Finite Group Databasebeta

← #34056587

Subgroups — #34056587

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#23750284C211yesmaximal, characteristic, complemented
2#23749982C211yesmaximal, characteristic, complemented
3#23749966C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749859C211yesmaximal, characteristic, complemented
7#23749852C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic, complemented
10#23749763C211yesmaximal, characteristic, complemented
11C4×#14558724C211yesmaximal, characteristic, complemented
12D4×#11924746C211yesmaximal, characteristic, complemented
13#23749619C211yesmaximal, characteristic, complemented
14C2×#18011834C211yesmaximal, characteristic, complemented
15#553×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C22×#11924746C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23#18011899C2211yescharacteristic
24#18011897—21no—
25#18011890C2211yescharacteristic
26#18011889—21no—
27#18011885C2211yescharacteristic
28#18011883—21no—
29C4×Dic298C2211yescharacteristic
30#18011871—21no—
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35#18011834C2211yescharacteristic
36#18011834C2211yescharacteristic
37#18011834C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011834C2211yescharacteristic
40#18011834C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48#126×C149—21no—
49#125×C149C2211yescharacteristic
50#123×C149—21no—
51#121×C149—21no—
52#121×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic
54C4×D4×C149—21no—
55C4×D4×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57#117×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—41no—
61C2×Dic298—22no—
62C2×Dic298—21no—
63C2×Dic298—41no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71#14558724—22no—
72#14558724—41no—
73#14558721—41no—
74C2×#11924746—41no—
75C2×#11924746—41no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83C22⋊Dic149—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87C4×Dic149—21no—
88C2×D4×C149—21no—
89C2×D4×C149—21no—
90C2×D4×C149D411yescharacteristic
91C2×D4×C149C2311yescharacteristic
92C22×C4×C149—21no—
93C22×C4×C149—21no—
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149D411yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149D411yescharacteristic
108C22⋊C4×C149D411yescharacteristic
109C42×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—42no—
116Dic298#4112yes—
117D596—21no—
118D596—21no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—42no—
125C4×D149—42no—
126#11924746—21no—
127#11924746—21no—
128#11924746—21no—
129#11924746—21no—
130C23×C149—21no—
131C23×C149C2×D411yescharacteristic
132C23×C149C2×D411yescharacteristic
133D4×C149—22no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—42no—
137D4×C149—81no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—81no—
146C2×C4×C149—81no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149#13512yes—
161C22×C149C22×D411yescharacteristic
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149C2×#4111yescharacteristic
173C4×C149H(5,𝔽2)11yescharacteristic
174Dic149—22no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—22no—
178C2×C149—41no—
179C2×C149—81no—
180C2×C149#54611yescharacteristic
181C2×C149C2×#13511yescharacteristic
182C2×C149#57711yescharacteristic
183D149—81no—
184C149#330111yescharacteristic, complemented, Sylow
185#3301—1491nomaximal, Sylow
186#553D14911yescharacteristic, complemented
187#548—1491no—
188#488—1491no—
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—21no—
209#125C2×D14911yescharacteristic
210#124—2981no—
211#124—1491no—
212#123—21no—
213C22⋊Q8—2981no—
214C22⋊Q8—1491no—
215#121—21no—
216#121—2981no—
217#121—1491no—
218#121C2×D14911yescharacteristic
219#121C2×D14911yescharacteristic
220C4×Q8—1491no—
221C4×D4—21no—
222C4×D4—2981no—
223C4×D4C2×D14911yescharacteristic
224C4×D4C2×D14911yescharacteristic
225#117C2×D14911yescharacteristic
226C2×C4⋊C4C2×D14911yescharacteristic
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#103—1491no—
236#103—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C4×C8—1491no—
244#41—2982no—
245#41—5961no—
246C2×Q8—2982no—
247C2×Q8—2981no—
248C2×Q8—5961no—
249C2×Q8—1491no—
250C2×Q8—1491no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4C22⋊D14911yescharacteristic
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4C22×D14911yescharacteristic
263C22×C4C22×D14911yescharacteristic
264SD16—2982no—
265SD16—5961no—
266D8—5961no—
267C2×C8—5961no—
268C2×C8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8—1491no—
272C2×C8—1491no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4C22⋊D14911yescharacteristic
280C4⋊C4C22×D14911yescharacteristic
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4C22⋊D14911yescharacteristic
292C22⋊C4C22⋊D14911yescharacteristic
293C42—21no—
294C42—2981no—
295C42C22×D14911yescharacteristic
296C23—21no—
297C23—2981no—
298C23C2×C22⋊D14911yescharacteristic
299C23C2×C22⋊D14911yescharacteristic
300Q8—2981no—
301Q8—2981no—
302Q8—2981no—
303Q8—5962no—
304Q8—1492no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—2981no—
311D4—2981no—
312D4—5962no—
313D4—5962no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—5962no—
327C2×C4—5962no—
328C2×C4C2×C22⋊D14911yescharacteristic
329C2×C4C2×C22⋊D14911yescharacteristic
330C2×C4C2×C22⋊D14911yescharacteristic
331C2×C4C2×C22⋊D14911yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—2981no—
334C8—2981no—
335C8—2981no—
336C8—2981no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5961no—
346C22—5961no—
347C22—5961no—
348C22#1801193112yes—
349C22C22×C22⋊D14911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2982no—
358C4—5961no—
359C4—5961no—
360C4#41×D14911yescharacteristic
361C4#1801195711yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—11921no—
366C2#2375026311yescharacteristic
367C2C2×#1801193111yescharacteristic
368C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#553×C149C2
socleC22×C149C22×D4
hypercenter#553D149
hypocenterC149#3301
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23750284C2semidirect
2. #23749982C2semidirect
3. #23749966C2semidirect
4. #23749943C2semidirect
5. #23749929C2semidirect
6. #23749859C2semidirect
7. #23749852C2semidirect
8. #23749840C2semidirect
9. #23749768C2semidirect
10. #23749763C2semidirect
11. C4×#14558724C2semidirect
12. D4×#11924746C2semidirect
13. #23749619C2semidirect
14. C2×#18011834C2semidirect
15. #553×C149C2semidirect
184. C149#3301semidirect
186. #553D149semidirect

Maximal subgroups

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

subgroupindex
#237502842
#237499822
#237499662
#237499432
#237499292
#237498592
#237498522
#237498402
#237497682
#237497632
C4×#145587242
D4×#119247462
#237496192
C2×#180118342
#553×C1492
#3301149