Finite Group Databasebeta

← #18081921

Subgroups — #18081921

Order 4864.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573957C211yesmaximal, characteristic
2#14563765C211yesmaximal, characteristic, complemented
3#14562200C211yesmaximal, characteristic, complemented
4#14562198C211yesmaximal, characteristic, complemented
5#14562195C211yesmaximal, characteristic
6#14561919C211yesmaximal, characteristic, complemented
7C19×#1517C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926898—21no—
10#11926898—21no—
11#11926894C411yescharacteristic, complemented
12#11926894C411yescharacteristic, complemented
13#11926890C411yescharacteristic, complemented
14#11926890C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16#11926540—21no—
17#11926540—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926410C2211yescharacteristic
20#11926306—21no—
21#11926306—21no—
22#11926282—22no—
23#11926280—22no—
24#11926278—22no—
25#11926266—21no—
26C8×C19⋊C8—21no—
27C19×#532C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#382C2211yescharacteristic
30C19×#327—22no—
31C2×#41×C19—21no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#127C2×C411yescharacteristic
34C19×#124—21no—
35C19×#121—21no—
36C19×#121—21no—
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19C2311yescharacteristic
41#10597372—21no—
42C2×C4⋊Dic19—21no—
43#10597370—21no—
44#10597370—21no—
45C22×C19⋊C8D411yescharacteristic
46C22×C19⋊C8D411yescharacteristic
47#10597316—21no—
48#10597315C2×C411yescharacteristic
49#10597315C2×C411yescharacteristic
50C4×Dic38—21no—
51C4×Dic38—21no—
52C19×C4⋊C8—21no—
53C19×C22⋊C8D412yes—
54C4×C8×C19—21no—
55C19×#95—21no—
56C19×#95—21no—
57#10597292—21no—
58#10597292—21no—
59#10597292—21no—
60#10597292—21no—
61#10597289—21no—
62#10597289—21no—
63#10597289—21no—
64#10597289—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C22⋊(C19⋊C8)D412yes—
68C4⋊(C19⋊C8)—21no—
69C4×C19⋊C8—21no—
70C4×C19⋊C8C2×C411yescharacteristic
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8D411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74#41×C19—41no—
75#41×C19—41no—
76#41×C19—41no—
77#41×C19—41no—
78C2×Q8×C19—21no—
79C2×D4×C19—21no—
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C2×D4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×Dic19—41no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×C8×C19—22no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C42×C19C22×C411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19#4111yescharacteristic
101C42×C19#4111yescharacteristic
102C22⋊Dic19—41no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109Dic19⋊C4—41no—
110Dic19⋊C4—41no—
111C4×Dic19—41no—
112C2×C19⋊C8—21no—
113C2×C19⋊C8—21no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8C22⋊C411yescharacteristic
118C2×C19⋊C8C22⋊C411yescharacteristic
119C2×C19⋊C8C22⋊C411yescharacteristic
120C2×C19⋊C8C22⋊C411yescharacteristic
121#9757—191nomaximal, Sylow
122C23×C19—41no—
123C23×C19#12711yescharacteristic
124Q8×C19—41no—
125Q8×C19—41no—
126D4×C19—41no—
127D4×C19—41no—
128D4×C19—81no—
129D4×C19—81no—
130D4×C19—81no—
131D4×C19—81no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—81no—
136C2×C4×C19—81no—
137C2×C4×C19—81no—
138C2×C4×C19—81no—
139C2×C4×C19—81no—
140C2×C4×C19C2×C22⋊C411yescharacteristic
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C2×C4×C19#12411yescharacteristic
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19#13511yescharacteristic
148C2×C4×C19#13511yescharacteristic
149C2×C4×C19#13511yescharacteristic
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—81no—
153C2×Dic19—81no—
154C2×Dic19—81no—
155Dic38—81no—
156Dic38—81no—
157C8×C19—42no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161C19⋊C8—21no—
162C19⋊C8—42no—
163#3131—191no—
164#1835—191no—
165#1518—191no—
166#1518—191no—
167#1517—191no—
168#1517D1911yescharacteristic
169#1450—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—81no—
173C22×C19—81no—
174C22×C19—81no—
175C22×C19#39011yescharacteristic
176C22×C19#49511yescharacteristic
177C22×C19#49511yescharacteristic
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—81no—
