Finite Group Databasebeta

← #34054811

Subgroups — #34054811

Order 19072.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750172C211yesmaximal, characteristic
2C4×Q8×D149C211yesmaximal, characteristic, complemented
3#23749940C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749919C211yesmaximal, characteristic, complemented
6#23749918C211yesmaximal, characteristic, complemented
7#23749824C211yesmaximal, characteristic, complemented
8#23749823C211yesmaximal, characteristic, complemented
9#23749765C211yesmaximal, characteristic, complemented
10#23749762C211yesmaximal, characteristic, complemented
11#23749727C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14#23749680C211yesmaximal, characteristic, complemented
15#440×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×Q8×D149C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011897—21no—
24#18011886C2211yescharacteristic
25#18011884—21no—
26#18011882C2211yescharacteristic
27Q8×Dic149C2211yescharacteristic
28C4×Dic298—21no—
29C4×Dic298C2211yescharacteristic
30#18011876—21no—
31#18011876C2211yescharacteristic
32C4×D596C2211yescharacteristic
33C4×C22⋊D149—21no—
34C4⋊C4×D149—21no—
35C4⋊C4×D149C2211yescharacteristic
36C42×D149—21no—
37C42×D149C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63Q8×D149—22no—
64Q8×D149—22no—
65C2×D596—21no—
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76#14558725—22no—
77#14558724—22no—
78#14558723—22no—
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100SD16×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149—21no—
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—24no—
112Dic298—21no—
113Dic298—42no—
114Dic298#4112yescomplemented
115D596—21no—
116D596—21no—
117D596—42no—
118C22⋊D149—42no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—24no—
128C4×D149—22no—
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—22no—
132C4×D149—42no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149#4112yescomplemented
139D4×C149—21no—
140D4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—42no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C8×C149—21no—
149C8×C149—21no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149C22×D411yescharacteristic
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149AGL(1,ℤ/8)12yes—
160C4×C149—22no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149C2×#4111yescharacteristic
166C4×C149C2×#4111yescharacteristic
167Dic149—22no—
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149#13712yes—
173C2×C149—81no—
174C2×C149#52511yescharacteristic
175C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C149C2×#13711yescharacteristic
177D149—22no—
178D149—81no—
179C149#311211yescharacteristic, complemented, Sylow
180#3112—1491nomaximal, Sylow
181#532—1491no—
182C2×C4×Q8—1491no—
183#480—1491no—
184#480—1491no—
185#477—1491no—
186#477—1491no—
187#460—1491no—
188#460—1491no—
189#448—1491no—
190#448—1491no—
191#440—1491no—
192#440—1491no—
193#440—1491no—
194#440D14911yescharacteristic, complemented
195#432—1491no—
196C2×#41—2981no—
197C22×Q8—1491no—
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×SD16C2×D14911yescharacteristic
202C4⋊Q8—1491no—
203#127—1491no—
204#124—2981no—
205#121—2981no—
206#121—1491no—
207#121—1491no—
208C4×Q8—2981no—
209C4×Q8—2981no—
210C4×Q8—1491no—
211C4×Q8—1491no—
212C4×Q8—1491no—
213C4×Q8C2×D14911yescharacteristic
214C4×D4—2981no—
215C4×D4—1491no—
216C4×D4C2×D14911yescharacteristic
217C2×C4⋊C4—2981no—
218C2×C4⋊C4—1491no—
219C2×C42—2981no—
220C2×C42—1491no—
221#107—1491no—
222#107—1491no—
223#107—1491no—
224#107C2×D14911yescharacteristic
225C4⋊C8—1491no—
226C4⋊C8—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103C2×D14911yescharacteristic
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102C2×D14911yescharacteristic
235C22⋊C8—1491no—
236C22⋊C8—1491no—
237#97—1491no—
238#97C2×D14911yescharacteristic
239#41—5964no—
240C2×Q8—2981no—
241C2×Q8—2981no—
242C2×Q8—2982no—
243C2×Q8—2982no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4C22×D14911yescharacteristic
252C22×C4—21no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—1491no—
257C22×C4—1491no—
258C22×C4—1491no—
259SD16—22no—
260SD16—2982no—
261SD16—2982no—
262SD16—2982no—
263C2×C8—1491no—
264C2×C8—1491no—
265C2×C8C22×D14911yescharacteristic
266C2×C8C22×D14911yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C42—21no—
282C42—2981no—
283C42—2981no—
284C42—2981no—
285C42—1491no—
286C42—1491no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—2981no—
291C23—1491no—
292Q8—21no—
293Q8—2984no—
294Q8—2981no—
295Q8—5962no—
296Q8—1492no—
297Q8#1455873612yescomplemented
298D4—21no—
299D4—21no—
300D4—2981no—
301D4—2981no—
302D4—5962no—
303D4—5962no—
304D4—5962no—
305D4—5962no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2984no—
311C2×C4—2982no—
312C2×C4—2982no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—5962no—
319C2×C4—5962no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4D4×D14911yescharacteristic
324C2×C4D4×D14911yescharacteristic
325C2×C4C23×D14911yescharacteristic
326C8—21no—
327C8—21no—
328C8—2981no—
329C8—2981no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2981no—
334C22—2981no—
335C22—5961no—
336C22—5961no—
337C22—5961no—
338C22—1492no—
339C22C2×D4×D14911yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—2981no—
346C4—2982no—
347C4—2981no—
348C4—5961no—
349C4—5961no—
350C4—1492no—
351C4#41×D14911yescharacteristic
352C4C2×#1455873611yescharacteristic
353C2—81no—
354C2—2982no—
355C2—11921no—
356C2#2375013411yescharacteristic
357C2AGL(1,ℤ/8)×D14911yescharacteristic
358C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
prime radical#23750172C2
hypercenter#440D149
hypocenterC149#3112
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D149C2semidirect
3. #23749940C2semidirect
4. #23749937C2semidirect
5. #23749919C2semidirect
6. #23749918C2semidirect
7. #23749824C2semidirect
8. #23749823C2semidirect
9. #23749765C2semidirect
10. #23749762C2semidirect
11. #23749727C2semidirect
12. #23749725C2semidirect
13. #23749723C2semidirect
14. #23749680C2semidirect
15. #440×C149C2semidirect
114. Dic298#41semidirect
138. Q8×C149#41semidirect
179. C149#3112semidirect
194. #440D149semidirect
297. Q8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237501722
C4×Q8×D1492
#237499402
#237499372
#237499192
#237499182
#237498242
#237498232
#237497652
#237497622
#237497272
#237497252
#237497232
#237496802
#440×C1492
#3112149