Finite Group Databasebeta

← #18077625

Subgroups — #18077625

Order 4864.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572197C211yesmaximal, characteristic
2#14566905C211yesmaximal, characteristic
3#14562064C211yesmaximal, characteristic, complemented
4#14561947C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic, complemented
6#14561536C211yesmaximal, characteristic, complemented
7C19×#1487C211yesmaximal, characteristic, complemented
8C2×M16×D19—21no—
9C2×#10597318C2211yescharacteristic
10#11926597C2211yescharacteristic
11#11926569—22no—
12#11926569—22no—
13#11926568C2211yescharacteristic
14#11926567—21no—
15#11926482C411yescharacteristic
16#11926479C411yescharacteristic
17#11926477—21no—
18#11926466—21no—
19#11926463C411yescharacteristic
20#11926455C411yescharacteristic
21C4×Dic19⋊C4—21no—
22C4×C4⋊Dic19C2211yescharacteristic
23C4×(C2×D19)⋊C4—21no—
24Q8⋊(C19⋊C8)—22no—
25#11926269—21no—
26#11926267—21no—
27C2×C4×Q8×C19C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×Q8⋊C8—22no—
31C22×Q8×C19C2×C411yescharacteristic
32C22×C4×D19D411yescharacteristic
33C2×M16×C19—21no—
34C4×Q8×C19—21no—
35C4×Q8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4C2×C411yescharacteristic
45C2×(C2×D19)⋊C4D411yescharacteristic
46C2×C4⋊Dic19—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4C2×C411yescharacteristic
50C2×Dic19⋊C4D411yescharacteristic
51C2×C4×Dic19—21no—
52C2×C4×Dic19D411yescharacteristic
53C2×#64520—21no—
54M16×D19—42no—
55M16×D19—42no—
56C2×#64515—22no—
57C2×C8×D19—22no—
58#10597318—21no—
59#10597318—21no—
60#10597318—21no—
61#10597318—21no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8D412yes—
65C19×C22⋊C8—21no—
66C4×C8×C19—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95C2×C411yescharacteristic
72C19⋊#95C2×C411yescharacteristic
73C22⋊(C19⋊C8)—21no—
74Dic19⋊C8—24no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)D412yes—
78C4×C19⋊C8—21no—
79C23×D19C22⋊C411yescharacteristic
80C2×Q8×C19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—42no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19C22⋊C411yescharacteristic
91C22×Dic19C22⋊C411yescharacteristic
92C22×Dic19C22⋊C411yescharacteristic
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×C4×D19SD1612yes—
98C2×C4×D19Q1612yes—
99M16×C19—41no—
100M16×C19—41no—
101C2×C8×C19—22no—
102C2×C8×C19—41no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C42×C19—41no—
108C42×C19—41no—
109C42×C19C2×D411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C42×C19#4111yescharacteristic
112C42×C19#4111yescharacteristic
113(C2×D19)⋊C4—21no—
114(C2×D19)⋊C4—21no—
115(C2×D19)⋊C4—21no—
116(C2×D19)⋊C4—21no—
117(C2×D19)⋊C4—42no—
118(C2×D19)⋊C4—42no—
119C4⋊Dic19—42no—
120Dic19⋊C4—21no—
121Dic19⋊C4—21no—
122Dic19⋊C4—21no—
123Dic19⋊C4—21no—
124Dic19⋊C4—42no—
125Dic19⋊C4—42no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130#64520—41no—
131#64520—41no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—41no—
134#64515—44no—
135C8×D19—44no—
136#9033—191nomaximal, Sylow
137C23×C19C2×C22⋊C411yescharacteristic
138C22×D19—21no—
139C22×D19—21no—
140C22×D19—41no—
141C22×D19—41no—
142C22×D19#10312yes—
143Q8×C19—22no—
144Q8×C19—22no—
145Q8×C19—41no—
146Q8×C19—41no—
147C2×C4×C19—22no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19C4×D411yescharacteristic
156C2×C4×C19C4×D411yescharacteristic
157C2×C4×C19#12011yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12311yescharacteristic
161C2×C4×C19C2×SD1611yescharacteristic
162C2×C4×C19C2×Q1611yescharacteristic
163C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C19#13711yescharacteristic
165C2×Dic19—21no—
166C2×Dic19—21no—
167C2×Dic19—22no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19#10312yes—
178C4×D19—22no—
179C4×D19—22no—
180C4×D19—22no—
181C4×D19—22no—
182C8×C19—42no—
183C8×C19—81no—
184C19⋊C8—42no—
185C19⋊C8—81no—
186#2905—191no—
187#2396—191no—
188#1487—191no—
189#1487D1911yescharacteristic, complemented
190#1458—191no—
191#1303—191no—
192#1303—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19#38611yescharacteristic
196C22×C19C2×#10311yescharacteristic
197C22×C19#41711yescharacteristic
198C2×D19—22no—
199C2×D19—41no—
200C2×D19—41no—
201C2×D19—42no—
202C2×D19—81no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—42no—
208C4×C19—81no—
209C4×C19#45011yescharacteristic
210C4×C19#45111yescharacteristic
211C4×C19#48311yescharacteristic
212C4×C19#48411yescharacteristic
213Dic19—22no—
214Dic19—42no—
215Dic19—41no—
216Dic19—41no—
