Finite Group Databasebeta

← #18075801

Subgroups — #18075801

Order 4864.

414 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572347C211yesmaximal, characteristic
2#14563772C211yesmaximal, characteristic, complemented
3C2×#11926294C211yesmaximal, characteristic, complemented
4#14562312C211yesmaximal, characteristic
5#14561510C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1547C211yesmaximal, characteristic
8C2×#10597394—21no—
9#11926622—21no—
10#11926622C412yes—
11D4×C19⋊C8—21no—
12D4×C19⋊C8C412yes—
13#11926568C2211yescharacteristic
14#11926568C2211yescharacteristic
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16#11926511—21no—
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926308—21no—
19#11926308—21no—
20#11926294—21no—
21#11926294—21no—
22#11926290—21no—
23#11926288—21no—
24C19×#532C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C19×#332—21no—
28C19×#331—21no—
29C2×#41×C19—21no—
30C2×M16×C19—21no—
31C22×C8×C19—21no—
32C19×C4⋊Q8D411yescharacteristic
33C19×#127D411yescharacteristic
34C19×#124—21no—
35C19×#121—21no—
36C19×#121Q812yes—
37C4×D4×C19—21no—
38C4×D4×C19C2×C412yes—
39C2×C42×C19C2311yescharacteristic
40#10597394—42no—
41#10597394—42no—
42C2×#64520—21no—
43C2×#64520—22no—
44C2×#64520—21no—
45C22×C19⋊C8—22no—
46C22×C19⋊C8—21no—
47C22×C19⋊C8D411yescharacteristic
48C22×C19⋊C8D411yescharacteristic
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)C2×C412yes—
61C4×C19⋊C8C2×C411yescharacteristic
62C4×C19⋊C8C2×C411yescharacteristic
63C4×C19⋊C8D411yescharacteristic
64C4×C19⋊C8D411yescharacteristic
65#41×C19—41no—
66#41×C19—41no—
67#41×C19—41no—
68#41×C19—41no—
69C2×Q8×C19—21no—
70C2×D4×C19—22no—
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19C4⋊C412yes—
74C22×C4×C19—22no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×Q811yescharacteristic
77C22×C4×C19#4111yescharacteristic
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—41no—
81C2×C8×C19—41no—
82C2×C8×C19—81no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19C4⋊C412yes—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C42×C19C22×C411yescharacteristic
88C42×C19C2×D411yescharacteristic
89C42×C19C2×D411yescharacteristic
90C42×C19#4111yescharacteristic
91#64520—44no—
92#64520—41no—
93#64520—41no—
94#64520—41no—
95#64520—41no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—22no—
101C2×C19⋊C8—44no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—81no—
105C2×C19⋊C8C22⋊C411yescharacteristic
106C2×C19⋊C8C22⋊C411yescharacteristic
107C2×C19⋊C8C22⋊C411yescharacteristic
108C2×C19⋊C8C22⋊C411yescharacteristic
109#8686—191nomaximal, Sylow
110C23×C19—22no—
111C23×C19C22⋊Q811yescharacteristic
112Q8×C19—41no—
113Q8×C19—41no—
114D4×C19—42no—
115D4×C19—42no—
116D4×C19—42no—
117D4×C19—41no—
118D4×C19—41no—
119D4×C19—41no—
120D4×C19—41no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—22no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C2×C4⋊C411yescharacteristic
129C2×C4×C19#11711yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19C22⋊Q811yescharacteristic
133C2×C4×C19#13511yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C8×C19—81no—
138C8×C19—81no—
139C19⋊C8—21no—
140C19⋊C8—21no—
141C19⋊C8—21no—
142C19⋊C8—21no—
143C19⋊C8—42no—
144C19⋊C8—81no—
145C19⋊C8—81no—
146#2931—191no—
147#1837—191no—
148C2×#334—191no—
149#1547—191no—
150#1547D1911yescharacteristic
151#1292—191no—
152#1292—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19—42no—
158C22×C19#38011yescharacteristic
159C22×C19#47811yescharacteristic
160C22×C19#47811yescharacteristic
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—42no—
165C4×C19#41611yescharacteristic
166C4×C19#41811yescharacteristic
167C4×C19#46311yescharacteristic
168C4×C19#46311yescharacteristic
169C4×C19#47111yescharacteristic
