Finite Group Databasebeta

← #34047183

Subgroups — #34047183

Order 19072.

524 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×#18011869C211yesmaximal, characteristic
2#23749517C211yesmaximal, characteristic
3#23749516C211yesmaximal, characteristic
4#23749515C211yesmaximal, characteristic
5#23749514C211yesmaximal, characteristic
6#23749511C211yesmaximal, characteristic, complemented
7#23749510C211yesmaximal, characteristic, complemented
8#23749508C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
10#23749476C211yesmaximal, characteristic, complemented
11#23749472C211yesmaximal, characteristic
12#23749472C211yesmaximal, characteristic
13#23749470C211yesmaximal, characteristic, complemented
14C42×Dic149C211yesmaximal, characteristic, complemented
15#387×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17#18011869C418yescomplemented
18C2×C4⋊Dic149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558713C2211yescharacteristic
23C2×#14558713C2211yescharacteristic
24C2×#14558713C2211yescharacteristic
25C2×#14558713C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C2×C4×Dic149C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31C2×C4×Dic149C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33C2×C4×Dic149C2211yescharacteristic
34C2×C4×Dic149C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
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×D149C2×C414yes—
63C4⋊Dic149—22no—
64C4⋊Dic149C2×C414yes—
65#14558715—22no—
66#14558715—22no—
67#14558713—22no—
68#14558713—22no—
69#14558713—22no—
70#14558713—22no—
71#14558713C2×C414yes—
72#14558713C2×C414yes—
73C4×Dic149—22no—
74C4×Dic149—22no—
75C4×Dic149—22no—
76C4×Dic149—22no—
77C4×Dic149—22no—
78C4×Dic149—22no—
79C4×Dic149—22no—
80C4×Dic149C2×C414yes—
81C4×Dic149C2×C414yes—
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×C414yes—
91C42×C149—22no—
92C22×D149—21no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149—21no—
97C22×D149—21no—
98C22×D149C22×C412yes—
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×Dic149C22×C412yes—
114C2×Dic149C22×C412yes—
115C2×Dic149C22×C412yes—
116C2×Dic149#4112yes—
117C2×Dic149#4112yes—
118C2×Dic149#4112yes—
119C2×Dic149#4112yes—
120C4×D149—28no—
121C23×C149C2411yescharacteristic
122C2×C4×C149—21no—
123C2×C4×C149—21no—
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×C149C22×C412yes—
139C2×C4×C149C22×C412yes—
140C2×C4×C149C22×C412yes—
141C2×C4×C149#4112yes—
142C2×C4×C149#4112yes—
143C22×C149C23×C411yescharacteristic
144C22×C149C2×#4111yescharacteristic
145C22×C149C2×#4111yescharacteristic
146C22×C149C2×#4111yescharacteristic
147C22×C149C2×#4111yescharacteristic
148C22×C149C2×#4111yescharacteristic
149C22×C149C2×#4111yescharacteristic
150C2×D149—22no—
151C2×D149—22no—
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C4×C149—22no—
158C4×C149—22no—
159C4×C149—22no—
160C4×C149—22no—
161C4×C149—22no—
162C4×C149—41no—
163C4×C149—41no—
164Dic149—22no—
165Dic149—22no—
166Dic149—22no—
167Dic149—22no—
168Dic149—41no—
169Dic149—41no—
170Dic149#11714yes—
171C2×C149C2×#11711yescharacteristic
172C2×C149C4×#4111yescharacteristic
173C2×C149C4×#4111yescharacteristic
174C2×C149#52911yescharacteristic
175C2×C149#52911yescharacteristic
176C2×C149#52911yescharacteristic
177C2×C149#52911yescharacteristic
178D149—42no—
179C149#229811yescharacteristic, complemented, Sylow
