Finite Group Databasebeta

← #34055785

Subgroups — #34055785

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#23750012C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749984C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749822C211yesmaximal, characteristic, complemented
9#23749817C211yesmaximal, characteristic, complemented
10#23749787C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749759C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#535×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic, complemented
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic, complemented
20C2×#14558723C2211yescharacteristic, complemented
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558721C2211yescharacteristic, complemented
24#18011911C2211yescharacteristic, complemented
25#18011906—21no—
26#18011899C2211yescharacteristic, complemented
27#18011897—21no—
28#18011893—21no—
29#18011890C2211yescharacteristic
30#18011889—21no—
31#18011885C2211yescharacteristic
32C4×Dic298C2211yescharacteristic, complemented
33C4×D596C2211yescharacteristic, complemented
34C4⋊#11924746C2211yescharacteristic, complemented
35C4⋊#11924746C2211yescharacteristic, complemented
36#18011835C2211yescharacteristic, complemented
37#18011835C2211yescharacteristic, complemented
38#18011832C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic, complemented
43#18011832C2211yescharacteristic, complemented
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48C2×#41×C149C2211yescharacteristic
49C22×D4×C149C2211yescharacteristic
50#127×C149C2211yescharacteristic
51#127×C149C2211yescharacteristic
52#124×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#121×C149—21no—
55#121×C149—21no—
56#120×C149—21no—
57#120×C149—21no—
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149—21no—
64#14558726—41no—
65#14558724—41no—
66#14558724—41no—
67#14558724—41no—
68#14558723—41no—
69#14558721—41no—
70#14558721—41no—
71#14558721—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81C22⋊Dic149—21no—
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86C4×Dic149—21no—
87C24×C149—21no—
88#41×C149—41no—
89#41×C149—41no—
90C2×Q8×C149C2311yescharacteristic
91C2×D4×C149—21no—
92C2×D4×C149—21no—
93C2×D4×C149—21no—
94C2×D4×C149—21no—
95C2×D4×C149—21no—
96C2×D4×C149—21no—
97C2×D4×C149—41no—
98C2×D4×C149—41no—
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104C4⋊C4×C149D411yescharacteristic
105C4⋊C4×C149D411yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C22⋊C4×C149D411yescharacteristic
111C22⋊C4×C149D411yescharacteristic
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—81no—
118D596—21no—
119D596—21no—
120C22⋊D149—81no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127#11924746—21no—
128#11924746—21no—
129C23×C149—21no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—42no—
133C23×C149—81no—
134C23×C149—81no—
135C23×C149C2×D411yescharacteristic
136Q8×C149—21no—
137Q8×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—21no—
143D4×C149—21no—
144D4×C149—42no—
145D4×C149—42no—
146D4×C149—81no—
147D4×C149—81no—
148D4×C149—81no—
149D4×C149—81no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—42no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2×D411yescharacteristic
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2411yescharacteristic
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×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—84no—
173C22×C149C22×D411yescharacteristic
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—41no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149—81no—
191C2×C149—81no—
192C2×C149#53511yescharacteristic
193C2×C149#57611yescharacteristic
194C2×C149#57711yescharacteristic
195D149—81no—
196C149#322411yescharacteristic, complemented, Sylow
197#3224—1491nomaximal, Sylow
198#542—1491no—
199#535D14911yescharacteristic, complemented
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#433—1491no—
213C2×#41C2×D14911yescharacteristic
214C22×D4C2×D14911yescharacteristic
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#127C2×D14911yescharacteristic
225#127C2×D14911yescharacteristic
226#126—2981no—
227#124—2981no—
228#124—1491no—
229#124C2×D14911yescharacteristic
230#124C2×D14911yescharacteristic
231#123—2981no—
232C22⋊Q8—2981no—
233C22⋊Q8—1491no—
234#121—21no—
235#121—21no—
236#121—1491no—
237#120—21no—
238#120—21no—
239C4×Q8—1491no—
240C4×D4—1491no—
241#117C2×D14911yescharacteristic
242C4⋊C8—1491no—
243C4⋊C8—1491no—
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⋊C8—1491no—
253C22⋊C8—1491no—
254#97—1491no—
255C4×C8—1491no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—2981no—
260C2×Q8—1491no—
261C2×Q8C22×D14911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—2981no—
271C2×D4—1491no—
272C2×D4C22×D14911yescharacteristic
273C2×D4C22×D14911yescharacteristic
274C2×D4C22×D14911yescharacteristic
275C22×C4—21no—
276C22×C4—2981no—
277C22×C4C22×D14911yescharacteristic
278Q16—5961no—
279SD16—5961no—
280SD16—5961no—
281SD16—5961no—
282SD16—5961no—
283D8—5961no—
284D8—5961no—
285D8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—1491no—
294C4⋊C4—1491no—
295C4⋊C4C22⋊D14911yescharacteristic
296C4⋊C4C22⋊D14911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4C22⋊D14911yescharacteristic
307C22⋊C4C22⋊D14911yescharacteristic
308C42—2981no—
309C42C22×D14911yescharacteristic
310C42C22×D14911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—2981no—
318C23C2×C22⋊D14911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2981no—
322Q8—2981no—
323Q8—11921no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—2981no—
337D4—2981no—
338D4—11921no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—11921no—
347C2×C4C2×C22⋊D14911yescharacteristic
348C2×C4C2×C22⋊D14911yescharacteristic
349C2×C4C2×C22⋊D14911yescharacteristic
350C2×C4C2×C22⋊D14911yescharacteristic
351C2×C4C2×C22⋊D14911yescharacteristic
352C2×C4C23×D14911yescharacteristic
353C8—2981no—
354C8—2981no—
355C8—2981no—
356C8—2981no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22C22×C22⋊D14911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—11921no—
390C2#2375019211yescharacteristic
391C2#2375042811yescharacteristic
392C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#535×C149C2
socleC22×C149C22×D4
hypercenter#535D149
hypocenterC149#3224
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23750246C2semidirect
2. #23750012C2semidirect
3. #23750007C2semidirect
4. #23749984C2semidirect
5. #23749971C2semidirect
6. #23749844C2semidirect
7. #23749837C2semidirect
8. #23749822C2semidirect
9. #23749817C2semidirect
10. #23749787C2semidirect
11. #23749776C2semidirect
12. #23749770C2semidirect
13. #23749759C2semidirect
14. #23749686C2semidirect
15. #535×C149C2semidirect
16. C2×#14558726C22semidirect
19. C2×#14558724C22semidirect
20. C2×#14558723C22semidirect
23. C2×#14558721C22semidirect
24. #18011911C22semidirect
26. #18011899C22semidirect
32. C4×Dic298C22semidirect
33. C4×D596C22semidirect
34. C4⋊#11924746C22semidirect
35. C4⋊#11924746C22semidirect
36. #18011835C22semidirect
37. #18011835C22semidirect
42. #18011832C22semidirect
43. #18011832C22semidirect
46. #18011822C22semidirect
47. C4×#11924746C22semidirect
196. C149#3224semidirect
199. #535D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237500122
#237500072
#237499842
#237499712
#237498442
#237498372
#237498222
#237498172
#237497872
#237497762
#237497702
#237497592
#237496862
#535×C1492
#3224149