Finite Group Databasebeta

← #18078913

Subgroups — #18078913

Order 4864.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926831C211yesmaximal, characteristic
2#14572370C211yesmaximal, characteristic
3#14564625C211yesmaximal, characteristic, complemented
4#14562061C211yesmaximal, characteristic
5#14561509C211yesmaximal, characteristic, complemented
6#14561484C211yesmaximal, characteristic, complemented
7C19×#1549C211yesmaximal, characteristic, complemented
8C2×M16×D19—21no—
9C2×C4×D76C2211yescharacteristic
10#11926831—21no—
11#11926831—21no—
12#11926831—21no—
13#11926831—21no—
14#11926621—21no—
15#11926614—22no—
16#11926609—21no—
17C2×#10597265C412yes—
18#11926568C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597266C412yes—
21#11926507—21no—
22C4×#64520C2211yescharacteristic
23#11926313—21no—
24#11926313—21no—
25#11926273—21no—
26#11926273—21no—
27C2×C19×C4⋊Q8C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×#332—22no—
31C22×Q8×C19—21no—
32C22×D76C2×C411yescharacteristic
33C22×C4×D19—21no—
34C2×M16×C19—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19C2×C412yes—
41C2×C42×C19C2311yescharacteristic
42C2×(C2×D19)⋊C4—21no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×#64520—21no—
45C2×#64520D411yescharacteristic
46C2×#64520D411yescharacteristic
47C22×C19⋊C8C2×C412yes—
48M16×D19—42no—
49M16×D19—42no—
50C2×#64515—22no—
51C2×C8×D19—22no—
52C4×D76—21no—
53C4×D76—21no—
54C4×D76D411yescharacteristic
55C4×D76D411yescharacteristic
56C4×D76D411yescharacteristic
57C4×D76D411yescharacteristic
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C19×C4⋊C8D412yes—
61C19×C22⋊C8—21no—
62C4×C8×C19—21no—
63(C2×D19)⋊C8—22no—
64(C2×D19)⋊C8—22no—
65#10597266—22no—
66#10597266—22no—
67#10597265—22no—
68#10597265—22no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73#10597260—21no—
74C4×C19⋊C8—21no—
75C23×D19—21no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—82no—
79C22×C4×C19—22no—
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×Dic19—21no—
84C2×D76—22no—
85C2×D76—21no—
86C2×D76—41no—
87C2×D76C22⋊C411yescharacteristic
88C2×D76C22⋊C411yescharacteristic
89C2×C4×D19—21no—
90C2×C4×D19—21no—
91C2×C4×D19—21no—
92C2×C4×D19—21no—
93C2×C4×D19—41no—
94C2×C4×D19—41no—
95C2×C4×D19—41no—
96C2×C4×D19—41no—
97M16×C19—41no—
98M16×C19—41no—
99C2×C8×C19—22no—
100C2×C8×C19—41no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19#4111yescharacteristic
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4—21no—
112(C2×D19)⋊C4—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19C22⋊C411yescharacteristic
115C4⋊Dic19C22⋊C411yescharacteristic
116#64520—21no—
117#64520—21no—
118#64520—21no—
119#64520—41no—
120#64520—41no—
121#64520SD1612yes—
122C2×C19⋊C8—21no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—21no—
125C2×C19⋊C8—42no—
126C2×C19⋊C8—41no—
127#64515—44no—
128C8×D19—44no—
129#9249—191nomaximal, Sylow
130C23×C19C4×D411yescharacteristic
131C22×D19—21no—
132C22×D19—21no—
133C22×D19—42no—
134C22×D19—41no—
135C22×D19—41no—
136C22×D19—81no—
137Q8×C19—82no—
138Q8×C19—82no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—82no—
144C2×C4×C19C2×C22⋊C411yescharacteristic
145C2×C4×C19C4×D411yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12311yescharacteristic
150C2×C4×C19C2×SD1611yescharacteristic
151C2×C4×C19#13511yescharacteristic
152C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C19#13711yescharacteristic
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158D76—21no—
159D76—21no—
160D76—21no—
161D76—42no—
162D76#10112yes—
163C4×D19—41no—
164C4×D19—41no—
165C4×D19—41no—
166C4×D19—41no—
167C4×D19—41no—
168C4×D19—41no—
169C4×D19—41no—
170C4×D19—41no—
171C8×C19—42no—
172C8×C19—81no—
173C19⋊C8—22no—
174C19⋊C8—42no—
175C19⋊C8—41no—
176C19⋊C8—81no—
177C2×#476—191no—
178D4×M16—191no—
179#1997—191no—
180#1549D1911yescharacteristic, complemented
181#1486—191no—
182#1292—191no—
183#1283—191no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19#38611yescharacteristic
187C22×C19C4×SD1611yescharacteristic
188C22×C19#44011yescharacteristic
189C2×D19—22no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—82no—
196C2×D19—82no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—82no—
201C4×C19C2×#10111yescharacteristic
202C4×C19#41311yescharacteristic
203C4×C19#45011yescharacteristic
