Finite Group Databasebeta

← #34055787

Subgroups — #34055787

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#23750246C211yesmaximal, characteristic, complemented
2#23750194C211yesmaximal, characteristic, complemented
3#23750014C211yesmaximal, characteristic, complemented
4#23750009C211yesmaximal, characteristic, complemented
5#23749985C211yesmaximal, characteristic, complemented
6#23749972C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749826C211yesmaximal, characteristic, complemented
10#23749821C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic, complemented
12#23749778C211yesmaximal, characteristic, complemented
13#23749772C211yesmaximal, characteristic, complemented
14#23749761C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×Dic596C2211yescharacteristic, complemented
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic, complemented
22C2×#14558725C2211yescharacteristic, complemented
23C2×D1192C2211yescharacteristic
24C2×D1192C2211yescharacteristic
25C2×D1192C2211yescharacteristic, complemented
26#18011911C2211yescharacteristic, complemented
27#18011908C2211yescharacteristic
28#18011908C2211yescharacteristic
29#18011906—21no—
30#18011899C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011899C2211yescharacteristic, complemented
33#18011897—21no—
34#18011893—21no—
35#18011890C2211yescharacteristic
36#18011889—21no—
37#18011886—21no—
38#18011886—21no—
39#18011885C2211yescharacteristic
40#18011881—21no—
41#18011881—21no—
42C4×Dic298C2211yescharacteristic, complemented
43C4×D596C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011836C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic, complemented
51#18011833C2211yescharacteristic, complemented
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic, complemented
54C4⋊C8×C149C2211yescharacteristic, complemented
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558736—41no—
61#14558736—41no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596—41no—
71C2×D596—41no—
72C2×D596C2311yescharacteristic
73C2×D596C2311yescharacteristic
74C2×D596C2311yescharacteristic
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80Dic596—41no—
81#14558725—41no—
82#14558725—41no—
83#14558725—41no—
84#14558725—41no—
85D1192—41no—
86D1192—41no—
87D1192—41no—
88C4⋊Dic149—21no—
89C4⋊Dic149C2311yescharacteristic
90C4⋊Dic149C2311yescharacteristic
91#14558715—21no—
92#14558715—21no—
93C22⋊Dic149—21no—
94#14558713—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—
103C22×C4×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149D411yescharacteristic
109C4⋊C4×C149D411yescharacteristic
110C22⋊C4×C149D411yescharacteristic
111C22⋊C4×C149D411yescharacteristic
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—42no—
119C22×D149—81no—
120C22×D149—81no—
121Dic298—21no—
122Dic298—21no—
123Dic298—21no—
124Dic298—21no—
125Dic298—81no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—21no—
130D596—21no—
131D596—21no—
132D596—21no—
133D596—21no—
134D596—42no—
135D596—81no—
136D596—81no—
137D596—81no—
138D596—81no—
139C22⋊D149—42no—
140C22⋊D149—81no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C4×D149—42no—
146C4×D149—81no—
147C23×C149C2×D411yescharacteristic
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2411yescharacteristic
156C8×C149—21no—
157C8×C149—21no—
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149C22×D411yescharacteristic
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
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—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149H(5,𝔽2)11yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—41no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149#53511yescharacteristic
190C2×C149#57611yescharacteristic
191C2×C149#57711yescharacteristic
192D149—81no—
193D149—81no—
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#449—1491no—
211#447—1491no—
212#433D14911yescharacteristic, complemented
213C2×#41—1491no—
214C22×D4—1491no—
