Finite Group Databasebeta

← #18077431

Subgroups — #18077431

Order 4864.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573090C211yesmaximal, characteristic
2#14572301C211yesmaximal, 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—
9#11927094C2211yescharacteristic
10#11926766—21no—
11#11926759—21no—
12#11926754C411yescharacteristic
13#11926749C411yescharacteristic
14#11926744C411yescharacteristic
15#11926739C411yescharacteristic
16#11926605—22no—
17#11926601—21no—
18#11926597—21no—
19#11926568C2211yescharacteristic
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22#11926538—21no—
23#11926511—21no—
24#11926500—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—
48C2×#64528—21no—
49C2×#64527—21no—
50C2×#64526—21no—
51C2×#64525—21no—
52#10597376—21no—
53#10597376—21no—
54C2×#64520—21no—
55C22×C19⋊C8—21no—
56C22×C19⋊C8—21no—
57#10597321—21no—
58#10597320C2×C411yescharacteristic
59C4×D76—21no—
60C4×D76—21no—
61#10597315C2×C411yescharacteristic
62C19×C4⋊C8—21no—
63C19×C22⋊C8—21no—
64C4×C8×C19—21no—
65C4×C8×C19—21no—
66C4×C8×C19—21no—
67C22⋊(C19⋊C8)—22no—
68C22⋊(C19⋊C8)—22no—
69#10597267—21no—
70#10597267—21no—
71#10597266—21no—
72#10597266—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)C2×C411yescharacteristic
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)D411yescharacteristic
79C4⋊(C19⋊C8)D411yescharacteristic
80C4⋊(C19⋊C8)D412yes—
81#10597260—22no—
82C4×C19⋊C8—22no—
83#41×C19—21no—
84#41×C19—21no—
85#41×C19—21no—
86#41×C19—21no—
87C2×Q8×C19C22⋊C411yescharacteristic
88C2×D4×C19—21no—
89C2×D4×C19C22⋊C411yescharacteristic
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C2×C22⋊D19—41no—
97#64541—41no—
98#64541—41no—
99#64541—41no—
100#64541—41no—
101C2×D76—21no—
102C2×D76—21no—
103C2×D76—21no—
104C2×C4×D19—41no—
105C2×Dic38—21no—
106C2×C8×C19—22no—
107C2×C8×C19—41no—
108C2×C8×C19—41no—
109C2×C8×C19—41no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C22⋊C4×C19—21no—
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C42×C19—21no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19C22×C411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D411yescharacteristic
124#64528—42no—
125#64527—42no—
126#64526—42no—
127#64525—42no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132#64520—41no—
133#64520—41no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—21no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—41no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143#8996—191nomaximal, Sylow
144C23×C19—21no—
145C23×C19#12311yescharacteristic
146C22×D19—41no—
147Q8×C19—21no—
148Q8×C19—21no—
149D4×C19—21no—
150D4×C19—21no—
151D4×C19—41no—
152D4×C19—41no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—81no—
164C2×C4×C19C2×C22⋊C411yescharacteristic
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#13511yescharacteristic
171C2×C4×C19#13511yescharacteristic
172C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
174C22⋊D19—81no—
175C22⋊D19—81no—
176C2×Dic19—41no—
177D76—42no—
178D76—41no—
179D76—41no—
180D76—41no—
181D76—41no—
182C4×D19—81no—
183C4×D19—81no—
184Dic38—41no—
185Dic38—41no—
186C8×C19—42no—
187C8×C19—81no—
188C19⋊C8—41no—
189C19⋊C8—41no—
190C19⋊C8—41no—
191C19⋊C8—41no—
192C19⋊C8—42no—
193#3035—191no—
194#2925—191no—
195#1492—191no—
196#1480—191no—
197#1476D1911yescharacteristic, complemented
198#1301—191no—
199#1277—191no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19#38611yescharacteristic
206C22×C19#48211yescharacteristic
207C22×C19#48211yescharacteristic
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—81no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—41no—
215C4×C19—41no—
216C4×C19—41no—
217C4×C19#41611yescharacteristic
218C4×C19#41811yescharacteristic
219C4×C19#44311yescharacteristic
220C4×C19#44411yescharacteristic
221C4×C19#44911yescharacteristic
222C4×C19#44911yescharacteristic
223Dic19—81no—
224C2×#135—381no—
225#532—191no—
226C4×#41C2×D1911yescharacteristic
227#464—381no—
228#463—381no—
229#462—191no—
230#461—191no—
231#460—191no—
232#459—191no—
233#433—382no—
234#432—381no—
235#431—381no—
236#431C2×D1911yescharacteristic
237#423—191no—
238C2×C4⋊C8—191no—
239C2×C4⋊C8—191no—
240#416—381no—
241#408—381no—
