Finite Group Databasebeta

← #34054950

Subgroups — #34054950

Order 19072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750244C211yesmaximal, characteristic, complemented
2#23750104C211yesmaximal, characteristic, complemented
3#23749959C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749921C211yesmaximal, characteristic, complemented
6#23749905C211yesmaximal, characteristic, complemented
7#23749844C211yesmaximal, characteristic, complemented
8#23749784C211yesmaximal, characteristic, complemented
9#23749767C211yesmaximal, characteristic
10#23749726C211yesmaximal, characteristic, complemented
11#23749722C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13D8×Dic149C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19#18011911C2211yescharacteristic
20#18011904—21no—
21#18011897—21no—
22#18011895—21no—
23#18011888—21no—
24#18011887C2211yescharacteristic
25#18011882C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic
27C4×Dic298C2211yescharacteristic
28#18011876C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31C4×C22⋊D149—21no—
32#18011871—21no—
33#18011868C2211yescharacteristic
34#18011867—21no—
35C2×#14558715—21no—
36C4⋊C4×D149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—22no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70#14558726—22no—
71#14558724—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713D411yescharacteristic
90#14558713D411yescharacteristic
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C2×Q8×C149C2311yescharacteristic
96C2×D4×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99SD16×C149—22no—
100D8×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149C2×D411yescharacteristic
109Dic298—21no—
110Dic298—81no—
111Dic298#4112yes—
112C22⋊D149—24no—
113C22⋊D149—81no—
114C2×Dic149—24no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C2×Dic149—81no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—81no—
127#11924746—21no—
128#11924746—21no—
129C23×C149—21no—
130C23×C149—21no—
131Q8×C149—21no—
132Q8×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149#4112yes—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—81no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C8×C149—21no—
144C8×C149—21no—
145C22×C149—22no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—41no—
158C4×C149—41no—
159C4×C149C2×#4111yescharacteristic
160C4×C149C2×#4111yescharacteristic
161Dic149—21no—
162Dic149—22no—
163Dic149—21no—
164Dic149—21no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168C2×C149—42no—
169C2×C149—81no—
170C2×C149#52511yescharacteristic
171C2×C149#57611yescharacteristic
172C2×C149#57811yescharacteristic
173D149—41no—
174C149#312411yescharacteristic, complemented, Sylow
175#3124—1491nomaximal, Sylow
176#542—1491no—
177#520—1491no—
178#484—1491no—
179#480—1491no—
180#477—1491no—
181#474—1491no—
182#464—1491no—
183#463D14911yescharacteristic, complemented
184#452—1491no—
185#449—1491no—
186#440—1491no—
187#440—1491no—
188C4×Q16—1491no—
189C4×D8—1491no—
190#433—1491no—
191C2×#41—1491no—
192C2×Q16—1491no—
193C2×SD16—1491no—
194C2×SD16C2×D14911yescharacteristic
195C2×D8C2×D14911yescharacteristic
196C4⋊Q8—1491no—
197#126—2981no—
198#124—2981no—
199#124C2×D14911yescharacteristic
200#123—2981no—
201C22⋊Q8—2981no—
202C22⋊Q8—1491no—
203#121—1491no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4C2×D14911yescharacteristic
212#117—2981no—
213#117—1491no—
214C2×C4⋊C4—2981no—
215C2×C4⋊C4—1491no—
216#107—1491no—
217#107—1491no—
218#107—1491no—
219#107—1491no—
220C4⋊C8—1491no—
221C4⋊C8C2×D14911yescharacteristic
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103C2×D14911yescharacteristic
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102C2×D14911yescharacteristic
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97—1491no—
233C4×C8—1491no—
234#41—2982no—
235#41—2982no—
236C2×Q8—2981no—
237C2×Q8—1491no—
238C2×Q8C22×D14911yescharacteristic
239C2×D4—2981no—
240C2×D4—2981no—
241C2×D4C22×D14911yescharacteristic
242C2×D4C22×D14911yescharacteristic
243C22×C4—21no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—1491no—
249Q16—2982no—
250SD16—22no—
251SD16—2982no—
252D8—22no—
253C2×C8—1491no—
254C2×C8—1491no—
255C2×C8C22×D14911yescharacteristic
256C2×C8C22×D14911yescharacteristic
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4C22×D14911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—1491no—
277C22⋊C4—1491no—
278C42—2981no—
279C42—2981no—
280C42—2981no—
281C42—1491no—
282C42C22×D14911yescharacteristic
283C23—21no—
284C23—21no—
285C23—1491no—
286Q8—21no—
287Q8—21no—
288Q8—2981no—
289Q8—1492no—
290Q8—11921no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—2984no—
295D4—11921no—
296D4#1455873512yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—2984no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4—1491no—
310C2×C4—11921no—
311C2×C4—11921no—
312C2×C4—11921no—
313C2×C4D4×D14911yescharacteristic
314C2×C4D4×D14911yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—21no—
317C8—21no—
318C8—2981no—
319C8—2981no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2981no—
327C22—2981no—
328C22—2981no—
329C22C2×D4×D14911yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—2981no—
335C4—2981no—
336C4—2981no—
337C4—2982no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C4#41×D14911yescharacteristic
342C4C2×#1455873511yescharacteristic
343C2—42no—
344C2—81no—
345C2—5961no—
346C2#2375013511yescharacteristic
347C2#2375042911yescharacteristic
348C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
prime radical#23749767C2
hypercenter#463D149
hypocenterC149#3124
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. #23750244C2semidirect
2. #23750104C2semidirect
3. #23749959C2semidirect
4. #23749937C2semidirect
5. #23749921C2semidirect
6. #23749905C2semidirect
7. #23749844C2semidirect
8. #23749784C2semidirect
10. #23749726C2semidirect
11. #23749722C2semidirect
12. #23749717C2semidirect
13. D8×Dic149C2semidirect
14. #23749685C2semidirect
15. #463×C149C2semidirect
174. C149#3124semidirect
183. #463D149semidirect

Maximal subgroups

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

subgroupindex
#237502442
#237501042
#237499592
#237499372
#237499212
#237499052
#237498442
#237497842
#237497672
#237497262
#237497222
#237497172
D8×Dic1492
#237496852
#463×C1492
#3124149