Finite Group Databasebeta

← #34054970

Subgroups — #34054970

Order 19072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750246C211yesmaximal, characteristic, complemented
2#23750105C211yesmaximal, characteristic, complemented
3#23749956C211yesmaximal, characteristic, complemented
4#23749944C211yesmaximal, characteristic, complemented
5#23749916C211yesmaximal, characteristic, complemented
6#23749911C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749789C211yesmaximal, characteristic, complemented
10#23749772C211yesmaximal, characteristic
11#23749738C211yesmaximal, characteristic, complemented
12#23749733C211yesmaximal, characteristic, complemented
13C4×#14558725C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011911C2211yescharacteristic
22#18011906—21no—
23#18011899C2211yescharacteristic
24#18011897—21no—
25#18011893—21no—
26#18011890C2211yescharacteristic
27#18011889—21no—
28#18011885C2211yescharacteristic
29C4×Dic298C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32C4×D596C2211yescharacteristic
33C4×D596C2211yescharacteristic
34C4×D596C2211yescharacteristic
35#18011871—21no—
36#18011871—21no—
37#18011869—21no—
38C2×C4⋊Dic149C2211yescharacteristic
39C4⋊C4×D149—21no—
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73Dic596—22no—
74#14558725—22no—
75#14558725—22no—
76D1192—22no—
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—81no—
114Dic298#4112yes—
115D596—21no—
116D596—21no—
117D596—21no—
118D596#4112yes—
119C22⋊D149—24no—
120C22⋊D149—81no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—81no—
128C4×D149—24no—
129C4×D149—81no—
130C4×D149—81no—
131C4×D149—81no—
132C23×C149C2×D411yescharacteristic
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C8×C149—21no—
142C8×C149—21no—
143C8×C149—21no—
144C8×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149C22×D411yescharacteristic
149C2×D149—22no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149C2×#4111yescharacteristic
161C4×C149C2×#4111yescharacteristic
162Dic149—22no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168C2×C149—41no—
169C2×C149#52511yescharacteristic
170C2×C149#57711yescharacteristic
171C2×C149#57711yescharacteristic
172D149—42no—
173D149—81no—
174C149#312511yescharacteristic, complemented, Sylow
175#3125—1491nomaximal, Sylow
176#542—1491no—
177#520—1491no—
178#483—1491no—
179#481—1491no—
180#476—1491no—
181#475—1491no—
182#464—1491no—
183#463—1491no—
184#452—1491no—
185#449—1491no—
186#442—1491no—
187#441—1491no—
188C4×SD16—1491no—
189C4×SD16—1491no—
190#433D14911yescharacteristic, complemented
191C2×#41—1491no—
192C2×Q16—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×D8—1491no—
196C4⋊Q8—1491no—
197#126—2981no—
198#124—2981no—
199#124—1491no—
200#123—2981no—
201C22⋊Q8—2981no—
202C22⋊Q8—1491no—
203#121—1491no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212#117—2981no—
213#117C2×D14911yescharacteristic
214C2×C4⋊C4—2981no—
215C2×C4⋊C4—1491no—
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8C2×D14911yescharacteristic
221C4⋊C8C2×D14911yescharacteristic
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8C2×D14911yescharacteristic
231C22⋊C8C2×D14911yescharacteristic
232#97C2×D14911yescharacteristic
233C4×C8C2×D14911yescharacteristic
234#41—2982no—
235#41—2982no—
236C2×Q8—2981no—
237C2×Q8—1491no—
238C2×Q8—1491no—
239C2×D4—2981no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4—1491no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4C22×D14911yescharacteristic
249Q16—2982no—
250SD16—2982no—
251SD16—2982no—
252D8—2982no—
253C2×C8C22×D14911yescharacteristic
254C2×C8C22×D14911yescharacteristic
255C2×C8C22×D14911yescharacteristic
256C2×C8C22×D14911yescharacteristic
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4D59611yescharacteristic
268C4⋊C4D59611yescharacteristic
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4D59611yescharacteristic
277C22⋊C4D59611yescharacteristic
278C42—2981no—
279C42—2981no—
280C42—2981no—
281C42C22×D14911yescharacteristic
282C42C22×D14911yescharacteristic
283C23—2981no—
284C23—2981no—
285C23C2×D59611yescharacteristic
286Q8—2981no—
287Q8—2981no—
288Q8—2981no—
289Q8—1492no—
290Q8—11921no—
291D4—2984no—
292D4—2981no—
293D4—2981no—
294D4—2981no—
295D4—1492no—
296D4—11921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2984no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—11921no—
307C2×C4—11921no—
308C2×C4—11921no—
309C2×C4—11921no—
310C2×C4C2×D59611yescharacteristic
311C2×C4C2×D59611yescharacteristic
312C2×C4C2×D59611yescharacteristic
313C2×C4C2×D59611yescharacteristic
314C2×C4C2×D59611yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—2982no—
324C22—5961no—
325C22—5961no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22C22×D59611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—2982no—
336C4—5961no—
337C4—5961no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C4#41×D14911yescharacteristic
342C4#41×D14911yescharacteristic
343C2—41no—
344C2—5962no—
345C2—11921no—
346C2#2375013711yescharacteristic
347C2#2375043711yescharacteristic
348C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radical#23749772C2
hypercenter#433D149
hypocenterC149#3125
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750105C2semidirect
3. #23749956C2semidirect
4. #23749944C2semidirect
5. #23749916C2semidirect
6. #23749911C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #23749789C2semidirect
11. #23749738C2semidirect
12. #23749733C2semidirect
13. C4×#14558725C2semidirect
14. C4×#14558725C2semidirect
15. #433×C149C2semidirect
174. C149#3125semidirect
190. #433D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237501052
#237499562
#237499442
#237499162
#237499112
#237498482
#237498412
#237497892
#237497722
#237497382
#237497332
C4×#145587252
#433×C1492
#3125149