Finite Group Databasebeta

← #18077984

Subgroups — #18077984

Order 4864.

456 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#14572718C211yesmaximal, characteristic
2C2×#11926652C211yesmaximal, characteristic
3#14562031C211yesmaximal, characteristic
4#14562029C211yesmaximal, characteristic
5#14561958C211yesmaximal, characteristic
6#14561466C211yesmaximal, characteristic
7C19×#1281C211yesmaximal, characteristic
8C22×Dic76C411yescharacteristic
9C2×C4×Dic38C2211yescharacteristic
10C2×C4×Dic38C2211yescharacteristic
11#11926674—22no—
12#11926671—22no—
13#11926652—22no—
14#11926652—22no—
15#11926598—22no—
16#11926597C2211yescharacteristic
17#11926597C2211yescharacteristic
18C2×#10597274C411yescharacteristic
19C2×#10597273C411yescharacteristic
20C2×#10597273C411yescharacteristic
21#11926276—22no—
22#11926274—22no—
23#11926269—22no—
24C19×#431C2211yescharacteristic
25C19×#431C2211yescharacteristic
26C2×C19×#97C2211yescharacteristic
27C22×Dic38C2×C411yescharacteristic
28C22×Dic38C2×C411yescharacteristic
29C22×C8×C19C2×C411yescharacteristic
30C22×C8×C19C2×C411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19C2×C411yescharacteristic
33C2×C4⋊Dic19C2×C411yescharacteristic
34C2×Dic19⋊C4—21no—
35C2×Dic19⋊C4—21no—
36C2×C4×Dic19—21no—
37C2×C4×Dic19—21no—
38C2×Dic76—22no—
39C2×Dic76—22no—
40C2×Dic76—22no—
41C4×Dic38—21no—
42C4×Dic38—21no—
43C4×Dic38—21no—
44C4×Dic38—21no—
45C4×Dic38—21no—
46C4×Dic38—21no—
47C4×Dic38D412yes—
48C4×Dic38D412yes—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C22⋊C8—21no—
52C19×C22⋊C8D412yes—
53C19×#97—21no—
54C19×#97—21no—
55C4×C8×C19—21no—
56C4×C8×C19—21no—
57C22⋊(C19⋊C8)—21no—
58C22⋊(C19⋊C8)—21no—
59#10597274—22no—
60#10597273—22no—
61#10597273—22no—
62#10597272—24no—
63Dic19⋊C8—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4×C19⋊C8—21no—
67C4×C19⋊C8D412yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4111yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C2×Dic38—21no—
76C2×Dic38—21no—
77C2×Dic38—21no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—21no—
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×Dic38—21no—
84C2×Dic38—21no—
85C2×Dic38C22⋊C412yes—
86C2×Dic38M1612yes—
87C2×C8×C19—21no—
88C2×C8×C19—21no—
89C2×C8×C19—21no—
90C2×C8×C19—22no—
91C2×C8×C19—21no—
92C2×C8×C19—21no—
93C2×C8×C19—41no—
94C2×C8×C19M1612yes—
95C42×C19C2×D411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4111yescharacteristic
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19C22⋊C412yes—
103Dic19⋊C4—22no—
104Dic19⋊C4—22no—
105Dic19⋊C4—41no—
106Dic19⋊C4—41no—
107C4×Dic19—22no—
108C4×Dic19—22no—
109C4×Dic19—41no—
110C4×Dic19—41no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113Dic76—28no—
114#9092—191nomaximal, Sylow
115C23×C19C4×D411yescharacteristic
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19C2×C22⋊C411yescharacteristic
119C2×C4×C19C4×D411yescharacteristic
120C2×C4×C19#12011yescharacteristic
121C2×C4×C19#12111yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19#12311yescharacteristic
124C2×C4×C19C2×M1611yescharacteristic
125C2×C4×C19C2×M1611yescharacteristic
126C2×C4×C19#13111yescharacteristic
127C2×C4×C19#13111yescharacteristic
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—81no—
137C2×Dic19—81no—
138Dic38—22no—
139Dic38—22no—
140Dic38—22no—
141Dic38—22no—
142Dic38—41no—
143Dic38—41no—
144Dic38—41no—
145Dic38—41no—
146C8×C19—22no—
147C8×C19—42no—
148C8×C19—41no—
149C8×C19—81no—
150C19⋊C8—42no—
151C19⋊C8—81no—
152#2983—191no—
153C2×#441—191no—
154#1479—191no—
155#1479—191no—
156#1461—191no—
157#1281D1911yescharacteristic
158#1275—191no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19#38611yescharacteristic
162C22×C19#43511yescharacteristic
163C22×C19#43611yescharacteristic
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19#40711yescharacteristic
169C4×C19#40811yescharacteristic
170C4×C19#43511yescharacteristic
