Finite Group Databasebeta

← #34047423

Subgroups — #34047423

Order 19072.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011887C211yesmaximal, characteristic
2#23749532C211yesmaximal, characteristic, complemented
3#23749522C211yesmaximal, characteristic, complemented
4#23749520C211yesmaximal, characteristic, complemented
5#23749510C211yesmaximal, characteristic, complemented
6#23749509C211yesmaximal, characteristic, complemented
7#23749508C211yesmaximal, characteristic, complemented
8#23749507C211yesmaximal, characteristic, complemented
9#23749499C211yesmaximal, characteristic
10#23749496C211yesmaximal, characteristic
11#23749484C211yesmaximal, characteristic
12C4×#14558713C211yesmaximal, characteristic
13#23749472C211yesmaximal, characteristic
14#95×D149C211yesmaximal, characteristic
15#391×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011887C418yescomplemented
20C2×C4⋊Dic149C2211yescharacteristic
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
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
45C22×Q8×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C42×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C23×D149C2311yescharacteristic
53C22×Dic149C2311yescharacteristic
54C22×Dic149C2311yescharacteristic
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C2×C4×D149—22no—
61C2×C4×D149—41no—
62C2×C4×D149—41no—
63C2×C4×D149—41no—
64C2×C4×D149—41no—
65C2×C4×D149—41no—
66C2×C4×D149—41no—
67C2×C4×D149C2×C414yes—
68C2×C4×D149Q814yescomplemented
69C4⋊Dic149—41no—
70C4⋊Dic149C2×C414yescomplemented
71#14558715—41no—
72#14558715—41no—
73#14558715—41no—
74#14558715—41no—
75#14558715C2×C414yescomplemented
76#14558715C2×C414yescomplemented
77#14558713—22no—
78#14558713—22no—
79#14558713C2×C414yes—
80#14558713C2×C414yes—
81C4×Dic149—41no—
82C4×Dic149—41no—
83C4×Dic149—41no—
84C2×Q8×C149—41no—
85C2×Q8×C149—41no—
86C2×Q8×C149C2×C414yescomplemented
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C4⋊C4×C149—41no—
95C42×C149—41no—
96C22×D149—21no—
97C22×D149—21no—
98C22×D149—21no—
99C22×D149—21no—
100C22×D149C22×C412yes—
101C22×D149C2×Q812yes—
102C22×D149#4112yes—
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—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149C22×C412yes—
121C2×Dic149C22×C412yes—
122C2×Dic149C22×C412yes—
123C2×Dic149C2×Q812yes—
124C4×D149—44no—
125C4×D149—44no—
126C4×D149—44no—
127C23×C149C2411yescharacteristic
128Q8×C149—44no—
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×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149C22×C412yes—
147C2×C4×C149C22×C412yes—
148C2×C4×C149C22×C412yes—
149C2×C4×C149C2×Q812yes—
150C22×C149C23×C411yescharacteristic
151C22×C149C22×Q811yescharacteristic
152C22×C149C2×#4111yescharacteristic
153C22×C149H(5,𝔽2)11yescharacteristic
154C22×C149H(5,𝔽2)11yescharacteristic
155C22×C149H(5,𝔽2)11yescharacteristic
156C22×C1492−1+411yescharacteristic
157C2×D149—22no—
158C2×D149—22no—
159C2×D149—22no—
160C2×D149—22no—
161C2×D149—22no—
162C2×D149—22no—
163C2×D149C4×Q814yes—
164C4×C149—22no—
165C4×C149—22no—
166C4×C149—22no—
167C4×C149—22no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149—41no—
171Dic149—22no—
172Dic149—22no—
173Dic149—22no—
174Dic149—22no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178C2×C149C2×C4×Q811yescharacteristic
179C2×C149#51811yescharacteristic
180C2×C149#52011yescharacteristic
181C2×C149#53811yescharacteristic
182C2×C149#53911yescharacteristic
183C2×C149#54311yescharacteristic
184C2×C149#54411yescharacteristic
185D149—24no—
186C149#232911yescharacteristic, complemented, Sylow
187#2329—1491nomaximal, Sylow
188C2×C22⋊Q8—1491no—
189#391—1491no—
190#391D14911yescharacteristic, complemented
191#389—1491no—
192#389—1491no—
193#387—1491no—
194#387—1491no—
195#387—1491no—
196#387—1491no—
