Finite Group Databasebeta

← #34055284

Subgroups — #34055284

Order 19072.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750172C211yesmaximal, characteristic, complemented
2#23750157C211yesmaximal, characteristic, complemented
3#23750033C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic, complemented
5#23749988C211yesmaximal, characteristic, complemented
6#23749983C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749875C211yesmaximal, characteristic, complemented
9#23749872C211yesmaximal, characteristic, complemented
10#23749870C211yesmaximal, characteristic, complemented
11C4×#14558725C211yesmaximal, characteristic, complemented
12C4×#14558724C211yesmaximal, characteristic, complemented
13C4×#14558721C211yesmaximal, characteristic, complemented
14C4×#14558719C211yesmaximal, characteristic, complemented
15C4×D8×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×#14558719C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011907C2211yescharacteristic
24#18011904—21no—
25#18011902C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011897—21no—
28#18011893—21no—
29#18011891C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011884—21no—
32#18011882C2211yescharacteristic
33#18011882C2211yescharacteristic
34C4×Dic298C2211yescharacteristic
35C4×D596C2211yescharacteristic
36C4×C22⋊D149—21no—
37C4×C22⋊D149—21no—
38#18011870—21no—
39C42×D149C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic
50#18011821C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149D411yescharacteristic
70C2×C4×D149D411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72#14558725—22no—
73#14558724—22no—
74#14558721—22no—
75#14558719—22no—
76#14558719—22no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100C22×C4×C149—21no—
101D8×C149—22no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—21no—
112Dic298—21no—
113Dic298—42no—
114D596—21no—
115D596—21no—
116D596—42no—
117C22⋊D149—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—22no—
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—41no—
131C4×D149—42no—
132#11924746—21no—
133#11924746#4112yescomplemented
134C23×C149—21no—
135C23×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—42no—
143C2×C4×C149—42no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149#4112yescomplemented
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149AGL(1,ℤ/8)12yes—
166C4×C149C2×#4111yescharacteristic
167C4×C149C2×#4111yescharacteristic
168Dic149—21no—
169Dic149—21no—
170Dic149—21no—
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174C2×C149—81no—
175C2×C149—81no—
176C2×C149#53211yescharacteristic
177C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C149#57511yescharacteristic
179D149—41no—
180D149—81no—
181C149#317111yescharacteristic, complemented, Sylow
182#3171—1491nomaximal, Sylow
183#532—1491no—
184#529—1491no—
185#501—1491no—
186#496—1491no—
187#490—1491no—
188#489—1491no—
189#469—1491no—
190#469—1491no—
191#468—1491no—
192#468—1491no—
193C4×SD16—1491no—
194C4×SD16—1491no—
195C4×D8—1491no—
196C4×D8D14911yescharacteristic, complemented
197C4×M16—1491no—
198C2×#41—2981no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C2×M16—1491no—
204C2×M16—1491no—
205C4⋊Q8—1491no—
206#127—1491no—
207#126—2981no—
208#125—1491no—
209#124—2981no—
210#124—1491no—
211#123—2981no—
212C22⋊Q8—1491no—
213#121—2981no—
214#121—1491no—
215#121—1491no—
216#121—1491no—
217C4×Q8—1491no—
218C4×D4—2981no—
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4C2×D14911yescharacteristic
222C4×D4C2×D14911yescharacteristic
223#117—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107C2×D14911yescharacteristic
227#106—1491no—
228#106—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102C2×D14911yescharacteristic
236#102C2×D14911yescharacteristic
237#97—1491no—
238#97—1491no—
239C4×C8—1491no—
240C4×C8C2×D14911yescharacteristic
241#41—5964no—
242C2×Q8—2981no—
243C2×Q8—1491no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—2981no—
249C2×D4—1491no—
250C2×D4C22×D14911yescharacteristic
251C2×D4C22×D14911yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—2981no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4—1491no—
258SD16—2982no—
259SD16—2982no—
260D8—22no—
261D8—2982no—
262M16—2982no—
263M16—2982no—
264C2×C8—1491no—
265C2×C8—1491no—
266C2×C8C22×D14911yescharacteristic
267C2×C8C22×D14911yescharacteristic
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—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—2981no—
287C42—1491no—
288C42—1491no—
289C42—1491no—
290C42C22×D14911yescharacteristic
291C23—21no—
292C23—21no—
293C23—2981no—
294C23—1491no—
295Q8—2981no—
296Q8—2981no—
297Q8—5962no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—2981no—
303D4—2981no—
304D4—5962no—
305D4—5962no—
306D4—5962no—
307D4—5962no—
308D4—5962no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2982no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—5961no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4D4×D14911yescharacteristic
325C2×C4D4×D14911yescharacteristic
326C2×C4C23×D14911yescharacteristic
327C8—21no—
328C8—2981no—
329C8—1492no—
330C8#1455873612yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2981no—
338C22—2981no—
339C22—2981no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—2981no—
350C4—5961no—
351C4—5961no—
352C4—5961no—
353C4#1801193512yes—
354C4#41×D14911yescharacteristic
355C4C2×#1455873611yescharacteristic
356C2—81no—
357C2—81no—
358C2—5961no—
359C2—11921no—
360C2#2375017211yescharacteristic
361C2C2×#1801193511yescharacteristic
362C2#2375042211yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3171
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750172C2semidirect
2. #23750157C2semidirect
3. #23750033C2semidirect
4. #23750013C2semidirect
5. #23749988C2semidirect
6. #23749983C2semidirect
7. #23749877C2semidirect
8. #23749875C2semidirect
9. #23749872C2semidirect
10. #23749870C2semidirect
11. C4×#14558725C2semidirect
12. C4×#14558724C2semidirect
13. C4×#14558721C2semidirect
14. C4×#14558719C2semidirect
15. C4×D8×C149C2semidirect
133. #11924746#41semidirect
148. C8×C149#41semidirect
181. C149#3171semidirect
196. C4×D8D149semidirect
330. C8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237501722
#237501572
#237500332
#237500132
#237499882
#237499832
#237498772
#237498752
#237498722
#237498702
C4×#145587252
C4×#145587242
C4×#145587212
C4×#145587192
C4×D8×C1492
#3171149