Finite Group Databasebeta

← #34057155

Subgroups — #34057155

Order 19072.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750279C211yesmaximal, characteristic, complemented
2#23750035C211yesmaximal, characteristic, complemented
3#23749949C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749941C211yesmaximal, characteristic, complemented
6#23749936C211yesmaximal, characteristic, complemented
7#23749922C211yesmaximal, characteristic, complemented
8#23749915C211yesmaximal, characteristic, complemented
9#23749876C211yesmaximal, characteristic, complemented
10#23749859C211yesmaximal, characteristic, complemented
11#23749735C211yesmaximal, characteristic, complemented
12#23749697C211yesmaximal, characteristic, complemented
13#23749668C211yesmaximal, characteristic, complemented
14C2×#18011842C211yesmaximal, characteristic, complemented
15#553×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558721C2211yescharacteristic
18C2×#14558720C2211yescharacteristic
19C22×#11924746C2211yescharacteristic
20#18011911C2211yescharacteristic
21#18011895—21no—
22#18011895—21no—
23#18011891—21no—
24#18011885C2211yescharacteristic
25#18011885C2211yescharacteristic
26C4×D596C2211yescharacteristic
27C2×C4⋊Dic149C2211yescharacteristic
28C2×C4⋊Dic149C2211yescharacteristic
29#18011844C2211yescharacteristic
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011842C2211yescharacteristic
37#18011842C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47#18011822C2211yescharacteristic
48#126×C149—21no—
49#125×C149C2211yescharacteristic
50#123×C149—21no—
51#121×C149—21no—
52#121×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic
54C4×D4×C149—21no—
55C4×D4×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57#117×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C2×C4×D149—21no—
67#14558721—22no—
68#14558720—22no—
69C2×#11924746—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558713—21no—
81#14558713—21no—
82#14558713—21no—
83C2×D4×C149—21no—
84C2×D4×C149—21no—
85C2×D4×C149D411yescharacteristic
86C2×D4×C149C2311yescharacteristic
87C22×C4×C149—21no—
88C22×C4×C149—21no—
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149D411yescharacteristic
95C4⋊C4×C149C2311yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149D411yescharacteristic
103C22⋊C4×C149D411yescharacteristic
104C42×C149—21no—
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107Dic298—42no—
108D596—21no—
109D596—21no—
110C22⋊D149—42no—
111C22⋊D149—42no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—42no—
116C2×Dic149—42no—
117C4×D149—42no—
118#11924746—21no—
119#11924746—21no—
120#11924746—21no—
121#11924746#4112yescomplemented
122C23×C149—21no—
123C23×C149C2×D411yescharacteristic
124C23×C149C2×D411yescharacteristic
125D4×C149—22no—
126D4×C149—21no—
127D4×C149—21no—
128D4×C149—42no—
129D4×C149—81no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—81no—
138C2×C4×C149—81no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149AGL(1,ℤ/8)12yes—
153C22×C149C22×D411yescharacteristic
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C1492−1+411yescharacteristic
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169C2×C149—22no—
170C2×C149—41no—
171C2×C149—81no—
172C2×C149#54711yescharacteristic
173C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C149#57711yescharacteristic
175D149—81no—
176C149#334511yescharacteristic, complemented, Sylow
177#3345—1491nomaximal, Sylow
178#553D14911yescharacteristic, complemented
179#547—1491no—
180#501—1491no—
181#482—1491no—
182#481—1491no—
183#481—1491no—
184#480—1491no—
185#478—1491no—
186#476—1491no—
187#469—1491no—
188#466—1491no—
189#442—1491no—
190#435—1491no—
191#428—1491no—
192C2×#106—1491no—
193C2×#41—2981no—
194C2×D8—1491no—
195C2×M16—1491no—
196C22×C8—1491no—
197C4⋊Q8—1491no—
198#126—21no—
199#125C2×D14911yescharacteristic
200#123—21no—
201#123—2981no—
202#123—2981no—
203C22⋊Q8—2981no—
204#121—21no—
205#121—1491no—
206#121—1491no—
207#121C2×D14911yescharacteristic
208#121C2×D14911yescharacteristic
209C4×D4—21no—
210C4×D4—1491no—
211C4×D4C2×D14911yescharacteristic
212C4×D4C2×D14911yescharacteristic
213#117C2×D14911yescharacteristic
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4C2×D14911yescharacteristic
217#107—1491no—
218#107—1491no—
219#107—1491no—
220#106—1491no—
221#106—1491no—
222#106—1491no—
223#106—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233C22⋊C8—1491no—
234C22⋊C8—1491no—
235#97—1491no—
236#41—5964no—
237C2×Q8—2981no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—1491no—
243C2×D4C22⋊D14911yescharacteristic
244C2×D4C22×D14911yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4C22×D14911yescharacteristic
251C22×C4C22×D14911yescharacteristic
252D8—2982no—
253M16—2982no—
254C2×C8—2982no—
255C2×C8—1491no—
256C2×C8—1491no—
257C2×C8—1491no—
258C2×C8—1491no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4C22⋊D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C4⋊C4C22×D14911yescharacteristic
271C4⋊C4C22×D14911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4C22⋊D14911yescharacteristic
280C22⋊C4C22⋊D14911yescharacteristic
281C42—21no—
282C42C22×D14911yescharacteristic
283C23—21no—
284C23—2981no—
285C23C2×C22⋊D14911yescharacteristic
286C23C2×C22⋊D14911yescharacteristic
287Q8—5962no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—2981no—
294D4—2981no—
295D4—5962no—
296D4—5962no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—5962no—
310C2×C4—5962no—
311C2×C4—5962no—
312C2×C4C2×C22⋊D14911yescharacteristic
313C2×C4C2×C22⋊D14911yescharacteristic
314C2×C4C2×C22⋊D14911yescharacteristic
315C2×C4C2×C22⋊D14911yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—2981no—
318C8—2981no—
319C8—2981no—
320C8—1492no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22#1801193612yes—
333C22C22×C22⋊D14911yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—5961no—
342C4—5961no—
343C4—5961no—
344C4#41×D14911yescharacteristic
345C4#1801195811yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—11921no—
350C2#2375027411yescharacteristic
351C2C2×#1801193611yescharacteristic
352C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#553×C149C2
socleC22×C149C22×D4
hypercenter#553D149
hypocenterC149#3345
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23750279C2semidirect
2. #23750035C2semidirect
3. #23749949C2semidirect
4. #23749943C2semidirect
5. #23749941C2semidirect
6. #23749936C2semidirect
7. #23749922C2semidirect
8. #23749915C2semidirect
9. #23749876C2semidirect
10. #23749859C2semidirect
11. #23749735C2semidirect
12. #23749697C2semidirect
13. #23749668C2semidirect
14. C2×#18011842C2semidirect
15. #553×C149C2semidirect
121. #11924746#41semidirect
176. C149#3345semidirect
178. #553D149semidirect

Maximal subgroups

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

subgroupindex
#237502792
#237500352
#237499492
#237499432
#237499412
#237499362
#237499222
#237499152
#237498762
#237498592
#237497352
#237496972
#237496682
C2×#180118422
#553×C1492
#3345149