Finite Group Databasebeta

← #34055302

Subgroups — #34055302

Order 19072.

362 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#23750246C211yesmaximal, characteristic, complemented
2#23750021C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749987C211yesmaximal, characteristic, complemented
5#23749984C211yesmaximal, characteristic, complemented
6#23749881C211yesmaximal, characteristic, complemented
7#23749876C211yesmaximal, characteristic
8#23749856C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749735C211yesmaximal, characteristic, complemented
11#23749730C211yesmaximal, characteristic, complemented
12C4×#14558723C211yesmaximal, characteristic, complemented
13C4×#14558724C211yesmaximal, characteristic, complemented
14#23749581C211yesmaximal, characteristic, complemented
15#542×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558720C2211yescharacteristic
21C22×#11924746C2211yescharacteristic
22#18011911C2211yescharacteristic
23#18011906—21no—
24#18011899C2211yescharacteristic
25#18011897—21no—
26#18011893—21no—
27#18011890C2211yescharacteristic
28#18011889—21no—
29#18011885C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×D596C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011834C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011822C2211yescharacteristic
45#18011822C2211yescharacteristic
46C4×#11924746C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#124×C149—21no—
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558726—22no—
65#14558724—22no—
66#14558723—22no—
67#14558721—22no—
68#14558720—22no—
69C2×#11924746—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80#14558713—21no—
81#14558713—21no—
82#14558713—21no—
83#14558713—21no—
84C4×Dic149—21no—
85C2×Q8×C149—21no—
86C2×Q8×C149C2311yescharacteristic
87C2×D4×C149—21no—
88C2×D4×C149C2311yescharacteristic
89C22×C4×C149—21no—
90C22×C4×C149C2311yescharacteristic
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149D411yescharacteristic
95C4⋊C4×C149D411yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—81no—
112D596—21no—
113D596—21no—
114C22⋊D149—81no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C4×D149—81no—
119#11924746—21no—
120#11924746—21no—
121#11924746#4112yes—
122#11924746#4112yes—
123C23×C149—21no—
124C23×C149C2×D411yescharacteristic
125Q8×C149—21no—
126Q8×C149—21no—
127Q8×C149—81no—
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×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149C22×D411yescharacteristic
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C149C2×#4111yescharacteristic
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—41no—
167C2×C149—81no—
168C2×C149#53211yescharacteristic
169C2×C149#57711yescharacteristic
170C2×C149#57711yescharacteristic
171D149—81no—
172C149#317311yescharacteristic, complemented, Sylow
173#3173—1491nomaximal, Sylow
174#542—1491no—
175#542D14911yescharacteristic, complemented
176#498—1491no—
177#495—1491no—
178#489—1491no—
179#489—1491no—
180#470—1491no—
181#469—1491no—
182#465—1491no—
183#465—1491no—
184#442—1491no—
185#441—1491no—
186C4×SD16—1491no—
187C4×SD16—1491no—
188#405—1491no—
189C2×Q16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192C2×D8—1491no—
193C2×M16—1491no—
194C22×C8—1491no—
195C4⋊Q8—1491no—
196C4⋊Q8C2×D14911yescharacteristic
197#126—21no—
198#126—2981no—
199#124—21no—
200#124—2981no—
201#124—1491no—
202#124C2×D14911yescharacteristic
203#123—21no—
204#123—2981no—
205C22⋊Q8—21no—
206C22⋊Q8—2981no—
207C22⋊Q8—1491no—
208C22⋊Q8C2×D14911yescharacteristic
209#121—1491no—
210#121C2×D14911yescharacteristic
211C4×Q8—1491no—
212C4×Q8C2×D14911yescharacteristic
213C4×D4—1491no—
214C4×D4C2×D14911yescharacteristic
215#117C2×D14911yescharacteristic
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220#103—1491no—
221#103—1491no—
222#103—1491no—
223#103—1491no—
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#97—1491no—
229#97—1491no—
230C4×C8—1491no—
231C4×C8—1491no—
232C2×Q8—21no—
233C2×Q8—2981no—
234C2×Q8—1491no—
235C2×Q8C22×D14911yescharacteristic
236C2×D4—21no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—21no—
241C22×C4—2981no—
242C22×C4C22×D14911yescharacteristic
243Q16—2982no—
244SD16—2982no—
245SD16—2982no—
246D8—2982no—
247M16—2982no—
248C2×C8—2982no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8—1491no—
252C2×C8—1491no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4C22⋊D14911yescharacteristic
262C4⋊C4C22⋊D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4C22⋊D14911yescharacteristic
276C22⋊C4C22⋊D14911yescharacteristic
277C42—21no—
278C42—2981no—
279C42C22×D14911yescharacteristic
280C42C22×D14911yescharacteristic
281C23—21no—
282C23—2981no—
283C23C2×C22⋊D14911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—2981no—
288Q8—2981no—
289Q8—11921no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—2981no—
294D4—2981no—
295D4—11921no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—11921no—
306C2×C4C2×C22⋊D14911yescharacteristic
307C2×C4C2×C22⋊D14911yescharacteristic
308C2×C4C2×C22⋊D14911yescharacteristic
309C2×C4C2×C22⋊D14911yescharacteristic
310C2×C4C2×C22⋊D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—2981no—
313C8—2981no—
314C8—1492no—
315C8—1492no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—5961no—
323C22—5961no—
324C22—5961no—
325C22C22×C22⋊D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4#41×D14911yescharacteristic
338C4#41×D14911yescharacteristic
339C2—41no—
340C2—81no—
341C2—11921no—
342C2#2375017111yescharacteristic
343C2#2375043311yescharacteristic
344C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#542×C149C2
socleC22×C149C22×D4
prime radical#23749876C2
hypercenter#542D149
hypocenterC149#3173
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750021C2semidirect
3. #23750007C2semidirect
4. #23749987C2semidirect
5. #23749984C2semidirect
6. #23749881C2semidirect
8. #23749856C2semidirect
9. #23749852C2semidirect
10. #23749735C2semidirect
11. #23749730C2semidirect
12. C4×#14558723C2semidirect
13. C4×#14558724C2semidirect
14. #23749581C2semidirect
15. #542×C149C2semidirect
172. C149#3173semidirect
175. #542D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237500212
#237500072
#237499872
#237499842
#237498812
#237498762
#237498562
#237498522
#237497352
#237497302
C4×#145587232
C4×#145587242
#237495812
#542×C1492
#3173149