Finite Group Databasebeta

← #34047463

Subgroups — #34047463

Order 19072.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011904C211yesmaximal, characteristic
2#23749523C211yesmaximal, characteristic, complemented
3#23749522C211yesmaximal, characteristic, complemented
4#23749513C211yesmaximal, characteristic
5#23749513C211yesmaximal, characteristic
6#23749512C211yesmaximal, characteristic, complemented
7#23749510C211yesmaximal, characteristic, complemented
8#23749506C211yesmaximal, characteristic, complemented
9#23749500C211yesmaximal, characteristic
10#23749497C211yesmaximal, characteristic
11#23749489C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
13C4×#14558715C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic149C211yesmaximal, characteristic
15#388×C149C211yesmaximal, characteristic
16C23×Dic149C2211yescharacteristic
17#18011904C418yescomplemented
18C2×C4⋊Dic149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×C4⋊Dic149C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31C2×C4×Dic149C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33C2×C4×Dic149C2211yescharacteristic
34C2×C4×Dic149C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C22×Dic149—22no—
53C22×Dic149—41no—
54C22×Dic149—41no—
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C4⋊Dic149—22no—
64C4⋊Dic149—41no—
65C4⋊Dic149C2×C414yescomplemented
66#14558715—22no—
67#14558715—41no—
68#14558715—41no—
69#14558715—41no—
70#14558715C2×C414yescomplemented
71#14558715C2×C414yescomplemented
72C22⋊Dic149—41no—
73C22⋊Dic149C2×C414yes—
74C22⋊Dic149C2×C414yes—
75C4×Dic149—22no—
76C4×Dic149—41no—
77C4×Dic149—41no—
78C4×Dic149—41no—
79C4×Dic149C2×C414yescomplemented
80C24×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—22no—
88C22⋊C4×C149—22no—
89C22⋊C4×C149—41no—
90C22⋊C4×C149C2×C414yes—
91C42×C149—41no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149—21no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C2×Dic149—21no—
98C2×Dic149—21no—
99C2×Dic149—21no—
100C2×Dic149—21no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149—21no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—44no—
112C2×Dic149C22×C412yes—
113C2×Dic149C22×C412yes—
114C2×Dic149C22×C412yes—
115C2×Dic149C22×C412yes—
116C2×Dic149#4112yes—
117C23×C149—21no—
118C23×C149—21no—
119C23×C149—21no—
120C23×C149—21no—
121C23×C149—21no—
122C23×C149—21no—
123C23×C149C22×C412yes—
124C23×C149C2411yescharacteristic
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149C22×C412yes—
141C2×C4×C149C22×C412yes—
142C2×C4×C149#4112yes—
143C22×C149—22no—
144C22×C149—22no—
145C22×C149—22no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149C23×C411yescharacteristic
151C22×C149C2×#4111yescharacteristic
152C22×C149C2×#4111yescharacteristic
153C22×C149H(5,𝔽2)11yescharacteristic
154C22×C149H(5,𝔽2)11yescharacteristic
155C22×C1492−1+411yescharacteristic
156C22×C1492−1+411yescharacteristic
157C4×C149—22no—
158C4×C149—22no—
159C4×C149—22no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163Dic149—22no—
164Dic149—22no—
165Dic149—22no—
166Dic149—22no—
167Dic149—22no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—42no—
172C2×C149C4×#4111yescharacteristic
173C2×C149#52011yescharacteristic
174C2×C149#52011yescharacteristic
175C2×C149#53811yescharacteristic
176C2×C149#53911yescharacteristic
177C2×C149#54111yescharacteristic
178C2×C149#54211yescharacteristic
179C149#233411yescharacteristic, complemented, Sylow
180#2334—1491nomaximal, Sylow
181C2×#126—1491no—
182#389—1491no—
183#389—1491no—
184#388—1491no—
185#388—1491no—