217Dic19—81no—
218C22×M16—381no—
219C2×C4×Q8C2×D1911yescharacteristic
220C2×#117—191no—
221#431—191no—
222#431C2×D1911yescharacteristic
223#424—382no—
224#424—382no—
225#423—191no—
226#423—381no—
227#423C2×D1911yescharacteristic
228#400—191no—
229#399—191no—
230#398—381no—
231#396—381no—
232#395—191no—
233#393—191no—
234C4×C4⋊C4—191no—
235C4×C4⋊C4—381no—
236C4×C22⋊C4—381no—
237Q8⋊C8—22no—
238Q8⋊C8—382no—
239#324—381no—
240#323—381no—
241C2×C19—21no—
242C2×C19—21no—
243C2×C19#187211yescharacteristic
244C2×C19#188411yescharacteristic
245C2×C19#189111yescharacteristic
246D19—42no—
247C22×Q8C4×D1911yescharacteristic
248C23×C4—191no—
249C2×M16—21no—
250C2×M16—382no—
251C2×M16—381no—
252C2×M16—762no—
253C2×M16—762no—
254C22×C8—382no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259#117—381no—
260#117—381no—
261#117—381no—
262#117—381no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—191no—
266C2×C4⋊C4—381no—
267C2×C4⋊C4—381no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4C4×D1911yescharacteristic
270C2×C22⋊C4—191no—
271C2×C22⋊C4—191no—
272C2×C22⋊C4—381no—
273C2×C22⋊C4—381no—
274C2×C42—21no—
275C2×C42—191no—
276C2×C42—381no—
277C2×C42C22×D1911yescharacteristic
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—192no—
281C4⋊C8—384no—
282C4⋊C8—381no—
283C4⋊C8—381no—
284C4⋊C8C22⋊D1912yes—
285C22⋊C8—21no—
286C22⋊C8—381no—
287C4×C8—21no—
288C4×C8—381no—
289#95—191no—
290#95—191no—
291#95—381no—
292#95—381no—
293#95—381no—
294#95—381no—
295C19#903311yescharacteristic, complemented, Sylow
296C24—191no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—191no—
303C22×C4—192no—
304C22×C4—192no—
305C22×C4—191no—
306C22×C4—191no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—381no—
311C22×C4—381no—
312C22×C4—381no—
313C22×C4C2×C4×D1911yescharacteristic
314C22×C4D4×D1911yescharacteristic
315C22×C4D4×D1911yescharacteristic
316M16—41no—
317M16—41no—
318M16—764no—
319M16—761no—
320M16—761no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—382no—
324C2×C8—764no—
325C2×C8—761no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—381no—
331C4⋊C4—381no—
332C4⋊C4—381no—
333C4⋊C4—381no—
334C4⋊C4—762no—
335C4⋊C4—762no—
336C4⋊C4—762no—
337C22⋊C4—381no—
338C22⋊C4—381no—
339C22⋊C4—381no—
340C22⋊C4—381no—
341C22⋊C4—762no—
342C22⋊C4—762no—
343C42—41no—
344C42—41no—
345C42—381no—
346C42—381no—
347C42—761no—
348C42—761no—
349C42#6454111yescharacteristic
350C42D4×D1911yescharacteristic
351C42#6454311yescharacteristic
352C42C2×C22⋊D1911yescharacteristic
353C23—192no—
354C23—381no—
355C23—381no—
356C23—761no—
357C23—761no—
358C23C22⋊C4×D1911yescharacteristic
359Q8—22no—
360Q8—22no—
361Q8—41no—
362Q8—41no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—192no—
372C2×C4—381no—
373C2×C4—381no—
374C2×C4—382no—
375C2×C4—382no—
376C2×C4—382no—
377C2×C4—382no—
378C2×C4—382no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—761no—
384C2×C4—761no—
385C2×C4—761no—
386C2×C4—761no—
387C2×C4—761no—
388C2×C4(C22⋊D19)⋊C411yescharacteristic
389C2×C4#1059732911yescharacteristic
390C2×C4#1059733011yescharacteristic
391C2×C4SD16×D1911yescharacteristic
392C2×C4#1059736011yescharacteristic
393C2×C4Q16×D1911yescharacteristic
394C2×C4#1059736411yescharacteristic
395C2×C4C4×C22⋊D1911yescharacteristic
396C2×C4#1059738311yescharacteristic
397C2×C4#1059738411yescharacteristic
398C8—42no—
399C8—81no—
400C8—762no—
401C8—1521no—
402C22—21no—
403C22—21no—
404C22—382no—
405C22—762no—
406C22—761no—
407C22—761no—
408C22—1521no—
409C22#1192642011yescharacteristic
410C22#103×D1911yescharacteristic
411C22#1192654411yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—382no—
419C4—762no—
420C4—761no—
421C4—761no—
422C4—1521no—
423C4#1192669311yescharacteristic
424C4#1192669811yescharacteristic
425C4#1192687311yescharacteristic
426C4#1192687811yescharacteristic
427C2—21no—
428C2—21no—
429C2—762no—
430C2#1456393911yescharacteristic
431C2#1456401511yescharacteristic
432C2#1456405011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1487C2
socleC22×C19#386
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1487D19
hypocenterC19#9033
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #14562064C2semidirect
5. #14561537C2semidirect
6. #14561536C2semidirect
7. C19×#1487C2semidirect
189. #1487D19semidirect
295. C19#9033semidirect

Maximal subgroups

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

subgroupindex
#145721972
#145669052
#145620642
#145619472
#145615372
#145615362
C19×#14872
#903319