Finite Group Databasebeta

← #34054794

Subgroups — #34054794

Order 19072.

392 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
1C4×#14558736C211yesmaximal, characteristic, complemented
2#23749963C211yesmaximal, characteristic, complemented
3#23749946C211yesmaximal, characteristic, complemented
4#23749929C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749785C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic
10#23749735C211yesmaximal, characteristic, complemented
11#23749730C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14#23749682C211yesmaximal, characteristic, complemented
15#529×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23C4×D596C2211yescharacteristic
24C4×D596C2211yescharacteristic
25C4×C22⋊D149—21no—
26C4×C22⋊D149—21no—
27#18011870C2211yescharacteristic
28#18011868—21no—
29C42×D149—21no—
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011834C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47#18011822C2211yescharacteristic
48#126×C149—21no—
49#125×C149C2211yescharacteristic
50#124×C149C2211yescharacteristic
51#123×C149—21no—
52C22⋊Q8×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×D4×C149—21no—
56C4×D4×C149C2211yescharacteristic
57#117×C149—21no—
58C2×C42×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67#14558726—22no—
68#14558724—22no—
69#14558723—22no—
70#14558721—22no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80#14558713—21no—
81#14558713—21no—
82C4×Dic149—21no—
83C4×Dic149—21no—
84C4×Dic149—21no—
85C2×Q8×C149C2311yescharacteristic
86C2×D4×C149—21no—
87C2×D4×C149C2311yescharacteristic
88C22×C4×C149—21no—
89C22×C4×C149D411yescharacteristic
90C22×C4×C149D411yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149C2311yescharacteristic
97C4⋊C4×C149C2311yescharacteristic
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C42×C149—21no—
104C42×C149D411yescharacteristic
105C42×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298#4112yes—
111D596—21no—
112D596#4112yes—
113C22⋊D149—24no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C4×D149—24no—
118C4×D149—42no—
119C4×D149—42no—
120#11924746—21no—
121#11924746—21no—
122#11924746—21no—
123#11924746—21no—
124C23×C149—21no—
125C23×C149C2×D411yescharacteristic
126Q8×C149—21no—
127Q8×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—42no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—41no—
137C2×C4×C149—41no—
138C2×C4×C149—42no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2411yescharacteristic
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149C22×D411yescharacteristic
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149C2×#4111yescharacteristic
164C4×C149C2×#4111yescharacteristic
165Dic149—22no—
166Dic149—41no—
167Dic149—41no—
168C2×C149—41no—
169C2×C149—81no—
170C2×C149#52511yescharacteristic
171C2×C149#57511yescharacteristic
172C2×C149#57511yescharacteristic
173D149—42no—
174C149#311111yescharacteristic, complemented, Sylow
175#3111—1491nomaximal, Sylow
176#529D14911yescharacteristic, complemented
177C4×#41—1491no—
178#485—1491no—
179#482—1491no—
180#479—1491no—
181#478—1491no—
182#464—1491no—
183#463—1491no—
184#452—1491no—
185#449—1491no—
186#442—1491no—
187#441—1491no—
188#440—1491no—
189#440—1491no—
190#432—1491no—
191C2×#41—1491no—
192C2×Q16—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×D8—1491no—
196#126—21no—
197#125C2×D14911yescharacteristic
198#124C2×D14911yescharacteristic
199#123—21no—
200C22⋊Q8C2×D14911yescharacteristic
201#121C2×D14911yescharacteristic
202C4×Q8—1491no—
203C4×Q8—1491no—
204C4×Q8C2×D14911yescharacteristic
205C4×D4—21no—
206C4×D4—2981no—
207C4×D4—2981no—
208C4×D4—1491no—
209C4×D4—1491no—
210C4×D4C2×D14911yescharacteristic
211#117—21no—
212#117—2981no—
213#117—1491no—
214C2×C42—2981no—
215C2×C42C2×D14911yescharacteristic
216#107—1491no—
217#107—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97—1491no—
233#97—1491no—
234#41—2982no—
235#41—2982no—
236C2×Q8—1491no—
237C2×Q8C22×D14911yescharacteristic
238C2×D4—21no—
239C2×D4—2981no—
240C2×D4—1491no—
241C2×D4C22×D14911yescharacteristic
242C22×C4—21no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4C22⋊D14911yescharacteristic
247C22×C4C22⋊D14911yescharacteristic
248C22×C4C22×D14911yescharacteristic
249Q16—2982no—
250SD16—2982no—
251SD16—2982no—
252D8—2982no—
253C2×C8—1491no—
254C2×C8—1491no—
255C2×C8—1491no—
256C2×C8—1491no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4C22×D14911yescharacteristic
266C4⋊C4C22×D14911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C42—21no—
276C42—2981no—
277C42—2981no—
278C42—2981no—
279C42C22⋊D14911yescharacteristic
280C42C22⋊D14911yescharacteristic
281C42C22×D14911yescharacteristic
282C42C22×D14911yescharacteristic
283C23—21no—
284C23—2981no—
285C23C2×C22⋊D14911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—2981no—
289Q8—1492no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—2984no—
294D4—2981no—
295D4—1492no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—2984no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—5962no—
309C2×C4—5962no—
310C2×C4C2×C22⋊D14911yescharacteristic
311C2×C4C2×C22⋊D14911yescharacteristic
312C2×C4C2×C22⋊D14911yescharacteristic
313C2×C4C2×C22⋊D14911yescharacteristic
314C2×C4C2×C22⋊D14911yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—2981no—
317C8—2981no—
318C8—2981no—
319C8—2981no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2982no—
327C22—5961no—
328C22—5961no—
329C22C22×C22⋊D14911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2982no—
339C4—5961no—
340C4—5961no—
341C4#41×D14911yescharacteristic
342C4#41×D14911yescharacteristic
343C2—41no—
344C2—81no—
345C2—5962no—
346C2#2375013211yescharacteristic
347C2#2375042311yescharacteristic
348C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#529×C149C2
socleC22×C149C22×D4
prime radical#23749768C2
hypercenter#529D149
hypocenterC149#3111
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#14558736C2semidirect
2. #23749963C2semidirect
3. #23749946C2semidirect
4. #23749929C2semidirect
5. #23749922C2semidirect
6. #23749844C2semidirect
7. #23749837C2semidirect
8. #23749785C2semidirect
10. #23749735C2semidirect
11. #23749730C2semidirect
12. #23749725C2semidirect
13. #23749723C2semidirect
14. #23749682C2semidirect
15. #529×C149C2semidirect
174. C149#3111semidirect
176. #529D149semidirect

Maximal subgroups

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

subgroupindex
C4×#145587362
#237499632
#237499462
#237499292
#237499222
#237498442
#237498372
#237497852
#237497682
#237497352
#237497302
#237497252
#237497232
#237496822
#529×C1492
#3111149