Finite Group Databasebeta

← #34055247

Subgroups — #34055247

Order 19072.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750179C211yesmaximal, characteristic, complemented
2#23750172C211yesmaximal, characteristic
3#23750022C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749974C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749857C211yesmaximal, characteristic, complemented
8#23749855C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11C4×#14558725C211yesmaximal, characteristic, complemented
12C4×#14558723C211yesmaximal, characteristic, complemented
13C4×#14558724C211yesmaximal, characteristic, complemented
14C4×C8×D149C211yesmaximal, characteristic, complemented
15C4×SD16×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011910C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011907C2211yescharacteristic
26#18011901—21no—
27#18011897—21no—
28#18011891C2211yescharacteristic
29#18011889—21no—
30#18011887C2211yescharacteristic
31#18011886C2211yescharacteristic
32#18011884—21no—
33#18011882C2211yescharacteristic
34C4×Dic298—21no—
35C4×Dic298C2211yescharacteristic
36C4×D596C2211yescharacteristic
37C4×C22⋊D149—21no—
38#18011868—21no—
39C42×D149C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49C4×#11924746C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149D411yescharacteristic
70C2×C4×D149D411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72#14558725—22no—
73#14558724—22no—
74#14558723—22no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C8×D149—22no—
78C8×D149—22no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100SD16×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149—21no—
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—21no—
112Dic298—21no—
113Dic298—42no—
114Dic298—42no—
115D596—21no—
116D596—21no—
117D596—42no—
118C22⋊D149—42no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—22no—
130C4×D149—42no—
131C4×D149SD1614yescomplemented
132#11924746—21no—
133#11924746#4112yescomplemented
134C23×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—42no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149#4112yescomplemented
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149C2×SD1612yes—
158C4×C149—21no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C2×SD1612yes—
163C4×C149C2×#4111yescharacteristic
164C4×C149C2×#4111yescharacteristic
165Dic149—21no—
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169Dic149C2×SD1612yes—
170Dic149#13512yes—
171C2×C149—81no—
172C2×C149#53211yescharacteristic
173C2×C149C22×SD1611yescharacteristic
174C2×C149C2×#13511yescharacteristic
175D149—22no—
176D149—81no—
177C149#316711yescharacteristic, complemented, Sylow
178#3167—1491nomaximal, Sylow
179#533—1491no—
180#532—1491no—
181#498—1491no—
182#492—1491no—
183#487—1491no—
184#486—1491no—
185#465—1491no—
186#465—1491no—
187#465—1491no—
188#465—1491no—
189C4×SD16—1491no—
190C4×SD16—1491no—
191C4×SD16—1491no—
192C4×SD16D14911yescharacteristic, complemented
193C2×C4×C8—1491no—
194C2×#41—2981no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16C2×D14911yescharacteristic
199C22×C8—1491no—
200C22×C8—1491no—
201C4⋊Q8—1491no—
202C4⋊Q8—1491no—
203C4⋊Q8—1491no—
204#127—1491no—
205#125—2981no—
206#124—2981no—
207C22⋊Q8—2981no—
208C22⋊Q8—1491no—
209C22⋊Q8—1491no—
210#121—2981no—
211#121—1491no—
212#121—1491no—
213C4×Q8—2981no—
214C4×Q8—1491no—
215C4×Q8C2×D14911yescharacteristic
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4C2×D14911yescharacteristic
219#117—2981no—
220C2×C42—1491no—
221#106—1491no—
222#106—1491no—
223#106—1491no—
224#106C2×D14911yescharacteristic
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103C2×D14911yescharacteristic
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102C2×D14911yescharacteristic
233C4×C8—1491no—
234C4×C8—1491no—
235C4×C8—1491no—
236C4×C8C2×D14911yescharacteristic
237#41—5964no—
238C2×Q8—2981no—
239C2×Q8—2981no—
240C2×Q8—1491no—
241C2×Q8C22×D14911yescharacteristic
242C2×D4—2981no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—1491no—
247C2×D4C22×D14911yescharacteristic
248C22×C4—21no—
249C22×C4—2981no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253SD16—22no—
254SD16—2982no—
255SD16—2982no—
256SD16—2982no—
257C2×C8—2982no—
258C2×C8—2982no—
259C2×C8—1491no—
260C2×C8—1491no—
261C2×C8C22×D14911yescharacteristic
262C2×C8C22×D14911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4C22×D14911yescharacteristic
274C4⋊C4C22×D14911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C42—21no—
282C42—2981no—
283C42—1491no—
284C42—1491no—
285C42—1491no—
286C42C22×D14911yescharacteristic
287C23—21no—
288C23—2981no—
289C23—1491no—
290Q8—21no—
291Q8—21no—
292Q8—2981no—
293Q8—2981no—
294Q8—5962no—
295Q8—5962no—
296D4—21no—
297D4—21no—
298D4—2981no—
299D4—2981no—
300D4—5962no—
301D4—5962no—
302D4—5962no—
303D4—5962no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2982no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—5962no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—1494no—
319C2×C4D4×D14911yescharacteristic
320C2×C4D4×D14911yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—2981no—
324C8—1492no—
325C8#1455873612yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2981no—
330C22—2981no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22—1492no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—5961no—
342C4—5961no—
343C4—5961no—
344C4—1492no—
345C4—1492no—
346C4SD16×D14912yes—
347C4#41×D14911yescharacteristic
348C4C2×#1455873611yescharacteristic
349C2—81no—
350C2—2982no—
351C2—11921no—
352C2#2375017211yescharacteristic
353C2C2×SD16×D14911yescharacteristic
354C2#135×D14911yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radical#23750172C2
hypercenterC4×SD16D149
hypocenterC149#3167
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23750179C2semidirect
3. #23750022C2semidirect
4. #23749996C2semidirect
5. #23749974C2semidirect
6. #23749970C2semidirect
7. #23749857C2semidirect
8. #23749855C2semidirect
9. #23749853C2semidirect
10. #23749851C2semidirect
11. C4×#14558725C2semidirect
12. C4×#14558723C2semidirect
13. C4×#14558724C2semidirect
14. C4×C8×D149C2semidirect
15. C4×SD16×C149C2semidirect
131. C4×D149SD16semidirect
133. #11924746#41semidirect
147. C8×C149#41semidirect
177. C149#3167semidirect
192. C4×SD16D149semidirect
325. C8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237501792
#237501722
#237500222
#237499962
#237499742
#237499702
#237498572
#237498552
#237498532
#237498512
C4×#145587252
C4×#145587232
C4×#145587242
C4×C8×D1492
C4×SD16×C1492
#3167149