Finite Group Databasebeta

← #34068029

Subgroups — #34068029

Order 19328.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752770C211yesmaximal, characteristic, complemented
2#23752348C211yesmaximal, characteristic, complemented
3#23752345C211yesmaximal, characteristic, complemented
4#23752122C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C22×D604—21no—
9C22×D604C2211yescharacteristic, complemented
10C2×D4×D151—21no—
11C2×D1208—21no—
12C2×#14558989—21no—
13#18012724—21no—
14#18012721—21no—
15#18012713C2211yescharacteristic
16#18012711—21no—
17#18012709—21no—
18#18012707—21no—
19C2×(C2×D151)⋊C4—21no—
20C2×(C2×D151)⋊C4C2211yescharacteristic
21#18012661—21no—
22#18012659—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic, complemented
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic, complemented
26#95×C151C2211yescharacteristic, complemented
27C23×D151—21no—
28C23×D151—21no—
29C23×D151D411yescharacteristic
30C2×D604—21no—
31C2×D604—21no—
32C2×D604—21no—
33C2×D604—42no—
34C2×D604—42no—
35C2×D604—42no—
36C2×D604—42no—
37C2×D604D411yescharacteristic, complemented
38C2×C22⋊D151—21no—
39C2×C22⋊D151—21no—
40C2×C22⋊D151—21no—
41D4×D151—42no—
42D4×D151—42no—
43C22×Dic151D411yescharacteristic
44C2×C4×D151—21no—
45D1208—42no—
46#14558989—42no—
47C2×C151⋊C8—21no—
48C4⋊Dic151D411yescharacteristic, complemented
49Dic151⋊C4—21no—
50C22⋊Dic151—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53(C2×D151)⋊C4—21no—
54(C2×D151)⋊C4—21no—
55(C2×D151)⋊C4—42no—
56C2×D4×C151—21no—
57C2×D4×C151D411yescharacteristic, complemented
58C22×C4×C151—21no—
59C22×C4×C151C2311yescharacteristic
60C2×C8×C151—21no—
61C4⋊C4×C151D411yescharacteristic, complemented
62C22⋊C4×C151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—22no—
66C22×D151—21no—
67C22×D151—42no—
68C22×D151—41no—
69C22×D151—41no—
70C22×D151—41no—
71C22×D151—41no—
72C22×D151—41no—
73C22×D151—41no—
74C22×D151—41no—
75C22×D151—41no—
76C22×D151—81no—
77C22×D151—81no—
78C22×D151D812yescomplemented
79D604—22no—
80D604—22no—
81D604—41no—
82D604—41no—
83D604—41no—
84D604—42no—
85D604—48no—
86C22⋊D151—42no—
87C22⋊D151—41no—
88C22⋊D151—41no—
89C22⋊D151—81no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151—41no—
93C4×D151—42no—
94C151⋊C8—41no—
95C23×C151—21no—
96C23×C151C2×D411yescharacteristic
97D4×C151—41no—
98D4×C151—41no—
99D4×C151—41no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2×D411yescharacteristic
107C8×C151—41no—
108C22×C151—21no—
109C22×C151—21no—
110C22×C151—41no—
111C22×C151—41no—
112C22×C151—41no—
113C22×C151#12011yescharacteristic
114C22×C151C2×D811yescharacteristic
115C22×C151AGL(1,ℤ/8)11yescharacteristic
116C2×D151—22no—
117C2×D151—41no—
118C2×D151—41no—
119C2×D151—42no—
120C2×D151—42no—
121C2×D151—42no—
122C2×D151—41no—
123C2×D151—41no—
124C2×D151—42no—
125C2×D151—41no—
126C2×D151—81no—
127C2×D151—84no—
128C2×D151—81no—
129C2×D151—81no—
130C2×D151—81no—
131C2×D151—81no—
132C4×C151—21no—
133C4×C151—21no—
134C4×C151—42no—
135C4×C151—41no—
136Dic151—41no—
137Dic151—41no—
138C2×C151—21no—
139C2×C151—21no—
140C2×C151—81no—
141C2×C151#44711yescharacteristic
142C2×C151#45311yescharacteristic
143C2×C151B(4,𝔽2)11yescharacteristic
144D151—42no—
145D151—82no—
146D151—81no—
147C151#159511yescharacteristic, complemented, Sylow
148#1595—1511nomaximal, Sylow
149#534—1511no—
