Finite Group Databasebeta

← #34057393

Subgroups — #34057393

Order 19072.

396 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
1#23750334C211yesmaximal, characteristic, complemented
2#23750295C211yesmaximal, characteristic, complemented
3#23749989C211yesmaximal, characteristic, complemented
4#23749988C211yesmaximal, characteristic, complemented
5#23749970C211yesmaximal, characteristic, complemented
6#23749926C211yesmaximal, characteristic, complemented
7#23749923C211yesmaximal, characteristic, complemented
8#23749913C211yesmaximal, characteristic, complemented
9#23749818C211yesmaximal, characteristic, complemented
10#23749818C211yesmaximal, characteristic, complemented
11#23749754C211yesmaximal, characteristic, complemented
12#23749737C211yesmaximal, characteristic, complemented
13#23749735C211yesmaximal, characteristic, complemented
14D8×Dic149C211yesmaximal, characteristic, complemented
15#459×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558721C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011907C2211yescharacteristic
20#18011907C2211yescharacteristic
21#18011903C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011890—21no—
24#18011888—21no—
25#18011888—21no—
26#18011883—21no—
27#18011883—21no—
28#18011882—21no—
29C4×Dic298C2211yescharacteristic
30C4×D596C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32D4×Dic149C2211yescharacteristic
33D4×Dic149C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35C2×#14558715—21no—
36#18011845C2211yescharacteristic
37#18011843C2211yescharacteristic
38#18011842C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011833C2211yescharacteristic
42#18011833C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#127×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×Dic298D411yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C22×Dic149—21no—
69C22×Dic149—21no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72#14558721—22no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715D411yescharacteristic
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149—21no—
95C2×D4×C149C2311yescharacteristic
96C2×D4×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99D8×C149—22no—
100D8×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107Dic298—22no—
108Dic298—81no—
109D596—21no—
110D596—21no—
111C22⋊D149—42no—
112C22⋊D149—42no—
113C22⋊D149—81no—
114C22⋊D149—81no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—42no—
119C2×Dic149—42no—
120C2×Dic149—42no—
121C2×Dic149—81no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—42no—
127#11924746—21no—
128#11924746—21no—
129C23×C149—21no—
130C23×C149—21no—
131C23×C149—21no—
132D4×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—42no—
138D4×C149—81no—
139D4×C149#4112yescomplemented
140C2×C4×C149—21no—
141C2×C4×C149—81no—
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2411yescharacteristic
145C8×C149—21no—
146C8×C149—21no—
147C22×C149—22no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149C22×D411yescharacteristic
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—41no—
163C4×C149C2×#4111yescharacteristic
164C4×C1492−1+411yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149AGL(1,ℤ/8)12yes—
172C2×C149—42no—
173C2×C149—81no—
174C2×C149—81no—
175C2×C149#54811yescharacteristic
176C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C149#57611yescharacteristic
178D149—81no—
179C149#336611yescharacteristic, complemented, Sylow
180#3366—1491nomaximal, Sylow
181#554—1491no—
182#550—1491no—
183#490—1491no—
184#490—1491no—
185#486—1491no—
186#478—1491no—
187#478—1491no—
188#476—1491no—
189#459—1491no—
190#459—1491no—
191#459D14911yescharacteristic, complemented
192#446—1491no—
193#442—1491no—
194#442—1491no—
195C4×D8—1491no—
196C2×#41—2981no—
197C2×D8—1491no—
198C2×D8C2×D14911yescharacteristic
199C2×D8C2×D14911yescharacteristic
200C4⋊Q8—1491no—
201#127—1491no—
202#127—1491no—
203#127C2×D14911yescharacteristic
204#125—1491no—
205#125—1491no—
206C22⋊Q8—2981no—
207C22⋊Q8—2981no—
208C22⋊Q8—2981no—
209#121—2981no—
210#121—2981no—
211#121—2981no—
212C4×Q8—1491no—
213C4×D4—1491no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218C4×D4C2×D14911yescharacteristic
219C2×C4⋊C4—2981no—
220#107—1491no—
221#106—1491no—
222#106—1491no—
223C4⋊C8—1491no—
224C4⋊C8—1491no—
225C4⋊C8C2×D14911yescharacteristic
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102C2×D14911yescharacteristic
235#102C2×D14911yescharacteristic
236#97—1491no—
237#97—1491no—
238C4×C8—1491no—
239#41—5964no—
240C2×Q8—2981no—
241C2×Q8—1491no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C2×D4C22×D14911yescharacteristic
252C22×C4—21no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258D8—22no—
259D8—22no—
260D8—2982no—
261C2×C8—1491no—
262C2×C8—1491no—
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—1491no—
284C42—1491no—
285C42C22×D14911yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—2981no—
290Q8—2982no—
291Q8—11921no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—2981no—
300D4—2981no—
301D4—5962no—
302D4—5962no—
303D4—11921no—
304D4—11921no—
305D4#1455873512yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—5962no—
312C2×C4—5962no—
313C2×C4—5962no—
314C2×C4—5962no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—11921no—
320C2×C4D4×D14911yescharacteristic
321C2×C4D4×D14911yescharacteristic
322C2×C4C23×D14911yescharacteristic
323C8—21no—
324C8—21no—
325C8—2981no—
326C8—2981no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22C2×D4×D14911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—2981no—
344C4—2981no—
345C4—2981no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4—1492no—
350C4C2×#1455873511yescharacteristic
351C4#1801195811yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—11921no—
356C2#2375028111yescharacteristic
357C2AGL(1,ℤ/8)×D14911yescharacteristic
358C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3366
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23750334C2semidirect
2. #23750295C2semidirect
3. #23749989C2semidirect
4. #23749988C2semidirect
5. #23749970C2semidirect
6. #23749926C2semidirect
7. #23749923C2semidirect
8. #23749913C2semidirect
9. #23749818C2semidirect
10. #23749818C2semidirect
11. #23749754C2semidirect
12. #23749737C2semidirect
13. #23749735C2semidirect
14. D8×Dic149C2semidirect
15. #459×C149C2semidirect
139. D4×C149#41semidirect
179. C149#3366semidirect
191. #459D149semidirect
305. D4#14558735semidirect

Maximal subgroups

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

subgroupindex
#237503342
#237502952
#237499892
#237499882
#237499702
#237499262
#237499232
#237499132
#237498182
#237497542
#237497372
#237497352
D8×Dic1492
#459×C1492
#3366149