Finite Group Databasebeta

← #34057193

Subgroups — #34057193

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#23750321C211yesmaximal, characteristic, complemented
3#23750034C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749950C211yesmaximal, characteristic, complemented
6#23749950C211yesmaximal, characteristic, complemented
7#23749939C211yesmaximal, characteristic, complemented
8#23749926C211yesmaximal, characteristic, complemented
9#23749906C211yesmaximal, characteristic, complemented
10#23749878C211yesmaximal, characteristic, complemented
11#23749861C211yesmaximal, characteristic, complemented
12#23749738C211yesmaximal, characteristic, complemented
13#23749667C211yesmaximal, characteristic, complemented
14#23749663C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×D1192C2211yescharacteristic
17#18011911C2211yescharacteristic
18#18011906—21no—
19#18011903C2211yescharacteristic
20#18011897—21no—
21#18011897—21no—
22#18011893—21no—
23#18011885C2211yescharacteristic
24#18011885C2211yescharacteristic
25#18011885C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011883—21no—
28#18011882—21no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic
31#18011871—21no—
32#18011870C2211yescharacteristic
33#18011870C2211yescharacteristic
34#18011870C2211yescharacteristic
35#18011869—21no—
36C2×C4⋊Dic149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011843C2211yescharacteristic
45#18011843C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C2×M16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69D1192—22no—
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80C22⋊Dic149—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C2×D4×C149D411yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95M16×C149—22no—
96C2×C8×C149—22no—
97C2×C8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149D411yescharacteristic
102C22⋊C4×C149D411yescharacteristic
103C22⋊C4×C149D411yescharacteristic
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106C22×D149—21no—
107Dic298—81no—
108D596—21no—
109D596—21no—
110D596—21no—
111D596—21no—
112C22⋊D149—42no—
113C22⋊D149—81no—
114C22⋊D149—81no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—81no—
123C4×D149—42no—
124C4×D149—81no—
125C23×C149C2×D411yescharacteristic
126C23×C149C2×D411yescharacteristic
127D4×C149—41no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2411yescharacteristic
137C8×C149—21no—
138C8×C149—21no—
139C8×C149—21no—
140C8×C149#4112yes—
141C22×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149C22×D411yescharacteristic
148C2×D149—41no—
149C2×D149—41no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149C2×#4111yescharacteristic
159C4×C1492−1+411yescharacteristic
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—41no—
167C2×C149—41no—
168C2×C149#54711yescharacteristic
169C2×C149#57511yescharacteristic
170C2×C149#57611yescharacteristic
171D149—81no—
172D149—81no—
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#442—1491no—
187#435D14911yescharacteristic, complemented
188#428—1491no—
189#427—1491no—
190C2×D8—1491no—
191C2×M16C2×D14911yescharacteristic
192C22×C8C2×D14911yescharacteristic
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×D4—1491no—
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#106—1491no—
223C4⋊C8C2×D14911yescharacteristic
224#102—1491no—
225#102—1491no—
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8C2×D14911yescharacteristic
231C22⋊C8C2×D14911yescharacteristic
232#97C2×D14911yescharacteristic
233C2×Q8—2981no—
234C2×D4—2981no—
235C2×D4—2981no—
236C2×D4—2981no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4—1491no—
240C2×D4D59611yescharacteristic
241C22×C4—2981no—
242C22×C4—2981no—
243C22×C4—2981no—
244C22×C4C22×D14911yescharacteristic
245C22×C4C22×D14911yescharacteristic
246D8—2982no—
247M16—22no—
248C2×C8—22no—
249C2×C8C22×D14911yescharacteristic
250C2×C8C22×D14911yescharacteristic
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⋊C4—1491no—
263C4⋊C4D59611yescharacteristic
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4D59611yescharacteristic
274C22⋊C4D59611yescharacteristic
275C42—2981no—
276C42—2981no—
277C42—2981no—
278C42C22×D14911yescharacteristic
279C23—2981no—
280C23—2981no—
281C23C2×D59611yescharacteristic
282C23C2×D59611yescharacteristic
283Q8—11921no—
284D4—41no—
285D4—2981no—
286D4—2981no—
287D4—2981no—
288D4—2981no—
289D4—5962no—
290D4—11921no—
291D4—11921no—
292D4—11921no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—5962no—
304C2×C4—11921no—
305C2×C4—11921no—
306C2×C4C2×D59611yescharacteristic
307C2×C4C2×D59611yescharacteristic
308C2×C4C2×D59611yescharacteristic
309C2×C4C2×D59611yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#1455873512yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—5961no—
322C22—5961no—
323C22—5961no—
324C22—5961no—
325C22—5961no—
326C22—5961no—
327C22C22×D59611yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—5961no—
333C4—5961no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4—5961no—
338C4C2×#1455873511yescharacteristic
339C4#1801195811yescharacteristic
340C2—41no—
341C2—41no—
342C2—11921no—
343C2—11921no—
344C2#2375027911yescharacteristic
345C2#2375042511yescharacteristic
346C2#2375043011yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
hypercenter#435D149
hypocenterC149#3347
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #23750340C2semidirect
2. #23750321C2semidirect
3. #23750034C2semidirect
4. #23749950C2semidirect
5. #23749950C2semidirect
6. #23749950C2semidirect
7. #23749939C2semidirect
8. #23749926C2semidirect
9. #23749906C2semidirect
10. #23749878C2semidirect
11. #23749861C2semidirect
12. #23749738C2semidirect
13. #23749667C2semidirect
14. #23749663C2semidirect
15. #435×C149C2semidirect
173. C149#3347semidirect
187. #435D149semidirect

Maximal subgroups

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

subgroupindex
#237503402
#237503212
#237500342
#237499502
#237499392
#237499262
#237499062
#237498782
#237498612
#237497382
#237496672
#237496632
#435×C1492
#3347149