171C4×C19#43611yescharacteristic
172Dic19—42no—
173Dic19—42no—
174Dic19—42no—
175Dic19—81no—
176C22×Q16—191no—
177C2×C4×Q8—191no—
178C2×C4×Q8—191no—
179#446—382no—
180#446—382no—
181#441—382no—
182#441—382no—
183#432—382no—
184#431—191no—
185#431—191no—
186#431C2×D1911yescharacteristic
187#431C2×D1911yescharacteristic
188C2×#106—191no—
189C2×#103—191no—
190C2×#103—191no—
191C2×#97C2×D1911yescharacteristic
192Q8⋊C8—382no—
193Q8⋊C8—382no—
194#324—382no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19#187011yescharacteristic
198C2×C19#190211yescharacteristic
199C2×C19#190511yescharacteristic
200C22×Q8—191no—
201C22×Q8—191no—
202C2×Q16—382no—
203C2×Q16—382no—
204C2×Q16—382no—
205C22×C8C4×D1911yescharacteristic
206C22×C8C4×D1911yescharacteristic
207C4×Q8—192no—
208C4×Q8—192no—
209C4×Q8—381no—
210C4×Q8—381no—
211C4×Q8—381no—
212C4×Q8—381no—
213C4×Q8—381no—
214C4×Q8—381no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—191no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C42—381no—
220C2×C42—381no—
221C2×C42C22×D1911yescharacteristic
222#106—382no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—384no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228#103—382no—
229#103—382no—
230C22⋊C8—21no—
231C22⋊C8—381no—
232C22⋊C8—381no—
233C22⋊C8D7612yes—
234#97—21no—
235#97—21no—
236#97—384no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—192no—
240C4×C8—381no—
241C19#909211yescharacteristic, complemented, Sylow
242C2×Q8—192no—
243C2×Q8—192no—
244C2×Q8—381no—
245C2×Q8—381no—
246C2×Q8—381no—
247C2×Q8—381no—
248C2×Q8—381no—
249C2×Q8—381no—
250C2×Q8—381no—
251C2×Q8—381no—
252C2×Q8—381no—
253C2×Q8—381no—
254C22×C4—381no—
255C22×C4—381no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4C2×C4×D1911yescharacteristic
259C22×C4C2×D7611yescharacteristic
260C22×C4#6454111yescharacteristic
261Q16—388no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—382no—
270C2×C8—761no—
271C2×C8#6451512yes—
272C4⋊C4—192no—
273C4⋊C4—382no—
274C4⋊C4—381no—
275C4⋊C4—382no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C42—382no—
281C42—382no—
282C42—761no—
283C42—761no—
284C42D4×D1911yescharacteristic
285C42D4×D1911yescharacteristic
286C42D4×D1911yescharacteristic
287C42#6454511yescharacteristic
288C23C4×D7611yescharacteristic
289Q8—382no—
290Q8—382no—
291Q8—382no—
292Q8—382no—
293Q8—761no—
294Q8—761no—
295Q8—761no—
296Q8—761no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—382no—
300C2×C4—382no—
301C2×C4—382no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—1521no—
308C2×C4—1521no—
309C2×C4C22⋊C4×D1911yescharacteristic
310C2×C4#1059732811yescharacteristic
311C2×C4#1059733011yescharacteristic
312C2×C4#1059733911yescharacteristic
313C2×C4#1059734011yescharacteristic
314C2×C4#1059734111yescharacteristic
315C2×C4C2×#6451511yescharacteristic
316C2×C4#1059734711yescharacteristic
317C2×C4M16×D1911yescharacteristic
318C2×C4#1059735311yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—762no—
324C8—1521no—
325C22—21no—
326C22—21no—
327C22#1192642211yescharacteristic
328C22#1192661711yescharacteristic
329C22#1192662311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—762no—
335C4—762no—
336C4—762no—
337C4—1521no—
338C4#1192650611yescharacteristic
339C4#1192650911yescharacteristic
340C4#1192661411yescharacteristic
341C4#1192662111yescharacteristic
342C2—21no—
343C2—21no—
344C2#1456393111yescharacteristic
345C2#1456410711yescharacteristic
346C2#1456412811yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1281C2
socleC22×C19#386
prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1281D19
hypocenterC19#9092
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
241. C19#9092semidirect

Maximal subgroups

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

subgroupindex
#145727182
C2×#119266522
#145620312
#145620292
#145619582
#145614662
C19×#12812
#909219