Finite Group Databasebeta

← #34056898

Subgroups — #34056898

Order 19072.

414 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#23750322C211yesmaximal, characteristic, complemented
2#23750266C211yesmaximal, characteristic, complemented
3#23749981C211yesmaximal, characteristic, complemented
4#23749963C211yesmaximal, characteristic, complemented
5#23749940C211yesmaximal, characteristic, complemented
6#23749928C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749769C211yesmaximal, characteristic, complemented
10#23749758C211yesmaximal, characteristic, complemented
11#23749705C211yesmaximal, characteristic, complemented
12#23749701C211yesmaximal, characteristic, complemented
13#23749631C211yesmaximal, characteristic, complemented
14#23749625C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21#18011904—21no—
22#18011902C2211yescharacteristic, complemented
23#18011900C2211yescharacteristic
24#18011896—21no—
25#18011892—21no—
26#18011886—21no—
27#18011886C2211yescharacteristic
28#18011882—21no—
29#18011882C2211yescharacteristic, complemented
30#18011881—21no—
31D4×Dic149C2211yescharacteristic, complemented
32#18011873C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34#18011871—21no—
35#18011870C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic, complemented
37C22⋊C4×D149—21no—
38#18011844C2211yescharacteristic, complemented
39#18011842C2211yescharacteristic, complemented
40#18011840C2211yescharacteristic, complemented
41#18011835C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic, complemented
53C2×M16×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#107×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558737—22no—
61#14558737—41no—
62C2×D596—22no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—41no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149D411yescharacteristic
71C22×Dic149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76#14558721—22no—
77#14558721—41no—
78#14558719—41no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715D411yescharacteristic
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713D411yescharacteristic
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149—21no—
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149C2311yescharacteristic
102SD16×C149—41no—
103M16×C149—41no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149—21no—
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117D596—21no—
118D596—21no—
119D596—21no—
120D596—42no—
121D596—42no—
122D596—81no—
123D596#4112yes—
124C22⋊D149—41no—
125C22⋊D149—42no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—81no—
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—42no—
135C4×D149—81no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140C23×C149C2×D411yescharacteristic
141Q8×C149—21no—
142Q8×C149—21no—
143D4×C149—21no—
144D4×C149—21no—
145D4×C149—81no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149C22×D411yescharacteristic
162C2×D149—21no—
163C2×D149—22no—
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—84no—
172C4×C149—21no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149C2×#4111yescharacteristic
177C4×C149H(5,𝔽2)11yescharacteristic
178Dic149—21no—
179Dic149—21no—
180Dic149—21no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—41no—
184C2×C149—81no—
185C2×C149#54611yescharacteristic
186C2×C149#57511yescharacteristic
187C2×C149#57611yescharacteristic
188D149—41no—
189D149—42no—
190D149—81no—
191C149#332211yescharacteristic, complemented, Sylow
192#3322—1491nomaximal, Sylow
193#553—1491no—
194#546—1491no—
195#488—1491no—
196#485—1491no—
197#480—1491no—
198#478—1491no—
199#469—1491no—
200#468D14911yescharacteristic, complemented
201#463—1491no—
202#449—1491no—
203#447—1491no—
204C4×D8—1491no—
205#436—1491no—
206#418—1491no—
207#417—1491no—
208C2×#41—1491no—
209C22×D4—1491no—
210C2×SD16C2×D14911yescharacteristic, complemented
211C2×D8—1491no—
212C2×D8—1491no—
213C2×M16—1491no—
214C2×M16C2×D14911yescharacteristic
215#126—2981no—
216#125—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8C2×D14911yescharacteristic
221#121—2981no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121C2×D14911yescharacteristic
226#120—2981no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4—1491no—
230C4×D4—1491no—
231#117—1491no—
232C2×C4⋊C4—1491no—
233C2×C22⋊C4—2981no—
234#107—1491no—
235#107C2×D14911yescharacteristic, complemented
236#106—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103C2×D14911yescharacteristic, complemented
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102C2×D14911yescharacteristic, complemented
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C4×C8—1491no—
251C24—2981no—
252#41—2982no—
253#41—5961no—
254C2×Q8C22×D14911yescharacteristic
255C2×D4—21no—
256C2×D4—2982no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—5961no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4C22×D14911yescharacteristic
266C22×C4—2981no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—1491no—
271C22×C4C22×D14911yescharacteristic
272SD16—41no—
273D8—2982no—
274D8—5961no—
275M16—41no—
276M16—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4—1491no—
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C42—2981no—
302C42—1491no—
303C23—21no—
304C23—2981no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—1491no—
309C23—11921no—
310C23D4×D14911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—2981no—
317D4—2981no—
318D4—2981no—
319D4—5962no—
320D4—5962no—
321D4—5961no—
322D4—5962no—
323D4—1492no—
324D4—11921no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—5962no—
335C2×C4—1491no—
336C2×C4—1491no—
337C2×C4—1491no—
338C2×C4—11921no—
339C2×C4—11921no—
340C2×C4—11921no—
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2981no—
354C22—2981no—
355C22—2981no—
356C22—2982no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—5961no—
362C22—11924no—
363C22C2×D4×D14911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2981no—
369C4—2981no—
370C4—2981no—
371C4—5961no—
372C4—5961no—
373C4#41×D14911yescharacteristic
374C4#1801195611yescharacteristic
375C2—41no—
376C2—81no—
377C2—5961no—
378C2—5962no—
379C2—11921no—
380C2#2375026411yescharacteristic
381C2#2375042411yescharacteristic
382C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
hypercenter#468D149
hypocenterC149#3322
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #23750322C2semidirect
2. #23750266C2semidirect
3. #23749981C2semidirect
4. #23749963C2semidirect
5. #23749940C2semidirect
6. #23749928C2semidirect
7. #23749877C2semidirect
8. #23749842C2semidirect
9. #23749769C2semidirect
10. #23749758C2semidirect
11. #23749705C2semidirect
12. #23749701C2semidirect
13. #23749631C2semidirect
14. #23749625C2semidirect
15. #468×C149C2semidirect
20. C2×#14558719C22semidirect
22. #18011902C22semidirect
29. #18011882C22semidirect
31. D4×Dic149C22semidirect
36. C4⋊C4×D149C22semidirect
38. #18011844C22semidirect
39. #18011842C22semidirect
40. #18011840C22semidirect
41. #18011835C22semidirect
42. #18011835C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
52. C2×SD16×C149C22semidirect
56. #107×C149C22semidirect
57. #103×C149C22semidirect
58. #102×C149C22semidirect
191. C149#3322semidirect
200. #468D149semidirect
210. C2×SD16C2×D149semidirect
235. #107C2×D149semidirect
240. #103C2×D149semidirect
247. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503222
#237502662
#237499812
#237499632
#237499402
#237499282
#237498772
#237498422
#237497692
#237497582
#237497052
#237497012
#237496312
#237496252
#468×C1492
#3322149