Finite Group Databasebeta

← #18078479

Subgroups — #18078479

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573107C211yesmaximal, characteristic
2#14566556C211yesmaximal, characteristic, complemented
3#14562196C211yesmaximal, characteristic
4#14562131C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic, complemented
6#14561494C211yesmaximal, characteristic, complemented
7C19×#1479C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9#11927094C2211yescharacteristic
10C2×Q8×Dic19—21no—
11#11926766—22no—
12#11926754C412yescomplemented
13#11926744C412yescomplemented
14#11926568C2211yescharacteristic
15#11926543—21no—
16#11926443—22no—
17#11926443—21no—
18#11926410—21no—
19#11926410C2211yescharacteristic
20C4×C4⋊Dic19—21no—
21C4×C4⋊Dic19C2211yescharacteristic
22#11926279—21no—
23#11926279—21no—
24#11926279—22no—
25C2×C4×Q8×C19C2211yescharacteristic
26C19×#431C2211yescharacteristic
27C19×#431C2211yescharacteristic
28C19×Q8⋊C8—22no—
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×C19D411yescharacteristic
37C2×C42×C19—21no—
38C2×C42×C19C2311yescharacteristic
39Q8×Dic19—42no—
40Q8×Dic19—42no—
41C2×#64528—22no—
42#10597388—42no—
43#10597388—42no—
44C2×#64527—22no—
45#10597376—21no—
46#10597376—21no—
47C2×C4⋊Dic19—22no—
48C2×C4⋊Dic19—22no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4×Dic19—22no—
52C2×C4×Dic19—21no—
53C2×#64520—21no—
54#10597321—21no—
55#10597320C2×C411yescharacteristic
56C4×D76—21no—
57C4×D76—21no—
58#10597315C2×C411yescharacteristic
59C19×C4⋊C8—21no—
60C19×C4⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C4×C8×C19—21no—
64C4×C8×C19—21no—
65C19⋊#95—22no—
66C19⋊#95—21no—
67C19⋊#95D411yescharacteristic
68C19⋊#95D411yescharacteristic
69C19⋊#95D412yes—
70#10597267—22no—
71#10597266—22no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)C2×C412yes—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19C22⋊C412yes—
78C2×Q8×C19D812yes—
79C2×Q8×C19SD1612yes—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C2×C22⋊D19—41no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89#64541—41no—
90#64541—41no—
91#64541—41no—
92#64541—41no—
93C2×D76—21no—
94C2×D76—21no—
95C2×D76—21no—
96C2×C4×D19—41no—
97C2×Dic38—21no—
98C2×C8×C19—41no—
99C2×C8×C19—41no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19C22⋊C412yes—
104C42×C19—22no—
105C42×C19—22no—
106C42×C19C22×C411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19#4111yescharacteristic
109C42×C19#4111yescharacteristic
110#64528—44no—
111#64527—44no—
112(C2×D19)⋊C4—41no—
113(C2×D19)⋊C4—41no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—42no—
117C4⋊Dic19—44no—
118C4⋊Dic19—44no—
119C4⋊Dic19—41no—
120C4⋊Dic19—41no—
121C4×Dic19—44no—
122C4×Dic19—41no—
123C4×Dic19—41no—
124#64520—41no—
125#64520—41no—
126C2×C19⋊C8—22no—
127#9180—191nomaximal, Sylow
128C23×C19#12011yescharacteristic
129C22×D19—41no—
130Q8×C19—22no—
131Q8×C19—22no—
132Q8×C19—22no—
133Q8×C19#10214yes—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19C4×D411yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12311yescharacteristic
147C2×C4×C19C2×D811yescharacteristic
148C2×C4×C19C2×SD1611yescharacteristic
149C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C19#13711yescharacteristic
151C22⋊D19—81no—
152C22⋊D19—81no—
153C2×Dic19—22no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—42no—
158C2×Dic19—41no—
159C2×Dic19—42no—
160C2×Dic19—41no—
161C2×Dic19—42no—
162C2×Dic19—41no—
163D76—41no—
164D76—41no—
165D76—81no—
166D76—81no—
167C4×D19—81no—
168C4×D19—81no—
169Dic38—41no—
170Dic38—41no—
171C8×C19—81no—
172C8×C19—81no—
173C19⋊C8—42no—
174#3037—191no—
175#2351—191no—
176#1517—191no—
177#1502—191no—
178#1479D1911yescharacteristic, complemented
179#1303—191no—
180#1286—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19#38611yescharacteristic
184C22×C19#44711yescharacteristic
185C22×C19#44811yescharacteristic
186C2×D19—81no—
187C2×D19—81no—
188C2×D19—81no—
189C4×C19—24no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—42no—
195C4×C19C2×#10211yescharacteristic
196C4×C19#41711yescharacteristic
197C4×C19#48011yescharacteristic
198C4×C19#48111yescharacteristic
199Dic19—42no—
200Dic19—82no—
201Dic19—81no—
202Dic19—81no—
203C2×#137—381no—
204#532—191no—
205C2×C4×Q8—381no—
206C2×C4×Q8C2×D1911yescharacteristic
