Finite Group Databasebeta

← #18077017

Subgroups — #18077017

Order 4864.

426 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#14572379C211yesmaximal, characteristic
2#14564411C211yesmaximal, characteristic, complemented
3#14562410C211yesmaximal, characteristic, complemented
4#14562086C211yesmaximal, characteristic
5#14561471C211yesmaximal, characteristic, complemented
6#14561469C211yesmaximal, characteristic, complemented
7C19×#1540C211yesmaximal, characteristic
8C2×#10597394—21no—
9#11926622—21no—
10#11926616—22no—
11D4×C19⋊C8—21no—
12C2×#10597276—21no—
13#11926568C2211yescharacteristic
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15#11926511—21no—
16C4×#64520C2211yescharacteristic
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926309—21no—
19#11926297—21no—
20#11926297—21no—
21D4⋊(C19⋊C8)—22no—
22C19×#532C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#332C411yescharacteristic
26C19×#332C411yescharacteristic
27C19×#331C411yescharacteristic
28C19×#331C411yescharacteristic
29C2×#41×C19—21no—
30C22×C8×C19—21no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×#127C2×C411yescharacteristic
33C19×#124—21no—
34C19×#121—21no—
35C19×#121Q812yes—
36C4×D4×C19—21no—
37C4×D4×C19D412yes—
38C2×C42×C19C2311yescharacteristic
39#10597394—42no—
40#10597394—42no—
41C2×#64520—22no—
42C2×#64520—21no—
43C2×#64520D411yescharacteristic
44C2×#64520D411yescharacteristic
45C22×C19⋊C8—22no—
46C22×C19⋊C8—21no—
47C22×C19⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8C2×C411yescharacteristic
50C19×C4⋊C8C2×C411yescharacteristic
51C19×C4⋊C8C2×C411yescharacteristic
52C19×C4⋊C8C2×C411yescharacteristic
53C19×C22⋊C8—21no—
54C4×C8×C19—21no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57#10597276—42no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)D411yescharacteristic
62C4⋊(C19⋊C8)D411yescharacteristic
63#10597260—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8—21no—
66C4×C19⋊C8—21no—
67#41×C19—41no—
68#41×C19—41no—
69#41×C19—41no—
70#41×C19—41no—
71C2×Q8×C19—21no—
72C2×D4×C19—22no—
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19C4⋊C412yes—
76C22×C4×C19—22no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×Q811yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—21no—
83C2×C8×C19—21no—
84C2×C8×C19—41no—
85C2×C8×C19—41no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19C4⋊C412yes—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C42×C19C22×C411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19C2×D411yescharacteristic
93C42×C19#4111yescharacteristic
94#64520—21no—
95#64520—21no—
96#64520—21no—
97#64520—44no—
98#64520—41no—
99#64520—41no—
100#64520D812yes—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—44no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112#8930—191nomaximal, Sylow
113C23×C19—22no—
114C23×C19C22⋊Q811yescharacteristic
115Q8×C19—41no—
116Q8×C19—41no—
117D4×C19—42no—
118D4×C19—42no—
119D4×C19—42no—
120D4×C19—41no—
121D4×C19—41no—
122D4×C19—41no—
123D4×C19—41no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19C2×C4⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19#12311yescharacteristic
136C2×C4×C19C2×D811yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C8×C19—41no—
141C8×C19—41no—
142C8×C19—41no—
143C8×C19—41no—
144C19⋊C8—22no—
145C19⋊C8—42no—
146C19⋊C8—41no—
147C19⋊C8—41no—
148C19⋊C8—41no—
149C19⋊C8—81no—
150#2935—191no—
151#1950—191no—
152#1571—191no—
153#1540D1911yescharacteristic
154#1492—191no—
155#1278—191no—
156#1277—191no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19—42no—
162C22×C19#38511yescharacteristic
163C22×C19#47411yescharacteristic
164C22×C19#47811yescharacteristic
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—42no—
169C4×C19C4×D811yescharacteristic
170C4×C19#44011yescharacteristic
171C4×C19#44311yescharacteristic
172C4×C19#44411yescharacteristic
