Finite Group Databasebeta

← #18078495

Subgroups — #18078495

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573107C211yesmaximal, characteristic
2#14562194C211yesmaximal, characteristic
3#14562129C211yesmaximal, characteristic
4#14562030C211yesmaximal, characteristic, complemented
5#14561538C211yesmaximal, characteristic, complemented
6#14561493C211yesmaximal, characteristic, complemented
7C19×#2356C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9#11927094C2211yescharacteristic
10#11926766—22no—
11#11926754C412yescomplemented
12#11926744C412yescomplemented
13#11926597C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926568C2211yescharacteristic
16#11926543—21no—
17#11926277—21no—
18#11926277—21no—
19#11926277—22no—
20Q8⋊(C19⋊C8)—22no—
21C2×C4×Q8×C19C2211yescharacteristic
22C19×#391—21no—
23C19×#387—22no—
24C19×#383—21no—
25C19×#382C2211yescharacteristic
26C4×C4⋊C4×C19—21no—
27C4×C4⋊C4×C19C2211yescharacteristic
28C19×#376—21no—
29C22×Q8×C19D411yescharacteristic
30C2×#64541—21no—
31C4×Q8×C19—21no—
32C4×Q8×C19—21no—
33C4×Q8×C19C2×C412yes—
34C4×Q8×C19D412yes—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C42×C19—21no—
40C2×C42×C19—22no—
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C2×#64528—22no—
44#10597388—42no—
45#10597388—42no—
46C2×#64527—22no—
47#10597376—21no—
48#10597376—21no—
49C2×#64520—21no—
50#10597321—21no—
51#10597320C2×C411yescharacteristic
52C4×D76—21no—
53C4×D76—21no—
54#10597315C2×C411yescharacteristic
55C19×#95—22no—
56C19×#95—22no—
57C19×#95—22no—
58C19×#95—21no—
59C19×#95D411yescharacteristic
60C19×#95D411yescharacteristic
61C19×#95D412yes—
62C22⋊(C19⋊C8)—21no—
63C22⋊(C19⋊C8)—21no—
64#10597267—22no—
65#10597266—22no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)C2×C412yes—
70C4×C19⋊C8—21no—
71C4×C19⋊C8—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19C22⋊C412yes—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—21no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C2×C22⋊D19—41no—
87#64541—41no—
88#64541—41no—
89#64541—41no—
90#64541—41no—
91C2×D76—21no—
92C2×D76—21no—
93C2×D76—21no—
94C2×C4×D19—41no—
95C2×Dic38—21no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—42no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19C22⋊C412yes—
103C42×C19—22no—
104C42×C19—22no—
105C42×C19—44no—
106C42×C19—41no—
107C42×C19—41no—
108C42×C19C22×C411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C42×C19#4111yescharacteristic
111C42×C19#4111yescharacteristic
112#64528—44no—
113#64527—44no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118#64520—41no—
119#64520—41no—
120C2×C19⋊C8—22no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123#9182—191nomaximal, Sylow
124C23×C19#12011yescharacteristic
125C22×D19—41no—
126Q8×C19—22no—
127Q8×C19—22no—
128Q8×C19—41no—
129Q8×C19—41no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19C2×C22⋊C411yescharacteristic
147C2×C4×C19C4×D411yescharacteristic
148C2×C4×C19C4×D411yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12311yescharacteristic
152C2×C4×C19#13511yescharacteristic
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
156C22⋊D19—81no—
157C22⋊D19—81no—
158C2×Dic19—41no—
159D76—41no—
160D76—41no—
161D76—81no—
162D76—81no—
163C4×D19—81no—
164C4×D19—81no—
165Dic38—41no—
166Dic38—41no—
167C19⋊C8—42no—
168C19⋊C8—81no—
169C19⋊C8—81no—
170#3037—191no—
171#2356D1911yescharacteristic, complemented
172#1517—191no—
173#1502—191no—
174#1479—191no—
175#1303—191no—
176#1286—191no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19#38611yescharacteristic
180C22×C19#44911yescharacteristic
181C22×C19#44911yescharacteristic
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—42no—
190C4×C19—42no—
191C4×C19—42no—
192C4×C19—81no—
193C4×C19—82no—
194C4×C19#41611yescharacteristic
195C4×C19#41811yescharacteristic
196C4×C19#48211yescharacteristic
197C4×C19#48211yescharacteristic
198Dic19—81no—
199C2×#137—381no—