207#464—382no—
208#462—192no—
209#460—192no—
210#431C2×D1911yescharacteristic
211#431C2×D1911yescharacteristic
212#423—191no—
213#417—381no—
214#389—382no—
215#389—381no—
216#382—191no—
217#382—381no—
218C4×C4⋊C4—191no—
219C4×C4⋊C4—381no—
220#327—381no—
221#327—381no—
222#327—382no—
223Q8⋊C8—22no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19#187411yescharacteristic
227C2×C19#190511yescharacteristic
228C2×C19#190611yescharacteristic
229D19—161no—
230C2×#41—381no—
231C22×Q8D7611yescharacteristic
232#137—762no—
233#137—762no—
234C2×Q16—382no—
235C2×SD16—382no—
236C2×M16—381no—
237C4⋊Q8—191no—
238#127—191no—
239#124—381no—
240#121—381no—
241#121—381no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—762no—
245C4×Q8—762no—
246C4×Q8C4×D1912yes—
247C4×Q8C22⋊D1912yes—
248C4×D4—381no—
249C4×D4—381no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—382no—
252C2×C4⋊C4—382no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4D7611yescharacteristic
256C2×C42—21no—
257C2×C42—382no—
258C2×C42—381no—
259C2×C42C22×D1911yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—192no—
263C4⋊C8—381no—
264#103—382no—
265#102—382no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270#95—191no—
271#95—191no—
272#95—192no—
273#95—382no—
274#95—381no—
275C19#918011yescharacteristic, complemented, Sylow
276#41—761no—
277#41—761no—
278#41—761no—
279#41—761no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—381no—
284C2×Q8#6451612yes—
285C2×Q8D15212yes—
286C2×Q8(C2×D19)⋊C412yes—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—761no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—382no—
296C22×C4—761no—
297C22×C4C2×D7611yescharacteristic
298C22×C4D4×D1911yescharacteristic
299C22×C4D4×D1911yescharacteristic
300Q16—764no—
301SD16—764no—
302M16—761no—
303M16—761no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—382no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—764no—
313C4⋊C4—762no—
314C4⋊C4—764no—
315C4⋊C4—761no—
316C4⋊C4—761no—
317C4⋊C4(C2×D19)⋊C412yes—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C42—22no—
321C42—22no—
322C42—764no—
323C42—761no—
324C42—761no—
325C42C2×C4×D1911yescharacteristic
326C42#6454311yescharacteristic
327C42#6454311yescharacteristic
328C42C2×C22⋊D1911yescharacteristic
329C23—761no—
330C23#1059732811yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—22no—
334Q8—761no—
335Q8—761no—
336Q8#1059727814yes—
337D4—761no—
338D4—761no—
339D4—1521no—
340D4—1521no—
341D4—1521no—
342D4—1521no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—382no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—762no—
355C2×C4—761no—
356C2×C4—762no—
357C2×C4—761no—
358C2×C4—762no—
359C2×C4—761no—
360C2×C4—1521no—
361C2×C4—1521no—
362C2×C4(C22⋊D19)⋊C411yescharacteristic
363C2×C4(C22⋊D19)⋊C411yescharacteristic
364C2×C4#1059733211yescharacteristic
365C2×C4C2×#6451611yescharacteristic
366C2×C4C2×D15211yescharacteristic
367C2×C4#1059735411yescharacteristic
368C2×C4#1059735511yescharacteristic
369C2×C4C2×(C2×D19)⋊C411yescharacteristic
370C2×C4#1059738511yescharacteristic
371C2×C4#1059738511yescharacteristic
372C8—81no—
373C8—81no—
374C8—762no—
375C22—21no—
376C22—21no—
377C22—1521no—
378C22—1521no—
379C22—1521no—
380C22#1192642111yescharacteristic
381C22#1192668011yescharacteristic
382C22#1192668511yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—24no—
388C4—42no—
389C4—762no—
390C4—1522no—
391C4—1521no—
392C4—1521no—
393C4C2×#1059727811yescharacteristic
394C4#1192654611yescharacteristic
395C4#1192685811yescharacteristic
396C4#1192686311yescharacteristic
397C2—21no—
398C2—21no—
399C2—3041no—
400C2#1456395011yescharacteristic
401C2#1456412711yescharacteristic
402C2#1456413411yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1479C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1479D19
hypocenterC19#9180
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #14566556C2semidirect
5. #14561537C2semidirect
6. #14561494C2semidirect
7. C19×#1479C2semidirect
12. #11926754C4semidirect
13. #11926744C4semidirect
178. #1479D19semidirect
275. C19#9180semidirect

Maximal subgroups

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

subgroupindex
#145731072
#145665562
#145621962
#145621312
#145615372
#145614942
C19×#14792
#918019