Finite Group Databasebeta

← #34070176

Subgroups — #34070176

Order 19328.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#23753010C211yesmaximal, characteristic, complemented
2#23752724C211yesmaximal, characteristic, complemented
3#23752719C211yesmaximal, characteristic, complemented
4#23752228C211yesmaximal, characteristic, complemented
5#23752175C211yesmaximal, characteristic, complemented
6#23751968C211yesmaximal, characteristic, complemented
7#421×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9C22×C4×D151C2211yescharacteristic
10#18012770—21no—
11#18012769—21no—
12#18012765—21no—
13#18012764—21no—
14#18012759—22no—
15C2×#14558988C2211yescharacteristic
16#18012723—21no—
17#18012720—21no—
18#18012719—21no—
19#18012715—21no—
20#18012714—21no—
21#18012710—21no—
22#18012709—21no—
23#18012707—21no—
24C4×D604—22no—
25C4×C22⋊D151—22no—
26#18012698C2211yescharacteristic
27#18012665—22no—
28(C2×D151)⋊C8—22no—
29C2×#41×C151C2211yescharacteristic
30C2×M16×C151C2211yescharacteristic
31#117×C151C2211yescharacteristic
32#104×C151—22no—
33C23×D151D411yescharacteristic
34#14559004—21no—
35#14559004—21no—
36#14559004—21no—
37#14559004—21no—
38C2×Dic302D411yescharacteristic, complemented
39C2×D604—22no—
40C2×D604D411yescharacteristic, complemented
41C2×C22⋊D151—22no—
42C2×C22⋊D151—21no—
43C22×Dic151D411yescharacteristic
44C2×C4×D151—21no—
45C2×C4×D151—21no—
46C2×C4×D151—21no—
47C2×C4×D151—21no—
48C2×C4×D151—21no—
49C2×C4×D151—21no—
50C2×C4×D151—21no—
51#14558994—22no—
52#14558992—22no—
53#14558991—22no—
54#14558989—22no—
55#14558988—21no—
56#14558988—21no—
57C2×C151⋊C8D412yescomplemented
58C4⋊Dic151—22no—
59C4⋊Dic151—21no—
60Dic151⋊C4—22no—
61C22⋊Dic151—22no—
62C22⋊Dic151—21no—
63(C2×D151)⋊C4—22no—
64(C2×D151)⋊C4—22no—
65(C2×D151)⋊C4—22no—
66C4×Dic151D412yescomplemented
67#41×C151—21no—
68#41×C151—21no—
69#41×C151—21no—
70#41×C151—21no—
71C2×Q8×C151D411yescharacteristic, complemented
72C2×D4×C151—21no—
73C2×D4×C151D411yescharacteristic, complemented
74C22×C4×C151—21no—
75C22×C4×C151C2311yescharacteristic
76M16×C151—21no—
77M16×C151—21no—
78C2×C8×C151—21no—
79C4⋊C4×C151—21no—
80C22⋊C4×C151—21no—
81C42×C151D412yescomplemented
82C22×D151—21no—
83C22×D151—21no—
84C22×D151—21no—
85C22×D151—21no—
86C22×D151—42no—
87Dic302—21no—
88Dic302—21no—
89D604—21no—
90D604—21no—
91D604—44no—
92C22⋊D151—44no—
93C22⋊D151—41no—
94C22⋊D151—41no—
95C2×Dic151—22no—
96C2×Dic151—21no—
97C2×Dic151—21no—
98C2×Dic151—21no—
99C2×Dic151—21no—
100C4×D151—41no—
101C4×D151—41no—
102C4×D151—41no—
103C4×D151—41no—
104C4×D151—41no—
105C4×D151—41no—
106C151⋊C8—22no—
107C23×C151—21no—
108C23×C151C2×D411yescharacteristic
109Q8×C151—21no—
110Q8×C151—21no—
111D4×C151—21no—
112D4×C151—21no—
113D4×C151—41no—
114D4×C151—41no—
115C2×C4×C151—21no—
116C2×C4×C151—22no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151#4111yescharacteristic
125C8×C151—41no—
126C22×C151—41no—
127C22×C151—42no—
128C22×C151—41no—
129C22×C151#12011yescharacteristic
130C22×C151#12011yescharacteristic
131C22×C151#12111yescharacteristic
132C2×D151—22no—
133C2×D151—22no—
134C2×D151—22no—
135C2×D151—41no—
136C2×D151—41no—
137C2×D151—41no—
138C2×D151—41no—
139C2×D151—42no—
140C2×D151—41no—
141C4×C151—42no—
142C4×C151—41no—
143C4×C151#12011yescharacteristic
144C4×C151#12111yescharacteristic
145C4×C151#12111yescharacteristic
146C4×C151#12711yescharacteristic
147Dic151—42no—
148Dic151—41no—
149Dic151—41no—
150C2×C151—21no—
151C2×C151—21no—
152C2×C151—21no—
153C2×C151—81no—
154C2×C151#39211yescharacteristic
155D151—42no—
156D151—81no—
157C151#201011yescharacteristic, complemented, Sylow
158#2010—1511nomaximal, Sylow
159#575—1511no—
160#525—1511no—