186#388D14911yescharacteristic
187#387—1491no—
188#387—1491no—
189#387—1491no—
190#385—1491no—
191#385—1491no—
192#382—1491no—
193C4×C4⋊C4—1491no—
194C4×C4⋊C4—1491no—
195C4×C22⋊C4—1491no—
196C23×C4—1491no—
197#126—1498no—
198C2×C4⋊C4—1491no—
199C2×C4⋊C4—1491no—
200C2×C4⋊C4—1491no—
201C2×C4⋊C4—1491no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4—1491no—
204C2×C4⋊C4—1491no—
205C2×C4⋊C4—1491no—
206C2×C4⋊C4—1491no—
207C2×C4⋊C4C2×D14911yescharacteristic
208C2×C22⋊C4—1491no—
209C2×C22⋊C4—1491no—
210C2×C22⋊C4—1491no—
211C2×C22⋊C4C2×D14911yescharacteristic
212C2×C22⋊C4C2×D14911yescharacteristic
213C2×C22⋊C4C2×D14911yescharacteristic
214C2×C42—1491no—
215C2×C42—1491no—
216C2×C42—1491no—
217C2×C42—1491no—
218C2×C42—1491no—
219C2×C42C2×D14911yescharacteristic
220#95—1491no—
221#95—1491no—
222#95—1491no—
223#95—1491no—
224#95—1491no—
225#95—1491no—
226#95—1491no—
227#95—1491no—
228#95—1491no—
229#95—1491no—
230#95C2×D14911yescharacteristic
231#95C2×D14911yescharacteristic
232C24C22×D14911yescharacteristic
233C22×C4—2982no—
234C22×C4—5961no—
235C22×C4—5961no—
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4—1491no—
239C22×C4—1491no—
240C22×C4—1491no—
241C22×C4—1491no—
242C22×C4—1491no—
243C22×C4—1491no—
244C22×C4C22×D14911yescharacteristic
245C22×C4C22×D14911yescharacteristic
246C22×C4C22×D14911yescharacteristic
247C22×C4C22×D14911yescharacteristic
248C22×C4C22×D14911yescharacteristic
249C22×C4C22×D14911yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—2982no—
252C4⋊C4—2982no—
253C4⋊C4—5961no—
254C4⋊C4—5961no—
255C4⋊C4—5961no—
256C4⋊C4—5961no—
257C4⋊C4—1494no—
258C4⋊C4—1494no—
259C4⋊C4—1494no—
260C22⋊C4—22no—
261C22⋊C4—41no—
262C22⋊C4—5961no—
263C22⋊C4—1494no—
264C22⋊C4—1494no—
265C22⋊C4C4×D14914yes—
266C42—41no—
267C42—2982no—
268C42—5961no—
269C42—5961no—
270C42—5961no—
271C42—1494no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D14912yes—
279C23C23×D14911yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—5964no—
315C2×C4—1492no—
316C2×C4—1492no—
317C2×C4—1492no—
318C2×C4—1492no—
319C2×C4—1492no—
320C2×C4C2×C4×D14912yes—
321C2×C4C2×C4×D14912yes—
322C2×C4#1455873512yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D14911yescharacteristic
331C22#41×D14911yescharacteristic
332C22C2×#1455873511yescharacteristic
333C22#1801195611yescharacteristic
334C22#1801195711yescharacteristic
335C22#1801195811yescharacteristic
336C22#1801195811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2982no—
344C4—2982no—
345C4—2982no—
346C4—2982no—
347C4—2982no—
348C4—5961no—
349C4—5961no—
350C4—5961no—
351C2—42no—
352C2C4×#1455873511yescharacteristic
353C2#2375010411yescharacteristic
354C2#2375010511yescharacteristic
355C2#2375021111yescharacteristic
356C2#2375022011yescharacteristic
357C2#2375023211yescharacteristic
358C2#2375024411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenter#388D149
hypocenterC149#2334
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #23749523C2semidirect
3. #23749522C2semidirect
6. #23749512C2semidirect
7. #23749510C2semidirect
8. #23749506C2semidirect
11. #23749489C2semidirect
12. C4⋊C4×Dic149C2semidirect
13. C4×#14558715C2semidirect
17. #18011904C4semidirect
65. C4⋊Dic149C2×C4semidirect
70. #14558715C2×C4semidirect
71. #14558715C2×C4semidirect
79. C4×Dic149C2×C4semidirect
179. C149#2334semidirect

Maximal subgroups

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

subgroupindex
C2×#180119042
#237495232
#237495222
#237495132
#237495122
#237495102
#237495062
#237495002
#237494972
#237494892
C4⋊C4×Dic1492
C4×#145587152
C22⋊C4×Dic1492
#388×C1492
#2334149