Finite Group Databasebeta

← #34047549

Subgroups — #34047549

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×#18011867C211yesmaximal, characteristic
2#23749512C211yesmaximal, characteristic, complemented
3#23749512C211yesmaximal, characteristic, complemented
4#23749506C211yesmaximal, characteristic, complemented
5#23749506C211yesmaximal, characteristic, complemented
6#23749500C211yesmaximal, characteristic
7#23749492C211yesmaximal, characteristic, complemented
8#23749490C211yesmaximal, characteristic, complemented
9#23749486C211yesmaximal, characteristic
10C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic149C211yesmaximal, characteristic
12C4×C22⋊Dic149C211yesmaximal, characteristic
13#23749470C211yesmaximal, characteristic, complemented
14C2×#18011818C211yesmaximal, characteristic
15#385×C149C211yesmaximal, characteristic
16C23×Dic149C2211yescharacteristic
17C23×Dic149C2211yescharacteristic
18#18011867C418yescomplemented
19C2×C4⋊Dic149C2211yescharacteristic
20C2×C4⋊Dic149C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×C22⋊Dic149C2211yescharacteristic
24C2×C22⋊Dic149C2211yescharacteristic
25C2×C4×Dic149C2211yescharacteristic
26C2×C4×Dic149C2211yescharacteristic
27C2×C4×Dic149C2211yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C2×C4×Dic149C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31#18011818C2211yescharacteristic
32#18011818C2211yescharacteristic
33#18011818C2211yescharacteristic
34#18011818C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C23×C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C22×Dic149—22no—
53C22×Dic149—22no—
54C22×Dic149—22no—
55C22×Dic149—22no—
56C22×Dic149—41no—
57C22×Dic149C2×C414yes—
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C4⋊Dic149—22no—
67C4⋊Dic149—41no—
68#14558715C2×C414yescomplemented
69#14558715C2×C414yescomplemented
70C22⋊Dic149—22no—
71C22⋊Dic149C2×C414yes—
72C4×Dic149—22no—
73C4×Dic149—22no—
74C4×Dic149—41no—
75C4×Dic149—41no—
76C4×Dic149C2×C414yescomplemented
77C4×Dic149C2×C414yescomplemented
78C24×C149C2311yescharacteristic
79C22×C4×C149—22no—
80C22×C4×C149—22no—
81C22×C4×C149—41no—
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C4⋊C4×C149—22no—
89C4⋊C4×C149—41no—
90C22⋊C4×C149—22no—
91C22⋊C4×C149C2×C414yes—
92C2×Dic149—28no—
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—21no—
112C2×Dic149—44no—
113C2×Dic149C22×C412yes—
114C2×Dic149C22×C412yes—
115C2×Dic149C22×C412yes—
116C2×Dic149C22×C412yes—
117C2×Dic149#4112yes—
118C23×C149—21no—
119C23×C149—21no—
120C23×C149—21no—
121C23×C149—21no—
122C23×C149C22×C412yes—
123C23×C149#4112yes—
124C23×C149#4112yes—
125C23×C149C2411yescharacteristic
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×C149—44no—
142C2×C4×C149C22×C412yes—
143C2×C4×C149C22×C412yes—
144C2×C4×C149#4112yes—
145C22×C149—22no—
146C22×C149—22no—
147C22×C149—22no—
148C22×C149—22no—
149C22×C149—22no—
150C22×C149—22no—
151C22×C149#11714yes—
152C22×C149C23×C411yescharacteristic
153C22×C149C2×#4111yescharacteristic
154C22×C149C2×#4111yescharacteristic
155C22×C149C2×#4111yescharacteristic
156C22×C149C2×#4111yescharacteristic
157C22×C149H(5,𝔽2)11yescharacteristic
158C22×C1492−1+411yescharacteristic
159C4×C149—22no—
160C4×C149—22no—
161C4×C149—22no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165Dic149—22no—
166Dic149—22no—
167Dic149—22no—
168Dic149—22no—
169Dic149—22no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173C2×C149—24no—
174C2×C149C2×#11711yescharacteristic
175C2×C149C4×#4111yescharacteristic
176C2×C149#52011yescharacteristic
