Finite Group Databasebeta

← #34045697

Subgroups — #34045697

Order 19072.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#14558725C211yesmaximal, characteristic, complemented
2C2×#18011891C211yesmaximal, characteristic, complemented
3C2×#18011886C211yesmaximal, characteristic
4C2×#18011834C211yesmaximal, characteristic, complemented
5C2×#18011831C211yesmaximal, characteristic, complemented
6C2×#18011823C211yesmaximal, characteristic, complemented
7#340×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C22×D596—21no—
10C22×D596C2211yescharacteristic
11C22×C4×D149C2211yescharacteristic
12C2×#14558725—22no—
13C2×#14558725—22no—
14C2×#14558725—22no—
15C22×#11924746C2211yescharacteristic
16#18011891—22no—
17#18011891—22no—
18#18011886—22no—
19#18011886—22no—
20C2×C4⋊Dic149—21no—
21C2×#14558713—21no—
22C2×#14558713—21no—
23#18011834—22no—
24#18011831—22no—
25#18011823—22no—
26C22×C8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29C23×D149—21no—
30C23×D149D411yescharacteristic
31C2×Dic298—21no—
32C2×Dic298—21no—
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×Dic298—21no—
36C2×Dic298D412yescomplemented
37C2×D596—24no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596—21no—
42C2×D596—21no—
43C2×D596—42no—
44C2×D596—42no—
45C2×D596D412yes—
46C22×Dic149—21no—
47C22×Dic149D411yescharacteristic
48C2×C4×D149—21no—
49C2×C4×D149—21no—
50C2×C4×D149—21no—
51C2×C4×D149—21no—
52C2×C4×D149—21no—
53C2×C4×D149—21no—
54#14558725—28no—
55C2×#11924746—21no—
56C2×#11924746—21no—
57C2×#11924746—21no—
58C4⋊Dic149—24no—
59#14558713—24no—
60#14558713—24no—
61C22×C4×C149—21no—
62C22×C4×C149—21no—
63C22×C4×C149C2311yescharacteristic
64C2×C8×C149—21no—
65C2×C8×C149—21no—
66C2×C8×C149D412yescomplemented
67C4⋊C4×C149—21no—
68C4⋊C4×C149—21no—
69C4⋊C4×C149D412yes—
70C4⋊C4×C149D412yescomplemented
71C22×D149—21no—
72C22×D149—21no—
73C22×D149—21no—
74C22×D149—21no—
75C22×D149—21no—
76C22×D149—21no—
77C22×D149—22no—
78C22×D149—41no—
79C22×D149—41no—
80C22×D149—41no—
81C22×D149—41no—
82C22×D149—41no—
83C22×D149—41no—
84C22×D149SD1612yescomplemented
85Dic298—22no—
86Dic298—22no—
87Dic298—41no—
88Dic298—41no—
89D596—22no—
90D596—22no—
91D596—48no—
92D596—41no—
93D596—41no—
94C2×Dic149—21no—
95C2×Dic149—21no—
96C2×Dic149—22no—
97C2×Dic149—21no—
98C2×Dic149—41no—
99C2×Dic149—41no—
100C4×D149—41no—
101C4×D149—41no—
102C4×D149—41no—
103C4×D149—41no—
104#11924746—41no—
105C23×C149C2×D411yescharacteristic
106C2×C4×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—41no—
109C2×C4×C149—41no—
110C2×C4×C149—41no—
111C2×C4×C149—41no—
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2×D411yescharacteristic
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149#4111yescharacteristic
118C8×C149—22no—
119C22×C149#12011yescharacteristic
120C22×C149#12011yescharacteristic
121C22×C149#12111yescharacteristic
122C22×C149C2×SD1611yescharacteristic
123C22×C149#13511yescharacteristic
124C22×C149AGL(1,ℤ/8)11yescharacteristic
125C22×C149#13711yescharacteristic
126C2×D149—22no—
127C2×D149—22no—
128C2×D149—22no—
129C2×D149—41no—
130C2×D149—41no—
131C2×D149—41no—
132C2×D149—41no—
133C2×D149—42no—
134C2×D149—42no—
135C2×D149—42no—
136C2×D149—81no—
137C2×D149—81no—
138C2×D149—81no—
139C2×D149—81no—
140C4×C149—42no—
141C4×C149—42no—
142C4×C149#12011yescharacteristic
143C4×C149#12111yescharacteristic
144C4×C149#12111yescharacteristic
145C4×C149#12711yescharacteristic
146Dic149—41no—
147Dic149—42no—
148C2×C149#39211yescharacteristic
149C2×C149#44811yescharacteristic
150C2×C149#44911yescharacteristic
151C2×C149#45011yescharacteristic
152C2×C149#45211yescharacteristic
153C2×C149#46511yescharacteristic
154C2×C149#46811yescharacteristic
155D149—42no—
156D149—82no—
157C149#200011yescharacteristic, complemented, Sylow
158#2000—1491nomaximal, Sylow
159C22×SD16—1491no—
