Finite Group Databasebeta

← #34055245

Subgroups — #34055245

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#23750177C211yesmaximal, characteristic, complemented
2#23750170C211yesmaximal, characteristic
3#23750022C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749974C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749856C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749716C211yesmaximal, characteristic, complemented
11SD16×Dic149C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749710C211yesmaximal, characteristic, complemented
14C2×C8×Dic149C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C22×#11924746C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011907C2211yescharacteristic
25#18011901—21no—
26#18011897—21no—
27#18011890C2211yescharacteristic
28#18011888—21no—
29#18011885C2211yescharacteristic
30#18011883—21no—
31Q8×Dic149C2211yescharacteristic
32#18011876—21no—
33#18011876C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011871—21no—
37#18011867—21no—
38C2×C4×Dic149C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48C8×Dic149C2211yescharacteristic
49C8×Dic149C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C22×Dic149D411yescharacteristic
69C22×Dic149D411yescharacteristic
70C2×C4×D149—21no—
71#14558725—22no—
72#14558724—22no—
73#14558723—22no—
74C2×#11924746—22no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149D411yescharacteristic
93C4×Dic149D411yescharacteristic
94C4×Dic149C2311yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100SD16×C149—22no—
101C2×C8×C149—22no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22×D149—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—42no—
113Dic298—42no—
114D596—21no—
115D596—21no—
116C22⋊D149—42no—
117C22⋊D149—42no—
118C22⋊D149—42no—
119C2×Dic149—22no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149SD1614yescomplemented
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—42no—
130#11924746—21no—
131#11924746#4112yescomplemented
132C23×C149—21no—
133C23×C149C2×D411yescharacteristic
134Q8×C149—21no—
135Q8×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—42no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149#4112yescomplemented
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149C2×SD1612yes—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C2×#4111yescharacteristic
163C4×C149C2×#4111yescharacteristic
164Dic149—21no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168Dic149C2×SD1612yes—
169Dic149C2×SD1612yes—
170Dic149#13512yes—
171C2×C149—22no—
172C2×C149—81no—
173C2×C149#53211yescharacteristic
174C2×C149C22×SD1611yescharacteristic
175C2×C149C2×#13511yescharacteristic
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#465D14911yescharacteristic, complemented
189C4×SD16—1491no—
190C4×SD16—1491no—
191C4×SD16—1491no—
192C4×SD16—1491no—
193C2×C4×C8—1491no—
194C2×#41—2981no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16C2×D14911yescharacteristic
199C22×C8—1491no—
200C22×C8C2×D14911yescharacteristic
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⋊Q8C2×D14911yescharacteristic
210#121—2981no—
211#121—1491no—
212#121C2×D14911yescharacteristic
213C4×Q8—2981no—
214C4×Q8—1491no—
215C4×Q8—1491no—
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4—1491no—
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×C8—1491no—
237#41—5964no—
238C2×Q8—2981no—
239C2×Q8—2981no—
240C2×Q8—1491no—
241C2×Q8C22×D14911yescharacteristic
242C2×D4—21no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—1491no—
247C2×D4C22×D14911yescharacteristic
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4C22×D14911yescharacteristic
253SD16—22no—
254SD16—2982no—
255SD16—2982no—
256SD16—2982no—
257C2×C8—22no—
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—21no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C42—2981no—
282C42—2981no—
283C42—1491no—
284C42—1491no—
285C42—1491no—
286C42—1491no—
287C23—21no—
288C23—2981no—
289C23D4×D14911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2981no—
293Q8—2981no—
294Q8—5962no—
295Q8—5962no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—2981no—
300D4—2981no—
301D4—5962no—
302D4—5962no—
303D4—5962no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2982no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—5962no—
314C2×C4—5962no—
315C2×C4—1491no—
316C2×C4—1494no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—1491no—
320C2×C4D4×D14911yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—2981no—
324C8—1492no—
325C8#1455873512yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—5961no—
332C22—5961no—
333C22—5961no—
334C22SD16×D14912yes—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—5961no—
342C4—5961no—
343C4—5961no—
344C4—1492no—
345C4—1492no—
346C4—1492no—
347C4#41×D14911yescharacteristic
348C4C2×#1455873511yescharacteristic
349C2—22no—
350C2—81no—
351C2—11921no—
352C2#2375017011yescharacteristic
353C2C2×SD16×D14911yescharacteristic
354C2#135×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
prime radical#23750170C2
hypercenter#465D149
hypocenterC149#3167
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23750177C2semidirect
3. #23750022C2semidirect
4. #23749996C2semidirect
5. #23749974C2semidirect
6. #23749970C2semidirect
7. #23749856C2semidirect
8. #23749854C2semidirect
9. #23749852C2semidirect
10. #23749716C2semidirect
11. SD16×Dic149C2semidirect
12. #23749712C2semidirect
13. #23749710C2semidirect
14. C2×C8×Dic149C2semidirect
15. #465×C149C2semidirect
124. C2×Dic149SD16semidirect
131. #11924746#41semidirect
147. C8×C149#41semidirect
177. C149#3167semidirect
188. #465D149semidirect
325. C8#14558735semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237501702
#237500222
#237499962
#237499742
#237499702
#237498562
#237498542
#237498522
#237497162
SD16×Dic1492
#237497122
#237497102
C2×C8×Dic1492
#465×C1492
#3167149