Finite Group Databasebeta

← #34055657

Subgroups — #34055657

Order 19072.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750160C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic, complemented
3#23750009C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749982C211yesmaximal, characteristic, complemented
6#23749850C211yesmaximal, characteristic, complemented
7#23749846C211yesmaximal, characteristic, complemented
8#23749843C211yesmaximal, characteristic, complemented
9#23749839C211yesmaximal, characteristic, complemented
10#23749782C211yesmaximal, characteristic, complemented
11#23749777C211yesmaximal, characteristic, complemented
12#23749765C211yesmaximal, characteristic, complemented
13#23749760C211yesmaximal, characteristic
14#23749676C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×Dic596C2211yescharacteristic, complemented
19C2×#14558726C2211yescharacteristic, complemented
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic, complemented
22C2×#14558724C2211yescharacteristic
23C2×#14558723C2211yescharacteristic, complemented
24C2×D1192C2211yescharacteristic
25C2×#14558721C2211yescharacteristic
26#18011906—21no—
27#18011900C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011899C2211yescharacteristic, complemented
30#18011898C2211yescharacteristic
31#18011897—21no—
32#18011897—21no—
33#18011896—21no—
34#18011891C2211yescharacteristic
35#18011886C2211yescharacteristic
36#18011876C2211yescharacteristic, complemented
37#18011873—21no—
38#18011873C2211yescharacteristic, complemented
39#18011869—21no—
40C22⋊C4×D149—21no—
41C22⋊C4×D149—21no—
42C42×D149C2211yescharacteristic
43#18011840C2211yescharacteristic, complemented
44#18011840C2211yescharacteristic, complemented
45#18011834C2211yescharacteristic, complemented
46#18011834C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51C4×#11924746C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic, complemented
55#103×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63Q8×D149—41no—
64Q8×D149—41no—
65C2×D596—21no—
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69D4×D149—41no—
70D4×D149—41no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76Dic596—41no—
77#14558726—41no—
78#14558725—41no—
79#14558725—41no—
80#14558724—41no—
81#14558723—41no—
82D1192—41no—
83#14558721—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C4⋊Dic149—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99C4×Dic149—21no—
100C4×Dic149D411yescharacteristic
101C4×Dic149D411yescharacteristic
102C4×Dic149C2311yescharacteristic
103C2×Q8×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149C2×D411yescharacteristic
120Dic298—21no—
121Dic298—21no—
122Dic298—21no—
123Dic298—21no—
124Dic298—42no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—42no—
130C22⋊D149—42no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C4×D149—22no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—41no—
140C4×D149—42no—
141C4×D149—42no—
142#11924746—21no—
143#11924746—21no—
144C23×C149—21no—
145Q8×C149—21no—
146Q8×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—84no—
170C2×D149#13512yes—
171C4×C149—21no—
172C4×C149—21no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149H(5,𝔽2)11yescharacteristic
177C4×C149H(5,𝔽2)11yescharacteristic
178Dic149—21no—
179Dic149—21no—
180Dic149—21no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—81no—
184C2×C149#53511yescharacteristic
185C2×C149C2×#13511yescharacteristic
186C2×C149#57511yescharacteristic
187D149—22no—
188D149—81no—
189D149—81no—
190C149#321111yescharacteristic, complemented, Sylow
191#3211—1491nomaximal, Sylow
192#529—1491no—
193C2×#124—1491no—
194#495—1491no—
195#495—1491no—
196#488—1491no—
197#488D14911yescharacteristic, complemented
198#464—1491no—
199#464—1491no—
200#463—1491no—
201#463—1491no—
202#451—1491no—
203#450—1491no—
204#448—1491no—
205#447—1491no—
206#431—1491no—
207C22×Q8—1491no—
208C22×D4—1491no—
209C2×Q16—1491no—
210C2×Q16—1491no—
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×SD16—1491no—
214C2×SD16—1491no—
