Finite Group Databasebeta

← #34056592

Subgroups — #34056592

Order 19072.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750328C211yesmaximal, characteristic, complemented
2#23750283C211yesmaximal, characteristic, complemented
3#23749964C211yesmaximal, characteristic, complemented
4#23749942C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749860C211yesmaximal, characteristic, complemented
7#23749857C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749771C211yesmaximal, characteristic, complemented
10#23749765C211yesmaximal, characteristic, complemented
11C4×#14558725C211yesmaximal, characteristic, complemented
12C8×D596C211yesmaximal, characteristic, complemented
13#23749618C211yesmaximal, characteristic, complemented
14#103×D149C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23#18011906—21no—
24#18011897—21no—
25#18011896—21no—
26#18011888—21no—
27#18011887C2211yescharacteristic
28#18011886—21no—
29#18011886C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011884—21no—
32#18011882C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34C4×D596C2211yescharacteristic
35C4×D596C2211yescharacteristic
36#18011873—21no—
37#18011871—21no—
38#18011869C2211yescharacteristic
39C4⋊C4×D149C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63Q8×D149—22no—
64Q8×D149—41no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596D411yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76C2×C4×D149C2311yescharacteristic
77#14558725—22no—
78#14558723—41no—
79#14558721—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C8×D149—41no—
83C8×D149—41no—
84C4⋊Dic149D411yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713D411yescharacteristic
97#14558713D411yescharacteristic
98C4×Dic149—21no—
99C4×Dic149—21no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149C2×D411yescharacteristic
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—42no—
116Dic298#4112yes—
117D596—22no—
118D596—21no—
119D596—21no—
120D596—42no—
121D596—81no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—42no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—42no—
135C4×D149—81no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142D4×C149—21no—
143D4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149#13512yes—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149C2×#4111yescharacteristic
171C4×C149H(5,𝔽2)11yescharacteristic
172Dic149—21no—
173Dic149—21no—
174Dic149—22no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—81no—
178C2×C149#54611yescharacteristic
179C2×C149C2×#13511yescharacteristic
180C2×C149#57711yescharacteristic
181D149—22no—
182D149—41no—
183D149—81no—
184C149#330111yescharacteristic, complemented, Sylow
185#3301—1491nomaximal, Sylow
186#553—1491no—
187#548—1491no—
188#488D14911yescharacteristic, complemented
189#485—1491no—
190#481—1491no—
191#479—1491no—
192#466—1491no—
193#465—1491no—
194#463—1491no—
195#449—1491no—
196#448—1491no—
197C4×SD16—1491no—
198C8×D4—1491no—
199#416—1491no—
200C2×#103—1491no—
201C2×#41—1491no—
202C22×Q8—1491no—
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C22×C8—1491no—
207C22×C8—1491no—
208#126—2981no—
209#125C2×D14911yescharacteristic
210#124—2981no—
211#124C2×D14911yescharacteristic
212#123—2981no—
213C22⋊Q8—2981no—
214C22⋊Q8—1491no—
215#121—2981no—
216#121—2981no—
217#121—1491no—
218#121—1491no—
219#121—1491no—
220C4×Q8—1491no—
221C4×D4—2981no—
222C4×D4—2981no—
223C4×D4—1491no—
224C4×D4—1491no—
225#117—1491no—
226C2×C4⋊C4—1491no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103C2×D14911yescharacteristic
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic
240#102C2×D14911yescharacteristic
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C4×C8C2×D14911yescharacteristic
244#41—2982no—
245#41—5961no—
246C2×Q8—2981no—
247C2×Q8—2982no—
248C2×Q8—5961no—
249C2×Q8—1491no—
250C2×Q8C22×D14911yescharacteristic
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4C22×D14911yescharacteristic
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4—1491no—
264SD16—2982no—
265SD16—5961no—
266D8—5961no—
267C2×C8—5961no—
268C2×C8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—1491no—
292C22⋊C4—1491no—
293C42—2981no—
294C42—2981no—
295C42C22×D14911yescharacteristic
296C23—21no—
297C23—2981no—
298C23—1491no—
299C23—1491no—
300Q8—21no—
301Q8—21no—
302Q8—2981no—
303Q8—5962no—
304Q8—1492no—
305D4—21no—
306D4—21no—
307D4—2982no—
308D4—2981no—
309D4—2981no—
310D4—5962no—
311D4—5962no—
312D4—5962no—
313D4—11921no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—5962no—
325C2×C4—5962no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—11921no—
329C2×C4—11921no—
330C2×C4D4×D14911yescharacteristic
331C2×C4D4×D14911yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—21no—
334C8—21no—
335C8—2981no—
336C8—2981no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—2981no—
341C22—2981no—
342C22—2981no—
343C22—2981no—
344C22—2981no—
345C22—5961no—
346C22—5961no—
347C22—5961no—
348C22—1492no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2981no—
356C4—2981no—
357C4—2982no—
358C4—5961no—
359C4—5961no—
360C4#41×D14911yescharacteristic
361C4#1801195711yescharacteristic
362C2—81no—
363C2—2982no—
364C2—5961no—
365C2—11921no—
366C2#2375026811yescharacteristic
367C2#135×D14911yescharacteristic
368C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
hypercenter#488D149
hypocenterC149#3301
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750328C2semidirect
2. #23750283C2semidirect
3. #23749964C2semidirect
4. #23749942C2semidirect
5. #23749929C2semidirect
6. #23749860C2semidirect
7. #23749857C2semidirect
8. #23749837C2semidirect
9. #23749771C2semidirect
10. #23749765C2semidirect
11. C4×#14558725C2semidirect
12. C8×D596C2semidirect
13. #23749618C2semidirect
14. #103×D149C2semidirect
15. #488×C149C2semidirect
184. C149#3301semidirect
188. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237503282
#237502832
#237499642
#237499422
#237499292
#237498602
#237498572
#237498372
#237497712
#237497652
C4×#145587252
C8×D5962
#237496182
#103×D1492
#488×C1492
#3301149