126C2×C149#39011yescharacteristic
127C2×C149C4×SD1612yes—
128D149—81no—
129D149#46512yes—
130D149#49211yescharacteristic
131D149#49511yescharacteristic
132C149#196811yescharacteristic, complemented, Sylow
133#1968—1491nomaximal, Sylow
134C22×SD16—1491no—
135C2×#106—1491no—
136C2×#103—1491no—
137C2×#102—1491no—
138C2×C4×C8—1491no—
139#391—1491no—
140#390—1491no—
141C22×Q8—1491no—
142C22×D4—1491no—
143C2×SD16—2982no—
144C2×SD16—2982no—
145C2×SD16—1491no—
146C2×SD16—1491no—
147C2×SD16—1491no—
148C2×SD16#1059701011yescharacteristic, complemented
149C22×C8—1491no—
150C22×C8—1491no—
151C2×C4⋊C4—1491no—
152C2×C4⋊C4—1491no—
153C2×C22⋊C4—2982no—
154C2×C42—1491no—
155#106—2982no—
156#103—2982no—
157#102—2982no—
158C4×C8—2982no—
159#95—2982no—
160C24—2981no—
161C2×Q8—2981no—
162C2×Q8—2981no—
163C2×Q8—2981no—
164C2×Q8—2981no—
165C2×Q8—2981no—
166C2×Q8—1491no—
167C2×Q8C2×#1059701011yescharacteristic
168C2×D4—2981no—
169C2×D4—2981no—
170C2×D4—2981no—
171C2×D4—2981no—
172C2×D4—2981no—
173C2×D4—1491no—
174C2×D4C2×#1059701011yescharacteristic
175C22×C4—2981no—
176C22×C4—2981no—
177C22×C4—2981no—
178C22×C4—1492no—
179C22×C4—1491no—
180SD16—22no—
181SD16—2982no—
182SD16—2982no—
183SD16—2982no—
184C2×C8—2981no—
185C2×C8—2981no—
186C2×C8—1492no—
187C2×C8—1491no—
188C2×C8—1492no—
189C2×C8—1492no—
190C2×C8C2×#1059701011yescharacteristic
191C4⋊C4—2981no—
192C4⋊C4—2981no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C22⋊C4—5964no—
196C42—2981no—
197C42—2981no—
198C23—21no—
199C23—2981no—
200C23—5962no—
201C23—5961no—
202C23—5961no—
203C23—5962no—
204C23—1491no—
205Q8—21no—
206Q8—21no—
207Q8—2981no—
208Q8—2981no—
209Q8—5961no—
210Q8—5961no—
211D4—21no—
212D4—21no—
213D4—2981no—
214D4—2981no—
215D4—5961no—
216D4—5961no—
217C2×C4—21no—
218C2×C4—2982no—
219C2×C4—2982no—
220C2×C4—2981no—
221C2×C4—5961no—
222C2×C4—5961no—
223C2×C4—5962no—
224C2×C4—5961no—
225C2×C4—5961no—
226C2×C4—5962no—
227C2×C4—1494no—
228C2×C4—1491no—
229C2×C4—1491no—
230C2×C4—1491no—
231C2×C4—1491no—
232C2×C4—1491no—
233C2×C4C22×#1059701011yescharacteristic
234C8—2982no—
235C8—1492no—
236C8C22⋊#1059701012yescomplemented
237C22—42no—
238C22—41no—
239C22—5962no—
240C22—5961no—
241C22—1492no—
242C22—1492no—
243C22—1491no—
244C22—1491no—
245C22—11922no—
246C22—11921no—
247C22—11921no—
248C22D4×#1059701011yescharacteristic
249C4—41no—
250C4—2984no—
251C4—5961no—
252C4—1491no—
253C4—1491no—
254C4—11921no—
255C4—11921no—
256C4C2×C22⋊#1059701011yescharacteristic
257C4D4×#1059701011yescharacteristic
258C2—81no—
259C2—1492no—
260C2—1491no—
261C2—1491no—
262C2—11921no—
263C2#2375057711yescharacteristic
264C2SD16×#1059701012yes—
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×SD16×C149C4
socleC22×C149C4×D4
prime radicalC2×D4×D149C22
cosocleC2×C4×D149C23
hypercenterC2×SD16#10597010
hypocenterC149#1968
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18011979C2semidirect
2. C2×#18011974C2semidirect
4. C2×C8×#10597010C2semidirect
5. (C2×#10597010)⋊Q8C2semidirect
20. C2×#14558725C4semidirect
21. C2×#14558724C4semidirect
22. C2×#14558723C4semidirect
26. C2×SD16×C149C4semidirect
71. C2×#10597010SD16semidirect
95. #11924746C22⋊C4semidirect
103. C8×C149C22⋊C4semidirect
132. C149#1968semidirect
148. C2×SD16#10597010semidirect
236. C8C22⋊#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119792
C2×#180119742
C2×#180119732
C2×C8×#105970102
(C2×#10597010)⋊Q82
#237505772
C2×SD16×D1492
#1968149