Finite Group Databasebeta

← #34057251

Subgroups — #34057251

Order 19072.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic
2#23750024C211yesmaximal, characteristic, complemented
3#23749963C211yesmaximal, characteristic, complemented
4#23749953C211yesmaximal, characteristic, complemented
5#23749949C211yesmaximal, characteristic, complemented
6#23749943C211yesmaximal, characteristic, complemented
7#23749932C211yesmaximal, characteristic, complemented
8#23749922C211yesmaximal, characteristic, complemented
9#23749873C211yesmaximal, characteristic, complemented
10#23749873C211yesmaximal, characteristic, complemented
11C4×#14558723C211yesmaximal, characteristic, complemented
12#23749703C211yesmaximal, characteristic, complemented
13#23749668C211yesmaximal, characteristic, complemented
14#23749665C211yesmaximal, characteristic, complemented
15#552×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C2×#14558720C2211yescharacteristic
19#18011906—21no—
20#18011903C2211yescharacteristic
21#18011893—21no—
22#18011885C2211yescharacteristic
23#18011885C2211yescharacteristic
24#18011883—21no—
25C4×D596C2211yescharacteristic
26#18011871—21no—
27#18011870C2211yescharacteristic
28C2×C4⋊Dic149C2211yescharacteristic
29#18011844C2211yescharacteristic
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011844C2211yescharacteristic
33#18011842C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011842C2211yescharacteristic
37#18011842C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011835C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48#126×C149—21no—
49#125×C149—21no—
50#125×C149C2211yescharacteristic
51#123×C149—21no—
52C22⋊Q8×C149C2211yescharacteristic
53C22⋊Q8×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56#117×C149—21no—
57#117×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59C2×D596C2311yescharacteristic
60C2×C22⋊D149—21no—
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C2×C4×D149—21no—
64#14558723—22no—
65#14558720—22no—
66#14558720—22no—
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77C22⋊Dic149—21no—
78#14558713—21no—
79#14558713—21no—
80#14558713—21no—
81C4×Dic149—21no—
82C2×Q8×C149C2311yescharacteristic
83C2×D4×C149D411yescharacteristic
84C22×C4×C149—21no—
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—21no—
88C4⋊C4×C149—21no—
89C4⋊C4×C149—21no—
90C4⋊C4×C149—21no—
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149D411yescharacteristic
94C4⋊C4×C149C2311yescharacteristic
95C4⋊C4×C149C2311yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C22⋊C4×C149—21no—
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149D411yescharacteristic
101C22⋊C4×C149D411yescharacteristic
102C42×C149—21no—
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106D596—21no—
107D596—21no—
108C22⋊D149—42no—
109C22⋊D149—81no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—81no—
114C4×D149—81no—
115#11924746—21no—
116#11924746—21no—
117#11924746—21no—
118#11924746#4112yes—
119C23×C149C2×D411yescharacteristic
120C23×C149C2×D411yescharacteristic
121Q8×C149—21no—
122Q8×C149—21no—
123D4×C149—41no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—42no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C22×C149—21no—
139C22×C149—21no—
140C22×C149—21no—
141C22×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149C22×D411yescharacteristic
145C2×D149—41no—
146C2×D149—41no—
147C2×D149—41no—
148C4×C149—21no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—21no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149C2×#4111yescharacteristic
157C4×C1492−1+411yescharacteristic
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161C2×C149—41no—
162C2×C149—41no—
163C2×C149#54711yescharacteristic
164C2×C149#57511yescharacteristic