150#447—1511no—
151#447—1511no—
152#392—1511no—
153#327—1511no—
154#327D15111yescharacteristic, complemented
155#323—1511no—
156C22×D4—3021no—
157C22×D4—3021no—
158C22×D4—1511no—
159C2×D8—3021no—
160C2×D8—3021no—
161#123—3021no—
162#123—3021no—
163#121—3021no—
164#121—1511no—
165#121C2×D15111yescharacteristic
166#120—3021no—
167#120—3021no—
168C2×C22⋊C4—3021no—
169C2×C22⋊C4—1511no—
170#102—3021no—
171#102—3021no—
172C22⋊C8—1511no—
173C22⋊C8C2×D15111yescharacteristic, complemented
174#95C2×D15111yescharacteristic, complemented
175C24—3021no—
176C24—3021no—
177C24—1511no—
178C2×D4—21no—
179C2×D4—3021no—
180C2×D4—3021no—
181C2×D4—3021no—
182C2×D4—3021no—
183C2×D4—3021no—
184C2×D4—3021no—
185C2×D4—6042no—
186C2×D4—6042no—
187C2×D4—6042no—
188C2×D4—6042no—
189C2×D4—6042no—
190C2×D4—6042no—
191C2×D4—1511no—
192C2×D4D60411yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—3021no—
195C22×C4—1511no—
196C22×C4C22×D15111yescharacteristic
197D8—6042no—
198D8—6042no—
199C2×C8—21no—
200C2×C8—3021no—
201C4⋊C4—3021no—
202C4⋊C4—1511no—
203C4⋊C4D60411yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C22⋊C4—3021no—
208C22⋊C4—3021no—
209C22⋊C4—3021no—
210C22⋊C4—6042no—
211C23—21no—
212C23—3022no—
213C23—3021no—
214C23—3021no—
215C23—3021no—
216C23—6041no—
217C23—6041no—
218C23—6041no—
219C23—6041no—
220C23—6041no—
221C23—6042no—
222C23—6041no—
223C23—6041no—
224C23—6041no—
225C23—1512no—
226C23—12081no—
227C23—12081no—
228C23D4×D15111yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—3022no—
233D4—3022no—
234D4—6041no—
235D4—6041no—
236D4—6041no—
237D4—6042no—
238D4—6048no—
239D4—6042no—
240D4—6041no—
241D4—6041no—
242D4—12081no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—3021no—
249C2×C4—3021no—
250C2×C4—6042no—
251C2×C4—6041no—
252C2×C4D4×D15111yescharacteristic
253C2×C4C2×D60411yescharacteristic
254C8—41no—
255C8—6041no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—3022no—
262C22—6042no—
263C22—6042no—
264C22—6042no—
265C22—6041no—
266C22—6041no—
267C22—6041no—
268C22—6041no—
269C22—6042no—
270C22—6041no—
271C22—12081no—
272C22—12081no—
273C22—12081no—
274C22—12084no—
275C22—12081no—
276C22—12081no—
277C22#1801270911yescharacteristic
278C22D8×D15111yescharacteristic
279C22#1801276611yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—6041no—
285C4—6041no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—6042no—
290C2—12082no—
291C2—12081no—
292C2#2375234711yescharacteristic
293C2#2375238111yescharacteristic
294C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
hypercenter#327D151
hypocenterC151#1595
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #23752770C2semidirect
2. #23752348C2semidirect
3. #23752345C2semidirect
4. #23752122C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #327×C151C2semidirect
9. C22×D604C22semidirect
23. C22⋊(C151⋊C8)C22semidirect
25. C22⋊C8×C151C22semidirect
26. #95×C151C22semidirect
37. C2×D604D4semidirect
48. C4⋊Dic151D4semidirect
57. C2×D4×C151D4semidirect
61. C4⋊C4×C151D4semidirect
78. C22×D151D8semidirect
147. C151#1595semidirect
154. #327D151semidirect
173. C22⋊C8C2×D151semidirect
174. #95C2×D151semidirect
192. C2×D4D604semidirect
203. C4⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237527702
#237523482
#237523452
#237521222
#237519452
#237519352
#327×C1512
#1595151