Finite Group Databasebeta

← #34057161

Subgroups — #34057161

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#23750321C211yesmaximal, characteristic, complemented
2#23750031C211yesmaximal, characteristic, complemented
3#23749946C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749941C211yesmaximal, characteristic, complemented
6#23749938C211yesmaximal, characteristic, complemented
7#23749925C211yesmaximal, characteristic, complemented
8#23749912C211yesmaximal, characteristic, complemented
9#23749876C211yesmaximal, characteristic, complemented
10#23749859C211yesmaximal, characteristic, complemented
11#23749735C211yesmaximal, characteristic, complemented
12#23749697C211yesmaximal, characteristic, complemented
13#23749665C211yesmaximal, characteristic, complemented
14C2×#18011842C211yesmaximal, characteristic, complemented
15#547×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
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#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
48C2×#41×C149—21no—
49C4⋊Q8×C149C2211yescharacteristic
50#123×C149—21no—
51#123×C149—21no—
52C22⋊Q8×C149—21no—
53#121×C149C2211yescharacteristic
54#121×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C2×C4⋊C4×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59C2×D596C2311yescharacteristic
60C2×C22⋊D149—21no—
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C2×C4×D149—21no—
64#14558721—22no—
65#14558720—22no—
66C2×#11924746—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—
82#41×C149—44no—
83C2×Q8×C149—21no—
84C2×D4×C149—21no—
85C2×D4×C149—21no—
86C2×D4×C149D411yescharacteristic
87C2×D4×C149C2311yescharacteristic
88C22×C4×C149—21no—
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C4⋊C4×C149—21no—
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149D411yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107D596—21no—
108D596—21no—
109C22⋊D149—42no—
110C22⋊D149—81no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—81no—
115C4×D149—81no—
116#11924746—21no—
117#11924746—21no—
118#11924746—21no—
119#11924746#4112yescomplemented
120C23×C149—21no—
121C23×C149C2×D411yescharacteristic
122C23×C149C2×D411yescharacteristic
123Q8×C149—42no—
124D4×C149—22no—
125D4×C149—21no—
126D4×C149—21no—
127D4×C149—42no—
128D4×C149—42no—
129C2×C4×C149—21no—
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—42no—
137C2×C4×C149—42no—
138C2×C4×C149—42no—
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#553—1491no—
179#547D14911yescharacteristic, complemented
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—21no—
194C2×D8—1491no—
195C2×M16—1491no—
196C22×C8—1491no—
197C4⋊Q8C2×D14911yescharacteristic
198#126—2981no—
199#125—1491no—
200#123—21no—
201#123—21no—
202#123—2981no—
203C22⋊Q8—21no—
204#121—2981no—
205#121—1491no—
206#121—1491no—
207#121C2×D14911yescharacteristic
208#121C2×D14911yescharacteristic
209C4×D4—2981no—
210C4×D4—1491no—
211C4×D4C2×D14911yescharacteristic
212C4×D4C2×D14911yescharacteristic
213#117—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4C2×D14911yescharacteristic
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—44no—
237C2×Q8—21no—
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—21no—
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—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4C22⋊D14911yescharacteristic
280C22⋊C4C22⋊D14911yescharacteristic
281C42—2981no—
282C42C22×D14911yescharacteristic
283C23—21no—
284C23—2981no—
285C23C2×C22⋊D14911yescharacteristic
286C23C2×C22⋊D14911yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—2981no—
294D4—2981no—
295D4—5962no—
296D4—11921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—11921no—
311C2×C4—11921no—
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#1801193712yes—
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×#1801193711yescharacteristic
352C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#547×C149C2
socleC22×C149C22×D4
hypercenter#547D149
hypocenterC149#3345
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #23750321C2semidirect
2. #23750031C2semidirect
3. #23749946C2semidirect
4. #23749943C2semidirect
5. #23749941C2semidirect
6. #23749938C2semidirect
7. #23749925C2semidirect
8. #23749912C2semidirect
9. #23749876C2semidirect
10. #23749859C2semidirect
11. #23749735C2semidirect
12. #23749697C2semidirect
13. #23749665C2semidirect
14. C2×#18011842C2semidirect
15. #547×C149C2semidirect
119. #11924746#41semidirect
176. C149#3345semidirect
179. #547D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237500312
#237499462
#237499432
#237499412
#237499382
#237499252
#237499122
#237498762
#237498592
#237497352
#237496972
#237496652
C2×#180118422
#547×C1492
#3345149