177C2×C149#55111yescharacteristic
178C2×C149#55111yescharacteristic
179C2×C149#55211yescharacteristic
180C2×C149#55211yescharacteristic
181C149#234311yescharacteristic, complemented, Sylow
182#2343—1491nomaximal, Sylow
183C2×#117—1491no—
184#387—1491no—
185#387—1491no—
186#387—1491no—
187#387—1491no—
188#385—1491no—
189#385D14911yescharacteristic
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×C4C2×D14911yescharacteristic
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⋊C4C2×D14911yescharacteristic
211C2×C22⋊C4C2×D14911yescharacteristic
212C2×C42—1491no—
213C2×C42—1491no—
214C2×C42—1491no—
215C2×C42—1491no—
216C2×C42—1491no—
217C2×C42—1491no—
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#95—1491no—
231#95—1491no—
232#95C2×D14911yescharacteristic
233#95C2×D14911yescharacteristic
234C24C22×D14911yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—2982no—
239C22×C4—2982no—
240C22×C4—2982no—
241C22×C4—2982no—
242C22×C4—5961no—
243C22×C4—1491no—
244C22×C4—1491no—
245C22×C4—1491no—
246C22×C4—1494no—
247C22×C4—1491no—
248C22×C4—1491no—
249C22×C4—1491no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4C22×D14911yescharacteristic
253C22×C4C22×D14911yescharacteristic
254C22×C4C22×D14911yescharacteristic
255C22×C4C22×D14911yescharacteristic
256C22×C4C22×D14911yescharacteristic
257C22×C4C22×D14911yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—2982no—
261C4⋊C4—5961no—
262C4⋊C4—1494no—
263C4⋊C4—1494no—
264C22⋊C4—22no—
265C22⋊C4—2982no—
266C22⋊C4—1494no—
267C22⋊C4C4×D14914yes—
268C42—2982no—
269C42—2982no—
270C42—5961no—
271C42—5961no—
272C42—1494no—
273C42—1494no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D14912yes—
279C23#1455873512yes—
280C23#1455873712yes—
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—44no—
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—2988no—
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—5964no—
319C2×C4—1492no—
320C2×C4—1492no—
321C2×C4—1492no—
322C2×C4—1492no—
323C2×C4—1492no—
324C2×C4C2×C4×D14912yes—
325C2×C4C2×C4×D14912yes—
326C2×C4#1455873512yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#1801186914yes—
334C22C22×C4×D14911yescharacteristic
335C22#41×D14911yescharacteristic
336C22C2×#1455873511yescharacteristic
337C22C2×#1455873511yescharacteristic
338C22C2×#1455873711yescharacteristic
339C22#1801195611yescharacteristic
340C22#1801195811yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2982no—
348C4—2982no—
349C4—2982no—
350C4—2982no—
351C4—2982no—
352C4—5961no—
353C4—5961no—
354C4—5961no—
355C2—24no—
356C2C2×#1801186911yescharacteristic
357C2C4×#1455873511yescharacteristic
358C2#2375010411yescharacteristic
359C2#2375030211yescharacteristic
360C2#2375030611yescharacteristic
361C2#2375031211yescharacteristic
362C2#2375031711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#385×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenter#385D149
hypocenterC149#2343
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #23749512C2semidirect
3. #23749512C2semidirect
4. #23749506C2semidirect
5. #23749506C2semidirect
7. #23749492C2semidirect
8. #23749490C2semidirect
10. C4⋊C4×Dic149C2semidirect
13. #23749470C2semidirect
18. #18011867C4semidirect
68. #14558715C2×C4semidirect
69. #14558715C2×C4semidirect
76. C4×Dic149C2×C4semidirect
77. C4×Dic149C2×C4semidirect
181. C149#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#180118672
#237495122
#237495062
#237495002
#237494922
#237494902
#237494862
C4⋊C4×Dic1492
C22⋊C4×Dic1492
C4×C22⋊Dic1492
#237494702
C2×#180118182
#385×C1492
#2343149