Finite Group Databasebeta

← #34047546

Subgroups — #34047546

Order 19072.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011869C211yesmaximal, characteristic
2#23749511C211yesmaximal, characteristic, complemented
3#23749510C211yesmaximal, characteristic, complemented
4#23749508C211yesmaximal, characteristic, complemented
5#23749499C211yesmaximal, characteristic
6#23749496C211yesmaximal, characteristic
7#23749492C211yesmaximal, characteristic, complemented
8#23749489C211yesmaximal, characteristic, complemented
9#23749487C211yesmaximal, characteristic
10C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
11C4×#14558713C211yesmaximal, characteristic
12#23749472C211yesmaximal, characteristic
13#23749471C211yesmaximal, characteristic, complemented
14#95×D149C211yesmaximal, characteristic
15#387×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011869C418yescomplemented
20C2×C4⋊Dic149C2211yescharacteristic
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558713C2211yescharacteristic
25C2×#14558713C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C2×C4×Dic149C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31C2×C4×Dic149C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33#18011818C2211yescharacteristic
34#18011818C2211yescharacteristic
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×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—22no—
62C2×C4×D149—22no—
63C2×C4×D149—22no—
64C2×C4×D149—22no—
65C2×C4×D149—22no—
66C2×C4×D149—41no—
67C2×C4×D149—41no—
68C2×C4×D149C2×C414yes—
69C4⋊Dic149—22no—
70C4⋊Dic149C2×C414yescomplemented
71#14558715—41no—
72#14558715—41no—
73#14558713—22no—
74#14558713—22no—
75#14558713C2×C414yes—
76#14558713C2×C414yes—
77C4×Dic149—22no—
78C4×Dic149—41no—
79C4×Dic149—41no—
80C4×Dic149C2×C414yescomplemented
81C4×Dic149C2×C414yescomplemented
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
89C4⋊C4×C149—22no—
90C4⋊C4×C149C2×C414yescomplemented
91C42×C149—22no—
92C22×D149—21no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149C22×C412yes—
97C22×D149#4112yes—
98C22×D149#4112yes—
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—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149C22×C412yes—
117C2×Dic149C22×C412yes—
118C2×Dic149C22×C412yes—
119C2×Dic149#4112yes—
120C4×D149—28no—
121C4×D149—44no—
122C4×D149—44no—
123C23×C149C2411yescharacteristic
124C2×C4×C149—21no—
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×C149—21no—
141C2×C4×C149C22×C412yes—
142C2×C4×C149C22×C412yes—
143C2×C4×C149C22×C412yes—
144C2×C4×C149#4112yes—
145C22×C149C23×C411yescharacteristic
146C22×C149C2×#4111yescharacteristic
147C22×C149C2×#4111yescharacteristic
148C22×C149C2×#4111yescharacteristic
149C22×C149C2×#4111yescharacteristic
150C22×C149H(5,𝔽2)11yescharacteristic
151C22×C1492−1+411yescharacteristic
152C2×D149—22no—
153C2×D149—22no—
154C2×D149—22no—
155C2×D149—22no—
156C2×D149—22no—
157C2×D149—22no—
158C2×D149#11714yes—
159C4×C149—22no—
160C4×C149—22no—
161C4×C149—22no—
162C4×C149—22no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149—41no—
166Dic149—22no—
167Dic149—22no—
168Dic149—22no—
169Dic149—22no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173C2×C149C2×#11711yescharacteristic
174C2×C149C4×#4111yescharacteristic
175C2×C149#52011yescharacteristic
176C2×C149#55111yescharacteristic
177C2×C149#55111yescharacteristic
178C2×C149#55211yescharacteristic
179C2×C149#55211yescharacteristic
180D149—24no—
181C149#234311yescharacteristic, complemented, Sylow
182#2343—1491nomaximal, Sylow
183C2×#117—1491no—
184#387—1491no—
185#387—1491no—
186#387—1491no—
187#387D14911yescharacteristic, complemented
188#385—1491no—
189#385—1491no—
190#383—1491no—
191#382—1491no—
