Finite Group Databasebeta

← #34056623

Subgroups — #34056623

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750346C211yesmaximal, characteristic, complemented
2#23750294C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749908C211yesmaximal, characteristic, complemented
7#23749856C211yesmaximal, characteristic, complemented
8#23749851C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749786C211yesmaximal, characteristic, complemented
11Q16×Dic149C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13#23749621C211yesmaximal, characteristic, complemented
14#23749620C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011910C2211yescharacteristic
21#18011907—21no—
22#18011907C2211yescharacteristic
23#18011906—21no—
24#18011904—21no—
25#18011897—21no—
26#18011887C2211yescharacteristic
27#18011885—21no—
28#18011885C2211yescharacteristic
29#18011882—21no—
30#18011882C2211yescharacteristic
31Q8×Dic149C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic
33#18011876—21no—
34C4×C22⋊D149—21no—
35C4×C22⋊D149C2211yescharacteristic
36#18011870C2211yescharacteristic
37#18011869C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011835C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61C2×Dic298—21no—
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149D411yescharacteristic
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558723—41no—
72C2×#11924746—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C8×D149—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149D411yescharacteristic
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96#41×C149—22no—
97#41×C149—41no—
98C2×Q8×C149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104Q16×C149—22no—
105SD16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22×D149—21no—
112C22×D149C2×D411yescharacteristic
113Dic298—42no—
114D596—21no—
115D596—21no—
116D596—42no—
117C22⋊D149—22no—
118C22⋊D149—42no—
119C22⋊D149—81no—
120C22⋊D149—81no—
121C22⋊D149—81no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—42no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149C2×D411yescharacteristic
135Q8×C149—21no—
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149#4112yes—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—42no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—42no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—22no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176Dic149#13512yes—
177C2×C149—41no—
178C2×C149—81no—
179C2×C149#54611yescharacteristic
180C2×C149C2×#13511yescharacteristic
181C2×C149#57711yescharacteristic
182D149—41no—
183D149—81no—
184C149#330411yescharacteristic, complemented, Sylow
185#3304—1491nomaximal, Sylow
186#556—1491no—
187#550—1491no—
188#486—1491no—
189#482—1491no—
190#482—1491no—
191#475—1491no—
192#465—1491no—
193#465—1491no—
194#460—1491no—
195#452—1491no—
196#452D14911yescharacteristic, complemented
197C4×Q16—1491no—
198C8×D4—1491no—
199#416—1491no—
200#416—1491no—
201C2×#41—1491no—
202C2×#41C2×D14911yescharacteristic
203C2×Q16C2×D14911yescharacteristic
204C2×SD16—1491no—
205C2×SD16C2×D14911yescharacteristic
206C22×C8—1491no—
207C22×C8—1491no—
208C4⋊Q8—1491no—
209#127—2981no—
210#127—1491no—
211#126—2981no—
212#126—2981no—
213#124—2981no—
214C22⋊Q8—1491no—
215C22⋊Q8C2×D14911yescharacteristic
216#121—2981no—
217#121—2981no—
218#121—1491no—
219#121—1491no—
220C4×Q8—2981no—
221C4×Q8—1491no—
222C4×Q8—1491no—
223C4×D4—2981no—
224C4×D4—1491no—
225#117—1491no—
226#117—1491no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103C2×D14911yescharacteristic
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102C2×D14911yescharacteristic
241C22⋊C8—1491no—
242C22⋊C8C2×D14911yescharacteristic
243C4×C8—1491no—
244#41—22no—
245#41—41no—
246#41—2982no—
247#41—5961no—
248C2×Q8—2981no—
249C2×Q8C22×D14911yescharacteristic
250C2×Q8C22×D14911yescharacteristic
251C2×D4—21no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—1491no—
258C2×D4—1491no—
259C2×D4C22×D14911yescharacteristic
260C22×C4—21no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—5961no—
267C2×C8—5961no—
268C2×C8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—1491no—
290C22⋊C4—1491no—
291C42—2981no—
292C42—2981no—
293C42—2981no—
294C42—2981no—
295C42—1491no—
296C23—21no—
297C23—2981no—
298C23—1491no—
299C23D4×D14911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—5962no—
304Q8#1455873512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—2982no—
309D4—2981no—
310D4—2981no—
311D4—5962no—
312D4—5962no—
313D4—11921no—
314D4—11921no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—5962no—
328C2×C4—1491no—
329C2×C4—1491no—
330C2×C4—1491no—
331C2×C4D4×D14911yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—21no—
334C8—21no—
335C8—2981no—
336C8—2981no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—2981no—
344C22—2981no—
345C22—2981no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—2981no—
355C4—2981no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4—1492no—
360C4C2×#1455873511yescharacteristic
361C4#1801195611yescharacteristic
362C2—41no—
363C2—81no—
364C2—5961no—
365C2—11921no—
366C2#2375026211yescharacteristic
367C2#135×D14911yescharacteristic
368C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23750294C2
hypercenter#452D149
hypocenterC149#3304
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23750346C2semidirect
3. #23749970C2semidirect
4. #23749950C2semidirect
5. #23749947C2semidirect
6. #23749908C2semidirect
7. #23749856C2semidirect
8. #23749851C2semidirect
9. #23749823C2semidirect
10. #23749786C2semidirect
11. Q16×Dic149C2semidirect
12. #23749688C2semidirect
13. #23749621C2semidirect
14. #23749620C2semidirect
15. #452×C149C2semidirect
184. C149#3304semidirect
196. #452D149semidirect

Maximal subgroups

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

subgroupindex
#237503462
#237502942
#237499702
#237499502
#237499472
#237499082
#237498562
#237498512
#237498232
#237497862
Q16×Dic1492
#237496882
#237496212
#237496202
#452×C1492
#3304149