165C2×C149#57711yescharacteristic
166D149—81no—
167C149#335111yescharacteristic, complemented, Sylow
168#3351—1491nomaximal, Sylow
169#553—1491no—
170#552D14911yescharacteristic, complemented
171#499—1491no—
172#485—1491no—
173#483—1491no—
174#482—1491no—
175#481—1491no—
176#479—1491no—
177#478—1491no—
178#468—1491no—
179#468—1491no—
180C4×SD16—1491no—
181#436—1491no—
182#428—1491no—
183#428—1491no—
184C2×SD16—1491no—
185C2×M16—1491no—
186C2×M16—1491no—
187#126—21no—
188#126—2981no—
189#125—21no—
190#125—1491no—
191#125C2×D14911yescharacteristic
192#123—21no—
193#123—2981no—
194C22⋊Q8C2×D14911yescharacteristic
195C22⋊Q8C2×D14911yescharacteristic
196#121—2981no—
197#121—1491no—
198#121—1491no—
199C4×Q8C2×D14911yescharacteristic
200C4×D4—2981no—
201C4×D4—1491no—
202C4×D4C2×D14911yescharacteristic
203#117—21no—
204#117—1491no—
205#117C2×D14911yescharacteristic
206C2×C4⋊C4—1491no—
207C2×C4⋊C4C2×D14911yescharacteristic
208#107—1491no—
209#107—1491no—
210#107—1491no—
211#107—1491no—
212#106—1491no—
213#106—1491no—
214#106—1491no—
215#106—1491no—
216#106—1491no—
217C4⋊C8—1491no—
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#102—1491no—
222#102—1491no—
223#102—1491no—
224C22⋊C8—1491no—
225C22⋊C8—1491no—
226C4×C8—1491no—
227C2×Q8C22×D14911yescharacteristic
228C2×D4—2981no—
229C2×D4—2981no—
230C2×D4—1491no—
231C2×D4C22⋊D14911yescharacteristic
232C22×C4—21no—
233C22×C4—2981no—
234C22×C4—2981no—
235C22×C4C22×D14911yescharacteristic
236C22×C4C22×D14911yescharacteristic
237SD16—2982no—
238M16—2982no—
239M16—2982no—
240C2×C8—1491no—
241C2×C8—1491no—
242C2×C8—1491no—
243C2×C8—1491no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—1491no—
254C4⋊C4—1491no—
255C4⋊C4—1491no—
256C4⋊C4C22⋊D14911yescharacteristic
257C4⋊C4C22×D14911yescharacteristic
258C4⋊C4C22×D14911yescharacteristic
259C4⋊C4C22×D14911yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4C22⋊D14911yescharacteristic
268C22⋊C4C22⋊D14911yescharacteristic
269C42—21no—
270C42—21no—
271C42—2981no—
272C42C22×D14911yescharacteristic
273C23—2981no—
274C23C2×C22⋊D14911yescharacteristic
275C23C2×C22⋊D14911yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—41no—
279D4—2981no—
280D4—2981no—
281D4—5962no—
282D4—11921no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—11921no—
296C2×C4—11921no—
297C2×C4C2×C22⋊D14911yescharacteristic
298C2×C4C2×C22⋊D14911yescharacteristic
299C2×C4C2×C22⋊D14911yescharacteristic
300C2×C4C2×C22⋊D14911yescharacteristic
301C2×C4C23×D14911yescharacteristic
302C8—2981no—
303C8—2981no—
304C8—2981no—
305C8—1492no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—5961no—
313C22—5961no—
314C22—5961no—
315C22C22×C22⋊D14911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—5961no—
325C4—5961no—
326C4—5961no—
327C4#41×D14911yescharacteristic
328C4#1801195811yescharacteristic
329C2—41no—
330C2—41no—
331C2—11921no—
332C2#2375027411yescharacteristic
333C2#2375042311yescharacteristic
334C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#552×C149C2
socleC22×C149C22×D4
prime radical#23750321C2
hypercenter#552D149
hypocenterC149#3351
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #23750024C2semidirect
3. #23749963C2semidirect
4. #23749953C2semidirect
5. #23749949C2semidirect
6. #23749943C2semidirect
7. #23749932C2semidirect
8. #23749922C2semidirect
9. #23749873C2semidirect
10. #23749873C2semidirect
11. C4×#14558723C2semidirect
12. #23749703C2semidirect
13. #23749668C2semidirect
14. #23749665C2semidirect
15. #552×C149C2semidirect
167. C149#3351semidirect
170. #552D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237500242
#237499632
#237499532
#237499492
#237499432
#237499322
#237499222
#237498732
C4×#145587232
#237497032
#237496682
#237496652
#552×C1492
#3351149