Finite Group Databasebeta

← #34077133

Subgroups — #34077133

Order 19328.

644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18012714C211yesmaximal, characteristic, complemented
2C2×#18012712C211yesmaximal, characteristic, complemented
3#23752141C212yesmaximal, complemented
4#23752138C211yesmaximal, characteristic, complemented
5#23752122C211yesmaximal, characteristic, complemented
6#23752122C212yesmaximal, complemented
7#23752121C212yesmaximal, complemented
8#23752121C212yesmaximal, complemented
9#23752121C211yesmaximal, characteristic, complemented
10#23752074C211yesmaximal, characteristic, complemented
11#397×C151C211yesmaximal, characteristic, complemented
12C22×D604C2212yes—
13C22×D604C2211yescharacteristic
14C22×D604C2211yescharacteristic
15C22×D604C2212yes—
16C22×C22⋊D151C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C22×C22⋊D151C2212yes—
19C22×C4×D151C2211yescharacteristic
20#18012714—24no—
21#18012712—24no—
22C2×Dic151⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2212yes—
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×(C2×D151)⋊C4C2212yes—
29C151⋊#95C2211yescharacteristic
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C23×D151C2311yescharacteristic
38C23×D151C2312yes—
39C23×D151C2311yescharacteristic
40C2×D604—22no—
41C2×D604—24no—
42C2×D604—22no—
43C2×D604—42no—
44C2×D604—42no—
45C2×D604—42no—
46C2×D604—42no—
47C2×D604—42no—
48C2×D604—42no—
49C2×D604—42no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—22no—
52C2×C22⋊D151—42no—
53C2×C22⋊D151—42no—
54C2×C22⋊D151—42no—
55C2×C22⋊D151—42no—
56C2×C22⋊D151—42no—
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2312yes—
59C22×Dic151C2311yescharacteristic
60C2×C4×D151—42no—
61C2×C4×D151D414yescomplemented
62Dic151⋊C4—22no—
63(C2×D151)⋊C4—24no—
64(C2×D151)⋊C4—22no—
65(C2×D151)⋊C4—42no—
66(C2×D151)⋊C4—42no—
67(C2×D151)⋊C4—42no—
68(C2×D151)⋊C4—42no—
69C24×C151C2311yescharacteristic
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2312yes—
72C22×C4×C151C2312yes—
73C22×C4×C151C2311yescharacteristic
74C4⋊C4×C151—22no—
75C22⋊C4×C151—22no—
76C22⋊C4×C151—42no—
77C22×D151—22no—
78C22×D151—22no—
79C22×D151—21no—
80C22×D151—21no—
81C22×D151—21no—
82C22×D151—22no—
83C22×D151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—22no—
88C22×D151—22no—
89C22×D151—22no—
90C22×D151—21no—
91C22×D151—22no—
92C22×D151—22no—
93C22×D151C2×D412yes—
94D604—44no—
95D604—44no—
96D604—48no—
97D604—48no—
98C22⋊D151—44no—
99C22⋊D151—44no—
100C22⋊D151—48no—
101C2×Dic151—22no—
102C2×Dic151—21no—
103C2×Dic151—22no—
104C2×Dic151—22no—
105C2×Dic151—22no—
106C2×Dic151—22no—
107C2×Dic151C2×D412yes—
108C4×D151—44no—
109C23×C151—21no—
110C23×C151—22no—
111C23×C151—21no—
112C23×C151—22no—
113C23×C151—21no—
114C23×C151C2411yescharacteristic
115C2×C4×C151—22no—
116C2×C4×C151—22no—
117C2×C4×C151—21no—
118C2×C4×C151—22no—
119C2×C4×C151—22no—
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—22no—
123C2×C4×C151—22no—
124C2×C4×C151C2×D412yes—
125C22×C151—41no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151—42no—
129C22×C151—42no—
130C22×C151C22×D411yescharacteristic
131C22×C151H(5,𝔽2)11yescharacteristic
132C22×C151H(5,𝔽2)12yes—
133C22×C151H(5,𝔽2)11yescharacteristic
134C22×C151H(5,𝔽2)12yes—
135C2×D151—22no—
136C2×D151—22no—
137C2×D151—22no—
138C2×D151—42no—
139C2×D151—42no—
140C2×D151—41no—
141C2×D151—42no—
142C2×D151—42no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151—42no—
146C2×D151—42no—
147C2×D151—42no—
148C2×D151—42no—
149C2×D151—42no—
150C2×D151—42no—
151C2×D151—42no—
152C4×C151—22no—
153C4×C151—42no—
154C4×C151—41no—
155C4×C151—42no—
156Dic151—22no—
157Dic151—41no—
158Dic151—42no—
159C2×C151—81no—
160C2×C151#53411yescharacteristic
161C2×C151#53511yescharacteristic