204C4×C19#45211yescharacteristic
205C4×C19#46111yescharacteristic
206C4×C19#46311yescharacteristic
207Dic19—41no—
208Dic19—41no—
209C22×M16—381no—
210C2×C4⋊Q8C2×D1911yescharacteristic
211C2×C4×D4—191no—
212#476—381no—
213#476—381no—
214#476—381no—
215#476—381no—
216#436—381no—
217#435—382no—
218C8×D4—381no—
219#431C2×D1911yescharacteristic
220C2×#106—192no—
221#423—191no—
222#423C2×D1911yescharacteristic
223C2×C4⋊C8—191no—
224C2×#102—192no—
225#407—381no—
226C4×M16—191no—
227#343—381no—
228#343—381no—
229#332—22no—
230D4⋊C8—381no—
231D4⋊C8—381no—
232C2×C19—21no—
233C2×C19—21no—
234C2×C19#187711yescharacteristic
235C2×C19#190111yescharacteristic
236C2×C19#190311yescharacteristic
237D19—42no—
238D19—81no—
239C22×Q8—21no—
240C22×D4—191no—
241C23×C4—381no—
242C2×M16—21no—
243C2×M16—191no—
244C2×M16—191no—
245C2×M16—382no—
246C2×M16—381no—
247C2×M16—762no—
248C2×M16—762no—
249C22×C8—192no—
250C22×C8—382no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4×D4—191no—
256C4×D4—191no—
257C4×D4—191no—
258C4×D4—191no—
259C4×D4—381no—
260C4×D4—381no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—191no—
263C2×C4⋊C4C4×D1912yes—
264C2×C22⋊C4—381no—
265C2×C42C22×D1911yescharacteristic
266#106—382no—
267#106—382no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—381no—
271C4⋊C8—381no—
272C4⋊C8—381no—
273C4⋊C8—381no—
274C4⋊C8C22⋊D1912yes—
275#102—382no—
276#102—382no—
277C22⋊C8—21no—
278C22⋊C8—382no—
279C22⋊C8—382no—
280#97—381no—
281C4×C8—21no—
282C4×C8—381no—
283C19#924911yescharacteristic, complemented, Sylow
284C24—381no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—191no—
289C2×D4—191no—
290C2×D4—382no—
291C2×D4—381no—
292C2×D4—761no—
293C22×C4—22no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—381no—
299C22×C4—761no—
300C22×C4—761no—
301C22×C4—761no—
302C22×C4—761no—
303C22×C4C2×C4×D1911yescharacteristic
304C22×C4D4×D1911yescharacteristic
305C22×C4#6454311yescharacteristic
306M16—41no—
307M16—41no—
308M16—192no—
309M16—381no—
310M16—381no—
311M16—381no—
312M16—764no—
313M16—761no—
314M16—761no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—381no—
318C2×C8—381no—
319C2×C8—382no—
320C2×C8—764no—
321C2×C8—762no—
322C2×C8—761no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—191no—
328C4⋊C4—191no—
329C4⋊C4—381no—
330C22⋊C4—381no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C42#6454111yescharacteristic
335C42D4×D1911yescharacteristic
336C42D4×D1911yescharacteristic
337C42C2×C22⋊D1911yescharacteristic
338C23—381no—
339C23—381no—
340C23—762no—
341C23—761no—
342C23—761no—
343C23—1521no—
344C23(C22⋊D19)⋊C411yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—192no—
348D4—381no—
349D4—381no—
350D4—381no—
351D4—762no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4C22⋊C4×D1911yescharacteristic
370C2×C4#1059732911yescharacteristic
371C2×C4#1059733011yescharacteristic
372C2×C4SD16×D1911yescharacteristic
373C2×C4#1059736011yescharacteristic
374C2×C4#1059736411yescharacteristic
375C2×C4#1059736511yescharacteristic
376C2×C4C4×C22⋊D1911yescharacteristic
377C2×C4#1059738311yescharacteristic
378C2×C4#1059738411yescharacteristic
379C8—42no—
380C8—81no—
381C8—382no—
382C8—761no—
383C8—762no—
384C8—1521no—
385C22—21no—
386C22—21no—
387C22—382no—
388C22—761no—
389C22—761no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—1522no—
394C22—1522no—
395C22#1192642011yescharacteristic
396C22#1192662911yescharacteristic
397C22#1192664711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—761no—
403C4—761no—
404C4#101×D1911yescharacteristic
405C4#1192652711yescharacteristic
406C4#1192669311yescharacteristic
407C4#1192670511yescharacteristic
408C4#1192674811yescharacteristic
409C4#1192676211yescharacteristic
410C2—21no—
411C2—21no—
412C2—762no—
413C2—1521no—
414C2#1456396611yescharacteristic
415C2#1456410011yescharacteristic
416C2#1456411211yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1549D19
hypocenterC19#9249
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. #14564625C2semidirect
5. #14561509C2semidirect
6. #14561484C2semidirect
7. C19×#1549C2semidirect
180. #1549D19semidirect
283. C19#9249semidirect

Maximal subgroups

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

subgroupindex
C2×#119268312
#145723702
#145646252
#145620612
#145615092
#145614842
C19×#15492
#924919