Finite Group Databasebeta

← #34054608

Subgroups — #34054608

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750137C211yesmaximal, characteristic
2#117×D149C211yesmaximal, characteristic, complemented
3#23749969C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749962C211yesmaximal, characteristic, complemented
6#23749957C211yesmaximal, characteristic, complemented
7#23749952C211yesmaximal, characteristic, complemented
8#23749951C211yesmaximal, characteristic, complemented
9#23749945C211yesmaximal, characteristic, complemented
10#23749940C211yesmaximal, characteristic, complemented
11#23749661C211yesmaximal, characteristic, complemented
12#23749622C211yesmaximal, characteristic, complemented
13#23749619C211yesmaximal, characteristic, complemented
14C2×#18011823C211yesmaximal, characteristic, complemented
15#427×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011895—21no—
20#18011891C2211yescharacteristic
21#18011891C2211yescharacteristic
22#18011886C2211yescharacteristic
23#18011886C2211yescharacteristic
24#18011881—21no—
25C4×D596—21no—
26C4×D596—21no—
27#18011870C2211yescharacteristic
28#18011869C2211yescharacteristic
29#18011869C2211yescharacteristic
30#18011868—21no—
31#18011867—21no—
32C4⋊C4×D149C2211yescharacteristic
33C4⋊C4×D149C2211yescharacteristic
34C22⋊C4×D149—21no—
35C42×D149—21no—
36#18011844C2211yescharacteristic, complemented
37#18011844C2211yescharacteristic, complemented
38#18011842C2211yescharacteristic, complemented
39#18011842C2211yescharacteristic, complemented
40#18011836C2211yescharacteristic, complemented
41#18011836C2211yescharacteristic, complemented
42#18011834C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C22×C8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#117×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic, complemented
56#107×C149C2211yescharacteristic, complemented
57#106×C149C2211yescharacteristic, complemented
58#106×C149C2211yescharacteristic, complemented
59C23×D149D411yescharacteristic
60#14558736—22no—
61#14558736—22no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C22×Dic149D411yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—22no—
72C2×C4×D149—22no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76C2×C4×D149C2311yescharacteristic
77C2×#11924746—22no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149—21no—
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C22×C4×C149C2311yescharacteristic
97C2×C8×C149—22no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C42×C149—21no—
107C42×C149—21no—
108C22×D149—22no—
109C22×D149—22no—
110C22×D149—21no—
111C22×D149—41no—
112C22×D149C2×D411yescharacteristic
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—21no—
116D596—21no—
117D596—21no—
118D596—42no—
119D596—42no—
120C22⋊D149—42no—
121C2×Dic149—22no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—22no—
128C4×D149—22no—
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—42no—
134C4×D149—42no—
135C4×D149—42no—
136#11924746—21no—
137#11924746—21no—
138C23×C149C2×D411yescharacteristic
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149#4112yes—
145C2×C4×C149#4112yes—
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149#12312yes—
152C22×C149C22×D411yescharacteristic
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—44no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149#13512yes—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149—41no—
167C4×C149#12312yes—
168C4×C149C2×#4111yescharacteristic
169C4×C149C2×#4111yescharacteristic
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173Dic149—41no—
174Dic149—41no—
175C2×C149—22no—
176C2×C149C2×#12311yescharacteristic
177C2×C149C2×#13511yescharacteristic
178C2×C149#57511yescharacteristic
179D149—22no—
180D149—41no—
181D149—81no—
182C149#309111yescharacteristic, complemented, Sylow
183#3091—1491nomaximal, Sylow
184#525—1491no—
185C2×#117—1491no—
186#485—1491no—
187#485—1491no—
188#484—1491no—
189#483—1491no—
190#482—1491no—
191#482—1491no—
192#481—1491no—
193#480—1491no—
194#427—1491no—
195#427D14911yescharacteristic, complemented
196#416—1491no—
197#416—1491no—
198C2×C22⋊C8—1491no—
