Finite Group Databasebeta

← #34055440

Subgroups — #34055440

Order 19072.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011882C211yesmaximal, characteristic, complemented
2#121×D149C211yesmaximal, characteristic, complemented
3#23749939C211yesmaximal, characteristic, complemented
4#23749937C212yesmaximal, complemented
5#23749936C211yesmaximal, characteristic, complemented
6#23749860C212yesmaximal, complemented
7#23749858C212yesmaximal, complemented
8#23749759C211yesmaximal, characteristic, complemented
9#23749757C212yesmaximal, complemented
10C22⋊C8×D149C211yesmaximal, characteristic, complemented
11#447×C149C211yesmaximal, characteristic, complemented
12C22×C22⋊D149—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2211yescharacteristic, complemented
15C22×C4×D149C2211yescharacteristic
16C2×#14558721C2212yescomplemented
17C2×C8×D149C2212yescomplemented
18#18011886C2211yescharacteristic, complemented
19#18011885C2211yescharacteristic
20#18011884—21no—
21#18011883—21no—
22#18011882—21no—
23#18011882—21no—
24#18011882C2212yes—
25#18011882C2211yescharacteristic, complemented
26#18011882C2212yescomplemented
27C2×C4⋊Dic149C2211yescharacteristic, complemented
28C4⋊C4×D149C2211yescharacteristic, complemented
29C2×C22⋊Dic149—21no—
30C22⋊C4×D149—21no—
31#18011845C2212yescomplemented
32#18011844C2212yescomplemented
33#18011833C2212yescomplemented
34#18011832C2212yescomplemented
35#18011832C2212yescomplemented
36C22⋊#11924746C2211yescharacteristic, complemented
37#18011823C2212yescomplemented
38C22×D4×C149C2211yescharacteristic, complemented
39C2×D8×C149C2212yescomplemented
40#121×C149C2211yescharacteristic
41#102×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44C23×D149D411yescharacteristic
45C2×D596—21no—
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—21no—
48C2×C22⋊D149—22no—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—21no—
51C2×C22⋊D149—21no—
52C2×C22⋊D149—44no—
53D4×D149—42no—
54D4×D149—44no—
55C22×Dic149—21no—
56C22×Dic149D411yescharacteristic
57C2×C4×D149—21no—
58C2×C4×D149—42no—
59C2×C4×D149D411yescharacteristic
60C2×C4×D149D411yescharacteristic
61C2×C4×D149C2311yescharacteristic
62C2×C4×D149C2311yescharacteristic
63#14558721—42no—
64C2×#11924746C2312yes—
65C8×D149—42no—
66C4⋊Dic149—21no—
67C4⋊Dic149C2311yescharacteristic
68C4⋊Dic149C2312yes—
69#14558715—21no—
70C22⋊Dic149—21no—
71C22⋊Dic149—22no—
72C22⋊Dic149—22no—
73#14558713—21no—
74#14558713—21no—
75C24×C149—21no—
76C2×D4×C149—21no—
77C2×D4×C149—21no—
78C2×D4×C149—42no—
79C2×D4×C149C2312yes—
80C2×D4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82D8×C149—42no—
83C2×C8×C149C2312yes—
84C4⋊C4×C149C2311yescharacteristic
85C22⋊C4×C149—21no—
86C22×D149—21no—
87C22×D149—41no—
88C22×D149—41no—
89C22×D149—42no—
90C22×D149—42no—
91C22×D149—42no—
92C22×D149D814yescomplemented
93C22×D149C2×D411yescharacteristic
94C22×D149C2×D411yescharacteristic
95D596—22no—
96D596—42no—
97C22⋊D149—42no—
98C22⋊D149—42no—
99C22⋊D149—42no—
100C22⋊D149—44no—
101C22⋊D149—44no—
102C2×Dic149—21no—
103C2×Dic149—22no—
104C2×Dic149—41no—
105C2×Dic149—42no—
106C2×Dic149C2×D411yescharacteristic
107C2×Dic149C2×D411yescharacteristic
108C4×D149—22no—
109C4×D149—22no—
110C4×D149—41no—
111C4×D149—41no—
112C4×D149—42no—
113#11924746—22no—
114C23×C149—21no—
115C23×C149—22no—
116C23×C149—42no—
117C23×C149—42no—
118C23×C149—42no—
119C23×C149C2×D411yescharacteristic
120D4×C149—22no—
121D4×C149—22no—
122D4×C149—22no—
123D4×C149—42no—
124D4×C149—42no—
125C2×C4×C149—22no—
126C2×C4×C149—21no—
127C2×C4×C149C2×D411yescharacteristic
128C2×C4×C149C2411yescharacteristic
129C8×C149—22no—
130C22×C149—21no—
131C22×C149—21no—
132C22×C149—42no—
133C22×C149—41no—
134C22×C149—41no—
135C22×C149—42no—
136C22×C149—42no—
137C22×C149—41no—
138C22×C149—84no—
139C22×C149C2×D812yes—
140C22×C149C22×D411yescharacteristic
141C2×D149—21no—
142C2×D149—21no—
143C2×D149—21no—
144C2×D149—21no—
145C2×D149—44no—
146C2×D149—41no—
147C2×D149—41no—
148C2×D149—41no—
149C2×D149—84no—
150C2×D149C2×D812yes—
151C2×D149C2×D812yes—
152C4×C149—21no—
153C4×C149—41no—
154C4×C149H(5,𝔽2)12yes—
155Dic149—21no—
156Dic149—21no—
157Dic149—41no—
158Dic149—42no—
159C2×C149—22no—
160C2×C149—81no—
161C2×C149—82no—
162C2×C149#53411yescharacteristic
163C2×C149C22×D811yescharacteristic
164C2×C149#57511yescharacteristic
