Finite Group Databasebeta

← #34057776

Subgroups — #34057776

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#23750361C211yesmaximal, characteristic, complemented
2#23750357C211yesmaximal, characteristic, complemented
3#23750013C211yesmaximal, characteristic, complemented
4#23750006C211yesmaximal, characteristic, complemented
5#23749845C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749842C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749818C211yesmaximal, characteristic, complemented
10#23749817C211yesmaximal, characteristic, complemented
11#23749753C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13#23749726C211yesmaximal, characteristic, complemented
14D8×Dic149C211yesmaximal, characteristic, complemented
15#496×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011907C2211yescharacteristic
22#18011900C2211yescharacteristic
23#18011898—21no—
24#18011898C2211yescharacteristic
25#18011898C2211yescharacteristic
26#18011897—21no—
27#18011895—21no—
28#18011893—21no—
29#18011892—21no—
30#18011892—21no—
31Q8×Dic149C2211yescharacteristic
32C4×Dic298C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34C4×D596C2211yescharacteristic
35D4×Dic149—21no—
36D4×Dic149C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38D4×Dic149C2211yescharacteristic
39#18011871—21no—
40#18011845C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic
56#127×C149C2211yescharacteristic
57#124×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68#14558726—41no—
69#14558725—22no—
70#14558724—41no—
71#14558721—41no—
72#14558721—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149—21no—
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102SD16×C149—22no—
103SD16×C149—41no—
104D8×C149—22no—
105D8×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—41no—
115D596—21no—
116D596—21no—
117C22⋊D149—42no—
118C22⋊D149—81no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—81no—
123C2×Dic149—81no—
124C2×Dic149—81no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—81no—
130#11924746—21no—
131#11924746—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—21no—
143D4×C149—42no—
144D4×C149—81no—
145C2×C4×C149—21no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149#4112yes—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149C2×#4111yescharacteristic
168C4×C149H(5,𝔽2)11yescharacteristic
169Dic149—21no—
170Dic149—21no—
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176C2×C149—81no—
177C2×C149—81no—
178C2×C149—81no—
179C2×C149#55011yescharacteristic
180C2×C149#57511yescharacteristic
181C2×C149#57611yescharacteristic
182D149—81no—
183C149#340311yescharacteristic, complemented, Sylow
184#3403—1491nomaximal, Sylow
185#559—1491no—
186#559—1491no—
187#496—1491no—
188#496D14911yescharacteristic, complemented
189#495—1491no—
190#464—1491no—
191#464—1491no—
192#463—1491no—
193#463—1491no—
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×SD16C2×D14911yescharacteristic
204C2×SD16C2×D14911yescharacteristic
205C2×D8—1491no—
206C2×D8—1491no—
207C2×D8C2×D14911yescharacteristic
208C2×D8C2×D14911yescharacteristic
209#127—1491no—
210#127C2×D14911yescharacteristic
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×D4—1491no—
230#107—1491no—
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233C4⋊C8—1491no—
234#103—1491no—
235#103—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#97—1491no—
241#97C2×D14911yescharacteristic
242C4×C8—1491no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4C22×D14911yescharacteristic
252C2×D4C22×D14911yescharacteristic
253C2×D4C22×D14911yescharacteristic
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—2981no—
258Q16—5961no—
259SD16—22no—
260SD16—41no—
261SD16—2982no—
262SD16—5961no—
263D8—22no—
264D8—41no—
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⋊C4—1491no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—2981no—
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—21no—
298C23—2981no—
299Q8—21no—
300Q8—21no—
301Q8—2981no—
302Q8—2981no—
303Q8—5961no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—2981no—
313D4—2981no—
314D4—5962no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—11921no—
325C2×C4—11921no—
326C2×C4—11921no—
327C2×C4—11921no—
328C2×C4D4×D14911yescharacteristic
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—2981no—
333C8—2981no—
334C8#1455873512yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—2981no—
352C4—2981no—
353C4—2981no—
354C4—2981no—
355C4—5961no—
356C4—5961no—
357C4—5961no—
358C4C2×#1455873511yescharacteristic
359C4#1801195611yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—11921no—
364C2#2375029511yescharacteristic
365C2#2375042111yescharacteristic
366C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#496×C149C2
socleC22×C149C22×D4
hypercenter#496D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23750361C2semidirect
2. #23750357C2semidirect
3. #23750013C2semidirect
4. #23750006C2semidirect
5. #23749845C2semidirect
6. #23749844C2semidirect
7. #23749842C2semidirect
8. #23749838C2semidirect
9. #23749818C2semidirect
10. #23749817C2semidirect
11. #23749753C2semidirect
12. #23749727C2semidirect
13. #23749726C2semidirect
14. D8×Dic149C2semidirect
15. #496×C149C2semidirect
183. C149#3403semidirect
188. #496D149semidirect

Maximal subgroups

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

subgroupindex
#237503612
#237503572
#237500132
#237500062
#237498452
#237498442
#237498422
#237498382
#237498182
#237498172
#237497532
#237497272
#237497262
D8×Dic1492
#496×C1492
#3403149