242#405—381no—
243C2×C4×C8C2×D1911yescharacteristic
244Q8⋊C8—21no—
245D4⋊C8—21no—
246D4⋊C8—381no—
247D4⋊C8—381no—
248D4⋊C8—382no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—81no—
252C2×C19#187511yescharacteristic
253C2×C19#187611yescharacteristic
254C2×C19#188111yescharacteristic
255D19—161no—
256C2×#41—381no—
257C2×#41D7611yescharacteristic
258#135—762no—
259#135—762no—
260C2×Q16—381no—
261C2×SD16—381no—
262C2×SD16—381no—
263C2×D8—381no—
264C2×M16—381no—
265C22×C8—21no—
266C22×C8—381no—
267C22×C8—381no—
268C4⋊Q8—191no—
269#127—191no—
270#124—381no—
271#121—381no—
272#121—381no—
273C4×Q8C4×D1911yescharacteristic
274C4×Q8C22⋊D1911yescharacteristic
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—381no—
278C4×D4—381no—
279C4×D4C4×D1911yescharacteristic
280C4×D4C22⋊D1911yescharacteristic
281#117—21no—
282#117D7611yescharacteristic
283C2×C42—21no—
284C2×C42C22×D1911yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—191no—
287C4⋊C8—191no—
288C4⋊C8—191no—
289C4⋊C8—191no—
290C4⋊C8—192no—
291C4⋊C8—381no—
292C4⋊C8—381no—
293C4⋊C8—381no—
294#103—381no—
295#103—381no—
296#102—381no—
297#102—381no—
298C22⋊C8—21no—
299C22⋊C8—382no—
300C22⋊C8—382no—
301#97—382no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—382no—
306C19#899611yescharacteristic, complemented, Sylow
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—761no—
312#41—761no—
313#41—761no—
314#41—761no—
315C2×Q8—381no—
316C2×Q8(C2×D19)⋊C411yescharacteristic
317C2×D4—21no—
318C2×D4—381no—
319C2×D4—381no—
320C2×D4—381no—
321C2×D4—761no—
322C2×D4(C2×D19)⋊C411yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—761no—
327C22×C4C2×D7611yescharacteristic
328C22×C4#6454311yescharacteristic
329C22×C4#6454311yescharacteristic
330Q16—762no—
331SD16—762no—
332SD16—762no—
333D8—762no—
334M16—761no—
335M16—761no—
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—381no—
341C2×C8—382no—
342C2×C8—381no—
343C2×C8—381no—
344C2×C8—381no—
345C2×C8—761no—
346C2×C8—761no—
347C2×C8—761no—
348C2×C8—761no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—381no—
352C4⋊C4—381no—
353C4⋊C4(C2×D19)⋊C411yescharacteristic
354C4⋊C4(C2×D19)⋊C411yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C2×C4×D1911yescharacteristic
364C42D4×D1911yescharacteristic
365C42D4×D1911yescharacteristic
366C42C2×C22⋊D1911yescharacteristic
367C23—21no—
368C23—761no—
369C23#1059733211yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—761no—
373Q8—761no—
374D4—21no—
375D4—21no—
376D4—41no—
377D4—41no—
378D4—762no—
379D4—761no—
380D4—761no—
381D4—761no—
382D4—761no—
383D4—1521no—
384D4—1521no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—761no—
397C2×C4—1521no—
398C2×C4—1521no—
399C2×C4(C22⋊D19)⋊C411yescharacteristic
400C2×C4(C22⋊D19)⋊C411yescharacteristic
401C2×C4#1059732811yescharacteristic
402C2×C4#1059735011yescharacteristic
403C2×C4#1059735011yescharacteristic
404C2×C4#1059735411yescharacteristic
405C2×C4#1059735411yescharacteristic
406C2×C4C2×(C2×D19)⋊C411yescharacteristic
407C2×C4#1059738511yescharacteristic
408C2×C4#1059738511yescharacteristic
409C8—42no—
410C8—81no—
411C8—761no—
412C8—761no—
413C8—761no—
414C8—761no—
415C8—762no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—1521no—
422C22—1521no—
423C22—1521no—
424C22#1192642111yescharacteristic
425C22#1192686911yescharacteristic
426C22#1192686911yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—1521no—
434C4#1192654111yescharacteristic
435C4#1192655011yescharacteristic
436C4#1192665811yescharacteristic
437C4#1192666311yescharacteristic
438C4#1192669111yescharacteristic
439C4#1192669111yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—3041no—
444C2#1456395511yescharacteristic
445C2#1456396011yescharacteristic
446C2#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#8996
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. #14572301C2semidirect
3. #14562087C2semidirect
4. #14562035C2semidirect
5. #14561531C2semidirect
6. #14561470C2semidirect
7. C19×#1476C2semidirect
197. #1476D19semidirect
306. C19#8996semidirect

Maximal subgroups

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

subgroupindex
#145730902
#145723012
#145620872
#145620352
#145615312
#145614702
C19×#14762
#899619