Finite Group Databasebeta

← #18077424

Subgroups — #18077424

Order 4864.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573090C211yesmaximal, characteristic
2#14572203C211yesmaximal, characteristic, complemented
3#14562087C211yesmaximal, characteristic, complemented
4#14562035C211yesmaximal, characteristic, complemented
5#14561531C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C19×#1476C211yesmaximal, characteristic, complemented
8C2×#10597396—21no—
9C2×#10597394—21no—
10#11927094C2211yescharacteristic
11#11926766—21no—
12#11926759—21no—
13#11926754C411yescharacteristic
14#11926749C411yescharacteristic
15#11926744C411yescharacteristic
16#11926739C411yescharacteristic
17#11926571—22no—
18#11926571—21no—
19#11926568—21no—
20#11926568C2211yescharacteristic
21C2×C4⋊(C19⋊C8)—21no—
22C2×C4⋊(C19⋊C8)C2211yescharacteristic
23C2×C4⋊(C19⋊C8)C2211yescharacteristic
24#11926538—21no—
25#11926273—22no—
26#11926273—21no—
27#11926273—21no—
28C4×#41×C19C2211yescharacteristic
29C19×#431C2211yescharacteristic
30C2×C4×C8×C19C2211yescharacteristic
31C19×Q8⋊C8—21no—
32C19×D4⋊C8—21no—
33C2×#41×C19D411yescharacteristic
34C2×#64541—21no—
35C22×C8×C19—21no—
36C4×Q8×C19C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19C2×C411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C19×#117—21no—
43C19×#117D411yescharacteristic
44C2×C42×C19—21no—
45C2×C42×C19C2311yescharacteristic
46#10597396—42no—
47#10597396—42no—
48#10597394—42no—
49#10597394—42no—
50C2×#64528—21no—
51C2×#64527—21no—
52C2×#64526—21no—
53C2×#64525—21no—
54#10597376—21no—
55#10597376—21no—
56C2×#64520—22no—
57C2×#64520—21no—
58C22×C19⋊C8—22no—
59C22×C19⋊C8—21no—
60C22×C19⋊C8—21no—
61#10597321—21no—
62#10597320C2×C411yescharacteristic
63C4×D76—21no—
64C4×D76—21no—
65#10597315C2×C411yescharacteristic
66C19×C4⋊C8—21no—
67C19×C22⋊C8—21no—
68C4×C8×C19—21no—
69C4×C8×C19—21no—
70C4×C8×C19—21no—
71#10597267—21no—
72#10597267—21no—
73#10597266—21no—
74#10597266—21no—
75C4⋊(C19⋊C8)—22no—
76C4⋊(C19⋊C8)—22no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4⋊(C19⋊C8)C2×C411yescharacteristic
82C4⋊(C19⋊C8)D411yescharacteristic
83C4⋊(C19⋊C8)D411yescharacteristic
84C4⋊(C19⋊C8)D412yes—
85#41×C19—21no—
86#41×C19—21no—
87#41×C19D812yes—
88#41×C19SD1612yes—
89C2×Q8×C19C22⋊C411yescharacteristic
90C2×D4×C19—21no—
91C2×D4×C19C22⋊C411yescharacteristic
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C2×C22⋊D19—41no—
99#64541—41no—
100#64541—41no—
101#64541—41no—
102#64541—41no—
103C2×D76—21no—
104C2×D76—21no—
105C2×D76—21no—
106C2×C4×D19—41no—
107C2×Dic38—21no—
108C2×C8×C19—22no—
109C2×C8×C19—41no—
110C2×C8×C19—41no—
111C2×C8×C19—41no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19C22⋊C411yescharacteristic
115C4⋊C4×C19C22⋊C411yescharacteristic
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19—21no—
122C42×C19C22×C411yescharacteristic
123C42×C19C2×D411yescharacteristic
124C42×C19C2×D411yescharacteristic
125C42×C19C2×D411yescharacteristic
126#64528—42no—
127#64527—42no—
128#64526—42no—
129#64525—42no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134#64520—44no—
135#64520—41no—
136#64520—41no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—44no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146C2×C19⋊C8—41no—
