Finite Group Databasebeta

← #34057779

Subgroups — #34057779

Order 19072.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750358C211yesmaximal, characteristic, complemented
2#23750357C211yesmaximal, characteristic, complemented
3#23750013C211yesmaximal, characteristic, complemented
4#23750011C211yesmaximal, characteristic, complemented
5#23750007C211yesmaximal, characteristic, complemented
6#23749850C211yesmaximal, characteristic, complemented
7#23749845C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749819C211yesmaximal, characteristic, complemented
10#23749818C211yesmaximal, characteristic, complemented
11#23749752C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749722C211yesmaximal, characteristic, complemented
14C4×#14558721C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23#18011907C2211yescharacteristic
24#18011907C2211yescharacteristic
25#18011900C2211yescharacteristic
26#18011899C2211yescharacteristic
27#18011898C2211yescharacteristic
28#18011897—21no—
29#18011897—21no—
30#18011895—21no—
31#18011894—21no—
32#18011893—21no—
33#18011893—21no—
34Q8×Dic149C2211yescharacteristic
35C4×Dic298C2211yescharacteristic
36#18011876C2211yescharacteristic
37C4×D596C2211yescharacteristic
38D4×Dic149C2211yescharacteristic
39#18011873C2211yescharacteristic
40C4×C22⋊D149—21no—
41#18011871—21no—
42#18011844C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic
50#18011821C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70#14558726—41no—
71#14558725—41no—
72#14558724—22no—
73#14558723—22no—
74D1192—41no—
75#14558721—22no—
76#14558721—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149D411yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—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×Dic149C2311yescharacteristic
97C4×Dic149C2311yescharacteristic
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102SD16×C149—41no—
103D8×C149—41no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—41no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120C22⋊D149—42no—
121C22⋊D149—42no—
122C22⋊D149—81no—
123C22⋊D149—81no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—81no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—81no—
132C4×D149—81no—
133#11924746—21no—
134#11924746#4112yes—
135C23×C149—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—81no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149C2×#4111yescharacteristic
169C4×C149H(5,𝔽2)11yescharacteristic
170Dic149—21no—
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176C2×C149—81no—
177C2×C149—81no—
178C2×C149#55011yescharacteristic
179C2×C149#57511yescharacteristic
180C2×C149#57611yescharacteristic
181D149—81no—
182D149—81no—
183C149#340311yescharacteristic, complemented, Sylow
184#3403—1491nomaximal, Sylow
185#559—1491no—
186#559—1491no—
187#496—1491no—
188#496—1491no—
189#495—1491no—
190#464—1491no—
191#464—1491no—
192#463—1491no—
193#463D14911yescharacteristic, complemented
194#459—1491no—
195#459—1491no—
196#446—1491no—
197#440—1491no—
198#440—1491no—
199C4×D8—1491no—
200C2×Q16—1491no—
201C2×SD16—1491no—
202C2×SD16—1491no—
203C2×SD16—1491no—
204C2×SD16C2×D14911yescharacteristic
205C2×D8—1491no—
206C2×D8—1491no—
207C2×D8—1491no—
208C2×D8C2×D14911yescharacteristic
209#127—1491no—
210#127—1491no—
211#124—2981no—
212#124—2981no—
213#124—1491no—
214#124—1491no—
215#124—1491no—
216#124C2×D14911yescharacteristic
217#123—2981no—
218#123—2981no—
219#123—2981no—
220#123—2981no—
221C4×Q8—1491no—
222C4×Q8—1491no—
223C4×Q8—1491no—
224C4×D4—2981no—
225C4×D4—2981no—
226C4×D4—1491no—
227C4×D4—1491no—
228C4×D4—1491no—
229C4×D4C2×D14911yescharacteristic
230#107—1491no—
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233C4⋊C8C2×D14911yescharacteristic
234#103—1491no—
235#103C2×D14911yescharacteristic
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic
240#97—1491no—
241#97—1491no—
242C4×C8—1491no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4—1491no—
252C2×D4C22×D14911yescharacteristic
253C2×D4C22×D14911yescharacteristic
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258Q16—5961no—
259SD16—41no—
260SD16—2982no—
261SD16—2982no—
262SD16—5961no—
263D8—41no—
264D8—2982no—
265D8—5961no—
266D8—5961no—
267C2×C8—1491no—
268C2×C8—1491no—
269C2×C8C22×D14911yescharacteristic
270C2×C8C22×D14911yescharacteristic
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4C22×D14911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C42—2981no—
291C42—2981no—
292C42—1491no—
293C42—1491no—
294C42C22×D14911yescharacteristic
295C23—21no—
296C23—21no—
297C23—2981no—
298C23—2981no—
299Q8—21no—
300Q8—21no—
301Q8—2981no—
302Q8—2981no—
303Q8—5961no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—2981no—
309D4—2981no—
310D4—2981no—
311D4—2981no—
312D4—5962no—
313D4—5962no—
314D4—11921no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1491no—
325C2×C4—11921no—
326C2×C4—11921no—
327C2×C4—11921no—
328C2×C4D4×D14911yescharacteristic
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—21no—
333C8—2981no—
334C8—1492no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2981no—
353C4—2981no—
354C4—2981no—
355C4—2981no—
356C4—5961no—
357C4—5961no—
358C4#41×D14911yescharacteristic
359C4#1801195611yescharacteristic
360C2—81no—
361C2—81no—
362C2—11921no—
363C2—11921no—
364C2#2375029311yescharacteristic
365C2#2375042211yescharacteristic
366C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750358C2semidirect
2. #23750357C2semidirect
3. #23750013C2semidirect
4. #23750011C2semidirect
5. #23750007C2semidirect
6. #23749850C2semidirect
7. #23749845C2semidirect
8. #23749841C2semidirect
9. #23749819C2semidirect
10. #23749818C2semidirect
11. #23749752C2semidirect
12. #23749728C2semidirect
13. #23749722C2semidirect
14. C4×#14558721C2semidirect
15. #463×C149C2semidirect
183. C149#3403semidirect
193. #463D149semidirect

Maximal subgroups

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

subgroupindex
#237503582
#237503572
#237500132
#237500112
#237500072
#237498502
#237498452
#237498412
#237498192
#237498182
#237497522
#237497282
#237497222
C4×#145587212
#463×C1492
#3403149