Finite Group Databasebeta

← #34056546

Subgroups — #34056546

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#23750325C211yesmaximal, characteristic, complemented
2#23750270C211yesmaximal, characteristic, complemented
3#23749980C211yesmaximal, characteristic, complemented
4#23749962C211yesmaximal, characteristic, complemented
5#23749952C211yesmaximal, characteristic, complemented
6#23749925C211yesmaximal, characteristic, complemented
7#23749860C211yesmaximal, characteristic, complemented
8#23749853C211yesmaximal, characteristic, complemented
9#23749840C211yesmaximal, characteristic, complemented
10#23749767C211yesmaximal, characteristic, complemented
11#23749757C211yesmaximal, characteristic, complemented
12C8×D596C211yesmaximal, characteristic, complemented
13#23749618C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15C4×D8×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558724C2211yescharacteristic, complemented
19C2×#14558721C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic, complemented
22#18011904—21no—
23#18011903C2211yescharacteristic, complemented
24#18011899C2211yescharacteristic
25#18011895—21no—
26#18011894—21no—
27#18011891C2211yescharacteristic
28#18011886C2211yescharacteristic
29#18011885—21no—
30#18011884—21no—
31#18011882C2211yescharacteristic
32#18011882C2211yescharacteristic, complemented
33#18011881—21no—
34C4×D596C2211yescharacteristic
35C4×C22⋊D149—21no—
36#18011869C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic
38C2×#14558713—21no—
39#18011844C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic, complemented
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic, complemented
55#107×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558735—22no—
61#14558735—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596D411yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70D4×D149—22no—
71D4×D149—41no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75C2×C4×D149C2311yescharacteristic
76#14558724—41no—
77#14558721—41no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C8×D149—41no—
81C8×D149—41no—
82C4⋊Dic149—21no—
83C4⋊Dic149D411yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713D411yescharacteristic
97#14558713D411yescharacteristic
98C4×Dic149—21no—
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102C22×C4×C149—21no—
103D8×C149—22no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—42no—
113C22×D149—42no—
114C22×D149—81no—
115C22×D149C2×D411yescharacteristic
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119D596—22no—
120D596—21no—
121D596—21no—
122D596—81no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—42no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—81no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149—21no—
142D4×C149—21no—
143D4×C149—21no—
144D4×C149—21no—
145D4×C149#4112yes—
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×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—22no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149C22×D411yescharacteristic
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—84no—
171C2×D149#13512yes—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149C2×#4111yescharacteristic
177C4×C149H(5,𝔽2)11yescharacteristic
178Dic149—21no—
179Dic149—21no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—42no—
184C2×C149—81no—
185C2×C149#54611yescharacteristic
186C2×C149C2×#13511yescharacteristic
187C2×C149#57611yescharacteristic
188D149—22no—
189D149—41no—
190D149—81no—
191C149#329711yescharacteristic, complemented, Sylow
192#3297—1491nomaximal, Sylow
193#553—1491no—
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×D8D14911yescharacteristic, complemented
205C8×D4—1491no—
206#416—1491no—
207C2×#102—1491no—
208C2×#41—1491no—
209C22×D4—1491no—
210C2×SD16—1491no—
211C2×D8—1491no—
212C2×D8C2×D14911yescharacteristic
213C22×C8—1491no—
214C22×C8—1491no—
215#126—2981no—
216#125—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8—1491no—
221#121—2981no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121—1491no—
226#120—2981no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4C2×D14911yescharacteristic
230C4×D4C2×D14911yescharacteristic, complemented
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#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102C2×D14911yescharacteristic
247#102C2×D14911yescharacteristic, complemented
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C4×C8C2×D14911yescharacteristic, complemented
251C24—2981no—
252#41—2982no—
253#41—5961no—
254C2×Q8—1491no—
255C2×D4—2981no—
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×D4C22×D14911yescharacteristic
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—1491no—
271C22×C4—1491no—
272SD16—5961no—
273D8—22no—
274D8—5961no—
275C2×C8—5961no—
276C2×C8—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—2981no—
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—
302C42C22×D14911yescharacteristic
303C23—21no—
304C23—21no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—1491no—
309C23—1491no—
310C23—11921no—
311Q8—2981no—
312Q8—2981no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2982no—
317D4—2981no—
318D4—2981no—
319D4—5962no—
320D4—5962no—
321D4—5962no—
322D4—11921no—
323D4—11921no—
324D4#1455873612yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—5962no—
337C2×C4—1491no—
338C2×C4—1491no—
339C2×C4—11921no—
340C2×C4D4×D14911yescharacteristic
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2981no—
354C22—2981no—
355C22—2981no—
356C22—2981no—
357C22—2981no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—1492no—
362C22—11924no—
363C22C2×D4×D14911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—2981no—
369C4—2981no—
370C4—5961no—
371C4—5961no—
372C4—5961no—
373C4C2×#1455873611yescharacteristic
374C4#1801195711yescharacteristic
375C2—42no—
376C2—81no—
377C2—2982no—
378C2—5961no—
379C2—11921no—
380C2#2375027111yescharacteristic
381C2#135×D14911yescharacteristic
382C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3297
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750325C2semidirect
2. #23750270C2semidirect
3. #23749980C2semidirect
4. #23749962C2semidirect
5. #23749952C2semidirect
6. #23749925C2semidirect
7. #23749860C2semidirect
8. #23749853C2semidirect
9. #23749840C2semidirect
10. #23749767C2semidirect
11. #23749757C2semidirect
12. C8×D596C2semidirect
13. #23749618C2semidirect
14. #102×D149C2semidirect
15. C4×D8×C149C2semidirect
18. C2×#14558724C22semidirect
21. C2×C8×D149C22semidirect
23. #18011903C22semidirect
32. #18011882C22semidirect
36. #18011869C22semidirect
39. #18011844C22semidirect
40. #18011842C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011836C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
51. #18011823C22semidirect
54. C4×D4×C149C22semidirect
55. #107×C149C22semidirect
57. #102×C149C22semidirect
58. C4×C8×C149C22semidirect
191. C149#3297semidirect
204. C4×D8D149semidirect
230. C4×D4C2×D149semidirect
235. #107C2×D149semidirect
247. #102C2×D149semidirect
250. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503252
#237502702
#237499802
#237499622
#237499522
#237499252
#237498602
#237498532
#237498402
#237497672
#237497572
C8×D5962
#237496182
#102×D1492
C4×D8×C1492
#3297149