215C2×D8—1491no—
216C2×D8—1491no—
217#126—2981no—
218#125C2×D14911yescharacteristic, complemented
219#124—2981no—
220#124—2981no—
221#124—1491no—
222#124—1491no—
223#124—1491no—
224#124—1491no—
225#124C2×D14911yescharacteristic
226#123—2981no—
227C22⋊Q8—1491no—
228#121—1491no—
229C4×Q8—1491no—
230C4×D4—2981no—
231C4×D4—1491no—
232#117—2981no—
233C2×C22⋊C4—2981no—
234C2×C22⋊C4—2981no—
235C2×C42—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103C2×D14911yescharacteristic, complemented
241#103C2×D14911yescharacteristic, complemented
242#102—1491no—
243#102—1491no—
244#102C2×D14911yescharacteristic
245#102C2×D14911yescharacteristic
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C4×C8—1491no—
249C4×C8C2×D14911yescharacteristic, complemented
250C24—2981no—
251C2×Q8—2981no—
252C2×Q8—5961no—
253C2×Q8—5961no—
254C2×Q8—1491no—
255C2×Q8—1491no—
256C2×Q8C22×D14911yescharacteristic
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—5961no—
260C2×D4—5961no—
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4C22×D14911yescharacteristic
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4—1491no—
269Q16—5961no—
270Q16—5961no—
271SD16—5961no—
272SD16—5961no—
273SD16—5961no—
274SD16—5961no—
275D8—5961no—
276D8—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4C22×D14911yescharacteristic
286C4⋊C4C22×D14911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C42—2981no—
301C42—1491no—
302C42—1491no—
303C42—1491no—
304C42C22×D14911yescharacteristic
305C23—21no—
306C23—2981no—
307C23—2981no—
308C23—5962no—
309C23—5962no—
310C23—5962no—
311C23—1491no—
312Q8—21no—
313Q8—21no—
314Q8—2981no—
315Q8—2981no—
316Q8—2981no—
317Q8—2981no—
318Q8—5962no—
319D4—21no—
320D4—21no—
321D4—2981no—
322D4—2981no—
323D4—2981no—
324D4—2981no—
325D4—5962no—
326D4—5962no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2982no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—5961no—
336C2×C4—5962no—
337C2×C4—5962no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4—1491no—
341C2×C4D4×D14911yescharacteristic
342C2×C4D4×D14911yescharacteristic
343C2×C4C23×D14911yescharacteristic
344C8—21no—
345C8—21no—
346C8—2981no—
347C8—2981no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2981no—
352C22—2981no—
353C22—5961no—
354C22—5961no—
355C22—5961no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—1492no—
360C22—11924no—
361C22C2×D4×D14911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—2981no—
368C4—2981no—
369C4—2981no—
370C4—5961no—
371C4—5961no—
372C4#1801195711yescharacteristic
373C4#1801195711yescharacteristic
374C2—81no—
375C2—2982no—
376C2—11921no—
377C2—11921no—
378C2#2375019311yescharacteristic
379C2#135×D14911yescharacteristic
380C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radical#23749760C2
hypercenter#488D149
hypocenterC149#3211
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750160C2semidirect
2. #124×D149C2semidirect
3. #23750009C2semidirect
4. #23750007C2semidirect
5. #23749982C2semidirect
6. #23749850C2semidirect
7. #23749846C2semidirect
8. #23749843C2semidirect
9. #23749839C2semidirect
10. #23749782C2semidirect
11. #23749777C2semidirect
12. #23749765C2semidirect
14. #23749676C2semidirect
15. #488×C149C2semidirect
18. C2×Dic596C22semidirect
19. C2×#14558726C22semidirect
21. C2×#14558725C22semidirect
23. C2×#14558723C22semidirect
29. #18011899C22semidirect
36. #18011876C22semidirect
38. #18011873C22semidirect
43. #18011840C22semidirect
44. #18011840C22semidirect
45. #18011834C22semidirect
46. #18011834C22semidirect
51. C4×#11924746C22semidirect
52. #125×C149C22semidirect
54. #103×C149C22semidirect
55. #103×C149C22semidirect
58. C4×C8×C149C22semidirect
190. C149#3211semidirect
197. #488D149semidirect
218. #125C2×D149semidirect
240. #103C2×D149semidirect
241. #103C2×D149semidirect
249. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501602
#124×D1492
#237500092
#237500072
#237499822
#237498502
#237498462
#237498432
#237498392
#237497822
#237497772
#237497652
#237497602
#237496762
#488×C1492
#3211149