165D149—22no—
166D149—22no—
167D149—81no—
168C149#318611yescharacteristic, complemented, Sylow
169#3186—1491nomaximal, Sylow
170C2×#121—1491no—
171C2×#121—1491no—
172#480—1491no—
173#480—1492no—
174#480—1491no—
175#466—1492no—
176#466—1492no—
177#447—1491no—
178#447—1492no—
179#447D14911yescharacteristic, complemented
180C2×C22⋊C8—1491no—
181C22×D4—2981no—
182C22×D4—2981no—
183C22×D4—1491no—
184C22×D4C2×D14911yescharacteristic, complemented
185C23×C4—1491no—
186C2×D8—1492no—
187C2×D8C2×D14912yescomplemented
188C22×C8—1492no—
189#121—2981no—
190#121—2981no—
191#121—2981no—
192#121—2981no—
193#121—1492no—
194#121—1491no—
195#121—1492no—
196#121—1491no—
197#121—1491no—
198#121C2×D14911yescharacteristic
199C2×C4⋊C4—1491no—
200C2×C4⋊C4—1491no—
201C2×C22⋊C4—2981no—
202C2×C22⋊C4—2981no—
203#107—1492no—
204#107—1492no—
205#102—1492no—
206#102—1492no—
207#102—1492no—
208#102C2×D14912yescomplemented
209C22⋊C8—1491no—
210C22⋊C8—1492no—
211C22⋊C8C2×D14911yescharacteristic, complemented
212C24—21no—
213C24—2981no—
214C24—1491no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—2981no—
219C2×D4—2981no—
220C2×D4—2982no—
221C2×D4—2982no—
222C2×D4—2981no—
223C2×D4—2981no—
224C2×D4—5962no—
225C2×D4—5964no—
226C2×D4—5964no—
227C2×D4—1491no—
228C2×D4C22×D14911yescharacteristic
229C2×D4C22×D14912yes—
230C22×C4—2981no—
231C22×C4—2981no—
232C22×C4—5962no—
233C22×C4—1491no—
234C22×C4—1491no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4C22×D14911yescharacteristic
239D8—42no—
240D8—5962no—
241C2×C8—5962no—
242C2×C8—1492no—
243C2×C8C22×D14912yes—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—1491no—
247C4⋊C4—1492no—
248C4⋊C4C22×D14911yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—2981no—
251C22⋊C4—2981no—
252C22⋊C4—2982no—
253C22⋊C4—2982no—
254C22⋊C4—2981no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—2981no—
261C23—5961no—
262C23—5961no—
263C23—5962no—
264C23—5962no—
265C23—5962no—
266C23—1491no—
267C23—1491no—
268C23—1494no—
269C23D4×D14911yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—2982no—
276D4—5962no—
277D4—5962no—
278D4—5962no—
279D4—5964no—
280D4—5964no—
281D4—5962no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—2982no—
285C2×C4—2982no—
286C2×C4—2981no—
287C2×C4—2982no—
288C2×C4—5961no—
289C2×C4—5961no—
290C2×C4—5962no—
291C2×C4—5961no—
292C2×C4—5962no—
293C2×C4—1491no—
294C2×C4—1491no—
295C2×C4D4×D14911yescharacteristic
296C2×C4C23×D14911yescharacteristic
297C8—22no—
298C8—2982no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—42no—
307C22—84no—
308C22—2981no—
309C22—2981no—
310C22—2981no—
311C22—2981no—
312C22—5964no—
313C22—5961no—
314C22—5961no—
315C22—5961no—
316C22—1492no—
317C22—1492no—
318C22—11924no—
319C22D8×D14912yes—
320C22C2×D4×D14911yescharacteristic
321C4—21no—
322C4—41no—
323C4—2981no—
324C4—2981no—
325C4—5961no—
326C4—5962no—
327C4#1801195612yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—2982no—
332C2—2982no—
333C2—11921no—
334C2#2375018511yescharacteristic
335C2C2×D8×D14911yescharacteristic
336C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3186
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#18011882C2semidirect
2. #121×D149C2semidirect
3. #23749939C2semidirect
4. #23749937C2semidirect
5. #23749936C2semidirect
6. #23749860C2semidirect
7. #23749858C2semidirect
8. #23749759C2semidirect
9. #23749757C2semidirect
10. C22⋊C8×D149C2semidirect
11. #447×C149C2semidirect
14. C2×D4×D149C22semidirect
16. C2×#14558721C22semidirect
17. C2×C8×D149C22semidirect
18. #18011886C22semidirect
25. #18011882C22semidirect
26. #18011882C22semidirect
27. C2×C4⋊Dic149C22semidirect
28. C4⋊C4×D149C22semidirect
31. #18011845C22semidirect
32. #18011844C22semidirect
33. #18011833C22semidirect
34. #18011832C22semidirect
35. #18011832C22semidirect
36. C22⋊#11924746C22semidirect
37. #18011823C22semidirect
38. C22×D4×C149C22semidirect
39. C2×D8×C149C22semidirect
41. #102×C149C22semidirect
42. C22⋊C8×C149C22semidirect
92. C22×D149D8semidirect
168. C149#3186semidirect
179. #447D149semidirect
184. C22×D4C2×D149semidirect
187. C2×D8C2×D149semidirect
208. #102C2×D149semidirect
211. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118822
#121×D1492
#237499392
#237499372
#237499362
#237498602
#237498582
#237497592
#237497572
C22⋊C8×D1492
#447×C1492
#3186149