Finite Group Databasebeta

← #34056580

Subgroups — #34056580

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750315C211yesmaximal, characteristic, complemented
2#23750284C211yesmaximal, characteristic
3#23749980C211yesmaximal, characteristic, complemented
4#23749967C211yesmaximal, characteristic, complemented
5#23749939C211yesmaximal, characteristic, complemented
6#23749933C211yesmaximal, characteristic, complemented
7#23749866C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749848C211yesmaximal, characteristic, complemented
10#23749789C211yesmaximal, characteristic, complemented
11#23749783C211yesmaximal, characteristic, complemented
12C4×Dic596C211yesmaximal, characteristic, complemented
13#23749622C211yesmaximal, characteristic, complemented
14C2×#18011836C211yesmaximal, characteristic, complemented
15C8×D4×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21#18011904—21no—
22#18011903C2211yescharacteristic
23#18011901—21no—
24#18011899C2211yescharacteristic
25#18011897—21no—
26#18011892—21no—
27#18011890C2211yescharacteristic
28#18011890C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011889—21no—
31#18011885C2211yescharacteristic
32#18011883—21no—
33C4×Dic298C2211yescharacteristic
34C4×Dic298C2211yescharacteristic
35#18011871—21no—
36#18011870C2211yescharacteristic
37#18011867—21no—
38C2×C4⋊Dic149C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C22×C8×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—41no—
61C2×Dic298—22no—
62C2×Dic298—21no—
63C2×Dic298—41no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73Dic596—22no—
74Dic596—41no—
75#14558725—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C2×D4×C149D411yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149—41no—
102C2×C8×C149—41no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149D411yescharacteristic
108C22⋊C4×C149D411yescharacteristic
109C22⋊C4×C149D411yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—42no—
118Dic298#4112yes—
119D596—21no—
120D596—21no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149—42no—
132C4×D149—42no—
133C23×C149C2×D411yescharacteristic
134C23×C149C2×D411yescharacteristic
135D4×C149—22no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2411yescharacteristic
145C8×C149—21no—
146C8×C149—21no—
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149#13512yes—
155C22×C149C22×D411yescharacteristic
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149C2×#4111yescharacteristic
164C4×C149H(5,𝔽2)11yescharacteristic
165Dic149—22no—
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149—22no—
173C2×C149—41no—
174C2×C149#54611yescharacteristic
175C2×C149C2×#13511yescharacteristic
176C2×C149#57811yescharacteristic
177D149—81no—
178C149#330011yescharacteristic, complemented, Sylow
179#3300—1491nomaximal, Sylow
180#552—1491no—
181#548—1491no—
182#488—1491no—
183#485—1491no—
184#480—1491no—
185#479—1491no—
186#467—1491no—
187#465—1491no—
188#464—1491no—
189#452—1491no—
190#451—1491no—
191C4×Q16—1491no—
192C8×D4D14911yescharacteristic, complemented
193#416—1491no—
194C2×#103—1491no—
195C2×#41—1491no—
196C22×Q8—1491no—
197C2×Q16—1491no—
198C2×Q16—1491no—
199C2×SD16—1491no—
200C22×C8C2×D14911yescharacteristic
201C22×C8C2×D14911yescharacteristic
202#126—2981no—
203#125—2981no—
204#125—1491no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210C22⋊Q8—1491no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—1491no—
214C4×Q8—1491no—
215C4×Q8—1491no—
216C4×D4—2981no—
217C4×D4C2×D14911yescharacteristic
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—1491no—
221#107—1491no—
222#107—1491no—
223#106—1491no—
224C4⋊C8C2×D14911yescharacteristic
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#103—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235C22⋊C8C2×D14911yescharacteristic
236C22⋊C8C2×D14911yescharacteristic
237C4×C8C2×D14911yescharacteristic
238#41—2982no—
239#41—5961no—
240C2×Q8—2982no—
241C2×Q8—2981no—
242C2×Q8—5961no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8—1491no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4D59611yescharacteristic
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4C22×D14911yescharacteristic
254C22×C4C22×D14911yescharacteristic
255Q16—2982no—
256Q16—5961no—
257SD16—5961no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4D59611yescharacteristic
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4D59611yescharacteristic
285C22⋊C4D59611yescharacteristic
286C42—2981no—
287C42—2981no—
288C42—2981no—
289C42C22×D14911yescharacteristic
290C23—2981no—
291C23C2×D59611yescharacteristic
292C23C2×D59611yescharacteristic
293Q8—2981no—
294Q8—2981no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—5962no—
299Q8—1492no—
300D4—22no—
301D4—2981no—
302D4—2981no—
303D4—5962no—
304D4—5962no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—5962no—
317C2×C4—5962no—
318C2×C4—5962no—
319C2×C4C2×D59611yescharacteristic
320C2×C4C2×D59611yescharacteristic
321C2×C4C2×D59611yescharacteristic
322C2×C4C2×D59611yescharacteristic
323C2×C4C23×D14911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22#1801193312yes—
337C22C22×D59611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—2982no—
343C4—5961no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4#41×D14911yescharacteristic
350C4#1801195611yescharacteristic
351C2—22no—
352C2—41no—
353C2—11921no—
354C2#2375027011yescharacteristic
355C2C2×#1801193311yescharacteristic
356C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC8×D4×C149C2
socleC22×C149C22×D4
prime radical#23750284C2
hypercenterC8×D4D149
hypocenterC149#3300
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23750315C2semidirect
3. #23749980C2semidirect
4. #23749967C2semidirect
5. #23749939C2semidirect
6. #23749933C2semidirect
7. #23749866C2semidirect
8. #23749854C2semidirect
9. #23749848C2semidirect
10. #23749789C2semidirect
11. #23749783C2semidirect
12. C4×Dic596C2semidirect
13. #23749622C2semidirect
14. C2×#18011836C2semidirect
15. C8×D4×C149C2semidirect
178. C149#3300semidirect
192. C8×D4D149semidirect

Maximal subgroups

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

subgroupindex
#237503152
#237502842
#237499802
#237499672
#237499392
#237499332
#237498662
#237498542
#237498482
#237497892
#237497832
C4×Dic5962
#237496222
C2×#180118362
C8×D4×C1492
#3300149