Finite Group Databasebeta

← #34057025

Subgroups — #34057025

Order 19072.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750330C211yesmaximal, characteristic, complemented
2#23750294C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749938C211yesmaximal, characteristic, complemented
5#23749937C211yesmaximal, characteristic, complemented
6#23749918C211yesmaximal, characteristic, complemented
7#23749871C211yesmaximal, characteristic, complemented
8#23749870C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749625C211yesmaximal, characteristic, complemented
15#417×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907—21no—
23#18011907C2211yescharacteristic
24#18011901—21no—
25#18011891C2211yescharacteristic
26#18011890—21no—
27#18011890C2211yescharacteristic
28#18011889—21no—
29#18011885—21no—
30#18011885C2211yescharacteristic
31#18011882—21no—
32#18011882C2211yescharacteristic
33Q8×Dic149C2211yescharacteristic
34#18011876C2211yescharacteristic
35C4×C22⋊D149—21no—
36C4×C22⋊D149—21no—
37C4×C22⋊D149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54C2×C4⋊C4×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149D411yescharacteristic
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149C2311yescharacteristic
73#14558726—22no—
74#14558725—41no—
75#14558724—41no—
76#14558719—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715D411yescharacteristic
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97#41×C149—22no—
98#41×C149—41no—
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149—21no—
104C22×C4×C149C2311yescharacteristic
105M16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—81no—
116D596—21no—
117D596—21no—
118D596—42no—
119C22⋊D149—22no—
120C22⋊D149—42no—
121C22⋊D149—81no—
122C22⋊D149—81no—
123C22⋊D149—81no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—42no—
133C4×D149—81no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137C23×C149C2×D411yescharacteristic
138Q8×C149—21no—
139Q8×C149#4112yes—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—42no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—42no—
149C2×C4×C149—81no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C8×C149—21no—
153C8×C149—21no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C4×C149—21no—
168C4×C149—22no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149C2×#4111yescharacteristic
172C4×C149H(5,𝔽2)11yescharacteristic
173Dic149—21no—
174Dic149—21no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178Dic149#13712yes—
179C2×C149—41no—
180C2×C149—81no—
181C2×C149#54611yescharacteristic
182C2×C149C2×#13711yescharacteristic
183C2×C149#57611yescharacteristic
184D149—41no—
185D149—81no—
186C149#333311yescharacteristic, complemented, Sylow
187#3333—1491nomaximal, Sylow
188#554—1491no—
189#550—1491no—
190#486—1491no—
191#480—1491no—
192#480—1491no—
193#477—1491no—
194#468—1491no—
195#468—1491no—
196#460—1491no—
197#452—1491no—
198#452—1491no—
199C4×Q16—1491no—
200#436—1491no—
201#417—1491no—
202#417D14911yescharacteristic, complemented
203C2×#41—1491no—
204C2×#41C2×D14911yescharacteristic
205C2×Q16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×M16—1491no—
209C2×M16C2×D14911yescharacteristic
210C4⋊Q8—1491no—
211#127—2981no—
212#127—1491no—
213#125—2981no—
214C22⋊Q8—2981no—
215C22⋊Q8—2981no—
216C22⋊Q8—1491no—
217C22⋊Q8—1491no—
218#121—2981no—
219#121—2981no—
220#121—1491no—
221#121—1491no—
222C4×Q8—1491no—
223C4×Q8—1491no—
224C4×D4—2981no—
225C4×D4—2981no—
226C4×D4—1491no—
227C2×C4⋊C4—1491no—
228C2×C4⋊C4C2×D14911yescharacteristic
229#107—1491no—
230#107—1491no—
231#107—1491no—
232C4⋊C8—1491no—
233#103—1491no—
234#103—1491no—
235#103C2×D14911yescharacteristic
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102C2×D14911yescharacteristic
242#102C2×D14911yescharacteristic
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245C4×C8—1491no—
246#41—22no—
247#41—41no—
248#41—2982no—
249#41—5961no—
250C2×Q8—2981no—
251C2×Q8—1491no—
252C2×Q8C22×D14911yescharacteristic
253C2×D4—21no—
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—1491no—
260C2×D4—1491no—
261C2×D4C22×D14911yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—1491no—
267C22×C4C22×D14911yescharacteristic
268Q16—2982no—
269SD16—5961no—
270SD16—5961no—
271M16—41no—
272M16—5961no—
273C2×C8—1491no—
274C2×C8—1491no—
275C2×C8C22×D14911yescharacteristic
276C2×C8C22×D14911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—1491no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4C22×D14911yescharacteristic
288C4⋊C4C22×D14911yescharacteristic
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—1491no—
294C22⋊C4—1491no—
295C42—2981no—
296C42—2981no—
297C42—1491no—
298C23—21no—
299C23—2981no—
300C23—1491no—
301C23D4×D14911yescharacteristic
302Q8—21no—
303Q8—2981no—
304Q8—2981no—
305Q8—11921no—
306Q8#1455873612yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—2982no—
311D4—2981no—
312D4—2981no—
313D4—5962no—
314D4—5962no—
315D4—11921no—
316D4—11921no—
317D4—11921no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—5962no—
331C2×C4—1491no—
332C2×C4—1491no—
333C2×C4—1491no—
334C2×C4—11921no—
335C2×C4D4×D14911yescharacteristic
336C2×C4C23×D14911yescharacteristic
337C8—21no—
338C8—21no—
339C8—2981no—
340C8—2981no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—2981no—
348C22—2981no—
349C22—2981no—
350C22—5961no—
351C22—5961no—
352C22—5961no—
353C22C2×D4×D14911yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—2981no—
359C4—2981no—
360C4—5961no—
361C4—5961no—
362C4—5961no—
363C4—1492no—
364C4C2×#1455873611yescharacteristic
365C4#1801195611yescharacteristic
366C2—41no—
367C2—81no—
368C2—5961no—
369C2—11921no—
370C2#2375026511yescharacteristic
371C2#137×D14911yescharacteristic
372C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#417×C149C2
socleC22×C149C22×D4
prime radical#23750294C2
hypercenter#417D149
hypocenterC149#3333
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #23750330C2semidirect
3. #23749970C2semidirect
4. #23749938C2semidirect
5. #23749937C2semidirect
6. #23749918C2semidirect
7. #23749871C2semidirect
8. #23749870C2semidirect
9. #23749824C2semidirect
10. #23749790C2semidirect
11. #23749787C2semidirect
12. #23749717C2semidirect
13. #23749701C2semidirect
14. #23749625C2semidirect
15. #417×C149C2semidirect
186. C149#3333semidirect
202. #417D149semidirect

Maximal subgroups

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

subgroupindex
#237503302
#237502942
#237499702
#237499382
#237499372
#237499182
#237498712
#237498702
#237498242
#237497902
#237497872
#237497172
#237497012
#237496252
#417×C1492
#3333149