Finite Group Databasebeta

← #34056014

Subgroups — #34056014

Order 19072.

398 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#23750154C211yesmaximal, characteristic, complemented
3#23749926C211yesmaximal, characteristic, complemented
4#23749925C211yesmaximal, characteristic, complemented
5#23749918C211yesmaximal, characteristic, complemented
6#23749913C211yesmaximal, characteristic, complemented
7#23749860C211yesmaximal, characteristic, complemented
8#23749858C211yesmaximal, characteristic, complemented
9#23749857C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749837C211yesmaximal, characteristic, complemented
12#23749823C211yesmaximal, characteristic, complemented
13#23749818C211yesmaximal, characteristic, complemented
14C4⋊C8×D149C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558723C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011904—21no—
24#18011903C2211yescharacteristic
25#18011897—21no—
26#18011893—21no—
27#18011887C2211yescharacteristic
28#18011886C2211yescharacteristic
29#18011884—21no—
30#18011882C2211yescharacteristic
31#18011882C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic
33C4×D596C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35C4×C22⋊D149—21no—
36#18011871—21no—
37#18011867—21no—
38C42×D149C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011832C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149D411yescharacteristic
70C2×C4×D149D411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72#14558723—41no—
73#14558721—41no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C8×D149—41no—
77C8×D149—41no—
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C4×Dic149D411yescharacteristic
94C4×Dic149D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100SD16×C149—41no—
101D8×C149—41no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—42no—
112D596—21no—
113D596—21no—
114D596—42no—
115C22⋊D149—42no—
116C22⋊D149—42no—
117C22⋊D149—42no—
118C22⋊D149—42no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—42no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—22no—
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—22no—
130C4×D149—42no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149—21no—
135Q8×C149—21no—
136Q8×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—42no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
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—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149AGL(1,ℤ/8)12yes—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149H(5,𝔽2)11yescharacteristic
167C4×C1492−1+411yescharacteristic
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173Dic149#13512yes—
174C2×C149—81no—
175C2×C149—81no—
176C2×C149#53711yescharacteristic
177C2×C149C2×#13511yescharacteristic
178C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
179D149—22no—
180D149—81no—
181C149#324711yescharacteristic, complemented, Sylow
182#3247—1491nomaximal, Sylow
183#532—1491no—
184#529—1491no—
185#478—1491no—
186#478—1491no—
187#477—1491no—
188#476—1491no—
189#466—1491no—
190#466—1491no—
191#465—1491no—
192#465—1491no—
193#463—1491no—
194#463D14911yescharacteristic, complemented
195#460—1491no—
196#459—1491no—
197C2×C4⋊C8—1491no—
198C2×#41—2981no—
199C2×SD16—1491no—
200C2×SD16C2×D14911yescharacteristic
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C22×C8—1491no—
204C22×C8—1491no—
205C4⋊Q8—1491no—
206#127—1491no—
207#126—2981no—
208#125—1491no—
209#124—2981no—
210#124C2×D14911yescharacteristic
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×D4—1491no—
222C4×D4C2×D14911yescharacteristic
223#117—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107—1491no—
227#106—1491no—
228#106—1491no—
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231C4⋊C8—1491no—
232C4⋊C8C2×D14911yescharacteristic
233#103—1491no—
234#103C2×D14911yescharacteristic
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102C2×D14911yescharacteristic
241#41—5964no—
242C2×Q8—2981no—
243C2×Q8C22×D14911yescharacteristic
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—2981no—
254C22×C4—2981no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4—1491no—
258SD16—41no—
259SD16—5961no—
260D8—41no—
261D8—5961no—
262C2×C8—5961no—
263C2×C8—5961no—
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⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
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—21no—
296Q8—21no—
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—2982no—
313C2×C4—2982no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—5962no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4D4×D14911yescharacteristic
325C2×C4D4×D14911yescharacteristic
326C2×C4C23×D14911yescharacteristic
327C8—21no—
328C8—21no—
329C8—2981no—
330C8—2981no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2981no—
338C22—2981no—
339C22—5961no—
340C22—5961no—
341C22—5961no—
342C22—1492no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—2981no—
349C4—2981no—
350C4—5961no—
351C4—5961no—
352C4—5961no—
353C4—1492no—
354C4#1801195611yescharacteristic
355C4#1801195811yescharacteristic
356C2—81no—
357C2—81no—
358C2—2982no—
359C2—11921no—
360C2#2375020411yescharacteristic
361C2#135×D14911yescharacteristic
362C2AGL(1,ℤ/8)×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3247
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750172C2semidirect
2. #23750154C2semidirect
3. #23749926C2semidirect
4. #23749925C2semidirect
5. #23749918C2semidirect
6. #23749913C2semidirect
7. #23749860C2semidirect
8. #23749858C2semidirect
9. #23749857C2semidirect
10. #23749851C2semidirect
11. #23749837C2semidirect
12. #23749823C2semidirect
13. #23749818C2semidirect
14. C4⋊C8×D149C2semidirect
15. #463×C149C2semidirect
181. C149#3247semidirect
194. #463D149semidirect

Maximal subgroups

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

subgroupindex
#237501722
#237501542
#237499262
#237499252
#237499182
#237499132
#237498602
#237498582
#237498572
#237498512
#237498372
#237498232
#237498182
C4⋊C8×D1492
#463×C1492
#3247149