Finite Group Databasebeta

← #18079080

Subgroups — #18079080

Order 4864.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574779C211yesmaximal, characteristic
2#14572582C211yesmaximal, characteristic
3#14562326C211yesmaximal, characteristic
4C2×#11926290C211yesmaximal, characteristic
5#14561530C211yesmaximal, characteristic
6#14561486C211yesmaximal, characteristic
7C19×#1966C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926940—21no—
10#11926896—21no—
11#11926874C414yes—
12#11926826—22no—
13#11926674—21no—
14#11926672—22no—
15C8×Dic38—21no—
16#11926597C2211yescharacteristic
17#11926572—21no—
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926502—21no—
21#11926292—21no—
22#11926290—21no—
23#11926290—21no—
24#11926289—21no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C19×#423C2211yescharacteristic
27C2×C19×#101—21no—
28C2×C19×#101—21no—
29C4×M16×C19C2211yescharacteristic
30C22×Q8×C19—21no—
31C2×M16×C19—21no—
32C2×M16×C19D411yescharacteristic
33C2×M16×C19D411yescharacteristic
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41#10597372—21no—
42#10597370—21no—
43#10597370C2×C412yes—
44C22×C19⋊C8—21no—
45C22×C19⋊C8—21no—
46#10597316—21no—
47#10597315D411yescharacteristic
48#10597315D411yescharacteristic
49C4×Dic38—21no—
50C4×Dic38D412yes—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×#101—42no—
54C19×#101—42no—
55C19×#97—21no—
56C4×C8×C19—21no—
57C22⋊(C19⋊C8)C2×C412yes—
58#10597272—22no—
59Dic19⋊C8—22no—
60Dic19⋊C8—22no—
61C8×Dic19—22no—
62#10597267—24no—
63#10597265—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)D411yescharacteristic
69C4⋊(C19⋊C8)D411yescharacteristic
70C4×C19⋊C8—21no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C2×Q8×C19—41no—
74C2×Q8×C19—41no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C22×C4×C19—22no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C22⋊C412yes—
83M16×C19—21no—
84M16×C19—21no—
85M16×C19—21no—
86M16×C19—41no—
87M16×C19—41no—
88M16×C19SD1612yes—
89C2×C8×C19—21no—
90C2×C8×C19—21no—
91C2×C8×C19—41no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19#4111yescharacteristic
100C22⋊Dic19—22no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19C22⋊C412yes—
105Dic19⋊C4—22no—
106Dic19⋊C4—22no—
107C4×Dic19—22no—
108C2×C19⋊C8—22no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—81no—
115#9272—191nomaximal, Sylow
116C23×C19C4×D411yescharacteristic
117Q8×C19—81no—
118Q8×C19—81no—
119Q8×C19—81no—
120Q8×C19—81no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12311yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C2×Dic19—22no—
138C2×Dic19—22no—
139Dic38—41no—
140Dic38—41no—
141Dic38—42no—
142C8×C19—22no—
143C8×C19—41no—
144C8×C19—81no—
145C19⋊C8—42no—
146C19⋊C8—41no—
147C19⋊C8—41no—
148C19⋊C8—81no—
149#3229—191no—
150#2962—191no—
151#1966D1911yescharacteristic
152#1550—191no—
153C2×#332—191no—
154#1301—191no—
155#1283—191no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19#38611yescharacteristic
159C22×C19C4×SD1611yescharacteristic
160C22×C19#44011yescharacteristic
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—82no—
165C4×C19#44811yescharacteristic
166C4×C19#44911yescharacteristic
167C4×C19#46011yescharacteristic
168C4×C19#46411yescharacteristic
169C4×C19#47111yescharacteristic
170C4×C19#47311yescharacteristic
171Dic19—42no—
172Dic19—42no—
173#533—191no—
174C2×C4⋊Q8C2×D1911yescharacteristic
175#498—381no—
176#487—381no—
177#483—194no—
178#475—382no—
179#446—381no—
180#446—382no—
181C8×Q8—381no—
182#431—191no—
183#424—381no—
184#423C2×D1911yescharacteristic
185C2×C4⋊C8—191no—
186C2×C4⋊C8—191no—
187C2×#101—21no—
188C2×#101—21no—
189#405—381no—
190C4×M16C2×D1911yescharacteristic
191#333—381no—
192#332—381no—
193#332—381no—
194#332—381no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19#188011yescharacteristic
198C2×C19#190811yescharacteristic
199C2×C19#191511yescharacteristic
200C22×Q8—21no—
201C2×M16—21no—
202C2×M16C22⋊D1911yescharacteristic
203C2×M16C22⋊D1911yescharacteristic
204C22×C8—381no—
205C22×C8—381no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—191no—
211C4⋊Q8—191no—
212#125—381no—
213C22⋊Q8—192no—
214C22⋊Q8—381no—
215C4×Q8—192no—
216C4×Q8—381no—
217#117—381no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C4×D1912yes—
220C2×C42C22×D1911yescharacteristic
221#106—384no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—191no—
225C4⋊C8—191no—
226C4⋊C8—382no—
227C4⋊C8—382no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232#103—384no—
233#101—42no—
234#101—42no—
235C22⋊C8—192no—
236#97—21no—
237#97—382no—
238C4×C8—21no—
239C4×C8—382no—
240C4×C8—381no—
241C19#927211yescharacteristic, complemented, Sylow
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—192no—
249C2×Q8—381no—
250C22×C4—22no—
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4#6454111yescharacteristic
253C22×C4C2×C22⋊D1911yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—41no—
258M16—41no—
259M16#6452612yes—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—382no—
266C2×C8—761no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—1521no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—192no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C4⋊C4—382no—
278C4⋊C4—382no—
279C4⋊C4—381no—
280C22⋊C4—382no—
281C42—382no—
282C42D4×D1911yescharacteristic
283C42D4×D1911yescharacteristic
284C42D4×D1911yescharacteristic
285C42#6454311yescharacteristic
286C23C4×C22⋊D1911yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—81no—
290Q8—81no—
291Q8—762no—
292Q8—761no—
293Q8—761no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—382no—
301C2×C4—382no—
302C2×C4C22⋊C4×D1911yescharacteristic
303C2×C4(C22⋊D19)⋊C411yescharacteristic
304C2×C4#1059732911yescharacteristic
305C2×C4#1059733011yescharacteristic
306C2×C4#1059737811yescharacteristic
307C2×C4C2×#6452611yescharacteristic
308C2×C4#1059738311yescharacteristic
309C2×C4#1059738411yescharacteristic
310C2×C4#1059739611yescharacteristic
311C2×C4#1059739711yescharacteristic
312C8—22no—
313C8—41no—
314C8—81no—
315C8—762no—
316C8—761no—
317C8—761no—
318C8—1521no—
319C22—21no—
320C22—21no—
321C22#1192642011yescharacteristic
322C22C4×#6452611yescharacteristic
323C22#1192664411yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—762no—
329C4—762no—
330C4#1192668211yescharacteristic
331C4#1192668711yescharacteristic
332C4#1192674111yescharacteristic
333C4#1192676311yescharacteristic
334C4#1192681011yescharacteristic
335C4#1192681811yescharacteristic
336C2—21no—
337C2—21no—
338C2#1456399311yescharacteristic
339C2#1456414711yescharacteristic
340C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1966C2
socleC22×C19#386
prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1966D19
hypocenterC19#9272
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
241. C19#9272semidirect

Maximal subgroups

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

subgroupindex
#145747792
#145725822
#145623262
C2×#119262902
#145615302
#145614862
C19×#19662
#927219