Finite Group Databasebeta

← #34056535

Subgroups — #34056535

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750271C211yesmaximal, characteristic, complemented
2#23749982C211yesmaximal, characteristic, complemented
3#23749960C211yesmaximal, characteristic, complemented
4#23749949C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749859C211yesmaximal, characteristic, complemented
7#23749852C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic, complemented
10#23749758C211yesmaximal, characteristic, complemented
11C4×#14558721C211yesmaximal, characteristic, complemented
12D4×#11924746C211yesmaximal, characteristic, complemented
13#23749619C211yesmaximal, characteristic, complemented
14C2×#18011831C211yesmaximal, characteristic, complemented
15#553×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×#14558724C2211yescharacteristic, complemented
19C2×#14558721C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C22×#11924746C2211yescharacteristic
22C22×#11924746C2211yescharacteristic, complemented
23#18011899C2211yescharacteristic
24#18011896—21no—
25#18011890C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011884—21no—
28#18011879—21no—
29C4×D596C2211yescharacteristic
30C22⋊C4×D149—21no—
31#18011844C2211yescharacteristic, complemented
32#18011844C2211yescharacteristic, complemented
33#18011842C2211yescharacteristic, complemented
34C4⋊#11924746C2211yescharacteristic, complemented
35#18011834C2211yescharacteristic, complemented
36#18011834C2211yescharacteristic, complemented
37#18011834C2211yescharacteristic, complemented
38#18011832C2211yescharacteristic, complemented
39#18011831C2211yescharacteristic
40#18011831C2211yescharacteristic
41#18011831C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48#126×C149—21no—
49#125×C149C2211yescharacteristic, complemented
50#123×C149—21no—
51#121×C149—21no—
52#121×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic, complemented
54C4×D4×C149—21no—
55C4×D4×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic, complemented
57#117×C149C2211yescharacteristic, complemented
58C2×C4⋊C4×C149C2211yescharacteristic
59C23×D149—21no—
60#14558736—22no—
61#14558736—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—41no—
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72#14558724—41no—
73#14558721—22no—
74#14558721—41no—
75C2×#11924746—41no—
76C2×#11924746—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83C22⋊Dic149—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88C2×D4×C149—21no—
89C2×D4×C149—21no—
90C2×D4×C149D411yescharacteristic
91C2×D4×C149C2311yescharacteristic
92C22×C4×C149—21no—
93C22×C4×C149—21no—
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149D411yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149D411yescharacteristic
108C22⋊C4×C149D411yescharacteristic
109C42×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116Dic298—21no—
117Dic298—21no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—42no—
122D596#4112yes—
123C22⋊D149—42no—
124C22⋊D149—81no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C4×D149—42no—
128C4×D149—81no—
129#11924746—21no—
130#11924746—21no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149C2×D411yescharacteristic
135C23×C149C2×D411yescharacteristic
136D4×C149—22no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—42no—
140D4×C149—81no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—81no—
149C2×C4×C149—81no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149#13512yes—
164C22×C149C22×D411yescharacteristic
165C2×D149—22no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—84no—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—21no—
175C4×C149—21no—
176C4×C149—41no—
177C4×C149—41no—
178C4×C149—41no—
179C4×C149C2×#4111yescharacteristic
180C4×C149H(5,𝔽2)11yescharacteristic
181Dic149—41no—
182Dic149—41no—
183C2×C149—22no—
184C2×C149—41no—
185C2×C149—81no—
186C2×C149#54611yescharacteristic
187C2×C149C2×#13511yescharacteristic
188C2×C149#57611yescharacteristic
189D149—42no—
190D149—81no—
191C149#329711yescharacteristic, complemented, Sylow
192#3297—1491nomaximal, Sylow
193#553D14911yescharacteristic, complemented
194#546—1491no—
195#488—1491no—