160C2×C22⋊Q8—1491no—
161C2×#121—1491no—
162C2×#103—1491no—
163C2×#102—1491no—
164C2×C22⋊C8—1491no—
165#340D14911yescharacteristic, complemented
166C22×Q8—1491no—
167C22×D4—2981no—
168C22×D4—1491no—
169C23×C4—1491no—
170C2×SD16—2982no—
171C2×SD16—2982no—
172C2×SD16—2982no—
173C22×C8—1491no—
174C22×C8C2×D14911yescharacteristic
175C22⋊Q8—2982no—
176C22⋊Q8—2982no—
177#121—2982no—
178#121—2982no—
179C2×C4⋊C4—2981no—
180C2×C4⋊C4C2×D14911yescharacteristic
181C2×C4⋊C4C2×D14911yescharacteristic
182C2×C22⋊C4—2981no—
183C2×C22⋊C4—2981no—
184#103—2982no—
185#102—2982no—
186C22⋊C8—2982no—
187C24—2981no—
188C24—1491no—
189C2×Q8—2981no—
190C2×Q8—2981no—
191C2×Q8—2981no—
192C2×Q8—2981no—
193C2×Q8—2981no—
194C2×Q8—1492no—
195C2×D4—2984no—
196C2×D4—2981no—
197C2×D4—2981no—
198C2×D4—2981no—
199C2×D4—2981no—
200C2×D4—2981no—
201C2×D4—5962no—
202C2×D4—5962no—
203C2×D4—1492no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—2981no—
207C22×C4—2981no—
208C22×C4—2981no—
209C22×C4—2981no—
210C22×C4—2981no—
211C22×C4—2981no—
212C22×C4—2981no—
213C22×C4—1491no—
214C22×C4C22×D14911yescharacteristic
215SD16—2988no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—2981no—
219C2×C8—2981no—
220C2×C8—2981no—
221C2×C8D59612yescomplemented
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—2984no—
225C4⋊C4D59612yes—
226C4⋊C4D59612yescomplemented
227C22⋊C4—2984no—
228C22⋊C4—2984no—
229C23—2981no—
230C23—2981no—
231C23—2981no—
232C23—2981no—
233C23—2981no—
234C23—2981no—
235C23—2982no—
236C23—5961no—
237C23—5961no—
238C23—5961no—
239C23—5961no—
240C23—5961no—
241C23—5961no—
242C23—1492no—
243C23D4×D14911yescharacteristic
244Q8—2982no—
245Q8—2982no—
246Q8—5961no—
247Q8—5961no—
248D4—2982no—
249D4—2982no—
250D4—5968no—
251D4—5961no—
252D4—5961no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—2981no—
260C2×C4—2982no—
261C2×C4—2981no—
262C2×C4—2981no—
263C2×C4—5961no—
264C2×C4—5961no—
265C2×C4—5961no—
266C2×C4—5961no—
267C2×C4—5961no—
268C2×C4—5961no—
269C2×C4D4×D14911yescharacteristic
270C2×C4D4×D14911yescharacteristic
271C2×C4C2×D59611yescharacteristic
272C2×C4C2×D59611yescharacteristic
273C2×C4C2×D59611yescharacteristic
274C2×C4#1455873711yescharacteristic
275C8—22no—
276C8—5961no—
277C22—2982no—
278C22—2982no—
279C22—2982no—
280C22—5961no—
281C22—5961no—
282C22—5961no—
283C22—5961no—
284C22—5962no—
285C22—5962no—
286C22—5962no—
287C22—11921no—
288C22—11921no—
289C22—11921no—
290C22—11921no—
291C22#1801188111yescharacteristic
292C22#1801188111yescharacteristic
293C22#1801188611yescharacteristic
294C22SD16×D14911yescharacteristic
295C22#1801193211yescharacteristic
296C22#1801193511yescharacteristic
297C22#1801194311yescharacteristic
298C4—42no—
299C4—42no—
300C4—5961no—
301C4—5962no—
302C4#1801188111yescharacteristic
303C4#1801188611yescharacteristic
304C4#1801188611yescharacteristic
305C4#1801190811yescharacteristic
306C2—5962no—
307C2—11922no—
308C2#2374953511yescharacteristic
309C2#2374976511yescharacteristic
310C2#2374977111yescharacteristic
311C2#2374977711yescharacteristic
312C2#2374979011yescharacteristic
313C2#2374985511yescharacteristic
314C2#2374987211yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011886C2
hypercenter#340D149
hypocenterC149#2000
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#14558725C2semidirect
2. C2×#18011891C2semidirect
4. C2×#18011834C2semidirect
5. C2×#18011831C2semidirect
6. C2×#18011823C2semidirect
7. #340×C149C2semidirect
36. C2×Dic298D4semidirect
66. C2×C8×C149D4semidirect
70. C4⋊C4×C149D4semidirect
84. C22×D149SD16semidirect
157. C149#2000semidirect
165. #340D149semidirect
221. C2×C8D596semidirect
226. C4⋊C4D596semidirect

Maximal subgroups

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

subgroupindex
C22×#145587252
C2×#180118912
C2×#180118862
C2×#180118342
C2×#180118312
C2×#180118232
#340×C1492
#2000149