Finite Group Databasebeta

← #34054840

Subgroups — #34054840

Order 19072.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750172C211yesmaximal, characteristic, complemented
2C4×#14558737C211yesmaximal, characteristic, complemented
3#23749952C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749908C211yesmaximal, characteristic, complemented
6#23749904C211yesmaximal, characteristic, complemented
7#23749823C211yesmaximal, characteristic, complemented
8#23749819C211yesmaximal, characteristic, complemented
9#23749773C211yesmaximal, characteristic, complemented
10#23749769C211yesmaximal, characteristic, complemented
11#23749738C211yesmaximal, characteristic, complemented
12#23749735C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14#23749680C211yesmaximal, characteristic, complemented
15#440×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736—21no—
18C2×#14558723C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011907C2211yescharacteristic
23#18011897—21no—
24#18011886C2211yescharacteristic
25#18011884—21no—
26#18011882C2211yescharacteristic
27Q8×Dic149C2211yescharacteristic
28C4×D596—21no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic
31#18011873—21no—
32#18011873C2211yescharacteristic
33C4×C22⋊D149—21no—
34#18011869—21no—
35#18011869C2211yescharacteristic
36C42×D149—21no—
37C42×D149C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
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#14558737—22no—
60#14558737—22no—
61#14558736—44no—
62C2×Dic298—21no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
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×D149—21no—
74C2×C4×D149D411yescharacteristic
75C2×C4×D149D411yescharacteristic
76C2×C4×D149C2311yescharacteristic
77#14558723—22no—
78D1192—22no—
79#14558721—22no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—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×D149—21no—
111C22×D149C2×D411yescharacteristic
112Dic298—42no—
113D596—24no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—42no—
118D596#4112yescomplemented
119C22⋊D149—42no—
120C22⋊D149—42no—
121C22⋊D149—42no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—24no—
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—22no—
131C4×D149—41no—
132C4×D149—42no—
133C4×D149—42no—
134C4×D149—42no—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138Q8×C149—21no—
139Q8×C149#4112yescomplemented
140D4×C149—21no—
141D4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—42no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—21no—
156C2×D149—22no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—22no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149C2×#4111yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149AGL(1,ℤ/8)12yes—
176C2×C149—81no—
177C2×C149#52511yescharacteristic
178C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C149#57511yescharacteristic
180D149—41no—
181D149—42no—
182D149—81no—
183C149#311511yescharacteristic, complemented, Sylow
184#3115—1491nomaximal, Sylow
185#532—1491no—
186C4×#41—1491no—
187#482—1491no—
188#482—1491no—
189#475—1491no—
190#474—1491no—
191#460—1491no—
192#459—1491no—
193#449—1491no—
194#449—1491no—
195#442—1491no—
196#442—1491no—
197#440—1491no—
198#440D14911yescharacteristic, complemented
199#432—1491no—
200C2×#41—2981no—
201C2×#41—1491no—
202C2×SD16—1491no—
203C2×SD16C2×D14911yescharacteristic
204C2×D8—1491no—
205C2×D8—1491no—
206C4⋊Q8—1491no—
207#127—1491no—
208#124—2981no—
209#121—2981no—
210#121—1491no—
211#121—1491no—
212C4×Q8—1491no—
213C4×Q8C2×D14911yescharacteristic
214C4×D4—2981no—
215C4×D4—2981no—
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4C2×D14911yescharacteristic
221#117—2981no—
222#117—1491no—
223C2×C42—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107C2×D14911yescharacteristic
227#106—1491no—
228#106—1491no—
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103C2×D14911yescharacteristic
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102—1491no—
238#102C2×D14911yescharacteristic
239C22⋊C8—1491no—
240C22⋊C8—1491no—
241#97—1491no—
242#97C2×D14911yescharacteristic
243#41—2982no—
244#41—2982no—
245#41—5964no—
246C2×Q8—2981no—
247C2×Q8C22×D14911yescharacteristic
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—1491no—
254C2×D4—1491no—
255C2×D4C22×D14911yescharacteristic
256C22×C4—21no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4—1491no—
264SD16—22no—
265SD16—2982no—
266D8—2982no—
267D8—2982no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4C22×D14911yescharacteristic
278C4⋊C4C22×D14911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—21no—
287C42—2981no—
288C42—2981no—
289C42—1491no—
290C42—1491no—
291C42—1491no—
292C42C22×D14911yescharacteristic
293C23—21no—
294C23—2981no—
295C23—2981no—
296C23—1491no—
297Q8—21no—
298Q8—5962no—
299Q8#1455873612yescomplemented
300D4—21no—
301D4—21no—
302D4—2984no—
303D4—2981no—
304D4—2981no—
305D4—2981no—
306D4—5962no—
307D4—5962no—
308D4—5962no—
309D4—5962no—
310D4—1492no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2984no—
316C2×C4—2982no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—5961no—
322C2×C4—5962no—
323C2×C4—5962no—
324C2×C4—5962no—
325C2×C4—1491no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4D4×D14911yescharacteristic
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—21no—
333C8—2981no—
334C8—2981no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2981no—
339C22—2981no—
340C22—2981no—
341C22—2982no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—22no—
351C4—41no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—5961no—
356C4—5961no—
357C4—1492no—
358C4#41×D14911yescharacteristic
359C4C2×#1455873611yescharacteristic
360C2—81no—
361C2—5961no—
362C2—5962no—
363C2—11921no—
364C2#2375013411yescharacteristic
365C2AGL(1,ℤ/8)×D14911yescharacteristic
366C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
hypercenter#440D149
hypocenterC149#3115
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
1. #23750172C2semidirect
2. C4×#14558737C2semidirect
3. #23749952C2semidirect
4. #23749948C2semidirect
5. #23749908C2semidirect
6. #23749904C2semidirect
7. #23749823C2semidirect
8. #23749819C2semidirect
9. #23749773C2semidirect
10. #23749769C2semidirect
11. #23749738C2semidirect
12. #23749735C2semidirect
13. #23749723C2semidirect
14. #23749680C2semidirect
15. #440×C149C2semidirect
118. D596#41semidirect
139. Q8×C149#41semidirect
183. C149#3115semidirect
198. #440D149semidirect
299. Q8#14558736semidirect

Maximal subgroups

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

subgroupindex
#237501722
C4×#145587372
#237499522
#237499482
#237499082
#237499042
#237498232
#237498192
#237497732
#237497692
#237497382
#237497352
#237497232
#237496802
#440×C1492
#3115149