161#525—1511no—
162#421—1511no—
163#421D15111yescharacteristic, complemented
164#407—1511no—
165H(3,ℤ/4)—1511no—
166C2×#41—1511no—
167C2×#41C2×D15111yescharacteristic
168C23×C4—1511no—
169#137—3021no—
170#137—3021no—
171AGL(1,ℤ/8)—3021no—
172AGL(1,ℤ/8)—3021no—
173#135—3022no—
174C2×M16—1511no—
175C2×M16C2×D15111yescharacteristic
176#123—3021no—
177#123—3021no—
178C22⋊Q8—3021no—
179C22⋊Q8—3021no—
180#121—3021no—
181#121—3021no—
182#120—3021no—
183#120—3021no—
184C4×D4—3022no—
185C4×D4—3022no—
186#117—1511no—
187#117C2×D15111yescharacteristic
188#104—22no—
189#104—3022no—
190C22⋊C8—3022no—
191C24—1511no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—3021no—
197#41—3021no—
198#41—3021no—
199#41—3021no—
200C2×Q8—1511no—
201C2×Q8D60411yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—3022no—
204C2×D4—3022no—
205C2×D4—3021no—
206C2×D4—1511no—
207C2×D4D60411yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—3021no—
210C22×C4—3021no—
211C22×C4—3021no—
212C22×C4—3021no—
213C22×C4—3021no—
214C22×C4—3021no—
215C22×C4—3021no—
216C22×C4—1511no—
217C22×C4C22×D15111yescharacteristic
218Q16—3022no—
219SD16—3022no—
220SD16—3022no—
221D8—3022no—
222M16—21no—
223M16—21no—
224M16—3021no—
225M16—3021no—
226C2×C8—21no—
227C2×C8—1512no—
228C4⋊C4—21no—
229C4⋊C4—3022no—
230C4⋊C4—3022no—
231C4⋊C4—3021no—
232C22⋊C4—21no—
233C22⋊C4—3022no—
234C22⋊C4—3022no—
235C22⋊C4—3022no—
236C22⋊C4—3022no—
237C22⋊C4—3021no—
238C42—1512no—
239C42C22⋊D15112yescomplemented
240C23—21no—
241C23—3021no—
242C23—3021no—
243C23—3021no—
244C23—3021no—
245C23—6042no—
246C23D4×D15111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—3021no—
250Q8—3021no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—3021no—
256D4—3021no—
257D4—6044no—
258D4—6044no—
259D4—6041no—
260D4—6041no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3021no—
266C2×C4—3021no—
267C2×C4—3022no—
268C2×C4—3021no—
269C2×C4—3021no—
270C2×C4—6041no—
271C2×C4—6041no—
272C2×C4—6041no—
273C2×C4—6041no—
274C2×C4—6041no—
275C2×C4—6041no—
276C2×C4D4×D15111yescharacteristic
277C2×C4D4×D15111yescharacteristic
278C2×C4D4×D15111yescharacteristic
279C2×C4C2×C22⋊D15111yescharacteristic
280C2×C4C2×D60411yescharacteristic
281C2×C4#1455900411yescharacteristic
282C8—41no—
283C8—3022no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—3022no—
288C22—3022no—
289C22—3022no—
290C22—6041no—
291C22—6041no—
292C22—6041no—
293C22—6042no—
294C22—6041no—
295C22—6041no—
296C22#1801270711yescharacteristic
297C22#1801270911yescharacteristic
298C22#1801271211yescharacteristic
299C4—42no—
300C4—41no—
301C4—6042no—
302C4—6041no—
303C4—6041no—
304C4#1801270911yescharacteristic
305C4#1801271211yescharacteristic
306C4#1801271311yescharacteristic
307C4#1801273511yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—6042no—
313C2—12081no—
314C2#2375212111yescharacteristic
subgroupG/H
centerC4#18012735
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#421×C151C2
socleC2×C151#392
hypercenter#421D151
hypocenterC151#2010
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #23753010C2semidirect
2. #23752724C2semidirect
3. #23752719C2semidirect
4. #23752228C2semidirect
5. #23752175C2semidirect
6. #23751968C2semidirect
7. #421×C151C2semidirect
38. C2×Dic302D4semidirect
40. C2×D604D4semidirect
57. C2×C151⋊C8D4semidirect
66. C4×Dic151D4semidirect
71. C2×Q8×C151D4semidirect
73. C2×D4×C151D4semidirect
81. C42×C151D4semidirect
157. C151#2010semidirect
163. #421D151semidirect
201. C2×Q8D604semidirect
207. C2×D4D604semidirect
239. C42C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530102
#237527242
#237527192
#237522282
#237521752
#237519682
#421×C1512
#2010151