Finite Group Databasebeta

← #34056595

Subgroups — #34056595

Order 19072.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic, complemented
2#23750284C211yesmaximal, characteristic, complemented
3#23749980C211yesmaximal, characteristic, complemented
4#23749967C211yesmaximal, characteristic, complemented
5#23749944C211yesmaximal, characteristic, complemented
6#23749933C211yesmaximal, characteristic, complemented
7#23749861C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749841C211yesmaximal, characteristic, complemented
10#23749772C211yesmaximal, characteristic, complemented
11#23749766C211yesmaximal, characteristic, complemented
12C4×#14558725C211yesmaximal, characteristic, complemented
13#23749622C211yesmaximal, characteristic, complemented
14C2×#18011836C211yesmaximal, characteristic, complemented
15C8×D4×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011906—21no—
22#18011903C2211yescharacteristic
23#18011899C2211yescharacteristic
24#18011897—21no—
25#18011893—21no—
26#18011890C2211yescharacteristic
27#18011889—21no—
28#18011885C2211yescharacteristic
29#18011885C2211yescharacteristic
30#18011885C2211yescharacteristic
31#18011883—21no—
32#18011883—21no—
33C4×Dic298C2211yescharacteristic
34C4×D596C2211yescharacteristic
35#18011871—21no—
36#18011871—21no—
37#18011870C2211yescharacteristic
38C2×C4⋊Dic149C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C22×C8×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—41no—
61C2×Dic298—22no—
62C2×Dic298—21no—
63C2×Dic298—41no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C22×Dic149—21no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76#14558725—22no—
77#14558725—41no—
78D1192—41no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C2×D4×C149D411yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149—41no—
102C2×C8×C149—41no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149D411yescharacteristic
108C22⋊C4×C149D411yescharacteristic
109C22⋊C4×C149D411yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117Dic298#4112yes—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—42no—
133C2×Dic149—81no—
134C4×D149—42no—
135C4×D149—81no—
136C23×C149C2×D411yescharacteristic
137C23×C149C2×D411yescharacteristic
138D4×C149—22no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C8×C149—21no—
149C8×C149—21no—
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149#13512yes—
158C22×C149C22×D411yescharacteristic
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149C2×#4111yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—22no—
172Dic149—41no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—22no—
178C2×C149—41no—
179C2×C149#54611yescharacteristic
180C2×C149C2×#13511yescharacteristic
181C2×C149#57711yescharacteristic
182D149—81no—
183D149—81no—
184C149#330111yescharacteristic, complemented, Sylow
185#3301—1491nomaximal, Sylow
186#553—1491no—
187#548—1491no—
188#488—1491no—
189#485—1491no—
190#481—1491no—
191#479—1491no—
192#466—1491no—
193#465—1491no—
194#463—1491no—
195#449—1491no—
196#448—1491no—
197C4×SD16—1491no—
198C8×D4D14911yescharacteristic, complemented
199#416—1491no—
200C2×#103—1491no—
201C2×#41—1491no—
202C22×Q8—1491no—
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C22×C8C2×D14911yescharacteristic
207C22×C8C2×D14911yescharacteristic
208#126—2981no—
209#125—1491no—
210#124—2981no—
211#124—1491no—
212#123—2981no—
213C22⋊Q8—2981no—
214C22⋊Q8—1491no—
215#121—2981no—
216#121—2981no—
217#121—1491no—
218#121—1491no—
219#121—1491no—
220C4×Q8—1491no—
221C4×D4—2981no—
222C4×D4—2981no—
223C4×D4—1491no—
224C4×D4C2×D14911yescharacteristic
225#117—1491no—
226C2×C4⋊C4—1491no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8C2×D14911yescharacteristic
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241C22⋊C8C2×D14911yescharacteristic
242C22⋊C8C2×D14911yescharacteristic
243C4×C8C2×D14911yescharacteristic
244#41—2982no—
245#41—5961no—
246C2×Q8—2982no—
247C2×Q8—2981no—
248C2×Q8—5961no—
249C2×Q8—1491no—
250C2×Q8—1491no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4D59611yescharacteristic
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4C22×D14911yescharacteristic
263C22×C4C22×D14911yescharacteristic
264SD16—2982no—
265SD16—5961no—
266D8—5961no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4D59611yescharacteristic
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4D59611yescharacteristic
292C22⋊C4D59611yescharacteristic
293C42—2981no—
294C42—2981no—
295C42C22×D14911yescharacteristic
296C23—2981no—
297C23—2981no—
298C23C2×D59611yescharacteristic
299C23C2×D59611yescharacteristic
300Q8—2981no—
301Q8—2981no—
302Q8—2981no—
303Q8—5962no—
304Q8—1492no—
305D4—22no—
306D4—2981no—
307D4—2981no—
308D4—2981no—
309D4—2981no—
310D4—5962no—
311D4—5962no—
312D4—5962no—
313D4—11921no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—5962no—
325C2×C4—5962no—
326C2×C4—11921no—
327C2×C4—11921no—
328C2×C4C2×D59611yescharacteristic
329C2×C4C2×D59611yescharacteristic
330C2×C4C2×D59611yescharacteristic
331C2×C4C2×D59611yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22—5961no—
348C22#1801193312yes—
349C22C22×D59611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—2982no—
355C4—5961no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4—5961no—
360C4#41×D14911yescharacteristic
361C4#1801195611yescharacteristic
362C2—22no—
363C2—41no—
364C2—11921no—
365C2—11921no—
366C2#2375027011yescharacteristic
367C2C2×#1801193311yescharacteristic
368C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC8×D4×C149C2
socleC22×C149C22×D4
hypercenterC8×D4D149
hypocenterC149#3301
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23750321C2semidirect
2. #23750284C2semidirect
3. #23749980C2semidirect
4. #23749967C2semidirect
5. #23749944C2semidirect
6. #23749933C2semidirect
7. #23749861C2semidirect
8. #23749854C2semidirect
9. #23749841C2semidirect
10. #23749772C2semidirect
11. #23749766C2semidirect
12. C4×#14558725C2semidirect
13. #23749622C2semidirect
14. C2×#18011836C2semidirect
15. C8×D4×C149C2semidirect
184. C149#3301semidirect
198. C8×D4D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237502842
#237499802
#237499672
#237499442
#237499332
#237498612
#237498542
#237498412
#237497722
#237497662
C4×#145587252
#237496222
C2×#180118362
C8×D4×C1492
#3301149