Finite Group Databasebeta

← #34057297

Subgroups — #34057297

Order 19072.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750323C211yesmaximal, characteristic, complemented
2#23750322C211yesmaximal, characteristic, complemented
3#23750026C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749940C211yesmaximal, characteristic, complemented
7#23749928C211yesmaximal, characteristic, complemented
8#23749927C211yesmaximal, characteristic, complemented
9#23749877C211yesmaximal, characteristic, complemented
10#23749876C211yesmaximal, characteristic, complemented
11#23749705C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749666C211yesmaximal, characteristic, complemented
14#23749665C211yesmaximal, characteristic, complemented
15#480×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19#18011906—21no—
20#18011904—21no—
21#18011902C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011896—21no—
24#18011892—21no—
25#18011886C2211yescharacteristic
26#18011885—21no—
27#18011885C2211yescharacteristic
28#18011882—21no—
29#18011882C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32C4×C22⋊D149—21no—
33C4×C22⋊D149C2211yescharacteristic
34#18011871—21no—
35#18011870C2211yescharacteristic
36#18011869C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011842C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×D596—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C2×C22⋊D149D411yescharacteristic
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149C2311yescharacteristic
68#14558721—22no—
69#14558720—22no—
70#14558719—22no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149D411yescharacteristic
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149C2311yescharacteristic
94C2×D4×C149—21no—
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22×D149—21no—
106C22×D149C2×D411yescharacteristic
107D596—21no—
108D596—21no—
109D596—81no—
110C22⋊D149—41no—
111C22⋊D149—42no—
112C22⋊D149—42no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—81no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C4×D149—21no—
121C4×D149—21no—
122C4×D149—81no—
123C4×D149—81no—
124#11924746—21no—
125#11924746#4112yes—
126C23×C149—21no—
127C23×C149C2×D411yescharacteristic
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—81no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—81no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2411yescharacteristic
139C8×C149—21no—
140C8×C149—21no—
141C22×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149—41no—
147C22×C149C22×D411yescharacteristic
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—21no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C4×C149—21no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149C2×#4111yescharacteristic
159C4×C1492−1+411yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—21no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—41no—
167C2×C149—81no—
168C2×C149#54711yescharacteristic
169C2×C149#57511yescharacteristic
170C2×C149#57611yescharacteristic
171D149—41no—
172D149—81no—
173C149#335511yescharacteristic, complemented, Sylow
174#3355—1491nomaximal, Sylow
175#553—1491no—
176#553—1491no—
177#499—1491no—
178#482—1491no—
179#482—1491no—
180#480—1491no—
181#480D14911yescharacteristic, complemented
182#478—1491no—
183#478—1491no—
184#469—1491no—
185#469—1491no—
186C4×D8—1491no—
187#436—1491no—
188#428—1491no—
189#428—1491no—
190C2×D8—1491no—
191C2×M16—1491no—
192C2×M16—1491no—
193#126—2981no—
194#126—2981no—
195#125—1491no—
196#125—1491no—
197#123—2981no—
198#123—2981no—
199#121—2981no—
200#121—2981no—
201#121—1491no—
202#121—1491no—
203#121—1491no—
204#121C2×D14911yescharacteristic
205C4×D4—2981no—
206C4×D4—2981no—
207C4×D4—1491no—
208C4×D4—1491no—
209C4×D4—1491no—
210#117—1491no—
211#117—1491no—
212C2×C4⋊C4—1491no—
213C2×C4⋊C4C2×D14911yescharacteristic
214#107—1491no—
215#107—1491no—
216#107—1491no—
217#107C2×D14911yescharacteristic
218#107C2×D14911yescharacteristic
219#106—1491no—
220#106—1491no—
221#106—1491no—
222#106—1491no—
223C4⋊C8—1491no—
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#102C2×D14911yescharacteristic
229#102C2×D14911yescharacteristic
230C22⋊C8—1491no—
231C22⋊C8C2×D14911yescharacteristic
232C4×C8—1491no—
233C2×D4—21no—
234C2×D4—2981no—
235C2×D4—2981no—
236C2×D4—2981no—
237C2×D4—1491no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—21no—
241C22×C4—2981no—
242C22×C4—2981no—
243C22×C4—2981no—
244C22×C4—1491no—
245C22×C4C22×D14911yescharacteristic
246D8—2982no—
247M16—2982no—
248M16—2982no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8C22×D14911yescharacteristic
252C2×C8C22×D14911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C4⋊C4C22×D14911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—1491no—
275C22⋊C4—1491no—
276C42—2981no—
277C42—2981no—
278C42—1491no—
279C23—21no—
280C23—2981no—
281C23—1491no—
282C23D4×D14911yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—2981no—
287D4—2981no—
288D4—5961no—
289D4—5962no—
290D4—5962no—
291D4—11921no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—1491no—
304C2×C4—1491no—
305C2×C4—1491no—
306C2×C4—11921no—
307C2×C4—11921no—
308C2×C4—11921no—
309C2×C4D4×D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—21no—
313C8—2981no—
314C8—1492no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2981no—
322C22—2981no—
323C22—2981no—
324C22—5961no—
325C22—5961no—
326C22—5961no—
327C22C2×D4×D14911yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—2981no—
333C4—2981no—
334C4—2981no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4#41×D14911yescharacteristic
339C4#1801195811yescharacteristic
340C2—41no—
341C2—81no—
342C2—5961no—
343C2—11921no—
344C2#2375027311yescharacteristic
345C2#2375042411yescharacteristic
346C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
hypercenter#480D149
hypocenterC149#3355
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23750323C2semidirect
2. #23750322C2semidirect
3. #23750026C2semidirect
4. #23749950C2semidirect
5. #23749947C2semidirect
6. #23749940C2semidirect
7. #23749928C2semidirect
8. #23749927C2semidirect
9. #23749877C2semidirect
10. #23749876C2semidirect
11. #23749705C2semidirect
12. #23749700C2semidirect
13. #23749666C2semidirect
14. #23749665C2semidirect
15. #480×C149C2semidirect
173. C149#3355semidirect
181. #480D149semidirect

Maximal subgroups

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

subgroupindex
#237503232
#237503222
#237500262
#237499502
#237499472
#237499402
#237499282
#237499272
#237498772
#237498762
#237497052
#237497002
#237496662
#237496652
#480×C1492
#3355149