Finite Group Databasebeta

← #34055525

Subgroups — #34055525

Order 19072.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750137C211yesmaximal, characteristic
2C22⋊Q8×D149C211yesmaximal, characteristic, complemented
3#23749966C211yesmaximal, characteristic, complemented
4#23749962C211yesmaximal, characteristic, complemented
5#23749945C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic, complemented
7#23749882C211yesmaximal, characteristic, complemented
8#23749874C211yesmaximal, characteristic, complemented
9#23749872C211yesmaximal, characteristic, complemented
10#23749789C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749782C211yesmaximal, characteristic, complemented
13#23749765C211yesmaximal, characteristic, complemented
14#23749587C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C2×Dic596C2211yescharacteristic, complemented
20C2×#14558726C2211yescharacteristic, complemented
21C2×#14558725C2211yescharacteristic, complemented
22C2×#14558723C2211yescharacteristic, complemented
23C2×#14558719C2211yescharacteristic
24C2×#14558719C2211yescharacteristic
25#18011895—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28#18011891C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011889—21no—
31#18011888—21no—
32#18011887C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011886C2211yescharacteristic
35#18011881—21no—
36C4×D596—21no—
37C4×D596—21no—
38C4⋊C4×D149—21no—
39C4⋊C4×D149C2211yescharacteristic
40C22⋊C4×D149—21no—
41#18011844C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011834C2211yescharacteristic, complemented
46#18011834C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
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×D149D411yescharacteristic
60#14558736—41no—
61#14558736—41no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65Q8×D149—41no—
66Q8×D149—41no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C22×Dic149D411yescharacteristic
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—41no—
76C2×C4×D149—41no—
77C2×C4×D149D411yescharacteristic
78C2×C4×D149D411yescharacteristic
79C2×C4×D149C2311yescharacteristic
80C2×C4×D149C2311yescharacteristic
81Dic596—41no—
82#14558726—41no—
83#14558725—41no—
84#14558723—41no—
85#14558719—41no—
86#14558719—41no—
87C2×#11924746C2311yescharacteristic
88C2×#11924746C2311yescharacteristic
89C4⋊Dic149—21no—
90C4⋊Dic149—21no—
91C4⋊Dic149—21no—
92C4⋊Dic149C2311yescharacteristic
93#14558715—21no—
94#14558715—21no—
95#14558715—21no—
96C22⋊Dic149—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713—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—22no—
115C22×D149—21no—
116C22×D149—41no—
117C22×D149—41no—
118C22×D149C2×D411yescharacteristic
119C22×D149C2×D411yescharacteristic
120Dic298—21no—
121Dic298—21no—
122Dic298—21no—
123Dic298—21no—
124Dic298—42no—
125D596—21no—
126D596—21no—
127D596—42no—
128D596—42no—
129C22⋊D149—42no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—41no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—41no—
141C4×D149—41no—
142C4×D149—42no—
143C4×D149—42no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149C2×D411yescharacteristic
148Q8×C149—21no—
149Q8×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149C22×D411yescharacteristic
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—44no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149#13712yes—
174C4×C149—21no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149—41no—
178C4×C149—41no—
179C4×C149H(5,𝔽2)11yescharacteristic
180C4×C149H(5,𝔽2)11yescharacteristic
181Dic149—21no—
182Dic149—21no—
183Dic149—41no—
184Dic149—41no—
185Dic149—41no—
186C2×C149—41no—
187C2×C149#53411yescharacteristic
188C2×C149C2×#13711yescharacteristic
189C2×C149#57511yescharacteristic
190D149—22no—
191D149—41no—
192D149—81no—
193C149#319611yescharacteristic, complemented, Sylow
194#3196—1491nomaximal, Sylow
195#525—1491no—
196C2×C22⋊Q8—1491no—
197#485—1491no—
198#485D14911yescharacteristic, complemented
199#484—1491no—
200#481—1491no—
201#470—1491no—
202#470—1491no—
203#468—1491no—
204#468—1491no—
205#452—1491no—
206#452—1491no—
207#451—1491no—