215C2×Q16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×D8—1491no—
221C2×D8—1491no—
222C2×D8—1491no—
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#121—1491no—
237#120—2981no—
238#120—2981no—
239C4×Q8—1491no—
240C4×D4—1491no—
241#117C2×D14911yescharacteristic
242C4⋊C8C2×D14911yescharacteristic, complemented
243C4⋊C8C2×D14911yescharacteristic, complemented
244#103—1491no—
245#103—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252C22⋊C8C2×D14911yescharacteristic
253C22⋊C8C2×D14911yescharacteristic
254#97C2×D14911yescharacteristic, complemented
255C4×C8C2×D14911yescharacteristic, complemented
256C24—2981no—
257#41—5961no—
258#41—5961no—
259C2×Q8—2981no—
260C2×Q8—1491no—
261C2×Q8—1491no—
262C2×D4—2981no—
263C2×D4—2981no—
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×D4—1491no—
274C2×D4—1491no—
275C22×C4—2981no—
276C22×C4—2981no—
277C22×C4C22×D14911yescharacteristic
278Q16—5961no—
279SD16—5961no—
280SD16—5961no—
281SD16—5961no—
282SD16—5961no—
283D8—5961no—
284D8—5961no—
285D8—5961no—
286C2×C8C22×D14911yescharacteristic
287C2×C8C22×D14911yescharacteristic
288C2×C8C22×D14911yescharacteristic
289C2×C8C22×D14911yescharacteristic
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—1491no—
294C4⋊C4—1491no—
295C4⋊C4D59611yescharacteristic
296C4⋊C4D59611yescharacteristic
297C22⋊C4—2981no—
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⋊C4D59611yescharacteristic
307C22⋊C4D59611yescharacteristic
308C42—2981no—
309C42C22×D14911yescharacteristic
310C42C22×D14911yescharacteristic
311C23—2981no—
312C23—2981no—
313C23—2981no—
314C23—2981no—
315C23—5962no—
316C23—11921no—
317C23—11921no—
318C23C2×D59611yescharacteristic
319Q8—2981no—
320Q8—2981no—
321Q8—2981no—
322Q8—2981no—
323Q8—11921no—
324D4—2981no—
325D4—2981no—
326D4—2981no—
327D4—2981no—
328D4—2981no—
329D4—2981no—
330D4—2981no—
331D4—2981no—
332D4—5962no—
333D4—5962no—
334D4—11921no—
335D4—11921no—
336D4—11921no—
337D4—11921no—
338D4—11921no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—5962no—
346C2×C4—11921no—
347C2×C4C2×D59611yescharacteristic
348C2×C4C2×D59611yescharacteristic
349C2×C4C2×D59611yescharacteristic
350C2×C4C2×D59611yescharacteristic
351C2×C4C2×D59611yescharacteristic
352C2×C4C23×D14911yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—5961no—
361C22—5961no—
362C22—5961no—
363C22—5961no—
364C22—5961no—
365C22—5961no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—11924no—
373C22C22×D59611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—5961no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195711yescharacteristic
384C4#1801195711yescharacteristic
385C2—41no—
386C2—11921no—
387C2—11921no—
388C2—11921no—
389C2—11921no—
390C2#2375019411yescharacteristic
391C2#2375043011yescharacteristic
392C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
hypercenter#433D149
hypocenterC149#3224
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750194C2semidirect
3. #23750014C2semidirect
4. #23750009C2semidirect
5. #23749985C2semidirect
6. #23749972C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. #23749826C2semidirect
10. #23749821C2semidirect
11. #23749789C2semidirect
12. #23749778C2semidirect
13. #23749772C2semidirect
14. #23749761C2semidirect
15. #433×C149C2semidirect
18. C2×Dic596C22semidirect
21. C2×#14558725C22semidirect
22. C2×#14558725C22semidirect
25. C2×D1192C22semidirect
26. #18011911C22semidirect
32. #18011899C22semidirect
42. C4×Dic298C22semidirect
43. C4×D596C22semidirect
44. #18011836C22semidirect
45. #18011836C22semidirect
50. #18011833C22semidirect
51. #18011833C22semidirect
53. C4⋊C8×C149C22semidirect
54. C4⋊C8×C149C22semidirect
57. #97×C149C22semidirect
58. C4×C8×C149C22semidirect
196. C149#3224semidirect
212. #433D149semidirect
242. C4⋊C8C2×D149semidirect
243. C4⋊C8C2×D149semidirect
254. #97C2×D149semidirect
255. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237501942
#237500142
#237500092
#237499852
#237499722
#237498482
#237498412
#237498262
#237498212
#237497892
#237497782
#237497722
#237497612
#433×C1492
#3224149