162C2×C151#53511yescharacteristic
163C2×C151#56012yes—
164C2×C151#56012yes—
165D151—42no—
166D151—81no—
167D151—82no—
168C151#281511yescharacteristic, complemented, Sylow
169#2815—1511nomaximal, Sylow
170C2×#121—1511no—
171C2×#121—1511no—
172#397—1511no—
173#397—1512no—
174#397D15111yescharacteristic, complemented
175#392—1512no—
176#392—1511no—
177#392—1512no—
178#392—1511no—
179#392—1512no—
180#381—1511no—
181C22×D4—1511no—
182C22×D4—1511no—
183C22×D4—1512no—
184C22×D4—1512no—
185C22×D4—1511no—
186C22×D4—1511no—
187C22×D4—1512no—
188C23×C4—1511no—
189#121—3024no—
190#121—3024no—
191C2×C4⋊C4—1511no—
192C2×C4⋊C4C2×D15111yescharacteristic
193C2×C22⋊C4—1512no—
194C2×C22⋊C4—1511no—
195C2×C22⋊C4—1512no—
196C2×C22⋊C4—1512no—
197C2×C22⋊C4—1512no—
198C2×C22⋊C4—1512no—
199C2×C22⋊C4C2×D15111yescharacteristic
200C2×C22⋊C4C2×D15112yes—
201#95—1511no—
202#95—1512no—
203#95—1512no—
204#95C2×D15111yescharacteristic
205#95C2×D15112yes—
206C24—1511no—
207C24—1512no—
208C24—1511no—
209C24C22×D15111yescharacteristic
210C2×D4—3022no—
211C2×D4—3024no—
212C2×D4—3022no—
213C2×D4—3022no—
214C2×D4—3022no—
215C2×D4—6042no—
216C2×D4—6042no—
217C2×D4—6042no—
218C2×D4—6042no—
219C2×D4—6042no—
220C2×D4—6042no—
221C2×D4—6042no—
222C2×D4—6042no—
223C2×D4—6042no—
224C2×D4—6042no—
225C2×D4—6042no—
226C2×D4—6042no—
227C22×C4—6042no—
228C22×C4—1512no—
229C22×C4—1511no—
230C22×C4—1511no—
231C22×C4—1514no—
232C22×C4C22×D15112yes—
233C22×C4C22×D15112yes—
234C22×C4C22×D15111yescharacteristic
235C22×C4C22×D15111yescharacteristic
236C4⋊C4—22no—
237C4⋊C4—3022no—
238C22⋊C4—22no—
239C22⋊C4—42no—
240C22⋊C4—3024no—
241C22⋊C4—3022no—
242C22⋊C4—6042no—
243C22⋊C4—6042no—
244C22⋊C4—6042no—
245C22⋊C4—6042no—
246C23—21no—
247C23—21no—
248C23—22no—
249C23—21no—
250C23—22no—
251C23—3021no—
252C23—3022no—
253C23—3021no—
254C23—3022no—
255C23—3022no—
256C23—3021no—
257C23—3022no—
258C23—3021no—
259C23—3021no—
260C23—3022no—
261C23—3022no—
262C23—3022no—
263C23—3022no—
264C23—3022no—
265C23—3022no—
266C23—3022no—
267C23—1512no—
268C23C23×D15111yescharacteristic
269D4—6044no—
270D4—6048no—
271D4—6044no—
272D4—6048no—
273D4—6044no—
274D4—6044no—
275D4—6048no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—3022no—
286C2×C4—3021no—
287C2×C4—3022no—
288C2×C4—3022no—
289C2×C4—3022no—
290C2×C4—3022no—
291C2×C4—6044no—
292C2×C4—1512no—
293C2×C4D4×D15112yes—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—3022no—
300C22—3022no—
301C22—3022no—
302C22—6042no—
303C22—6042no—
304C22—6042no—
305C22—6041no—
306C22—6042no—
307C22—6041no—
308C22—6041no—
309C22—6042no—
310C22—6042no—
311C22—6042no—
312C22—6042no—
313C22—6042no—
314C22—6042no—
315C22—6042no—
316C22C2×D4×D15111yescharacteristic
317C22#1801278411yescharacteristic
318C22#1801278512yes—
319C22#1801278511yescharacteristic
320C22#1801278512yes—
321C4—22no—
322C4—42no—
323C4—41no—
324C4—42no—
325C4—3022no—
326C4—6041no—
327C4—6042no—
328C2—81no—
329C2—6042no—
330C2—12082no—
331C2—12081no—
332C2#2375277311yescharacteristic
333C2#2375277811yescharacteristic
334C2#2375278011yescharacteristic
335C2#2375295212yes—
336C2#2375295312yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
hypercenter#397D151
hypocenterC151#2815
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#18012714C2semidirect
2. C2×#18012712C2semidirect
3. #23752141C2semidirect
4. #23752138C2semidirect
5. #23752122C2semidirect
6. #23752122C2semidirect
7. #23752121C2semidirect
8. #23752121C2semidirect
9. #23752121C2semidirect
10. #23752074C2semidirect
11. #397×C151C2semidirect
61. C2×C4×D151D4semidirect
168. C151#2815semidirect
174. #397D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127142
C2×#180127122
#237521412
#237521382
#237521222
#237521212
#237520742
#397×C1512
#2815151