196#484—1491no—
197#482—1491no—
198#478—1491no—
199#466—1491no—
200#465—1491no—
201#463—1491no—
202#449—1491no—
203#447—1491no—
204C4×D8—1491no—
205C8×D4—1491no—
206#416—1491no—
207C2×#102—1491no—
208C2×#41—1491no—
209C22×D4—1491no—
210C2×SD16—1491no—
211C2×D8—1491no—
212C2×D8—1491no—
213C22×C8—1491no—
214C22×C8—1491no—
215#126—21no—
216#125C2×D14911yescharacteristic, complemented
217#124—1491no—
218#123—21no—
219#123—2981no—
220C22⋊Q8—1491no—
221#121—21no—
222#121—2981no—
223#121—1491no—
224#121C2×D14911yescharacteristic
225#121C2×D14911yescharacteristic, complemented
226#120—2981no—
227C4×D4—21no—
228C4×D4—1491no—
229C4×D4C2×D14911yescharacteristic
230C4×D4C2×D14911yescharacteristic, complemented
231#117C2×D14911yescharacteristic, complemented
232C2×C4⋊C4C2×D14911yescharacteristic
233C2×C22⋊C4—2981no—
234#107—1491no—
235#107—1491no—
236#106—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C4×C8—1491no—
251C24—2981no—
252#41—2982no—
253#41—5961no—
254C2×Q8—1491no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2982no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—5961no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4C22⋊D14911yescharacteristic
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272SD16—5961no—
273D8—2982no—
274D8—5961no—
275C2×C8—5961no—
276C2×C8—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8—1491no—
280C2×C8—1491no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4C22⋊D14911yescharacteristic
287C4⋊C4C22×D14911yescharacteristic
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4C22⋊D14911yescharacteristic
300C22⋊C4C22⋊D14911yescharacteristic
301C42—21no—
302C42C22×D14911yescharacteristic
303C23—21no—
304C23—2981no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—11921no—
309C23C2×C22⋊D14911yescharacteristic
310C23C2×C22⋊D14911yescharacteristic
311Q8—2981no—
312Q8—2981no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—2981no—
319D4—2981no—
320D4—2981no—
321D4—5962no—
322D4—5962no—
323D4—1492no—
324D4—11921no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—5962no—
337C2×C4—11921no—
338C2×C4C2×C22⋊D14911yescharacteristic
339C2×C4C2×C22⋊D14911yescharacteristic
340C2×C4C2×C22⋊D14911yescharacteristic
341C2×C4C2×C22⋊D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—2981no—
344C8—2981no—
345C8—2981no—
346C8—2981no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2982no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—11924no—
362C22#1801193112yes—
363C22C22×C22⋊D14911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—5961no—
372C4—5961no—
373C4#41×D14911yescharacteristic
374C4#1801195711yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—5962no—
379C2—11921no—
380C2#2375026311yescharacteristic
381C2C2×#1801193111yescharacteristic
382C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#553×C149C2
socleC22×C149C22×D4
hypercenter#553D149
hypocenterC149#3297
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. #23750271C2semidirect
2. #23749982C2semidirect
3. #23749960C2semidirect
4. #23749949C2semidirect
5. #23749922C2semidirect
6. #23749859C2semidirect
7. #23749852C2semidirect
8. #23749840C2semidirect
9. #23749768C2semidirect
10. #23749758C2semidirect
11. C4×#14558721C2semidirect
12. D4×#11924746C2semidirect
13. #23749619C2semidirect
14. C2×#18011831C2semidirect
15. #553×C149C2semidirect
18. C2×#14558724C22semidirect
22. C22×#11924746C22semidirect
31. #18011844C22semidirect
32. #18011844C22semidirect
33. #18011842C22semidirect
34. C4⋊#11924746C22semidirect
35. #18011834C22semidirect
36. #18011834C22semidirect
37. #18011834C22semidirect
38. #18011832C22semidirect
46. C22⋊#11924746C22semidirect
47. C4×#11924746C22semidirect
49. #125×C149C22semidirect
53. #121×C149C22semidirect
56. C4×D4×C149C22semidirect
57. #117×C149C22semidirect
191. C149#3297semidirect
193. #553D149semidirect
216. #125C2×D149semidirect
225. #121C2×D149semidirect
230. C4×D4C2×D149semidirect
231. #117C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502712
#237499822
#237499602
#237499492
#237499222
#237498592
#237498522
#237498402
#237497682
#237497582
C4×#145587212
D4×#119247462
#237496192
C2×#180118312
#553×C1492
#3297149