Finite Group Databasebeta

← #34057191

Subgroups — #34057191

Order 19072.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic, complemented
2#23750031C211yesmaximal, characteristic, complemented
3#23749949C211yesmaximal, characteristic, complemented
4#23749949C211yesmaximal, characteristic, complemented
5#23749946C211yesmaximal, characteristic, complemented
6#23749936C211yesmaximal, characteristic, complemented
7#23749925C211yesmaximal, characteristic, complemented
8#23749902C211yesmaximal, characteristic, complemented
9#23749876C211yesmaximal, characteristic, complemented
10#23749859C211yesmaximal, characteristic, complemented
11#23749735C211yesmaximal, characteristic, complemented
12#23749697C211yesmaximal, characteristic, complemented
13#23749668C211yesmaximal, characteristic, complemented
14#23749661C211yesmaximal, characteristic, complemented
15#555×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011906—21no—
20#18011903C2211yescharacteristic
21#18011893—21no—
22#18011885C2211yescharacteristic
23#18011885C2211yescharacteristic
24#18011883—21no—
25C4×D596C2211yescharacteristic
26#18011871—21no—
27#18011870C2211yescharacteristic
28C2×C4⋊Dic149C2211yescharacteristic
29#18011844C2211yescharacteristic
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011844C2211yescharacteristic
33#18011844C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011842C2211yescharacteristic
37#18011842C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47#18011822C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#124×C149—21no—
50#124×C149—21no—
51#121×C149—21no—
52#121×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56#117×C149—21no—
57#117×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×D596C2311yescharacteristic
60C2×C22⋊D149—21no—
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C2×C4×D149—21no—
64#14558721—22no—
65#14558720—22no—
66C2×#11924746—22no—
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77C22⋊Dic149—21no—
78#14558713—21no—
79#14558713—21no—
80#14558713—21no—
81C4×Dic149—21no—
82C2×Q8×C149—21no—
83C2×D4×C149—21no—
84C2×D4×C149—21no—
85C2×D4×C149D411yescharacteristic
86C2×D4×C149C2311yescharacteristic
87C22×C4×C149—21no—
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C4⋊C4×C149—21no—
91C4⋊C4×C149D411yescharacteristic
92C4⋊C4×C149C2311yescharacteristic
93C4⋊C4×C149C2311yescharacteristic
94C4⋊C4×C149C2311yescharacteristic
95C22⋊C4×C149—21no—
96C22⋊C4×C149—21no—
97C22⋊C4×C149—21no—
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149D411yescharacteristic
101C22⋊C4×C149D411yescharacteristic
102C42×C149—21no—
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106D596—21no—
107D596—21no—
108C22⋊D149—42no—
109C22⋊D149—81no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—81no—
114C4×D149—81no—
115#11924746—21no—
116#11924746—21no—
117#11924746—21no—
118#11924746#4112yes—
119C23×C149—21no—
120C23×C149C2×D411yescharacteristic
121C23×C149C2×D411yescharacteristic
122Q8×C149—81no—
123D4×C149—21no—
124D4×C149—21no—
125D4×C149—41no—
126D4×C149—81no—
127D4×C149—81no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—42no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C22×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149C22×D411yescharacteristic
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C1492−1+411yescharacteristic
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—41no—
167C2×C149—41no—
168C2×C149—81no—
169C2×C149#54711yescharacteristic
170C2×C149#57511yescharacteristic
171C2×C149#57611yescharacteristic
172D149—81no—
173C149#334711yescharacteristic, complemented, Sylow
174#3347—1491nomaximal, Sylow
175#555D14911yescharacteristic, complemented
176#553—1491no—
177#501—1491no—
178#482—1491no—
179#482—1491no—
180#482—1491no—
181#480—1491no—
182#478—1491no—
183#474—1491no—
184#469—1491no—
185#466—1491no—
186#442—1491no—
187#435—1491no—
188#428—1491no—
189#427—1491no—
190C2×D8—1491no—
191C2×M16—1491no—
192C22×C8—1491no—
193C4⋊Q8C2×D14911yescharacteristic
194#126—2981no—
195#125—1491no—
196#124—21no—
197#124—21no—
198#123—2981no—
199#121—21no—
200#121—2981no—
201#121—1491no—
202#121—1491no—
203#121C2×D14911yescharacteristic
204#121C2×D14911yescharacteristic
205C4×D4—2981no—
206C4×D4—1491no—
207C4×D4C2×D14911yescharacteristic
208C4×D4C2×D14911yescharacteristic
209#117—21no—
210#117—1491no—
211#117C2×D14911yescharacteristic
212#117C2×D14911yescharacteristic
213C2×C4⋊C4—1491no—
214#107—1491no—
215#107—1491no—
216#107—1491no—
217#107—1491no—
218#107—1491no—
219#106—1491no—
220#106—1491no—
221#106—1491no—
222#106—1491no—
223C4⋊C8—1491no—
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97—1491no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—2981no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22⋊D14911yescharacteristic
240C2×D4C22×D14911yescharacteristic
241C22×C4—21no—
242C22×C4—2981no—
243C22×C4—2981no—
244C22×C4C22×D14911yescharacteristic
245C22×C4C22×D14911yescharacteristic
246D8—2982no—
247M16—2982no—
248C2×C8—2982no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8—1491no—
252C2×C8—1491no—
253C4⋊C4—21no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4C22⋊D14911yescharacteristic
261C4⋊C4C22×D14911yescharacteristic
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4C22⋊D14911yescharacteristic
274C22⋊C4C22⋊D14911yescharacteristic
275C42—21no—
276C42—21no—
277C42—2981no—
278C42C22×D14911yescharacteristic
279C23—21no—
280C23—2981no—
281C23C2×C22⋊D14911yescharacteristic
282C23C2×C22⋊D14911yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—2981no—
290D4—2981no—
291D4—5962no—
292D4—11921no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—11921no—
305C2×C4—11921no—
306C2×C4C2×C22⋊D14911yescharacteristic
307C2×C4C2×C22⋊D14911yescharacteristic
308C2×C4C2×C22⋊D14911yescharacteristic
309C2×C4C2×C22⋊D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—2981no—
312C8—2981no—
313C8—2981no—
314C8—1492no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—5961no—
325C22—5961no—
326C22—5961no—
327C22C22×C22⋊D14911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4#41×D14911yescharacteristic
339C4#1801195811yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—11921no—
344C2#2375027411yescharacteristic
345C2#2375042311yescharacteristic
346C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#555×C149C2
socleC22×C149C22×D4
hypercenter#555D149
hypocenterC149#3347
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #23750321C2semidirect
2. #23750031C2semidirect
3. #23749949C2semidirect
4. #23749949C2semidirect
5. #23749946C2semidirect
6. #23749936C2semidirect
7. #23749925C2semidirect
8. #23749902C2semidirect
9. #23749876C2semidirect
10. #23749859C2semidirect
11. #23749735C2semidirect
12. #23749697C2semidirect
13. #23749668C2semidirect
14. #23749661C2semidirect
15. #555×C149C2semidirect
173. C149#3347semidirect
175. #555D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237500312
#237499492
#237499462
#237499362
#237499252
#237499022
#237498762
#237498592
#237497352
#237496972
#237496682
#237496612
#555×C1492
#3347149