180#2298—1491nomaximal, Sylow
181C2×#117—1491no—
182#388—1491no—
183#388—1491no—
184#388—1491no—
185#388—1491no—
186#387—1491no—
187#387—1491no—
188#387—1491no—
189#387D14911yescharacteristic, complemented
190C4×C4⋊C4—1491no—
191C4×C4⋊C4—1491no—
192C4×C22⋊C4—1491no—
193C4×C22⋊C4—1491no—
194#376—1491no—
195C43—1491no—
196C23×C4—1491no—
197#117—1498no—
198C2×C4⋊C4—1491no—
199C2×C4⋊C4—1491no—
200C2×C4⋊C4—1491no—
201C2×C4⋊C4—1491no—
202C2×C4⋊C4C2×D14911yescharacteristic
203C2×C4⋊C4C2×D14911yescharacteristic
204C2×C22⋊C4—1491no—
205C2×C22⋊C4—1491no—
206C2×C22⋊C4—1491no—
207C2×C22⋊C4—1491no—
208C2×C22⋊C4—1491no—
209C2×C22⋊C4—1491no—
210C2×C42—1491no—
211C2×C42—1491no—
212C2×C42—1491no—
213C2×C42—1491no—
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#95C2×D14911yescharacteristic
229#95C2×D14911yescharacteristic
230#95C2×D14911yescharacteristic
231#95C2×D14911yescharacteristic
232C24—1491no—
233C22×C4—2982no—
234C22×C4—2982no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4—1491no—
239C22×C4—1491no—
240C22×C4—1491no—
241C22×C4—1494no—
242C22×C4—1491no—
243C22×C4C22×D14911yescharacteristic
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—2982no—
254C4⋊C4—1494no—
255C4⋊C4C4×D14914yes—
256C22⋊C4—2982no—
257C22⋊C4—2982no—
258C22⋊C4—2982no—
259C22⋊C4—2982no—
260C22⋊C4—1494no—
261C22⋊C4—1494no—
262C42—22no—
263C42—2982no—
264C42—2982no—
265C42—2982no—
266C42—2982no—
267C42—2982no—
268C42—2982no—
269C42—2982no—
270C42—1494no—
271C42—1494no—
272C23—2981no—
273C23—2981no—
274C23—2981no—
275C23—2981no—
276C23—2981no—
277C23—2981no—
278C23—1492no—
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—21no—
296C2×C4—2988no—
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—1492no—
312C2×C4—1492no—
313C2×C4—1492no—
314C2×C4—1492no—
315C2×C4—1492no—
316C2×C4—1492no—
317C2×C4—1492no—
318C2×C4C2×C4×D14912yes—
319C2×C4C2×C4×D14912yes—
320C2×C4C2×C4×D14912yes—
321C2×C4#1455873512yes—
322C2×C4#1455873712yes—
323C22—2982no—
324C22—2982no—
325C22—2982no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22C22×C4×D14911yescharacteristic
331C22#41×D14911yescharacteristic
332C22#41×D14911yescharacteristic
333C22#41×D14911yescharacteristic
334C22#41×D14911yescharacteristic
335C22C2×#1455873511yescharacteristic
336C22C2×#1455873711yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—2982no—
345C4—2982no—
346C4—2982no—
347C4—2982no—
348C4—5961no—
349C4—5961no—
350C4—1494no—
351C2—5962no—
352C2#117×D14911yescharacteristic
353C2C4×#1455873511yescharacteristic
354C2C4×#1455873711yescharacteristic
355C2#2375015211yescharacteristic
356C2#2375015811yescharacteristic
357C2#2375016011yescharacteristic
358C2#2375016111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#387×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenter#387D149
hypocenterC149#2298
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
6. #23749511C2semidirect
7. #23749510C2semidirect
8. #23749508C2semidirect
9. C4⋊C4×Dic149C2semidirect
10. #23749476C2semidirect
13. #23749470C2semidirect
14. C42×Dic149C2semidirect
15. #387×C149C2semidirect
17. #18011869C4semidirect
179. C149#2298semidirect
189. #387D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118692
#237495172
#237495162
#237495152
#237495142
#237495112
#237495102
#237495082
C4⋊C4×Dic1492
#237494762
#237494722
#237494702
C42×Dic1492
#387×C1492
#2298149