199C2×#41—1491no—
200C23×C4—1491no—
201C22×C8—1491no—
202C22×C8C2×D14911yescharacteristic
203#123—2981no—
204C22⋊Q8—1491no—
205C22⋊Q8—1491no—
206#121—1491no—
207#121—1491no—
208#120—2981no—
209C4×D4—2981no—
210C4×D4—2981no—
211#117—2981no—
212#117—2981no—
213#117—1491no—
214#117—1491no—
215#117—1491no—
216#117C2×D14911yescharacteristic
217#117C2×D14911yescharacteristic
218C2×C4⋊C4—1491no—
219C2×C4⋊C4—1491no—
220C2×C22⋊C4—2981no—
221C2×C42—2981no—
222#107—1491no—
223#107—1491no—
224#107C2×D14911yescharacteristic, complemented
225#107C2×D14911yescharacteristic, complemented
226#106—1491no—
227#106—1491no—
228#106C2×D14911yescharacteristic, complemented
229#106C2×D14911yescharacteristic, complemented
230#103—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238C22⋊C8—1491no—
239C22⋊C8—1491no—
240C22⋊C8—1491no—
241C22⋊C8—1491no—
242C24—1491no—
243#41—2982no—
244#41—2982no—
245C2×Q8—1491no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—1491no—
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2982no—
253C22×C4—2982no—
254C22×C4—2981no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4—1491no—
258C22×C4—1491no—
259C22×C4—1491no—
260C22×C4C22×D14911yescharacteristic
261C2×C8—22no—
262C2×C8—2982no—
263C2×C8—1491no—
264C2×C8—1491no—
265C2×C8C22×D14911yescharacteristic
266C2×C8C22×D14911yescharacteristic
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4C22×D14911yescharacteristic
274C4⋊C4C22×D14911yescharacteristic
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—21no—
287C42—21no—
288C42—2981no—
289C42—2981no—
290C42—2981no—
291C23—2982no—
292C23—2982no—
293C23—2981no—
294C23—5961no—
295C23—1491no—
296C23—1491no—
297C23D4×D14911yescharacteristic
298Q8—2981no—
299Q8—2981no—
300D4—2981no—
301D4—2981no—
302D4—5962no—
303D4—5962no—
304D4—5962no—
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—2981no—
314C2×C4—2982no—
315C2×C4—2982no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—5962no—
320C2×C4—5962no—
321C2×C4—5962no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4D4×D14911yescharacteristic
325C2×C4#1455873612yes—
326C2×C4#1455873712yes—
327C2×C4C23×D14911yescharacteristic
328C8—21no—
329C8—21no—
330C8—2981no—
331C8—2981no—
332C22—21no—
333C22—21no—
334C22—2981no—
335C22—2981no—
336C22—2981no—
337C22—2981no—
338C22—2981no—
339C22—5964no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22—1492no—
344C22#1801189612yes—
345C22C2×D4×D14911yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2981no—
351C4—2981no—
352C4—5961no—
353C4—5961no—
354C4—5961no—
355C4#1801189612yes—
356C4C2×#1455873611yescharacteristic
357C4C2×#1455873711yescharacteristic
358C2—22no—
359C2—2982no—
360C2—5961no—
361C2—11921no—
362C2C2×#1801189611yescharacteristic
363C2#135×D14911yescharacteristic
364C2#2375042211yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#427×C149C2
socleC22×C149C22×D4
prime radical#23750137C2
hypercenter#427D149
hypocenterC149#3091
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D149C2semidirect
3. #23749969C2semidirect
4. #23749968C2semidirect
5. #23749962C2semidirect
6. #23749957C2semidirect
7. #23749952C2semidirect
8. #23749951C2semidirect
9. #23749945C2semidirect
10. #23749940C2semidirect
11. #23749661C2semidirect
12. #23749622C2semidirect
13. #23749619C2semidirect
14. C2×#18011823C2semidirect
15. #427×C149C2semidirect
36. #18011844C22semidirect
37. #18011844C22semidirect
38. #18011842C22semidirect
39. #18011842C22semidirect
40. #18011836C22semidirect
41. #18011836C22semidirect
42. #18011834C22semidirect
43. #18011834C22semidirect
44. #18011833C22semidirect
45. #18011833C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
55. #107×C149C22semidirect
56. #107×C149C22semidirect
57. #106×C149C22semidirect
58. #106×C149C22semidirect
182. C149#3091semidirect
195. #427D149semidirect
224. #107C2×D149semidirect
225. #107C2×D149semidirect
228. #106C2×D149semidirect
229. #106C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501372
#117×D1492
#237499692
#237499682
#237499622
#237499572
#237499522
#237499512
#237499452
#237499402
#237496612
#237496222
#237496192
C2×#180118232
#427×C1492
#3091149