Finite Group Databasebeta

← #34055562

Subgroups — #34055562

Order 19072.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750198C211yesmaximal, characteristic, complemented
2#23750194C211yesmaximal, characteristic
3#23749966C211yesmaximal, characteristic, complemented
4#23749952C211yesmaximal, characteristic, complemented
5#23749951C211yesmaximal, characteristic, complemented
6#23749874C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749857C211yesmaximal, characteristic, complemented
9#23749855C211yesmaximal, characteristic, complemented
10#23749778C211yesmaximal, characteristic, complemented
11#23749775C211yesmaximal, characteristic, complemented
12#23749765C211yesmaximal, characteristic, complemented
13#23749765C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic, complemented
18C22×D596C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558719C2211yescharacteristic, complemented
24C2×C8×D149C2211yescharacteristic, complemented
25#18011910—21no—
26#18011908—21no—
27#18011899—21no—
28#18011897—21no—
29#18011896—21no—
30#18011893—21no—
31#18011891C2211yescharacteristic, complemented
32#18011890C2211yescharacteristic
33#18011887C2211yescharacteristic, complemented
34#18011886C2211yescharacteristic
35#18011886C2211yescharacteristic
36#18011886C2211yescharacteristic
37#18011886C2211yescharacteristic
38#18011881—21no—
39#18011881—21no—
40#18011869C2211yescharacteristic, complemented
41#18011844C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149—21no—
60#14558736—41no—
61#14558736—41no—
62C2×Dic298—21no—
63C2×Dic298D411yescharacteristic
64C2×Dic298C2311yescharacteristic
65Q8×D149—41no—
66Q8×D149—41no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596—21no—
71C2×D596—21no—
72C2×D596—41no—
73C2×D596—41no—
74C2×D596D411yescharacteristic
75C2×D596C2311yescharacteristic
76C2×D596C2311yescharacteristic
77C2×C22⋊D149D411yescharacteristic
78C2×C22⋊D149D411yescharacteristic
79C2×C4×D149—21no—
80C2×C4×D149C2311yescharacteristic
81C2×C4×D149C2311yescharacteristic
82#14558725—41no—
83#14558725—41no—
84#14558723—41no—
85#14558723—41no—
86#14558719—41no—
87C2×#11924746C2311yescharacteristic
88C2×#11924746C2311yescharacteristic
89C8×D149—41no—
90C4⋊Dic149—21no—
91C4⋊Dic149C2311yescharacteristic
92#14558715—21no—
93#14558715—21no—
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×Q8×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×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—
124Dic298—42no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—41no—
130D596—42no—
131D596—81no—
132D596—81no—
133D596—81no—
134D596—81no—
135C22⋊D149—41no—
136C22⋊D149—41no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—21no—
144C4×D149—21no—
145C4×D149—42no—
146#11924746—21no—
147#11924746—21no—
148C23×C149C2×D411yescharacteristic
149Q8×C149—21no—
150Q8×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—84no—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—21no—
186Dic149—21no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—41no—
190C2×C149#53411yescharacteristic
191C2×C149#57711yescharacteristic
192C2×C149#57711yescharacteristic
193D149—41no—
194D149—41no—
195D149—81no—
196D149—81no—
197C149#320011yescharacteristic, complemented, Sylow
198#3200—1491nomaximal, Sylow
199#536—1491no—
200#535—1491no—
201#485—1491no—
202#485D14911yescharacteristic, complemented
203#482—1491no—
204#482—1491no—
205#468—1491no—
206#468—1491no—
207#465—1491no—
208#465—1491no—
209#450—1491no—
210#450—1491no—
211#448—1491no—
212#448—1491no—
213#408—1491no—
214C2×#41—1491no—
215C22×Q8—1491no—
216C22×D4—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×SD16—1491no—
221C2×M16—1491no—
222C22×C8—1491no—
223C4⋊Q8—2981no—
224#127—2981no—
225#124—2981no—
226#124—2981no—
227#123—2981no—
228#123—2981no—
229C22⋊Q8—1491no—
230C22⋊Q8—1491no—
231C22⋊Q8—1491no—
232C22⋊Q8C2×D14911yescharacteristic
233#121—1491no—
234#121—1491no—
235#121—1491no—
236#121—1491no—
237#120—2981no—
238#120—2981no—
239#117—1491no—
240#117C2×D14911yescharacteristic
241#107—1491no—
242#107C2×D14911yescharacteristic, complemented
243#106—1491no—
244#106C2×D14911yescharacteristic, complemented
245#103—1491no—
246#103—1491no—
247#103C2×D14911yescharacteristic, complemented
248#103C2×D14911yescharacteristic, complemented
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8C2×D14911yescharacteristic
257C24—2981no—
258#41—5961no—
259#41—5961no—
260C2×Q8—2981no—
261C2×Q8—5961no—
262C2×Q8—5961no—
263C2×Q8—1491no—
264C2×Q8—1491no—
265C2×Q8C22×D14911yescharacteristic
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—5961no—
272C2×D4—5961no—
273C2×D4—1491no—
274C2×D4—1491no—
275C2×D4—1491no—
276C2×D4—1491no—
277C2×D4—1491no—
278C22×C4—2981no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4C22×D14911yescharacteristic
282SD16—5961no—
283SD16—5961no—
284SD16—5961no—
285SD16—5961no—
286M16—5961no—
287C2×C8—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4C22×D14911yescharacteristic
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C42—21no—
311C42—2981no—
312C23—2981no—
313C23—2981no—
314C23—5962no—
315C23—1491no—
316C23—1491no—
317C23—11921no—
318C23—11921no—
319C23D4×D14911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2981no—
323Q8—2981no—
324Q8—5961no—
325Q8—5962no—
326D4—2981no—
327D4—2981no—
328D4—2981no—
329D4—2981no—
330D4—5961no—
331D4—5962no—
332D4—5961no—
333D4—5961no—
334D4—11921no—
335D4—11921no—
336D4—11921no—
337D4—11921no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—5962no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4D4×D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C8—21no—
356C8—21no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—2981no—
363C22—2981no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22—11924no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2981no—
382C4—2981no—
383C4—5961no—
384C4—5961no—
385C4#1801195711yescharacteristic
386C4#1801195711yescharacteristic
387C2—41no—
388C2—5961no—
389C2—5961no—
390C2—11921no—
391C2—11921no—
392C2#2375018611yescharacteristic
393C2#2375043211yescharacteristic
394C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radical#23750194C2
hypercenter#485D149
hypocenterC149#3200
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23750198C2semidirect
3. #23749966C2semidirect
4. #23749952C2semidirect
5. #23749951C2semidirect
6. #23749874C2semidirect
7. #23749872C2semidirect
8. #23749857C2semidirect
9. #23749855C2semidirect
10. #23749778C2semidirect
11. #23749775C2semidirect
12. #23749765C2semidirect
13. #23749765C2semidirect
14. #23749590C2semidirect
15. #485×C149C2semidirect
17. C2×Q8×D149C22semidirect
23. C2×#14558719C22semidirect
24. C2×C8×D149C22semidirect
31. #18011891C22semidirect
33. #18011887C22semidirect
40. #18011869C22semidirect
41. #18011844C22semidirect
42. #18011842C22semidirect
43. #18011834C22semidirect
44. #18011834C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
197. C149#3200semidirect
202. #485D149semidirect
242. #107C2×D149semidirect
244. #106C2×D149semidirect
247. #103C2×D149semidirect
248. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501982
#237501942
#237499662
#237499522
#237499512
#237498742
#237498722
#237498572
#237498552
#237497782
#237497752
#237497652
#237495902
#485×C1492
#3200149