Finite Group Databasebeta

← #34056139

Subgroups — #34056139

Order 19072.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750238C211yesmaximal, characteristic, complemented
2#23750226C211yesmaximal, characteristic
3#23749935C211yesmaximal, characteristic, complemented
4#23749931C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749872C211yesmaximal, characteristic, complemented
7#23749870C211yesmaximal, characteristic, complemented
8#23749855C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749831C211yesmaximal, characteristic, complemented
11#23749830C211yesmaximal, characteristic, complemented
12#23749824C211yesmaximal, characteristic, complemented
13#23749824C211yesmaximal, characteristic, complemented
14#23749650C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011911C2211yescharacteristic
23#18011907C2211yescharacteristic
24#18011906—21no—
25#18011906—21no—
26#18011902—21no—
27#18011902—21no—
28#18011902C2211yescharacteristic
29#18011894—21no—
30#18011893—21no—
31#18011891C2211yescharacteristic
32#18011891C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011885—21no—
35#18011884—21no—
36#18011882C2211yescharacteristic
37#18011876C2211yescharacteristic
38#18011876C2211yescharacteristic
39C4×D596C2211yescharacteristic
40#18011868C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011831C2211yescharacteristic
51#18011831C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149C2311yescharacteristic
68#14558725—41no—
69#14558725—41no—
70#14558724—41no—
71#14558724—41no—
72#14558719—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C8×D149—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86#14558715D411yescharacteristic
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114D596—21no—
115D596—21no—
116D596—81no—
117C22⋊D149—81no—
118C22⋊D149—81no—
119C22⋊D149—81no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—81no—
129#11924746—21no—
130#11924746—21no—
131C23×C149—21no—
132D4×C149—21no—
133D4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—81no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C8×C149—21no—
142C8×C149—21no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149H(5,𝔽2)11yescharacteristic
159C4×C1492−1+411yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—21no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—81no—
167C2×C149#53711yescharacteristic
168C2×C149#57711yescharacteristic
169C2×C149#57711yescharacteristic
170D149—41no—
171D149—81no—
172C149#326011yescharacteristic, complemented, Sylow
173#3260—1491nomaximal, Sylow
174#541—1491no—
175#540—1491no—
176#479—1491no—
177#479—1491no—
178#478—1491no—
179#478D14911yescharacteristic, complemented
180#468—1491no—
181#468—1491no—
182#465—1491no—
183#465—1491no—
184#461—1491no—
185#461—1491no—
186#460—1491no—
187#460—1491no—
188#424—1491no—
189C2×SD16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192C2×SD16—1491no—
193C2×M16—1491no—
194C22×C8—1491no—
195C4⋊Q8—1491no—
196#127—1491no—
197#126—2981no—
198#126—2981no—
199#125—2981no—
200#125—2981no—
201#125—1491no—
202#125C2×D14911yescharacteristic
203#123—2981no—
204#123—2981no—
205C22⋊Q8—1491no—
206C22⋊Q8—1491no—
207#121—2981no—
208#121—2981no—
209#121—1491no—
210#121—1491no—
211C4×Q8—1491no—
212C4×Q8—1491no—
213C4×D4—1491no—
214C4×D4C2×D14911yescharacteristic
215#117—1491no—
216#107—1491no—
217#107C2×D14911yescharacteristic
218#106—1491no—
219#106C2×D14911yescharacteristic
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222C4⋊C8—1491no—
223C4⋊C8C2×D14911yescharacteristic
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#102—1491no—
229#102—1491no—
230#102C2×D14911yescharacteristic
231#102C2×D14911yescharacteristic
232C2×Q8—1491no—
233C2×Q8—1491no—
234C2×D4—2981no—
235C2×D4—2981no—
236C2×D4—2981no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—21no—
241C22×C4—2981no—
242C22×C4—1491no—
243SD16—5961no—
244SD16—5961no—
245SD16—5961no—
246SD16—5961no—
247M16—5961no—
248C2×C8—5961no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8C22×D14911yescharacteristic
252C2×C8C22×D14911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4C22×D14911yescharacteristic
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—1491no—
276C22⋊C4—1491no—
277C42—2981no—
278C42—2981no—
279C42—1491no—
280C42C22×D14911yescharacteristic
281C23—21no—
282C23—2981no—
283C23—1491no—
284Q8—2981no—
285Q8—2981no—
286Q8—2981no—
287Q8—2981no—
288D4—21no—
289D4—21no—
290D4—2981no—
291D4—2981no—
292D4—11921no—
293D4—11921no—
294D4—11921no—
295D4—11921no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—11921no—
309C2×C4D4×D14911yescharacteristic
310C2×C4D4×D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—21no—
313C8—21no—
314C8—2981no—
315C8—2981no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—2981no—
320C22—2981no—
321C22—2981no—
322C22—5961no—
323C22—5961no—
324C22—5961no—
325C22C2×D4×D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2981no—
332C4—2981no—
333C4—2981no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4#1801195711yescharacteristic
338C4#1801195911yescharacteristic
339C2—81no—
340C2—5961no—
341C2—11921no—
342C2#2375020511yescharacteristic
343C2#2375043211yescharacteristic
344C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radical#23750226C2
hypercenter#478D149
hypocenterC149#3260
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750238C2semidirect
3. #23749935C2semidirect
4. #23749931C2semidirect
5. #23749922C2semidirect
6. #23749872C2semidirect
7. #23749870C2semidirect
8. #23749855C2semidirect
9. #23749853C2semidirect
10. #23749831C2semidirect
11. #23749830C2semidirect
12. #23749824C2semidirect
13. #23749824C2semidirect
14. #23749650C2semidirect
15. #478×C149C2semidirect
172. C149#3260semidirect
179. #478D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237502262
#237499352
#237499312
#237499222
#237498722
#237498702
#237498552
#237498532
#237498312
#237498302
#237498242
#237496502
#478×C1492
#3260149