200#532—191no—
201C2×C4×Q8C2×D1911yescharacteristic
202#464—382no—
203#462—192no—
204#460—192no—
205#431—191no—
206#431—191no—
207#423—191no—
208#417—381no—
209#391—21no—
210#387—22no—
211#383—21no—
212#382C2×D1911yescharacteristic
213C4×C4⋊C4—21no—
214C4×C4⋊C4C2×D1911yescharacteristic
215#376—21no—
216#327—381no—
217#327—381no—
218#327—382no—
219Q8⋊C8—382no—
220C2×C19—21no—
221C2×C19—21no—
222C2×C19#187511yescharacteristic
223C2×C19#190511yescharacteristic
224C2×C19#190611yescharacteristic
225D19—161no—
226C2×#41—381no—
227C22×Q8C22⋊D1911yescharacteristic
228#137—762no—
229#137—762no—
230C2×Q16—382no—
231C2×SD16—382no—
232C2×M16—381no—
233C4⋊Q8—191no—
234#127—191no—
235#124—381no—
236#121—381no—
237#121—381no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8C4×D1912yes—
241C4×Q8D7612yes—
242C4×D4—381no—
243C4×D4—381no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4C22⋊D1911yescharacteristic
248C2×C42—21no—
249C2×C42—22no—
250C2×C42—21no—
251C2×C42C22×D1911yescharacteristic
252C4⋊C8—192no—
253C4⋊C8—381no—
254C4⋊C8—381no—
255C4⋊C8—381no—
256#103—382no—
257#102—382no—
258C22⋊C8—381no—
259C22⋊C8—381no—
260C4×C8—381no—
261C4×C8—381no—
262#95—22no—
263#95—22no—
264#95—22no—
265#95—21no—
266#95C22⋊D1911yescharacteristic
267#95C22⋊D1911yescharacteristic
268#95C22⋊D1912yes—
269C19#918211yescharacteristic, complemented, Sylow
270#41—761no—
271#41—761no—
272#41—761no—
273#41—761no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—381no—
280C2×Q8(C2×D19)⋊C412yes—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4—761no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—761no—
291C22×C4C2×C22⋊D1911yescharacteristic
292C22×C4C2×C22⋊D1911yescharacteristic
293C22×C4C2×C22⋊D1911yescharacteristic
294Q16—764no—
295SD16—764no—
296M16—761no—
297M16—761no—
298C2×C8—382no—
299C2×C8—761no—
300C2×C8—761no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4(C2×D19)⋊C412yes—
310C22⋊C4—761no—
311C22⋊C4—761no—
312C42—22no—
313C42—22no—
314C42—44no—
315C42—41no—
316C42—41no—
317C42C2×C4×D1911yescharacteristic
318C42C2×D7611yescharacteristic
319C42#6454111yescharacteristic
320C42#6454111yescharacteristic
321C23—761no—
322C23#1059739911yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—761no—
328Q8—761no—
329D4—761no—
330D4—761no—
331D4—1521no—
332D4—1521no—
333D4—1521no—
334D4—1521no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—761no—
352C2×C4—1521no—
353C2×C4—1521no—
354C2×C4C2×(C2×D19)⋊C411yescharacteristic
355C2×C4C4×C22⋊D1911yescharacteristic
356C2×C4C4×C22⋊D1911yescharacteristic
357C2×C4#1059737511yescharacteristic
358C2×C4#1059737611yescharacteristic
359C2×C4#1059737611yescharacteristic
360C2×C4#1059739511yescharacteristic
361C2×C4#1059739511yescharacteristic
362C2×C4#1059739611yescharacteristic
363C2×C4#1059739611yescharacteristic
364C8—762no—
365C8—1521no—
366C8—1521no—
367C22—21no—
368C22—21no—
369C22—1521no—
370C22—1521no—
371C22—1521no—
372C22#1192642311yescharacteristic
373C22#1192668911yescharacteristic
374C22#1192668911yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4—81no—
383C4—82no—
384C4—1521no—
385C4#1192653811yescharacteristic
386C4#1192654811yescharacteristic
387C4#1192686811yescharacteristic
388C4#1192686811yescharacteristic
389C2—21no—
390C2—21no—
391C2—3041no—
392C2#1456395711yescharacteristic
393C2#1456412911yescharacteristic
394C2#1456413611yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2356C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#2356D19
hypocenterC19#9182
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
4. #14562030C2semidirect
5. #14561538C2semidirect
6. #14561493C2semidirect
7. C19×#2356C2semidirect
11. #11926754C4semidirect
12. #11926744C4semidirect
171. #2356D19semidirect
269. C19#9182semidirect

Maximal subgroups

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

subgroupindex
#145731072
#145621942
#145621292
#145620302
#145615382
#145614932
C19×#23562
#918219