Finite Group Databasebeta

← #34055548

Subgroups — #34055548

Order 19072.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750206C211yesmaximal, characteristic, complemented
2#23750191C211yesmaximal, characteristic, complemented
3#23749969C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749938C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749870C211yesmaximal, characteristic, complemented
8#23749860C211yesmaximal, characteristic, complemented
9#23749855C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749772C211yesmaximal, characteristic, complemented
12#23749768C211yesmaximal, characteristic, complemented
13#23749760C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#481×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558736C2211yescharacteristic, complemented
18C2×D4×D149C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×D1192C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558719C2211yescharacteristic, complemented
24C2×C8×D149C2211yescharacteristic, complemented
25#18011907—21no—
26#18011897—21no—
27#18011891—21no—
28#18011891C2211yescharacteristic
29#18011891C2211yescharacteristic, complemented
30#18011886—21no—
31#18011886C2211yescharacteristic
32#18011886C2211yescharacteristic
33#18011886C2211yescharacteristic, complemented
34#18011885—21no—
35#18011885—21no—
36#18011885C2211yescharacteristic
37#18011882C2211yescharacteristic
38#18011881—21no—
39#18011879—21no—
40#18011869C2211yescharacteristic
41#18011844C2211yescharacteristic, complemented
42#18011844C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic, complemented
54#106×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558736—41no—
61#14558736—41no—
62#14558736—41no—
63#14558736—41no—
64C2×Dic298D411yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596D411yescharacteristic
70C2×D596C2311yescharacteristic
71C2×D596C2311yescharacteristic
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149D411yescharacteristic
77C2×C22⋊D149D411yescharacteristic
78D4×D149—41no—
79D4×D149—41no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82C2×C4×D149C2311yescharacteristic
83#14558725—41no—
84#14558724—41no—
85D1192—41no—
86#14558721—41no—
87#14558719—41no—
88C2×#11924746C2311yescharacteristic
89C2×#11924746C2311yescharacteristic
90C8×D149—41no—
91C4⋊Dic149—21no—
92C4⋊Dic149—21no—
93C4⋊Dic149C2311yescharacteristic
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102C4×Dic149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106C22×C4×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—81no—
118C22×D149—81no—
119C22×D149C2×D411yescharacteristic
120C22×D149C2×D411yescharacteristic
121Dic298—21no—
122Dic298—21no—
123Dic298—41no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—41no—
129D596—81no—
130D596—81no—
131D596—81no—
132C22⋊D149—41no—
133C22⋊D149—41no—
134C22⋊D149—42no—
135C22⋊D149—42no—
136C22⋊D149—81no—
137C22⋊D149—81no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149C2×D411yescharacteristic
141C2×Dic149C2×D411yescharacteristic
142C4×D149—21no—
143C4×D149—21no—
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—42no—
147#11924746—21no—
148#11924746—21no—
149C23×C149—21no—
150C23×C149C2×D411yescharacteristic
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—81no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—81no—
160C2×C4×C149C2×D411yescharacteristic
161C2×C4×C149C2411yescharacteristic
162C8×C149—21no—
163C8×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149C22×D411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—84no—
184C4×C149—21no—
185C4×C149—41no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149H(5,𝔽2)11yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—21no—
192Dic149—41no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—81no—
196C2×C149#53411yescharacteristic
197C2×C149#57611yescharacteristic
198C2×C149#57711yescharacteristic
199D149—41no—
200D149—41no—
201D149—81no—
202D149—81no—
203C149#319811yescharacteristic, complemented, Sylow
204#3198—1491nomaximal, Sylow
205#537—1491no—
206#535—1491no—
207#485—1491no—
208#482—1491no—
209#481D14911yescharacteristic, complemented
210#480—1491no—
211#469—1491no—
212#468—1491no—
213#466—1491no—
214#465—1491no—
215#450—1491no—
216#449—1491no—
