Finite Group Databasebeta

← #34054890

Subgroups — #34054890

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750230C211yesmaximal, characteristic, complemented
2#23749943C211yesmaximal, characteristic, complemented
3#23749938C211yesmaximal, characteristic, complemented
4#23749932C211yesmaximal, characteristic, complemented
5#23749925C211yesmaximal, characteristic, complemented
6#23749825C211yesmaximal, characteristic, complemented
7#23749820C211yesmaximal, characteristic, complemented
8#23749770C211yesmaximal, characteristic, complemented
9#23749770C211yesmaximal, characteristic, complemented
10#23749735C211yesmaximal, characteristic, complemented
11#23749723C211yesmaximal, characteristic, complemented
12C4×#14558723C211yesmaximal, characteristic, complemented
13C4×#14558721C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#520×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20#18011908C2211yescharacteristic
21#18011903C2211yescharacteristic
22#18011896—21no—
23#18011896—21no—
24#18011885C2211yescharacteristic
25#18011885C2211yescharacteristic
26#18011884—21no—
27#18011884—21no—
28C4×D596C2211yescharacteristic
29C4×D596C2211yescharacteristic
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011832C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011831C2211yescharacteristic
41#18011831C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C2×#41×C149C2211yescharacteristic
49C4×Q8×C149C2211yescharacteristic
50C4×Q8×C149C2211yescharacteristic
51C4×D4×C149—21no—
52C4×D4×C149—21no—
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#117×C149—21no—
56#117×C149C2211yescharacteristic
57C2×C4⋊C4×C149—21no—
58C2×C4⋊C4×C149C2211yescharacteristic
59C2×D596—21no—
60C2×D596—21no—
61C2×D596C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67#14558723—22no—
68#14558723—22no—
69#14558721—22no—
70#14558721—22no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558713—21no—
80#14558713—21no—
81#14558713—21no—
82#14558713—21no—
83#41×C149—22no—
84#41×C149—22no—
85C2×Q8×C149C2311yescharacteristic
86C2×D4×C149—21no—
87C2×D4×C149C2311yescharacteristic
88C22×C4×C149—21no—
89C22×C4×C149—21no—
90C22×C4×C149—21no—
91C22×C4×C149—21no—
92C22×C4×C149C2311yescharacteristic
93C4⋊C4×C149—21no—
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149D411yescharacteristic
97C4⋊C4×C149D411yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149D411yescharacteristic
103C22⋊C4×C149D411yescharacteristic
104C42×C149—21no—
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110D596—21no—
111D596—21no—
112D596—21no—
113D596—21no—
114D596—81no—
115D596—81no—
116C22⋊D149—81no—
117C22⋊D149—81no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C4×D149—81no—
121C4×D149—81no—
122#11924746—21no—
123#11924746—21no—
124#11924746—21no—
125#11924746—21no—
126C23×C149—21no—
127C23×C149C2×D411yescharacteristic
128Q8×C149—21no—
129Q8×C149#4112yes—
130D4×C149—24no—
131D4×C149—21no—
132D4×C149#4112yes—
133C2×C4×C149—24no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—81no—
140C2×C4×C149—81no—
141C2×C4×C149—81no—
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C22×C149—21no—
149C22×C149—22no—
150C22×C149—21no—
151C22×C149—21no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—22no—
163C4×C149—21no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149C2×#4111yescharacteristic
171Dic149—41no—
172Dic149—41no—
173C2×C149—41no—
174C2×C149—42no—
175C2×C149#52511yescharacteristic
176C2×C149#57611yescharacteristic
177C2×C149#57711yescharacteristic
178D149—81no—
179D149—81no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520D14911yescharacteristic, complemented
184#481—1491no—
185#480—1491no—
186#479—1491no—
187#478—1491no—
188#460—1491no—
189#459—1491no—
190#449—1491no—
191#449—1491no—
192#442—1491no—
193#440—1491no—
194C4×SD16—1491no—
195C4×D8—1491no—
196#433—1491no—
197C2×#41C2×D14911yescharacteristic
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×D8—1491no—
201C2×D8—1491no—
202#127—1491no—
203#125—1491no—
204#123—2981no—
205#123—2981no—
206#121—2981no—
207#121—2981no—
208#121—1491no—
209#121—1491no—
210C4×Q8C2×D14911yescharacteristic
211C4×Q8C2×D14911yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4C2×D14911yescharacteristic
217C4×D4C2×D14911yescharacteristic
218#117—21no—
219#117C2×D14911yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D14911yescharacteristic
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236C22⋊C8—1491no—
237C22⋊C8—1491no—
238#97—1491no—
239C4×C8—1491no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D14911yescharacteristic
243C2×D4—21no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4C22×D14911yescharacteristic
258SD16—2982no—
259SD16—2982no—
260D8—2982no—
261D8—2982no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8—1491no—
265C2×C8—1491no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4C22⋊D14911yescharacteristic
274C4⋊C4C22⋊D14911yescharacteristic
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4C22⋊D14911yescharacteristic
284C22⋊C4C22⋊D14911yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D14911yescharacteristic
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—2981no—
291C23—2981no—
292C23C2×C22⋊D14911yescharacteristic
293Q8—21no—
294Q8#1455873612yes—
295D4—24no—
296D4—21no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—2981no—
301D4—11921no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305D4#1455873612yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—11921no—
318C2×C4—11921no—
319C2×C4C2×C22⋊D14911yescharacteristic
320C2×C4C2×C22⋊D14911yescharacteristic
321C2×C4C2×C22⋊D14911yescharacteristic
322C2×C4C2×C22⋊D14911yescharacteristic
323C2×C4C2×C22⋊D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—2981no—
326C8—2981no—
327C8—2981no—
328C8—2981no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—5961no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C22×C22⋊D14911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—22no—
348C4—41no—
349C4—41no—
350C4—5961no—
351C4—5961no—
352C4C2×#1455873611yescharacteristic
353C4C2×#1455873611yescharacteristic
354C2—41no—
355C2—42no—
356C2—11921no—
357C2—11921no—
358C2#2375013611yescharacteristic
359C2#2375042811yescharacteristic
360C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#520×C149C2
socleC22×C149C22×D4
hypercenter#520D149
hypocenterC149#3119
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #23750230C2semidirect
2. #23749943C2semidirect
3. #23749938C2semidirect
4. #23749932C2semidirect
5. #23749925C2semidirect
6. #23749825C2semidirect
7. #23749820C2semidirect
8. #23749770C2semidirect
9. #23749770C2semidirect
10. #23749735C2semidirect
11. #23749723C2semidirect
12. C4×#14558723C2semidirect
13. C4×#14558721C2semidirect
14. #23749686C2semidirect
15. #520×C149C2semidirect
180. C149#3119semidirect
183. #520D149semidirect

Maximal subgroups

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

subgroupindex
#237502302
#237499432
#237499382
#237499322
#237499252
#237498252
#237498202
#237497702
#237497352
#237497232
C4×#145587232
C4×#145587212
#237496862
#520×C1492
#3119149