170C4×C19#47111yescharacteristic
171C2×#131—381no—
172#532C2×D1911yescharacteristic
173#436—192no—
174#436—381no—
175C8×D4—192no—
176C8×D4—381no—
177#423—191no—
178#423—191no—
179#423C2×D1911yescharacteristic
180C2×C4⋊C8—191no—
181C2×C4⋊C8C2×D1911yescharacteristic
182#408—381no—
183C2×C4×C8—191no—
184#341—381no—
185#341—381no—
186#334—381no—
187#334—381no—
188#332—21no—
189#332—381no—
190#331—21no—
191#331—381no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19—82no—
195C2×C19#180411yescharacteristic
196C2×C19#181311yescharacteristic
197C2×C19#181511yescharacteristic
198C2×#41—21no—
199#131—762no—
200#131—762no—
201C2×M16—21no—
202C2×M16—382no—
203C2×M16—381no—
204C2×M16—381no—
205C22×C8—21no—
206C22×C8—191no—
207C22×C8—191no—
208C22×C8—382no—
209C22×C8—381no—
210C4⋊Q8C22⋊D1911yescharacteristic
211#127C22⋊D1911yescharacteristic
212#124—21no—
213#121—21no—
214#121Dic3812yes—
215C4×D4—21no—
216C4×D4C4×D1912yes—
217C2×C42C22×D1911yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—192no—
223C4⋊C8—381no—
224C4⋊C8—381no—
225C4⋊C8—381no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C22⋊C8—382no—
229C22⋊C8—382no—
230C4×C8—191no—
231C4×C8—191no—
232C4×C8—191no—
233C4×C8—191no—
234C19#868611yescharacteristic, complemented, Sylow
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4Dic19⋊C412yes—
244C22×C4—22no—
245C22×C4C2×Dic3811yescharacteristic
246C22×C4D4×D1911yescharacteristic
247C22×C4#6454311yescharacteristic
248M16—41no—
249M16—41no—
250M16—764no—
251M16—761no—
252M16—761no—
253M16—761no—
254M16—761no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—81no—
258C2×C8—191no—
259C2×C8—191no—
260C2×C8—191no—
261C2×C8—191no—
262C2×C8—381no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—382no—
267C2×C8—764no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—1521no—
271C4⋊C4—21no—
272C4⋊C4Dic19⋊C412yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C42C2×C4×D1911yescharacteristic
276C42D4×D1911yescharacteristic
277C42#6454311yescharacteristic
278C42C2×C22⋊D1911yescharacteristic
279C23—22no—
280C23#1059732411yescharacteristic
281Q8—41no—
282Q8—41no—
283D4—42no—
284D4—42no—
285D4—42no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4#1059732311yescharacteristic
297C2×C4#1059732411yescharacteristic
298C2×C4C22⋊C4×D1911yescharacteristic
299C2×C4#1059735711yescharacteristic
300C2×C4#1059735811yescharacteristic
301C2×C4#1059736011yescharacteristic
302C2×C4#1059736211yescharacteristic
303C2×C4C2×Dic19⋊C411yescharacteristic
304C2×C4#1059738511yescharacteristic
305C2×C4#1059738511yescharacteristic
306C8—81no—
307C8—81no—
308C8—381no—
309C8—381no—
310C8—381no—
311C8—381no—
312C8—762no—
313C8—1521no—
314C8—1521no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22#1192640211yescharacteristic
321C22#1192684211yescharacteristic
322C22#1192684611yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4#1192653711yescharacteristic
328C4#1192654711yescharacteristic
329C4#1192675711yescharacteristic
330C4#1192676111yescharacteristic
331C4#1192680511yescharacteristic
332C4#1192680911yescharacteristic
333C2—21no—
334C2—21no—
335C2—82no—
336C2#1456364311yescharacteristic
337C2#1456368311yescharacteristic
338C2#1456369211yescharacteristic
subgroupG/H
centerC22#11926402
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1547C2
socleC22×C19#380
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1547D19
hypocenterC19#8686
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #14563772C2semidirect
3. C2×#11926294C2semidirect
5. #14561510C2semidirect
6. #14561509C2semidirect
234. C19#8686semidirect

Maximal subgroups

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

subgroupindex
#145723472
#145637722
C2×#119262942
#145623122
#145615102
#145615092
C19×#15472
#868619