Finite Group Databasebeta

← #34055879

Subgroups — #34055879

Order 19072.

368 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750172C211yesmaximal, characteristic
2#125×D149C211yesmaximal, characteristic, complemented
3#23750033C211yesmaximal, characteristic, complemented
4#23750032C211yesmaximal, characteristic, complemented
5#23749988C211yesmaximal, characteristic, complemented
6#23749988C211yesmaximal, characteristic, complemented
7#23749945C211yesmaximal, characteristic, complemented
8#23749942C211yesmaximal, characteristic, complemented
9#23749940C211yesmaximal, characteristic, complemented
10#23749937C211yesmaximal, characteristic, complemented
11#23749926C211yesmaximal, characteristic, complemented
12#23749925C211yesmaximal, characteristic, complemented
13#23749922C211yesmaximal, characteristic, complemented
14#23749681C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17#18011910C2211yescharacteristic
18#18011907C2211yescharacteristic
19#18011903C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011901—21no—
23#18011901—21no—
24#18011897—21no—
25#18011886C2211yescharacteristic
26#18011884—21no—
27#18011882C2211yescharacteristic
28C4×D596C2211yescharacteristic
29C4×C22⋊D149—21no—
30C4⋊C4×D149—21no—
31C4⋊C4×D149—21no—
32C4⋊C4×D149C2211yescharacteristic
33C4⋊C4×D149C2211yescharacteristic
34C42×D149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011833C2211yescharacteristic
43#18011833C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149D411yescharacteristic
70C2×C4×D149D411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89C4×Dic149D411yescharacteristic
90C4×Dic149D411yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×D4×C149C2311yescharacteristic
93C22×C4×C149—21no—
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C22⋊C4×C149—21no—
102C42×C149C2311yescharacteristic
103C22×D149—21no—
104C22×D149C2×D411yescharacteristic
105Dic298—42no—
106D596—21no—
107D596—21no—
108D596—42no—
109C22⋊D149—42no—
110C22⋊D149—42no—
111C22⋊D149—42no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C4×D149—22no—
119C4×D149—21no—
120C4×D149—21no—
121C4×D149—41no—
122C4×D149—42no—
123C4×D149—42no—
124C4×D149—42no—
125#11924746—21no—
126#11924746—21no—
127C23×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—42no—
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2411yescharacteristic
137C8×C149—21no—
138C8×C149—21no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149C22×D411yescharacteristic
143C2×D149—21no—
144C2×D149—21no—
145C2×D149—41no—
146C2×D149—41no—
147C2×D149—41no—
148C2×D149AGL(1,ℤ/8)12yes—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C1492−1+411yescharacteristic
155C4×C1492−1+411yescharacteristic
156Dic149—21no—
157Dic149—21no—
158Dic149—21no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162C2×C149—81no—
163C2×C149#53611yescharacteristic
164C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C149#57511yescharacteristic
166D149—22no—
167D149—81no—
168C149#323411yescharacteristic, complemented, Sylow
169#3234—1491nomaximal, Sylow
170#532—1491no—
171C2×#125—1491no—
172#501—1491no—
173#501—1491no—
174#490—1491no—
175#490—1491no—
176#481—1491no—
177#481—1491no—
178#480—1491no—
179#480—1491no—
180#478—1491no—
181#478—1491no—
182#478—1491no—
183#478D14911yescharacteristic, complemented
184#432—1491no—
185C2×#41—2981no—
186C4⋊Q8—1491no—
187#127—1491no—
188#125—2981no—
189#125—2981no—
190#125—1491no—
191#125—1491no—
192#125—1491no—
193#125C2×D14911yescharacteristic
194#124—2981no—
195#121—2981no—
196#121—1491no—
197#121—1491no—
198C4×D4—2981no—
199C4×D4—1491no—
200C4×D4C2×D14911yescharacteristic
201C2×C4⋊C4—2981no—
202C2×C4⋊C4—2981no—
203C2×C4⋊C4—1491no—
204C2×C4⋊C4—1491no—
205C2×C42—1491no—
206#107—1491no—
207#107—1491no—
208#107—1491no—
209#107C2×D14911yescharacteristic
210#106—1491no—
211#106—1491no—
212#106—1491no—
213#106C2×D14911yescharacteristic
214C4⋊C8—1491no—
215C4⋊C8C2×D14911yescharacteristic
216#102—1491no—
217#102—1491no—
218#102—1491no—
219#102—1491no—
220#102—1491no—
221#102—1491no—
222#102C2×D14911yescharacteristic
223#102C2×D14911yescharacteristic
224C22⋊C8—1491no—
225C22⋊C8—1491no—
226#97—1491no—
227#97—1491no—
228#41—5964no—
229C2×Q8—2981no—
230C2×D4—2981no—
231C2×D4—2981no—
232C2×D4—2981no—
233C2×D4—2981no—
234C2×D4—1491no—
235C2×D4C22×D14911yescharacteristic
236C22×C4—21no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4—2981no—
240C22×C4—1491no—
241C22×C4—1491no—
242C22×C4—1491no—
243C2×C8—1491no—
244C2×C8—1491no—
245C2×C8C22×D14911yescharacteristic
246C2×C8C22×D14911yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4C22×D14911yescharacteristic
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C42—1491no—
269C42—1491no—
270C42—1491no—
271C42C22×D14911yescharacteristic
272C23—21no—
273C23—2981no—
274C23—1491no—
275Q8—5962no—
276D4—21no—
277D4—21no—
278D4—2981no—
279D4—2981no—
280D4—5962no—
281D4—5962no—
282D4—5962no—
283D4—5962no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—2982no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—5961no—
295C2×C4—5962no—
296C2×C4—5962no—
297C2×C4—5962no—
298C2×C4—1491no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4D4×D14911yescharacteristic
302C2×C4D4×D14911yescharacteristic
303C2×C4C23×D14911yescharacteristic
304C8—21no—
305C8—21no—
306C8—2981no—
307C8—2981no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—2981no—
312C22—2981no—
313C22—5961no—
314C22—5961no—
315C22—5961no—
316C22—1492no—
317C22C2×D4×D14911yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2981no—
324C4—2981no—
325C4—2981no—
326C4—5961no—
327C4—5961no—
328C4—5961no—
329C4#1801195811yescharacteristic
330C4#1801195911yescharacteristic
331C2—81no—
332C2—2982no—
333C2—11921no—
334C2#2375019811yescharacteristic
335C2AGL(1,ℤ/8)×D14911yescharacteristic
336C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radical#23750172C2
hypercenter#478D149
hypocenterC149#3234
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
2. #125×D149C2semidirect
3. #23750033C2semidirect
4. #23750032C2semidirect
5. #23749988C2semidirect
6. #23749988C2semidirect
7. #23749945C2semidirect
8. #23749942C2semidirect
9. #23749940C2semidirect
10. #23749937C2semidirect
11. #23749926C2semidirect
12. #23749925C2semidirect
13. #23749922C2semidirect
14. #23749681C2semidirect
15. #478×C149C2semidirect
168. C149#3234semidirect
183. #478D149semidirect

Maximal subgroups

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

subgroupindex
#237501722
#125×D1492
#237500332
#237500322
#237499882
#237499452
#237499422
#237499402
#237499372
#237499262
#237499252
#237499222
#237496812
#478×C1492
#3234149