Finite Group Databasebeta

← #34057163

Subgroups — #34057163

Order 19072.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic, complemented
2#23750279C211yesmaximal, characteristic, complemented
3#23750034C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749944C211yesmaximal, characteristic, complemented
6#23749944C211yesmaximal, characteristic, complemented
7#23749939C211yesmaximal, characteristic, complemented
8#23749926C211yesmaximal, characteristic, complemented
9#23749916C211yesmaximal, characteristic, complemented
10#23749878C211yesmaximal, characteristic, complemented
11#23749861C211yesmaximal, characteristic, complemented
12#23749738C211yesmaximal, characteristic, complemented
13#23749667C211yesmaximal, characteristic, complemented
14C2×#18011843C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×D1192C2211yescharacteristic
18#18011911C2211yescharacteristic
19#18011906—21no—
20#18011903C2211yescharacteristic
21#18011895—21no—
22#18011895—21no—
23#18011893—21no—
24#18011891—21no—
25#18011885C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011885C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011883—21no—
30C4×D596C2211yescharacteristic
31C4×D596C2211yescharacteristic
32#18011871—21no—
33#18011870C2211yescharacteristic
34C2×C4⋊Dic149C2211yescharacteristic
35C2×C4⋊Dic149C2211yescharacteristic
36C2×C4⋊Dic149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
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
59#14558735—44no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C22×Dic149—21no—
68C22×Dic149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72D1192—22no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C2×D4×C149D411yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96M16×C149—22no—
97C2×C8×C149—22no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C22⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107C22×D149—21no—
108Dic298—42no—
109D596—21no—
110D596—21no—
111D596—21no—
112D596—21no—
113C22⋊D149—42no—
114C22⋊D149—42no—
115C22⋊D149—42no—
116C22⋊D149—81no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149—42no—
125C2×Dic149—81no—
126C4×D149—42no—
127C4×D149—81no—
128C23×C149C2×D411yescharacteristic
129C23×C149C2×D411yescharacteristic
130D4×C149—22no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149—21no—
142C8×C149—21no—
143C8×C149#4112yescomplemented
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149AGL(1,ℤ/8)12yes—
150C22×C149C22×D411yescharacteristic
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149C2×#4111yescharacteristic
162C4×C1492−1+411yescharacteristic
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169C2×C149—22no—
170C2×C149—41no—
171C2×C149#54711yescharacteristic
172C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C149#57711yescharacteristic
174D149—81no—
175D149—81no—
176C149#334511yescharacteristic, complemented, Sylow
177#3345—1491nomaximal, Sylow
178#553—1491no—
179#547—1491no—
180#501—1491no—
181#482—1491no—
182#481—1491no—
183#481—1491no—
184#480—1491no—
185#478—1491no—
186#476—1491no—
187#469—1491no—
188#466—1491no—
189#442—1491no—
190#435D14911yescharacteristic, complemented
191#428—1491no—
192C2×#106—1491no—
193C2×#41—2981no—
194C2×D8—1491no—
195C2×M16C2×D14911yescharacteristic
196C22×C8C2×D14911yescharacteristic
197C4⋊Q8—1491no—
198#126—2981no—
199#125—1491no—
200#123—2981no—
201#123—2981no—
202#123—2981no—
203C22⋊Q8—2981no—
204#121—2981no—
205#121—1491no—
206#121—1491no—
207#121—1491no—
208#121—1491no—
209C4×D4—2981no—
210C4×D4—1491no—
211C4×D4—1491no—
212C4×D4C2×D14911yescharacteristic
213#117—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4—1491no—
217#107—1491no—
218#107—1491no—
219#107—1491no—
220#106—1491no—
221#106—1491no—
222#106—1491no—
223#106—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8C2×D14911yescharacteristic
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233C22⋊C8C2×D14911yescharacteristic
234C22⋊C8C2×D14911yescharacteristic
235#97C2×D14911yescharacteristic
236#41—5964no—
237C2×Q8—2981no—
238C2×D4—2981no—
239C2×D4—2981no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—1491no—
243C2×D4—1491no—
244C2×D4D59611yescharacteristic
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4C22×D14911yescharacteristic
251C22×C4C22×D14911yescharacteristic
252D8—2982no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D14911yescharacteristic
256C2×C8C22×D14911yescharacteristic
257C2×C8C22×D14911yescharacteristic
258C2×C8C22×D14911yescharacteristic
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4D59611yescharacteristic
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4D59611yescharacteristic
280C22⋊C4D59611yescharacteristic
281C42—2981no—
282C42C22×D14911yescharacteristic
283C23—2981no—
284C23—2981no—
285C23C2×D59611yescharacteristic
286C23C2×D59611yescharacteristic
287Q8—5962no—
288D4—22no—
289D4—2981no—
290D4—2981no—
291D4—2981no—
292D4—2981no—
293D4—5962no—
294D4—5962no—
295D4—5962no—
296D4—11921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—5962no—
308C2×C4—5962no—
309C2×C4—5962no—
310C2×C4—11921no—
311C2×C4—11921no—
312C2×C4C2×D59611yescharacteristic
313C2×C4C2×D59611yescharacteristic
314C2×C4C2×D59611yescharacteristic
315C2×C4C2×D59611yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1455873512yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22#1801193912yes—
333C22C22×D59611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C4—5961no—
342C4—5961no—
343C4—5961no—
344C4C2×#1455873511yescharacteristic
345C4#1801195811yescharacteristic
346C2—22no—
347C2—41no—
348C2—11921no—
349C2—11921no—
350C2#2375027911yescharacteristic
351C2C2×#1801193911yescharacteristic
352C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
hypercenter#435D149
hypocenterC149#3345
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. #23750321C2semidirect
2. #23750279C2semidirect
3. #23750034C2semidirect
4. #23749950C2semidirect
5. #23749944C2semidirect
6. #23749944C2semidirect
7. #23749939C2semidirect
8. #23749926C2semidirect
9. #23749916C2semidirect
10. #23749878C2semidirect
11. #23749861C2semidirect
12. #23749738C2semidirect
13. #23749667C2semidirect
14. C2×#18011843C2semidirect
15. #435×C149C2semidirect
143. C8×C149#41semidirect
176. C149#3345semidirect
190. #435D149semidirect
320. C8#14558735semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237502792
#237500342
#237499502
#237499442
#237499392
#237499262
#237499162
#237498782
#237498612
#237497382
#237496672
C2×#180118432
#435×C1492
#3345149