Finite Group Databasebeta

← #34055783

Subgroups — #34055783

Order 19072.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750242C211yesmaximal, characteristic, complemented
2#23750189C211yesmaximal, characteristic, complemented
3#23750013C211yesmaximal, characteristic, complemented
4#23750006C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749818C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749778C211yesmaximal, characteristic, complemented
13#23749758C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×#14558726C2211yescharacteristic, complemented
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic, complemented
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23#18011910C2211yescharacteristic, complemented
24#18011907C2211yescharacteristic
25#18011907C2211yescharacteristic
26#18011904—21no—
27#18011900C2211yescharacteristic
28#18011900C2211yescharacteristic
29#18011898—21no—
30#18011898C2211yescharacteristic, complemented
31#18011892—21no—
32#18011890C2211yescharacteristic
33#18011888—21no—
34#18011885—21no—
35#18011885—21no—
36#18011879—21no—
37#18011879—21no—
38#18011876C2211yescharacteristic, complemented
39D4×Dic149C2211yescharacteristic, complemented
40#18011870C2211yescharacteristic
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic, complemented
54C2×D8×C149C2211yescharacteristic, complemented
55#121×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—41no—
64C2×D596—41no—
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72#14558726—41no—
73#14558725—41no—
74#14558725—41no—
75#14558724—41no—
76#14558721—41no—
77#14558721—41no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149D411yescharacteristic
81C4⋊Dic149D411yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91C22⋊Dic149D411yescharacteristic
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149—21no—
107C22×C4×C149C2311yescharacteristic
108SD16×C149—41no—
109D8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—81no—
118C22×D149—81no—
119Dic298—21no—
120Dic298—21no—
121Dic298—81no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—42no—
127C22⋊D149—81no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C22⋊D149—81no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—81no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149—21no—
142C23×C149C2×D411yescharacteristic
143Q8×C149—21no—
144Q8×C149—21no—
145D4×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149D4×C149—42no—
150D4×C149—81no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—42no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149C22×D411yescharacteristic
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—84no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149H(5,𝔽2)11yescharacteristic
181C4×C149H(5,𝔽2)11yescharacteristic
182Dic149—21no—
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149—81no—
191C2×C149#53511yescharacteristic
192C2×C149#57611yescharacteristic
193C2×C149#57711yescharacteristic
194D149—81no—
195D149—81no—
196C149#322411yescharacteristic, complemented, Sylow
197#3224—1491nomaximal, Sylow
198#542—1491no—
199#535—1491no—
200#496—1491no—
201#495—1491no—
202#489—1491no—
203#486—1491no—
204#464—1491no—
205#463—1491no—
206#460—1491no—
207#459—1491no—
208#452—1491no—
209#450—1491no—
210#449D14911yescharacteristic, complemented
211#447—1491no—
212#433—1491no—
213C2×#41C2×D14911yescharacteristic
214C22×D4—1491no—
215C2×Q16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16C2×D14911yescharacteristic, complemented
220C2×D8—1491no—
221C2×D8—1491no—
222C2×D8C2×D14911yescharacteristic, complemented
223C4⋊Q8—1491no—
224#127—1491no—
225#127—1491no—
226#126—2981no—
227#124—2981no—
228#124—1491no—
229#124—1491no—
230#124—1491no—
231#123—2981no—
232C22⋊Q8—2981no—
233C22⋊Q8—1491no—
234#121—2981no—
235#121—2981no—
236#121C2×D14911yescharacteristic
237#120—2981no—
238#120—2981no—
239C4×Q8—1491no—
240C4×D4—1491no—
241#117—1491no—
242C4⋊C8—1491no—
243C4⋊C8—1491no—
244#103—1491no—
245#103C2×D14911yescharacteristic, complemented
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102C2×D14911yescharacteristic, complemented
252C22⋊C8—1491no—
253C22⋊C8C2×D14911yescharacteristic
254#97—1491no—
255C4×C8—1491no—
256C24—2981no—
257#41—41no—
258#41—41no—
259C2×Q8—2981no—
260C2×Q8—1491no—
261C2×Q8C22×D14911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—5961no—
270C2×D4—5961no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4C22×D14911yescharacteristic
274C2×D4C22×D14911yescharacteristic
275C22×C4—21no—
276C22×C4—2981no—
277C22×C4C22×D14911yescharacteristic
278Q16—5961no—
279SD16—41no—
280SD16—5961no—
281SD16—5961no—
282SD16—5961no—
283D8—41no—
284D8—5961no—
285D8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8C22×D14911yescharacteristic
289C2×C8C22×D14911yescharacteristic
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—1491no—
294C4⋊C4—1491no—
295C4⋊C4—1491no—
296C4⋊C4C22×D14911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C42—2981no—
309C42—1491no—
310C42—1491no—
311C23—21no—
312C23—21no—
313C23—2981no—
314C23—2981no—
315C23—5962no—
316C23—11921no—
317C23—11921no—
318C23D4×D14911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2981no—
322Q8—2981no—
323Q8—11921no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—2981no—
331D4—2981no—
332D4—2981no—
333D4—2981no—
334D4—5962no—
335D4—11921no—
336D4—11921no—
337D4—11921no—
338D4—11921no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—11921no—
351C2×C4D4×D14911yescharacteristic
352C2×C4C23×D14911yescharacteristic
353C8—21no—
354C8—21no—
355C8—2981no—
356C8—2981no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—11924no—
373C22C2×D4×D14911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—2981no—
378C4—2981no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—11921no—
389C2—11921no—
390C2#2375019011yescharacteristic
391C2#2375042911yescharacteristic
392C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3224
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750242C2semidirect
2. #23750189C2semidirect
3. #23750013C2semidirect
4. #23750006C2semidirect
5. #23749986C2semidirect
6. #23749970C2semidirect
7. #23749850C2semidirect
8. #23749842C2semidirect
9. #23749824C2semidirect
10. #23749818C2semidirect
11. #23749787C2semidirect
12. #23749778C2semidirect
13. #23749758C2semidirect
14. #23749683C2semidirect
15. #449×C149C2semidirect
17. C2×#14558726C22semidirect
20. C2×#14558724C22semidirect
23. #18011910C22semidirect
30. #18011898C22semidirect
38. #18011876C22semidirect
39. D4×Dic149C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011835C22semidirect
46. #18011832C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
53. C2×SD16×C149C22semidirect
54. C2×D8×C149C22semidirect
56. #103×C149C22semidirect
57. #102×C149C22semidirect
196. C149#3224semidirect
210. #449D149semidirect
219. C2×SD16C2×D149semidirect
222. C2×D8C2×D149semidirect
245. #103C2×D149semidirect
251. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502422
#237501892
#237500132
#237500062
#237499862
#237499702
#237498502
#237498422
#237498242
#237498182
#237497872
#237497782
#237497582
#237496832
#449×C1492
#3224149