217#449—1491no—
218#447—1491no—
219#408—1491no—
220C2×#41—1491no—
221C2×#41—1491no—
222C22×D4—1491no—
223C2×SD16—1491no—
224C2×SD16—1491no—
225C2×D8—1491no—
226C2×D8—1491no—
227C2×M16—1491no—
228C22×C8—1491no—
229#127—2981no—
230#124—2981no—
231C22⋊Q8—2981no—
232C22⋊Q8—1491no—
233C22⋊Q8—1491no—
234#121—2981no—
235#121—2981no—
236#121—2981no—
237#121—1491no—
238#121—1491no—
239#121—1491no—
240#121—1491no—
241#121—1491no—
242#121C2×D14911yescharacteristic
243#120—2981no—
244#120—2981no—
245#117—1491no—
246C2×C4⋊C4C2×D14911yescharacteristic, complemented
247#107—1491no—
248#107—1491no—
249#106C2×D14911yescharacteristic, complemented
250#106C2×D14911yescharacteristic, complemented
251#103—1491no—
252#103—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102—1491no—
257#102C2×D14911yescharacteristic
258#102C2×D14911yescharacteristic
259C22⋊C8—1491no—
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262C22⋊C8C2×D14911yescharacteristic, complemented
263C24—2981no—
264#41—5961no—
265#41—5961no—
266#41—5961no—
267#41—5961no—
268C2×Q8—1491no—
269C2×Q8—1491no—
270C2×D4—21no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—5961no—
279C2×D4—5961no—
280C2×D4—1491no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4—1491no—
284C2×D4—1491no—
285C2×D4C22×D14911yescharacteristic
286C22×C4—21no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4—1491no—
290C22×C4C22×D14911yescharacteristic
291SD16—5961no—
292SD16—5961no—
293D8—5961no—
294D8—5961no—
295M16—5961no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—1491no—
305C4⋊C4C22×D14911yescharacteristic
306C4⋊C4C22×D14911yescharacteristic
307C4⋊C4C22×D14911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C42—2981no—
318C23—21no—
319C23—2981no—
320C23—2981no—
321C23—5962no—
322C23—1491no—
323C23—1491no—
324C23—11921no—
325C23—11921no—
326C23D4×D14911yescharacteristic
327Q8—2981no—
328Q8—2981no—
329Q8—5961no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—2981no—
334D4—2981no—
335D4—2981no—
336D4—2981no—
337D4—5961no—
338D4—5961no—
339D4—5961no—
340D4—5962no—
341D4—5962no—
342D4—11921no—
343D4—11921no—
344D4—11921no—
345D4—11921no—
346D4—11921no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—5962no—
360C2×C4—1491no—
361C2×C4—1491no—
362C2×C4D4×D14911yescharacteristic
363C2×C4C23×D14911yescharacteristic
364C8—21no—
365C8—21no—
366C8—2981no—
367C8—2981no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—2981no—
375C22—2981no—
376C22—2981no—
377C22—2981no—
378C22—2981no—
379C22—2981no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—11924no—
387C22C2×D4×D14911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—2981no—
393C4—2981no—
394C4—5961no—
395C4—5961no—
396C4#1801195711yescharacteristic
397C4#1801195711yescharacteristic
398C2—41no—
399C2—81no—
400C2—5961no—
401C2—5961no—
402C2—11921no—
403C2—11921no—
404C2#2375018611yescharacteristic
405C2#2375042911yescharacteristic
406C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#481×C149C2
socleC22×C149C22×D4
hypercenter#481D149
hypocenterC149#3198
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23750206C2semidirect
2. #23750191C2semidirect
3. #23749969C2semidirect
4. #23749951C2semidirect
5. #23749938C2semidirect
6. #23749879C2semidirect
7. #23749870C2semidirect
8. #23749860C2semidirect
9. #23749855C2semidirect
10. #23749777C2semidirect
11. #23749772C2semidirect
12. #23749768C2semidirect
13. #23749760C2semidirect
14. #23749590C2semidirect
15. #481×C149C2semidirect
17. C2×#14558736C22semidirect
23. C2×#14558719C22semidirect
24. C2×C8×D149C22semidirect
29. #18011891C22semidirect
33. #18011886C22semidirect
41. #18011844C22semidirect
42. #18011844C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
45. #18011833C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
53. C2×C4⋊C4×C149C22semidirect
54. #106×C149C22semidirect
55. #106×C149C22semidirect
58. C22⋊C8×C149C22semidirect
203. C149#3198semidirect
209. #481D149semidirect
246. C2×C4⋊C4C2×D149semidirect
249. #106C2×D149semidirect
250. #106C2×D149semidirect
262. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502062
#237501912
#237499692
#237499512
#237499382
#237498792
#237498702
#237498602
#237498552
#237497772
#237497722
#237497682
#237497602
#237495902
#481×C1492
#3198149