Finite Group Databasebeta

← #34054521

Subgroups — #34054521

Order 19072.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750255C211yesmaximal, characteristic, complemented
2#23750097C211yesmaximal, characteristic
3#23749927C211yesmaximal, characteristic, complemented
4#23749924C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749916C211yesmaximal, characteristic, complemented
7#23749913C211yesmaximal, characteristic, complemented
8#23749905C211yesmaximal, characteristic, complemented
9#23749904C211yesmaximal, characteristic, complemented
10#23749666C211yesmaximal, characteristic, complemented
11#23749660C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic
14#102×D149C211yesmaximal, characteristic
15#478×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×#14558719C2211yescharacteristic
18C2×C8×D149C2211yescharacteristic
19#18011911C2211yescharacteristic, complemented
20#18011910—21no—
21#18011910C2211yescharacteristic, complemented
22#18011902C2211yescharacteristic, complemented
23#18011901—21no—
24#18011891—21no—
25#18011889—21no—
26C4×D596C2211yescharacteristic
27D4×Dic149C2211yescharacteristic
28#18011873C2211yescharacteristic
29C4×C22⋊D149—21no—
30#18011871—21no—
31#18011869C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011868C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35C2×#14558713—21no—
36C22⋊C4×D149—21no—
37#18011844C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43C4⋊#11924746C2211yescharacteristic, complemented
44#18011840C2211yescharacteristic, complemented
45#18011840C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011831C2211yescharacteristic
51#18011831C2211yescharacteristic
52#125×C149C2211yescharacteristic, complemented
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64D4×D149—22no—
65D4×D149Q814yescomplemented
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558719—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C8×D149—22no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91#14558713D411yescharacteristic
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149—21no—
97C2×C8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C4⋊C4×C149—21no—
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107C22×D149—24no—
108C22×D149—81no—
109C22×D149—81no—
110C22×D149C2×D411yescharacteristic
111Dic298—81no—
112Dic298—81no—
113D596—21no—
114D596C2×Q812yes—
115C22⋊D149—24no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—81no—
124C4×D149—81no—
125C4×D149—81no—
126C4×D149C2×Q812yes—
127C4×D149#4112yes—
128#11924746—21no—
129#11924746—21no—
130C23×C149—21no—
131D4×C149—21no—
132D4×C149C2×Q812yes—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—81no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149—21no—
142C22×C149—22no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149C22×D411yescharacteristic
146C2×D149—21no—
147C2×D149—21no—
148C2×D149—22no—
149C2×D149—41no—
150C2×D149—41no—
151C2×D149—84no—
152C2×D149C22⋊Q812yes—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149C22×Q811yescharacteristic
159C4×C149C2×#4111yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149C22⋊Q812yes—
166C2×C149—42no—
167C2×C149C2×C22⋊Q811yescharacteristic
168C2×C149#57611yescharacteristic
169C2×C149#57711yescharacteristic
170D149—22no—
171D149—42no—
172C149#308111yescharacteristic, complemented, Sylow
173#3081—1491nomaximal, Sylow
174#544—1491no—
175#518—1491no—
176#478—1491no—
177#478—1491no—
178#478—1491no—
179#478D14911yescharacteristic, complemented
180#476—1491no—
181#476—1491no—
182#474—1491no—
183#474—1491no—
184#428—1491no—
185#427—1491no—
186#424—1491no—
187#418—1491no—
188C2×#102—1491no—
189C22×D4—1491no—
190C2×M16—1491no—
191C22×C8—1491no—
192C4⋊Q8—2981no—
193C4⋊Q8—1491no—
194C4⋊Q8—1491no—
195#125—2981no—
196#125—1491no—
197#125C2×D14911yescharacteristic, complemented
198C22⋊Q8—2981no—
199C22⋊Q8—2981no—
200C4×D4—2981no—
201C4×D4—2981no—
202C4×D4—1491no—
203C4×D4—1491no—
204C4×D4—1491no—
205C4×D4C2×D14911yescharacteristic
206#117—1491no—
207#117—1491no—
208#117—1491no—
209C2×C4⋊C4—1491no—
210C2×C22⋊C4—2981no—
211C2×C22⋊C4—2981no—
212#107—1491no—
213#107—1491no—
214#107—1491no—
215#107C2×D14911yescharacteristic, complemented
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106C2×D14911yescharacteristic, complemented
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222C4⋊C8—1491no—
223C4⋊C8C2×D14911yescharacteristic, complemented
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102C2×D14911yescharacteristic
231#102C2×D14911yescharacteristic
232C24—2981no—
233C2×Q8—2981no—
234C2×Q8—2981no—
235C2×D4—2982no—
236C2×D4—2981no—
237C2×D4—1494no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—21no—
241C22×C4—2981no—
242C22×C4—2981no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—1491no—
246M16—2982no—
247C2×C8—2982no—
248C2×C8—1491no—
249C2×C8—1491no—
250C2×C8C22×D14911yescharacteristic
251C2×C8C22×D14911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4—1491no—
264C4⋊C4C22×D14911yescharacteristic
265C4⋊C4C22×D14911yescharacteristic
266C4⋊C4C22×D14911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—1491no—
274C22⋊C4—1491no—
275C42—2981no—
276C42—2981no—
277C42—1491no—
278C42C22×D14911yescharacteristic
279C23—21no—
280C23—2984no—
281C23—2981no—
282C23—1491no—
283C23—11921no—
284C23—11921no—
285Q8—11921no—
286Q8—11921no—
287D4—21no—
288D4—2984no—
289D4—2981no—
290D4—1492no—
291D4Q8×D14912yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—1492no—
303C2×C4—1492no—
304C2×C4—11921no—
305C2×C4—11921no—
306C2×C4—11921no—
307C2×C4—11921no—
308C2×C4D4×D14911yescharacteristic
309C2×C4D4×D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—21no—
313C8—2981no—
314C8—2981no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2981no—
319C22—2981no—
320C22—2982no—
321C22—5961no—
322C22—5961no—
323C22—1492no—
324C22—11924no—
325C22C2×D4×D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2981no—
332C4—2981no—
333C4—5961no—
334C4—5961no—
335C4—5961no—
336C4—1492no—
337C4C2×Q8×D14911yescharacteristic
338C4#41×D14911yescharacteristic
339C2—42no—
340C2—2982no—
341C2—5962no—
342C2C22⋊Q8×D14911yescharacteristic
343C2#2375042911yescharacteristic
344C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#478D149
hypocenterC149#3081
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750255C2semidirect
3. #23749927C2semidirect
4. #23749924C2semidirect
5. #23749922C2semidirect
6. #23749916C2semidirect
7. #23749913C2semidirect
8. #23749905C2semidirect
9. #23749904C2semidirect
10. #23749666C2semidirect
11. #23749660C2semidirect
12. #23749650C2semidirect
15. #478×C149C2semidirect
19. #18011911C22semidirect
21. #18011910C22semidirect
22. #18011902C22semidirect
37. #18011844C22semidirect
38. #18011844C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. C4⋊#11924746C22semidirect
44. #18011840C22semidirect
45. #18011840C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
65. D4×D149Q8semidirect
172. C149#3081semidirect
179. #478D149semidirect
197. #125C2×D149semidirect
215. #107C2×D149semidirect
219. #106C2×D149semidirect
223. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237500972
#237499272
#237499242
#237499222
#237499162
#237499132
#237499052
#237499042
#237496662
#237496602
#237496502
#237496282
#102×D1492
#478×C1492
#3081149