208#448—1491no—
209#407—1491no—
210C2×#41—1491no—
211C22×Q8—1491no—
212C23×C4—1491no—
213C2×Q16—1491no—
214C2×Q16—1491no—
215C2×SD16—1491no—
216C2×SD16—1491no—
217C2×M16—1491no—
218C2×M16—1491no—
219#123—2981no—
220C22⋊Q8—2981no—
221C22⋊Q8—2981no—
222C22⋊Q8—1491no—
223C22⋊Q8—1491no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8C2×D14911yescharacteristic
228#121—1491no—
229#121—1491no—
230#120—2981no—
231C4×D4—2981no—
232C4×D4—2981no—
233#117C2×D14911yescharacteristic
234C2×C4⋊C4—2981no—
235C2×C4⋊C4—1491no—
236C2×C22⋊C4—2981no—
237#107—1491no—
238#107C2×D14911yescharacteristic, complemented
239#106—1491no—
240#106C2×D14911yescharacteristic, complemented
241#103—1491no—
242#103—1491no—
243#103—1491no—
244#103—1491no—
245#103C2×D14911yescharacteristic, complemented
246#103C2×D14911yescharacteristic, complemented
247#102—1491no—
248#102—1491no—
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8—1491no—
252C22⋊C8C2×D14911yescharacteristic
253C24—1491no—
254#41—5961no—
255#41—5961no—
256C2×Q8—2981no—
257C2×Q8—5961no—
258C2×Q8—5961no—
259C2×Q8—1491no—
260C2×Q8—1491no—
261C2×Q8C22×D14911yescharacteristic
262C2×D4—2981no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4—1491no—
266C22×C4—2981no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—5961no—
270C22×C4—5961no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4C22×D14911yescharacteristic
277Q16—5961no—
278Q16—5961no—
279SD16—5961no—
280SD16—5961no—
281M16—5961no—
282M16—5961no—
283C2×C8—1491no—
284C2×C8—1491no—
285C2×C8C22×D14911yescharacteristic
286C2×C8C22×D14911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—1491no—
295C4⋊C4C22×D14911yescharacteristic
296C4⋊C4C22×D14911yescharacteristic
297C4⋊C4C22×D14911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C42—21no—
308C23—2982no—
309C23—2981no—
310C23—5961no—
311C23—5961no—
312C23—1491no—
313C23—1491no—
314C23D4×D14911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—2981no—
318Q8—2981no—
319Q8—2981no—
320Q8—2981no—
321Q8—5962no—
322D4—2981no—
323D4—2981no—
324D4—5962no—
325D4—5962no—
326D4—5962no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—5961no—
341C2×C4—5961no—
342C2×C4—5962no—
343C2×C4—5962no—
344C2×C4—5962no—
345C2×C4—5961no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4D4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—2981no—
353C8—2981no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—2981no—
358C22—2981no—
359C22—2981no—
360C22—2981no—
361C22—2981no—
362C22—5964no—
363C22—5961no—
364C22—5961no—
365C22—5961no—
366C22—1492no—
367C22C2×D4×D14911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—2981no—
374C4—2981no—
375C4—5961no—
376C4—5961no—
377C4—5961no—
378C4#1801195711yescharacteristic
379C4#1801195711yescharacteristic
380C2—41no—
381C2—2982no—
382C2—5961no—
383C2—11921no—
384C2#2375018611yescharacteristic
385C2#137×D14911yescharacteristic
386C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radical#23750137C2
hypercenter#485D149
hypocenterC149#3196
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
2. C22⋊Q8×D149C2semidirect
3. #23749966C2semidirect
4. #23749962C2semidirect
5. #23749945C2semidirect
6. #23749884C2semidirect
7. #23749882C2semidirect
8. #23749874C2semidirect
9. #23749872C2semidirect
10. #23749789C2semidirect
11. #23749785C2semidirect
12. #23749782C2semidirect
13. #23749765C2semidirect
14. #23749587C2semidirect
15. #485×C149C2semidirect
19. C2×Dic596C22semidirect
20. C2×#14558726C22semidirect
21. C2×#14558725C22semidirect
22. C2×#14558723C22semidirect
41. #18011844C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
45. #18011834C22semidirect
46. #18011834C22semidirect
47. #18011833C22semidirect
48. #18011831C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
193. C149#3196semidirect
198. #485D149semidirect
238. #107C2×D149semidirect
240. #106C2×D149semidirect
245. #103C2×D149semidirect
246. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501372
C22⋊Q8×D1492
#237499662
#237499622
#237499452
#237498842
#237498822
#237498742
#237498722
#237497892
#237497852
#237497822
#237497652
#237495872
#485×C1492
#3196149