Finite Group Databasebeta

← #34057196

Subgroups — #34057196

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#23750340C211yesmaximal, characteristic, complemented
2#23750325C211yesmaximal, characteristic, complemented
3#23750034C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749948C211yesmaximal, characteristic, complemented
6#23749947C211yesmaximal, characteristic, complemented
7#23749937C211yesmaximal, characteristic, complemented
8#23749925C211yesmaximal, characteristic, complemented
9#23749905C211yesmaximal, characteristic, complemented
10#23749875C211yesmaximal, characteristic, complemented
11#23749858C211yesmaximal, characteristic, complemented
12#23749698C211yesmaximal, characteristic, complemented
13#23749664C211yesmaximal, characteristic, complemented
14#23749660C211yesmaximal, characteristic, complemented
15#442×C149C211yesmaximal, characteristic, complemented
16C2×#14558719C2211yescharacteristic
17C2×C8×D149C2211yescharacteristic
18#18011911C2211yescharacteristic
19#18011904—21no—
20#18011903C2211yescharacteristic
21#18011897—21no—
22#18011897—21no—
23#18011894—21no—
24#18011885—21no—
25#18011884—21no—
26#18011882C2211yescharacteristic
27#18011882C2211yescharacteristic
28#18011882C2211yescharacteristic
29#18011882C2211yescharacteristic
30C4×D596C2211yescharacteristic
31C4×C22⋊D149—21no—
32#18011870—21no—
33#18011869C2211yescharacteristic
34#18011869C2211yescharacteristic
35#18011869C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011842C2211yescharacteristic
45C4⋊#11924746C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596D411yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67C2×C4×D149C2311yescharacteristic
68#14558719—22no—
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C8×D149—22no—
72C4⋊Dic149—21no—
73C4⋊Dic149D411yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713D411yescharacteristic
89#14558713D411yescharacteristic
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C2×D4×C149C2311yescharacteristic
94C2×D4×C149C2311yescharacteristic
95C22×C4×C149—21no—
96C22×C4×C149—21no—
97D8×C149—22no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149C2×D411yescharacteristic
106C22×D149C2×D411yescharacteristic
107Dic298—81no—
108D596—41no—
109C22⋊D149—42no—
110C22⋊D149—81no—
111C22⋊D149—81no—
112C22⋊D149—81no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C4×D149—21no—
120C4×D149—21no—
121C4×D149—21no—
122C4×D149—21no—
123C4×D149—81no—
124#11924746—21no—
125#11924746—21no—
126C23×C149—21no—
127C23×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—21no—
131D4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—42no—
135C2×C4×C149—81no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2411yescharacteristic
139C8×C149—21no—
140C8×C149#4112yes—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149—41no—
147C22×C149C22×D411yescharacteristic
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—21no—
151C2×D149—21no—
152C2×D149—21no—
153C2×D149—21no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149C2×#4111yescharacteristic
159C4×C1492−1+411yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—81no—
167C2×C149—81no—
168C2×C149#54711yescharacteristic
169C2×C149#57511yescharacteristic
170C2×C149#57611yescharacteristic
171D149—41no—
172D149—41no—
173C149#334711yescharacteristic, complemented, Sylow
174#3347—1491nomaximal, Sylow
175#555—1491no—
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#442D14911yescharacteristic, complemented
187#435—1491no—
188#428—1491no—
189#427—1491no—
190C2×D8C2×D14911yescharacteristic
191C2×M16—1491no—
192C22×C8—1491no—
193C4⋊Q8—1491no—
194#126—2981no—
195#125—1491no—
196#124—2981no—
197#124—2981no—
198#123—2981no—
199#121—2981no—
200#121—2981no—
201#121—1491no—
202#121—1491no—
203#121—1491no—
204#121—1491no—
205C4×D4—2981no—
206C4×D4—1491no—
207C4×D4C2×D14911yescharacteristic
208C4×D4C2×D14911yescharacteristic
209#117—2981no—
210#117—1491no—
211#117—1491no—
212#117—1491no—
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#106C2×D14911yescharacteristic
223C4⋊C8—1491no—
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#102C2×D14911yescharacteristic
229#102C2×D14911yescharacteristic
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97C2×D14911yescharacteristic
233C2×Q8—2981no—
234C2×D4—2981no—
235C2×D4—2981no—
236C2×D4—2981no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C2×D4C22×D14911yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—2981no—
244C22×C4—1491no—
245C22×C4—1491no—
246D8—22no—
247M16—2982no—
248C2×C8—2982no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8C22×D14911yescharacteristic
252C2×C8C22×D14911yescharacteristic
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
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—2981no—
278C42C22×D14911yescharacteristic
279C23—21no—
280C23—21no—
281C23—1491no—
282C23—1491no—
283Q8—11921no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—5961no—
289D4—5962no—
290D4—11921no—
291D4—11921no—
292D4—11921no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—11921no—
308C2×C4D4×D14911yescharacteristic
309C2×C4D4×D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—2981no—
313C8—2981no—
314C8#1455873612yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2981no—
322C22—2981no—
323C22—2981no—
324C22—2981no—
325C22—2981no—
326C22—2981no—
327C22C2×D4×D14911yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—2981no—
333C4—2981no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4C2×#1455873611yescharacteristic
339C4#1801195811yescharacteristic
340C2—81no—
341C2—81no—
342C2—5961no—
343C2—5961no—
344C2#2375028011yescharacteristic
345C2#2375042111yescharacteristic
346C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
hypercenter#442D149
hypocenterC149#3347
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23750340C2semidirect
2. #23750325C2semidirect
3. #23750034C2semidirect
4. #23749948C2semidirect
5. #23749948C2semidirect
6. #23749947C2semidirect
7. #23749937C2semidirect
8. #23749925C2semidirect
9. #23749905C2semidirect
10. #23749875C2semidirect
11. #23749858C2semidirect
12. #23749698C2semidirect
13. #23749664C2semidirect
14. #23749660C2semidirect
15. #442×C149C2semidirect
173. C149#3347semidirect
186. #442D149semidirect

Maximal subgroups

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

subgroupindex
#237503402
#237503252
#237500342
#237499482
#237499472
#237499372
#237499252
#237499052
#237498752
#237498582
#237496982
#237496642
#237496602
#442×C1492
#3347149