183C4×C19—161no—
184C4×C19#41611yescharacteristic
185C4×C19#41611yescharacteristic
186C4×C19#48811yescharacteristic
187C4×C19#48811yescharacteristic
188Dic19—81no—
189Dic19—81no—
190Dic19—161no—
191#533—191no—
192#532C2×D1911yescharacteristic
193#488—381no—
194#488—381no—
195#487—191no—
196#487—191no—
197#486—191no—
198#486—191no—
199#431—191no—
200#431C2×D1911yescharacteristic
201#416—381no—
202#416—381no—
203C2×C4×C8—191no—
204#382—191no—
205#382C2×D1911yescharacteristic
206#340—381no—
207#340—381no—
208#328—382no—
209#328—382no—
210#327—22no—
211#327—382no—
212#322—381no—
213C82—381no—
214C2×C19—21no—
215C2×C19—21no—
216C2×C19—161no—
217C2×C19#195811yescharacteristic
218C2×C19#197611yescharacteristic
219C2×C19#197611yescharacteristic
220C2×#41—21no—
221C22×C8—191no—
222C22×C8—191no—
223C4⋊Q8—191no—
224C4⋊Q8—191no—
225C4⋊Q8C4×D1911yescharacteristic
226#127C4×D1911yescharacteristic
227#125—381no—
228#124—21no—
229C22⋊Q8—381no—
230C22⋊Q8—381no—
231#121—21no—
232#121—21no—
233C4×Q8—381no—
234C4×Q8—381no—
235C4×D4—21no—
236C4×D4—21no—
237#117—381no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—381no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—381no—
243#103—381no—
244#103—381no—
245#103—381no—
246#103—381no—
247#102—381no—
248#102—381no—
249#102—381no—
250#102—381no—
251C22⋊C8—192no—
252C22⋊C8C22⋊D1912yes—
253C4×C8—21no—
254C4×C8—191no—
255C4×C8—191no—
256C4×C8—191no—
257C4×C8—191no—
258C4×C8—381no—
259#95—21no—
260#95—21no—
261#95—381no—
262#95—381no—
263C19#975711yescharacteristic, complemented, Sylow
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—381no—
270C2×Q8—381no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—761no—
278C22×C4D4×D1911yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4C2×C22⋊D1911yescharacteristic
281C2×C8—22no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—191no—
285C2×C8—191no—
286C2×C8—381no—
287C2×C8—381no—
288C2×C8—381no—
289C2×C8—381no—
290C2×C8—382no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4—381no—
299C4⋊C4—761no—
300C4⋊C4—761no—
301C4⋊C4—761no—
302C4⋊C4—761no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—761no—
306C42—761no—
307C42C2×C4×D1911yescharacteristic
308C42#6454111yescharacteristic
309C42D4×D1911yescharacteristic
310C42#6454311yescharacteristic
311C23—41no—
312C23#1059738611yescharacteristic
313Q8—41no—
314Q8—41no—
315Q8—1521no—
316Q8—1521no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—1521no—
334C2×C4—1521no—
335C2×C4—1521no—
336C2×C4C22⋊C4×D1911yescharacteristic
337C2×C4(C22⋊D19)⋊C411yescharacteristic
338C2×C4#1059733011yescharacteristic
339C2×C4#1059733111yescharacteristic
340C2×C4#1059735811yescharacteristic
341C2×C4#1059735811yescharacteristic
342C2×C4#1059736211yescharacteristic
343C2×C4#1059736211yescharacteristic
344C2×C4C4×C22⋊D1911yescharacteristic
345C2×C4#1059738511yescharacteristic
346C8—42no—
347C8—381no—
348C8—381no—
349C8—381no—
350C8—381no—
351C8—762no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1192644411yescharacteristic
358C22#1192692511yescharacteristic
359C22#1192692711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—161no—
366C4—3041no—
367C4—1521no—
368C4—1521no—
369C4#1192653711yescharacteristic
370C4#1192653711yescharacteristic
371C4#1192689711yescharacteristic
372C4#1192689711yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2#1456444511yescharacteristic
377C2#1456453011yescharacteristic
378C2#1456453211yescharacteristic
subgroupG/H
centerC22#11926444
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1517C2
socleC22×C19#390
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1517D19
hypocenterC19#9757
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #14563765C2semidirect
3. #14562200C2semidirect
4. #14562198C2semidirect
6. #14561919C2semidirect
11. #11926894C4semidirect
12. #11926894C4semidirect
13. #11926890C4semidirect
14. #11926890C4semidirect
263. C19#9757semidirect

Maximal subgroups

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

subgroupindex
#145739572
#145637652
#145622002
#145621982
#145621952
#145619192
C19×#15172
#975719