197#385—1491no—
198#385—1491no—
199#380—1491no—
200C4×C22⋊C4—1491no—
201C4×C22⋊C4—1491no—
202C2×#95—1491no—
203C22×Q8C2×D14911yescharacteristic
204C23×C4—1491no—
205C23×C4—1491no—
206C23×C4—1491no—
207C22⋊Q8—1498no—
208C2×C4⋊C4—1491no—
209C2×C4⋊C4—1491no—
210C2×C4⋊C4—1491no—
211C2×C4⋊C4—1491no—
212C2×C4⋊C4—1491no—
213C2×C4⋊C4—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4C2×D14911yescharacteristic
217C2×C22⋊C4—1491no—
218C2×C22⋊C4—1491no—
219C2×C22⋊C4—1491no—
220C2×C22⋊C4—1491no—
221C2×C42—1491no—
222C2×C42—1491no—
223C2×C42—1491no—
224C2×C42C2×D14911yescharacteristic
225#95—1491no—
226#95—1491no—
227#95—1491no—
228#95—1491no—
229#95—1491no—
230#95—1491no—
231#95—1491no—
232#95—1491no—
233#95—1491no—
234#95—1491no—
235#95C2×D14911yescharacteristic
236#95C2×D14911yescharacteristic
237#95C2×D14911yescharacteristic
238#95C2×D14911yescharacteristic
239C24—1491no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8C4×D14914yescomplemented
243C22×C4—2982no—
244C22×C4—5961no—
245C22×C4—5961no—
246C22×C4—5961no—
247C22×C4—5961no—
248C22×C4—5961no—
249C22×C4—5961no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253C22×C4—1491no—
254C22×C4—1491no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4—1494no—
258C22×C4—1494no—
259C22×C4C22×D14911yescharacteristic
260C22×C4C22×D14911yescharacteristic
261C22×C4C22×D14911yescharacteristic
262C22×C4C22×D14911yescharacteristic
263C22×C4C22×D14911yescharacteristic
264C22×C4C22×D14911yescharacteristic
265C22×C4C22×D14911yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—5961no—
268C4⋊C4—5961no—
269C4⋊C4—5961no—
270C4⋊C4—5961no—
271C4⋊C4—5961no—
272C4⋊C4—1494no—
273C4⋊C4—1494no—
274C4⋊C4—1494no—
275C22⋊C4—2982no—
276C22⋊C4—2982no—
277C22⋊C4—1494no—
278C22⋊C4—1494no—
279C42—41no—
280C42—5961no—
281C42—5961no—
282C42—5961no—
283C23—2981no—
284C23—2981no—
285C23—2981no—
286C23—2981no—
287C23—1492no—
288C23—1492no—
289C23—1492no—
290C23C23×D14911yescharacteristic
291Q8—44no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—5964no—
327C2×C4—5964no—
328C2×C4—5964no—
329C2×C4—1492no—
330C2×C4—1492no—
331C2×C4—1492no—
332C2×C4—1492no—
333C2×C4C2×C4×D14912yes—
334C2×C4C2×C4×D14912yes—
335C2×C4C2×C4×D14912yes—
336C2×C4Q8×D14912yes—
337C22—2982no—
338C22—2982no—
339C22—2982no—
340C22—2982no—
341C22—2982no—
342C22—2982no—
343C22—1494no—
344C22C22×C4×D14911yescharacteristic
345C22C2×Q8×D14911yescharacteristic
346C22#41×D14911yescharacteristic
347C22#1801195611yescharacteristic
348C22#1801195611yescharacteristic
349C22#1801195711yescharacteristic
350C22#1801195911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2982no—
359C4—2982no—
360C4—2982no—
361C4—2982no—
362C4—5961no—
363C4—5961no—
364C4—5961no—
365C2—2984no—
366C2C4×Q8×D14911yescharacteristic
367C2#2375009811yescharacteristic
368C2#2375010711yescharacteristic
369C2#2375020911yescharacteristic
370C2#2375022111yescharacteristic
371C2#2375025011yescharacteristic
372C2#2375025211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#391×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenter#391D149
hypocenterC149#2329
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #23749532C2semidirect
3. #23749522C2semidirect
4. #23749520C2semidirect
5. #23749510C2semidirect
6. #23749509C2semidirect
7. #23749508C2semidirect
8. #23749507C2semidirect
15. #391×C149C2semidirect
19. #18011887C4semidirect
68. C2×C4×D149Q8semidirect
70. C4⋊Dic149C2×C4semidirect
75. #14558715C2×C4semidirect
76. #14558715C2×C4semidirect
86. C2×Q8×C149C2×C4semidirect
186. C149#2329semidirect
190. #391D149semidirect
242. C2×Q8C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118872
#237495322
#237495222
#237495202
#237495102
#237495092
#237495082
#237495072
#237494992
#237494962
#237494842
C4×#145587132
#237494722
#95×D1492
#391×C1492
#2329149