Finite Group Databasebeta

← #34060684

Subgroups — #34060684

Order 19072.

402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#10597010C211yesmaximal, characteristic
2C2×#18011974C211yesmaximal, characteristic, complemented
3C2×#18011973C211yesmaximal, characteristic
4(C2×#10597010)⋊Q8C211yesmaximal, characteristic, complemented
5#23750499C211yesmaximal, characteristic, complemented
6(C2×#10597010)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×D149C211yesmaximal, characteristic
8C23×#10597010—21no—
9C2×D149⋊C8C2211yescharacteristic
10D4×#10597010—22no—
11D4×#10597010—22no—
12C2×C4⋊#10597010C2211yescharacteristic
13C2×C4⋊#10597010C2211yescharacteristic
14C2×C22⋊#10597010—21no—
15C2×C4×#10597010C2211yescharacteristic
16#18011974—22no—
17#18011973—22no—
18(C2×#10597010)⋊C4—21no—
19(C2×#10597010)⋊C4—21no—
20C2×Q8×D149C2211yescharacteristic
21C2×D4×D149C2211yescharacteristic
22C2×#14558725C411yescharacteristic, complemented
23C2×#14558724C411yescharacteristic, complemented
24C2×#14558723C411yescharacteristic, complemented
25SD16×D149—22no—
26SD16×D149—22no—
27C2×C8×D149C2211yescharacteristic
28C2×SD16×C149C411yescharacteristic, complemented
29C22×#10597010—24no—
30C22×#10597010—21no—
31C22×#10597010—21no—
32C22×#10597010—42no—
33C22×#10597010—42no—
34C22×#10597010D411yescharacteristic
35C22×#10597010D411yescharacteristic
36D149⋊C8—21no—
37D149⋊C8—21no—
38C2×#11924753—21no—
39C4⋊#10597010—21no—
40C4⋊#10597010—21no—
41C4⋊#10597010—21no—
42C4⋊#10597010D412yes—
43C22⋊#10597010—24no—
44C4×#10597010—21no—
45C4×#10597010—21no—
46C23×D149—21no—
47C2×Dic298—21no—
48C2×Dic298C2×C411yescharacteristic, complemented
49Q8×D149—21no—
50Q8×D149—21no—
51Q8×D149—21no—
52Q8×D149—21no—
53C2×D596C2×C411yescharacteristic
54C2×C22⋊D149—21no—
55D4×D149—21no—
56D4×D149—21no—
57D4×D149D412yes—
58D4×D149D412yes—
59C2×C4×D149—21no—
60C2×C4×D149C2311yescharacteristic
61#14558725—22no—
62#14558724—22no—
63#14558723—22no—
64C2×#11924746C2×C411yescharacteristic, complemented
65C8×D149—21no—
66C8×D149—21no—
67C2×Q8×C149C2×C411yescharacteristic, complemented
68C2×D4×C149C2×C411yescharacteristic
69SD16×C149—22no—
70C2×C8×C149C2×C411yescharacteristic, complemented
71C2×#10597010—21no—
72C2×#10597010—21no—
73C2×#10597010—21no—
74C2×#10597010—22no—
75C2×#10597010—21no—
76C2×#10597010—21no—
77C2×#10597010—48no—
78C2×#10597010—41no—
79C2×#10597010—41no—
80C2×#10597010—41no—
81C2×#10597010—41no—
82C2×#10597010—41no—
83C2×#10597010SD1612yescomplemented
84#11924753—41no—
85C22×D149—21no—
86C22×D149—22no—
87C22×D149—22no—
88C22×D149—41no—
89C22×D149—41no—
90C22×D149—41no—
91C22×D149—41no—
92C22×D149C2×D411yescharacteristic
93Dic298—21no—
94Dic298—21no—
95Dic298—41no—
96Dic298—41no—
97D596—21no—
98D596C22⋊C412yes—
99C22⋊D149—22no—
100C22⋊D149—22no—
101C2×Dic149—21no—
102C2×Dic149#4111yescharacteristic
103C4×D149—41no—
104C4×D149—41no—
105C4×D149C2×D411yescharacteristic
106C4×D149C2×D411yescharacteristic
107C4×D149C2×D411yescharacteristic
108C4×D149#4111yescharacteristic
109#11924746—21no—
110C23×C149—21no—
111Q8×C149—21no—
112Q8×C149—21no—
113D4×C149—21no—
114D4×C149C22⋊C412yes—
115C2×C4×C149—21no—
116C2×C4×C149C22×C411yescharacteristic
117C8×C149—21no—
118C22×C149—22no—
119C22×C149—41no—
120C22×C149—41no—
121C22×C149C4×D411yescharacteristic
122C2×D149—22no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—42no—
126C2×D149—42no—
127C2×D149—42no—
128C2×D149—42no—
129C2×D149#12011yescharacteristic
130C2×D149#12111yescharacteristic
131C2×D149C2×SD1611yescharacteristic
132C2×D149#13511yescharacteristic
133C2×D149AGL(1,ℤ/8)11yescharacteristic
134C2×D149#13711yescharacteristic
135#10597010—22no—
136#10597010—42no—
137#10597010—41no—
138#10597010—81no—
139C4×C149—41no—
140C4×C149C2×C22⋊C411yescharacteristic
141C4×C149C4×D411yescharacteristic
142Dic149—41no—
143Dic149#12111yescharacteristic
144Dic149#12311yescharacteristic