147#8995—191nomaximal, Sylow
148C23×C19—21no—
149C23×C19#12311yescharacteristic
150C22×D19—41no—
151Q8×C19—21no—
152Q8×C19#10212yes—
153D4×C19—22no—
154D4×C19—22no—
155D4×C19—21no—
156D4×C19#10212yes—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—81no—
168C2×C4×C19C2×C22⋊C411yescharacteristic
169C2×C4×C19C4×D411yescharacteristic
170C2×C4×C19C4×D411yescharacteristic
171C2×C4×C19#12011yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19C2×D811yescharacteristic
175C2×C4×C19C2×SD1611yescharacteristic
176C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C19#13711yescharacteristic
178C22⋊D19—81no—
179C22⋊D19—81no—
180C2×Dic19—41no—
181D76—42no—
182D76—41no—
183D76—41no—
184D76—41no—
185D76—41no—
186C4×D19—81no—
187C4×D19—81no—
188Dic38—41no—
189Dic38—41no—
190C8×C19—42no—
191C8×C19—81no—
192C19⋊C8—41no—
193C19⋊C8—41no—
194C19⋊C8—41no—
195C19⋊C8—42no—
196C19⋊C8—41no—
197#3035—191no—
198#2906—191no—
199#1492—191no—
200#1480—191no—
201#1476D1911yescharacteristic, complemented
202#1301—191no—
203#1277—191no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—22no—
207C22×C19—41no—
208C22×C19—41no—
209C22×C19#38611yescharacteristic
210C22×C19#48011yescharacteristic
211C22×C19#48111yescharacteristic
212C2×D19—81no—
213C2×D19—81no—
214C2×D19—81no—
215C4×C19—22no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—41no—
220C4×C19—41no—
221C4×C19C2×#10211yescharacteristic
222C4×C19#41711yescharacteristic
223C4×C19#44311yescharacteristic
224C4×C19#44411yescharacteristic
225C4×C19#44711yescharacteristic
226C4×C19#44811yescharacteristic
227Dic19—81no—
228C2×#135—381no—
229C2×#131—381no—
230#532—191no—
231C4×#41C2×D1911yescharacteristic
232#464—381no—
233#463—381no—
234#462—191no—
235#461—191no—
236#460—191no—
237#459—191no—
238#431C2×D1911yescharacteristic
239#424—382no—
240#424—381no—
241#423—191no—
242#423—381no—
243C2×C4⋊C8—191no—
244C2×C4⋊C8—191no—
245C2×C4⋊C8—381no—
246#416—381no—
247C2×C4×C8C2×D1911yescharacteristic
248Q8⋊C8—21no—
249D4⋊C8—21no—
250D4⋊C8—381no—
251D4⋊C8—381no—
252D4⋊C8—382no—
253C2×C19—21no—
254C2×C19—21no—
255C2×C19—42no—
256C2×C19#187411yescharacteristic
257C2×C19#187611yescharacteristic
258C2×C19#188111yescharacteristic
259D19—161no—
260C2×#41—381no—
261C2×#41D7611yescharacteristic
262#135—762no—
263#135—762no—
264C2×Q16—381no—
265C2×SD16—381no—
266C2×SD16—381no—
267C2×D8—381no—
268#131—762no—
269#131—762no—
270C2×M16—382no—
271C2×M16—381no—
272C22×C8—21no—
273C22×C8—382no—
274C22×C8—381no—
275C22×C8—381no—
276C4⋊Q8—191no—
277#127—191no—
278#124—381no—
279#121—381no—
280#121—381no—
281C4×Q8C4×D1911yescharacteristic
282C4×Q8C22⋊D1911yescharacteristic
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—381no—
286C4×D4—381no—
287C4×D4C4×D1911yescharacteristic
288C4×D4C22⋊D1911yescharacteristic
289#117—21no—
290#117D7611yescharacteristic
291C2×C42—21no—
292C2×C42C22×D1911yescharacteristic
293C4⋊C8—21no—
294C4⋊C8—191no—
295C4⋊C8—191no—
296C4⋊C8—191no—
297C4⋊C8—191no—
298C4⋊C8—192no—
299C4⋊C8—382no—
300C4⋊C8—382no—
301C4⋊C8—381no—
302C4⋊C8—381no—
303C4⋊C8—381no—
304#103—381no—
305#103—381no—
306#102—381no—
307#102—381no—
308C22⋊C8—21no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8—21no—