192#381—1491no—
193C4×C4⋊C4—1491no—
194C4×C22⋊C4—1491no—
195C4×C22⋊C4—1491no—
196#376—1491no—
197C2×#95—1491no—
198C23×C4—1491no—
199C23×C4—1491no—
200C23×C4—1491no—
201#117—1498no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4—1491no—
204C2×C4⋊C4—1491no—
205C2×C4⋊C4—1491no—
206C2×C4⋊C4C2×D14911yescharacteristic
207C2×C4⋊C4C2×D14911yescharacteristic
208C2×C22⋊C4—1491no—
209C2×C22⋊C4—1491no—
210C2×C22⋊C4—1491no—
211C2×C22⋊C4—1491no—
212C2×C42—1491no—
213C2×C42—1491no—
214C2×C42—1491no—
215C2×C42—1491no—
216C2×C42—1491no—
217C2×C42C2×D14911yescharacteristic
218#95—1491no—
219#95—1491no—
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
232#95C2×D14911yescharacteristic
233#95C2×D14911yescharacteristic
234C24—1491no—
235C22×C4—2982no—
236C22×C4—2982no—
237C22×C4—2982no—
238C22×C4—2982no—
239C22×C4—2982no—
240C22×C4—2982no—
241C22×C4—5961no—
242C22×C4—5961no—
243C22×C4—1491no—
244C22×C4—1491no—
245C22×C4—1491no—
246C22×C4—1491no—
247C22×C4—1491no—
248C22×C4—1491no—
249C22×C4—1491no—
250C22×C4—1494no—
251C22×C4C22×D14911yescharacteristic
252C22×C4C22×D14911yescharacteristic
253C22×C4C22×D14911yescharacteristic
254C22×C4C22×D14911yescharacteristic
255C22×C4C22×D14911yescharacteristic
256C22×C4C22×D14911yescharacteristic
257C22×C4C22×D14911yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—2982no—
260C4⋊C4—5961no—
261C4⋊C4—5961no—
262C4⋊C4—1494no—
263C4⋊C4C4×D14914yescomplemented
264C22⋊C4—2982no—
265C22⋊C4—2982no—
266C22⋊C4—1494no—
267C22⋊C4—1494no—
268C42—22no—
269C42—2982no—
270C42—5961no—
271C42—5961no—
272C42—1494no—
273C42—1494no—
274C23—2981no—
275C23—2981no—
276C23—2981no—
277C23—2981no—
278C23—1492no—
279C23—1492no—
280C23—1492no—
281C23C23×D14911yescharacteristic
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—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2988no—
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—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—5964no—
318C2×C4—5964no—
319C2×C4—1492no—
320C2×C4—1492no—
321C2×C4—1492no—
322C2×C4—1492no—
323C2×C4C2×C4×D14912yes—
324C2×C4C2×C4×D14912yes—
325C2×C4C2×C4×D14912yes—
326C2×C4#1455873512yes—
327C22—2982no—
328C22—2982no—
329C22—2982no—
330C22—2982no—
331C22—2982no—
332C22—2982no—
333C22—1494no—
334C22C22×C4×D14911yescharacteristic
335C22#41×D14911yescharacteristic
336C22#41×D14911yescharacteristic
337C22#41×D14911yescharacteristic
338C22C2×#1455873511yescharacteristic
339C22#1801195711yescharacteristic
340C22#1801195911yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2982no—
349C4—2982no—
350C4—2982no—
351C4—2982no—
352C4—5961no—
353C4—5961no—
354C4—5961no—
355C2—2984no—
356C2#117×D14911yescharacteristic
357C2C4×#1455873511yescharacteristic
358C2#2375010711yescharacteristic
359C2#2375029811yescharacteristic
360C2#2375030011yescharacteristic
361C2#2375030711yescharacteristic
362C2#2375030911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#387×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenter#387D149
hypocenterC149#2343
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #23749511C2semidirect
3. #23749510C2semidirect
4. #23749508C2semidirect
7. #23749492C2semidirect
8. #23749489C2semidirect
10. C4⋊C4×Dic149C2semidirect
13. #23749471C2semidirect
15. #387×C149C2semidirect
19. #18011869C4semidirect
70. C4⋊Dic149C2×C4semidirect
80. C4×Dic149C2×C4semidirect
81. C4×Dic149C2×C4semidirect
90. C4⋊C4×C149C2×C4semidirect
181. C149#2343semidirect
187. #387D149semidirect
263. C4⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118692
#237495112
#237495102
#237495082
#237494992
#237494962
#237494922
#237494892
#237494872
C4⋊C4×Dic1492
C4×#145587132
#237494722
#237494712
#95×D1492
#387×C1492
#2343149