145C2×C149—42no—
146C2×C149#38611yescharacteristic
147C2×C149C4×SD1611yescharacteristic
148C2×C149#44011yescharacteristic
149D149—42no—
150D149#45011yescharacteristic
151D149#45211yescharacteristic
152D149#46111yescharacteristic
153D149#46311yescharacteristic
154C149#187711yescharacteristic, complemented, Sylow
155#1877—1491nomaximal, Sylow
156C22×SD16—1491no—
157C2×C4×D4—1491no—
158C2×#103—1491no—
159C2×#102—1491no—
160#391—1491no—
161#340—1491no—
162#336—1491no—
163C22×Q8—1491no—
164C22×D4—1491no—
165C23×C4—2981no—
166C2×SD16—2982no—
167C2×SD16—2982no—
168C2×SD16—1491no—
169C2×SD16—1491no—
170C2×SD16—1491no—
171C2×SD16#1059701011yescharacteristic, complemented
172C22×C8—1491no—
173C22×C8—1491no—
174C4×D4—2982no—
175C4×D4—2982no—
176C2×C4⋊C4—1491no—
177C2×C4⋊C4—1491no—
178C2×C22⋊C4—2981no—
179C2×C42—1491no—
180#103—2982no—
181#102—2982no—
182#95—2981no—
183#95—2981no—
184C24—2981no—
185C2×Q8—2981no—
186C2×Q8—2981no—
187C2×Q8—2981no—
188C2×Q8—2981no—
189C2×Q8—2981no—
190C2×Q8—1491no—
191C2×Q8C2×#1059701011yescharacteristic, complemented
192C2×D4—2981no—
193C2×D4—2981no—
194C2×D4—2981no—
195C2×D4—1492no—
196C2×D4—1492no—
197C2×D4—1491no—
198C2×D4C2×#1059701011yescharacteristic
199C22×C4—2981no—
200C22×C4—2984no—
201C22×C4—2981no—
202C22×C4—2981no—
203C22×C4—5962no—
204C22×C4—5962no—
205C22×C4—1491no—
206C22×C4—1491no—
207C22×C4—1491no—
208SD16—22no—
209SD16—2982no—
210SD16—2982no—
211SD16—2982no—
212C2×C8—2981no—
213C2×C8—2981no—
214C2×C8—2981no—
215C2×C8—2981no—
216C2×C8—2981no—
217C2×C8—1491no—
218C2×C8C2×#1059701011yescharacteristic, complemented
219C4⋊C4—2981no—
220C4⋊C4—2981no—
221C4⋊C4—2981no—
222C4⋊C4—1492no—
223C22⋊C4—2984no—
224C42—2981no—
225C42—2981no—
226C23—21no—
227C23—2982no—
228C23—2982no—
229C23—2981no—
230C23—5961no—
231C23—5961no—
232C23—5961no—
233C23—5961no—
234C23—1491no—
235Q8—21no—
236Q8—21no—
237Q8—2981no—
238Q8—2981no—
239Q8—5961no—
240Q8—5961no—
241D4—21no—
242D4—2982no—
243D4—2982no—
244D4—2981no—
245D4—1492no—
246D4C22⋊#1059701012yes—
247C2×C4—21no—
248C2×C4—2981no—
249C2×C4—2981no—
250C2×C4—2981no—
251C2×C4—2982no—
252C2×C4—2981no—
253C2×C4—2981no—
254C2×C4—2981no—
255C2×C4—5961no—
256C2×C4—5961no—
257C2×C4—5968no—
258C2×C4—5961no—
259C2×C4—5961no—
260C2×C4—5961no—
261C2×C4—5961no—
262C2×C4—5961no—
263C2×C4—1492no—
264C2×C4—1491no—
265C2×C4—1491no—
266C2×C4—1491no—
267C2×C4—1491no—
268C2×C4—1491no—
269C2×C4C22×#1059701011yescharacteristic
270C8—21no—
271C8—2981no—
272C8—5961no—
273C22—22no—
274C22—41no—
275C22—41no—
276C22—2982no—
277C22—5962no—
278C22—5962no—
279C22—5962no—
280C22—5962no—
281C22—5961no—
282C22—5961no—
283C22—1491no—
284C22—1491no—
285C22—1491no—
286C22—1491no—
287C22—1491no—
288C22—1491no—
289C22D4×#1059701011yescharacteristic
290C4—41no—
291C4—2982no—
292C4—5961no—
293C4—5962no—
294C4—5961no—
295C4—1491no—
296C4—1491no—
297C4—11921no—
298C4C2×C22⋊#1059701011yescharacteristic
299C4D4×#1059701011yescharacteristic
300C2—42no—
301C2—5962no—
302C2—1491no—
303C2—1491no—
304C2—1491no—
305C2—1491no—
306C2#2375057311yescharacteristic
307C2SD16×#1059701011yescharacteristic
308C2#2375066411yescharacteristic
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#1877
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
2. C2×#18011974C2semidirect
4. (C2×#10597010)⋊Q8C2semidirect
5. #23750499C2semidirect
6. (C2×#10597010)⋊C8C2semidirect
22. C2×#14558725C4semidirect
23. C2×#14558724C4semidirect
24. C2×#14558723C4semidirect
28. C2×SD16×C149C4semidirect
48. C2×Dic298C2×C4semidirect
64. C2×#11924746C2×C4semidirect
67. C2×Q8×C149C2×C4semidirect
70. C2×C8×C149C2×C4semidirect
83. C2×#10597010SD16semidirect
154. C149#1877semidirect
171. C2×SD16#10597010semidirect
191. C2×Q8C2×#10597010semidirect
218. C2×C8C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#105970102
C2×#180119742
C2×#180119732
(C2×#10597010)⋊Q82
#237504992
(C2×#10597010)⋊C82
C2×SD16×D1492
#1877149