173C4×C19#44711yescharacteristic
174C4×C19#45211yescharacteristic
175C2×#131—381no—
176#532C2×D1911yescharacteristic
177#436—381no—
178#435—382no—
179C8×D4—381no—
180#431C2×D1911yescharacteristic
181C2×#108—381no—
182#423—191no—
183C2×C4⋊C8—191no—
184C2×C4⋊C8C2×D1911yescharacteristic
185#408—381no—
186C4×M16—191no—
187C2×C4×C8—191no—
188#341—381no—
189#335—381no—
190#335—381no—
191#332Dic1911yescharacteristic
192#332Dic1911yescharacteristic
193#331Dic1911yescharacteristic
194#331Dic1911yescharacteristic
195D4⋊C8—382no—
196C2×C19—21no—
197C2×C19—21no—
198C2×C19—82no—
199C2×C19#185811yescharacteristic
200C2×C19#186211yescharacteristic
201C2×C19#186611yescharacteristic
202C2×#41—21no—
203#131—762no—
204#131—762no—
205C2×M16—191no—
206C2×M16—191no—
207C2×M16—382no—
208C2×M16—381no—
209C22×C8—21no—
210C22×C8—382no—
211C22×C8—381no—
212C22×C8—381no—
213C4⋊Q8C2×Dic1911yescharacteristic
214#127C2×Dic1911yescharacteristic
215#124—21no—
216#121—21no—
217#121Dic3812yes—
218C4×D4—21no—
219C4×D4D7612yes—
220C2×C42C22×D1911yescharacteristic
221#108—762no—
222C4⋊C8—21no—
223C4⋊C8—191no—
224C4⋊C8—191no—
225C4⋊C8—381no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C4⋊C8C2×Dic1911yescharacteristic
229C4⋊C8C2×Dic1911yescharacteristic
230C4⋊C8C2×Dic1911yescharacteristic
231C4⋊C8C2×Dic1911yescharacteristic
232C22⋊C8—21no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235#97—381no—
236C4×C8—21no—
237C4×C8—381no—
238C4×C8—381no—
239C4×C8—381no—
240C19#893011yescharacteristic, complemented, Sylow
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C4⋊Dic1912yes—
250C22×C4—22no—
251C22×C4C2×Dic3811yescharacteristic
252C22×C4D4×D1911yescharacteristic
253C22×C4#6454311yescharacteristic
254M16—192no—
255M16—381no—
256M16—381no—
257M16—381no—
258M16—764no—
259M16—761no—
260M16—761no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—381no—
268C2×C8—382no—
269C2×C8—381no—
270C2×C8—381no—
271C2×C8—381no—
272C2×C8—764no—
273C2×C8—761no—
274C2×C8—761no—
275C2×C8—761no—
276C2×C8—761no—
277C2×C8—761no—
278C4⋊C4—21no—
279C4⋊C4C4⋊Dic1912yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C42C2×D7611yescharacteristic
283C42D4×D1911yescharacteristic
284C42#6454311yescharacteristic
285C42C22×Dic1911yescharacteristic
286C23—22no—
287C23#1059732411yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4#1059732411yescharacteristic
304C2×C4#1059732811yescharacteristic
305C2×C4#1059733211yescharacteristic
306C2×C4D8×D1911yescharacteristic
307C2×C4#1059735811yescharacteristic
308C2×C4#1059736011yescharacteristic
309C2×C4#1059736111yescharacteristic
310C2×C4C2×C4⋊Dic1911yescharacteristic
311C2×C4D4×Dic1911yescharacteristic
312C2×C4D4×Dic1911yescharacteristic
313C8—41no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—382no—
318C8—762no—
319C8—761no—
320C8—761no—
321C8—761no—
322C8—1521no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1192641911yescharacteristic
329C22#1192682211yescharacteristic
330C22#1192684211yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4D8×Dic1911yescharacteristic
336C4#1192664511yescharacteristic
337C4#1192666111yescharacteristic
338C4#1192666611yescharacteristic
339C4#1192667911yescharacteristic
340C4#1192670711yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1456385711yescharacteristic
345C2#1456388411yescharacteristic
346C2#1456391211yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1540C2
socleC22×C19#385
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1540D19
hypocenterC19#8930
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #14564411C2semidirect
3. #14562410C2semidirect
5. #14561471C2semidirect
6. #14561469C2semidirect
240. C19#8930semidirect

Maximal subgroups

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

subgroupindex
#145723792
#145644112
#145624102
#145620862
#145614712
#145614692
C19×#15402
#893019