312C19#899511yescharacteristic, complemented, Sylow
313#41—21no—
314#41—21no—
315#41—761no—
316#41—761no—
317#41—761no—
318#41—761no—
319#41#6451612yes—
320#41D15212yes—
321C2×Q8—381no—
322C2×Q8(C2×D19)⋊C411yescharacteristic
323C2×D4—21no—
324C2×D4—381no—
325C2×D4—381no—
326C2×D4—381no—
327C2×D4—761no—
328C2×D4(C2×D19)⋊C411yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—761no—
333C22×C4C2×D7611yescharacteristic
334C22×C4#6454311yescharacteristic
335C22×C4#6454311yescharacteristic
336Q16—762no—
337SD16—762no—
338SD16—762no—
339D8—762no—
340M16—764no—
341M16—761no—
342M16—761no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—381no—
348C2×C8—381no—
349C2×C8—382no—
350C2×C8—381no—
351C2×C8—381no—
352C2×C8—764no—
353C2×C8—761no—
354C2×C8—761no—
355C2×C8—761no—
356C2×C8—761no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—381no—
360C4⋊C4—381no—
361C4⋊C4(C2×D19)⋊C411yescharacteristic
362C4⋊C4(C2×D19)⋊C411yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—761no—
367C22⋊C4—761no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42C2×C4×D1911yescharacteristic
372C42D4×D1911yescharacteristic
373C42D4×D1911yescharacteristic
374C42C2×C22⋊D1911yescharacteristic
375C23—21no—
376C23—761no—
377C23#1059733211yescharacteristic
378Q8—21no—
379Q8—761no—
380Q8—761no—
381Q8#1059727812yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—762no—
386D4—761no—
387D4—761no—
388D4—761no—
389D4—761no—
390D4—1521no—
391D4—1521no—
392D4#1059727812yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—761no—
405C2×C4—1521no—
406C2×C4—1521no—
407C2×C4(C22⋊D19)⋊C411yescharacteristic
408C2×C4(C22⋊D19)⋊C411yescharacteristic
409C2×C4#1059732811yescharacteristic
410C2×C4C2×#6451611yescharacteristic
411C2×C4C2×D15211yescharacteristic
412C2×C4#1059735411yescharacteristic
413C2×C4#1059735511yescharacteristic
414C2×C4C2×(C2×D19)⋊C411yescharacteristic
415C2×C4#1059738511yescharacteristic
416C2×C4#1059738511yescharacteristic
417C8—42no—
418C8—81no—
419C8—761no—
420C8—761no—
421C8—761no—
422C8—762no—
423C8—761no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—1521no—
430C22—1521no—
431C22—1521no—
432C22#1192642111yescharacteristic
433C22#1192685811yescharacteristic
434C22#1192686311yescharacteristic
435C4—22no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—1521no—
442C4C2×#1059727811yescharacteristic
443C4#1192654611yescharacteristic
444C4#1192665811yescharacteristic
445C4#1192666311yescharacteristic
446C4#1192668011yescharacteristic
447C4#1192668511yescharacteristic
448C2—21no—
449C2—21no—
450C2—42no—
451C2—3041no—
452C2#1456395011yescharacteristic
453C2#1456396011yescharacteristic
454C2#1456399511yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1476C2
socleC22×C19#386
prime radical#14573090C2
cosocleC2×C42×C19C23
hypercenter#1476D19
hypocenterC19#8995
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #14572203C2semidirect
3. #14562087C2semidirect
4. #14562035C2semidirect
5. #14561531C2semidirect
6. #14561470C2semidirect
7. C19×#1476C2semidirect
201. #1476D19semidirect
312. C19#8995semidirect

Maximal subgroups

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

subgroupindex
#145730902
#145722032
#145620872
#145620352
#145615312
#145614702
C19×#14762
#899519