Finite Group Databasebeta

← #18075781

Subgroups — #18075781

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572347C211yesmaximal, characteristic
2#14563806C211yesmaximal, 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—
13C2×#10597279—21no—
14C2×#10597279—21no—
15#11926568C2211yescharacteristic
16#11926568C2211yescharacteristic
17C2×C4⋊(C19⋊C8)C2211yescharacteristic
18#11926511—21no—
19C2×C4×C19⋊C8C2211yescharacteristic
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—
55#10597279—42no—
56#10597279—42no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)C2×C412yes—
63C4×C19⋊C8C2×C411yescharacteristic
64C4×C19⋊C8C2×C411yescharacteristic
65C4×C19⋊C8D411yescharacteristic
66C4×C19⋊C8D411yescharacteristic
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
80M16×C19—41no—
81M16×C19—41no—
82C2×C8×C19—41no—
83C2×C8×C19—41no—
84C2×C8×C19—81no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19C4⋊C412yes—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C42×C19C22×C411yescharacteristic
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93#64520—41no—
94#64520—41no—
95#64520—44no—
96#64520—41no—
97#64520—41no—
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
109C2×C19⋊C8D812yes—
110C2×C19⋊C8SD1612yes—
111#8682—191nomaximal, Sylow
112C23×C19—22no—
113C23×C19C22⋊Q811yescharacteristic
114Q8×C19—41no—
115Q8×C19—41no—
116D4×C19—42no—
117D4×C19—42no—
118D4×C19—42no—
119D4×C19—41no—
120D4×C19—41no—
121D4×C19—41no—
122D4×C19—41no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19C2×C22⋊C411yescharacteristic
130C2×C4×C19C2×C4⋊C411yescharacteristic
131C2×C4×C19#11711yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19C2×D811yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C8×C19—81no—
140C8×C19—81no—
141C19⋊C8—21no—
142C19⋊C8—21no—
143C19⋊C8—42no—
144C19⋊C8—81no—
145C19⋊C8—81no—
146C19⋊C8#10212yes—
147C19⋊C8#10212yes—
148#2931—191no—
149#1848—191no—
150C2×#334—191no—
151#1547—191no—
152#1547D1911yescharacteristic
153#1292—191no—
154#1292—191no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—42no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19#38011yescharacteristic
161C22×C19#47411yescharacteristic
162C22×C19#47611yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—42no—
167C4×C19C2×#10211yescharacteristic
168C4×C19#41711yescharacteristic
169C4×C19#45911yescharacteristic
170C4×C19#46111yescharacteristic
171C4×C19#47111yescharacteristic
172C4×C19#47111yescharacteristic
173C2×#131—381no—
174#532C2×D1911yescharacteristic
175#436—192no—
176#436—381no—
177C8×D4—192no—
178C8×D4—381no—
179C2×#108—381no—
180C2×#108—381no—
181#423—191no—
182#423—191no—
183#423C2×D1911yescharacteristic
184C2×C4⋊C8—191no—
185C2×C4⋊C8C2×D1911yescharacteristic
186#408—381no—
187C2×C4×C8—191no—
188#334—381no—
189#334—381no—
190#332—21no—
191#332—381no—
192#331—21no—
193#331—381no—
194C2×C19—21no—
195C2×C19—21no—
196C2×C19—82no—
197C2×C19#180211yescharacteristic
198C2×C19#181311yescharacteristic
199C2×C19#181511yescharacteristic
200C2×#41—21no—
201#131—762no—
202#131—762no—
203C2×M16—21no—
204C2×M16—382no—
205C2×M16—381no—
206C2×M16—381no—
207C22×C8—21no—
208C22×C8—191no—
209C22×C8—191no—
210C22×C8—382no—
211C22×C8—381no—
212C4⋊Q8C22⋊D1911yescharacteristic
213#127C22⋊D1911yescharacteristic
214#124—21no—
215#121—21no—
216#121Dic3812yes—
217C4×D4—21no—
218C4×D4C4×D1912yes—
219C2×C42C22×D1911yescharacteristic
220#108—762no—
221#108—762no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—192no—
227C4⋊C8—381no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C22⋊C8—382no—
233C22⋊C8—382no—
234C4×C8—191no—
235C4×C8—191no—
236C4×C8—191no—
237C4×C8—191no—
238C19#868211yescharacteristic, complemented, Sylow
239#41—41no—
240#41—41no—
241#41—41no—
242#41—41no—
243C2×Q8—21no—
244C2×D4—22no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4Dic19⋊C412yes—
248C22×C4—22no—
249C22×C4C2×Dic3811yescharacteristic
250C22×C4D4×D1911yescharacteristic
251C22×C4#6454311yescharacteristic
252M16—41no—
253M16—41no—
254M16—764no—
255M16—761no—
256M16—761no—
257M16—761no—
258M16—761no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—81no—
262C2×C8—191no—
263C2×C8—191no—
264C2×C8—192no—
265C2×C8—192no—
266C2×C8—191no—
267C2×C8—191no—
268C2×C8—381no—
269C2×C8—381no—
270C2×C8—382no—
271C2×C8—764no—
272C2×C8—761no—
273C2×C8—761no—
274C2×C8—1521no—
275C4⋊C4—21no—
276C4⋊C4Dic19⋊C412yes—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C42C2×C4×D1911yescharacteristic
280C42D4×D1911yescharacteristic
281C42#6454311yescharacteristic
282C42C2×C22⋊D1911yescharacteristic
283C23—22no—
284C23#1059732411yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—42no—
288D4—42no—
289D4—42no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—41no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4#1059732311yescharacteristic
301C2×C4#1059732411yescharacteristic
302C2×C4C22⋊C4×D1911yescharacteristic
303C2×C4D8×D1911yescharacteristic
304C2×C4#1059735711yescharacteristic
305C2×C4SD16×D1911yescharacteristic
306C2×C4#1059736111yescharacteristic
307C2×C4C2×Dic19⋊C411yescharacteristic
308C2×C4#1059738511yescharacteristic
309C2×C4#1059738511yescharacteristic
310C8—81no—
311C8—81no—
312C8—192no—
313C8—192no—
314C8—381no—
315C8—381no—
316C8—762no—
317C8—1521no—
318C8—1521no—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22#1192640211yescharacteristic
325C22#1192682211yescharacteristic
326C22#1192683211yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4#102×D1911yescharacteristic
332C4#1192654211yescharacteristic
333C4#1192673711yescharacteristic
334C4#1192674711yescharacteristic
335C4#1192680511yescharacteristic
336C4#1192680911yescharacteristic
337C2—21no—
338C2—21no—
339C2—82no—
340C2#1456363311yescharacteristic
341C2#1456368311yescharacteristic
342C2#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#8682
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. #14563806C2semidirect
3. C2×#11926294C2semidirect
5. #14561510C2semidirect
6. #14561509C2semidirect
238. C19#8682semidirect

Maximal subgroups

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

subgroupindex
#145723472
#145638062
C2×#119262942
#145623122
#145615102
#145615092
C19×#15472
#868219