Finite Group Databasebeta

← #18077732

Subgroups — #18077732

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573631C211yesmaximal, characteristic
2#14564433C211yesmaximal, characteristic, complemented
3#14562284C211yesmaximal, characteristic, complemented
4#14562059C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561480C211yesmaximal, characteristic, complemented
7C19×#2932C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9#11926855C412yes—
10#11926821—21no—
11#11926736—21no—
12#11926677C412yes—
13C4×#64525—22no—
14#11926597C2211yescharacteristic
15#11926597C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C2×(C2×D19)⋊C8—21no—
18C2×(C2×D19)⋊C8—21no—
19#11926290—21no—
20#11926288—21no—
21#11926271—22no—
22C2×C19×#131—21no—
23C19×#532C2211yescharacteristic
24C19×#435—22no—
25C19×#435—22no—
26C19×#423C2211yescharacteristic
27C19×#408—21no—
28C2×C19×#97C2211yescharacteristic
29C2×#41×C19—21no—
30C22×D76C2×C411yescharacteristic
31C22×C4×D19—21no—
32C19×#131—42no—
33C19×#131—42no—
34C2×M16×C19—22no—
35C2×M16×C19—21no—
36C22×C8×C19—22no—
37C22×C8×C19D411yescharacteristic
38C22×C8×C19D411yescharacteristic
39C19×C4⋊Q8D411yescharacteristic
40C19×#127D411yescharacteristic
41C19×#124—21no—
42C19×#121—21no—
43C19×#121C2×C412yes—
44C4×D4×C19—21no—
45C4×D4×C19D412yes—
46C2×C42×C19C2311yescharacteristic
47C2×#64525—22no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19C2×C411yescharacteristic
50C22×C19⋊C8—21no—
51C4×D76—21no—
52C4×D76—21no—
53C4×D76—21no—
54C4×D76—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8D412yes—
57C19×C22⋊C8—24no—
58C19×#97—21no—
59C19×#97—21no—
60#10597289—22no—
61C22⋊(C19⋊C8)—21no—
62C22⋊(C19⋊C8)C2×C412yes—
63(C2×D19)⋊C8—42no—
64(C2×D19)⋊C8—42no—
65#10597266—22no—
66#10597264—22no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4×C19⋊C8—21no—
72C4×C19⋊C8—21no—
73C23×D19—21no—
74#41×C19—41no—
75#41×C19—41no—
76#41×C19—41no—
77#41×C19—41no—
78C2×Q8×C19—21no—
79C2×D4×C19—22no—
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C2×D4×C19C22⋊C412yes—
83C22×C4×C19—22no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C22×Dic19—21no—
88C2×D76—21no—
89C2×D76—21no—
90C2×D76—42no—
91C2×C4×D19—41no—
92C2×C4×D19—41no—
93C2×C4×D19—41no—
94C2×C4×D19—41no—
95C2×C4×D19—41no—
96C2×C4×D19—41no—
97M16×C19—44no—
98M16×C19—41no—
99M16×C19—41no—
100C2×C8×C19—21no—
101C2×C8×C19—21no—
102C2×C8×C19—22no—
103C2×C8×C19—21no—
104C2×C8×C19—21no—
105C2×C8×C19—21no—
106C2×C8×C19—44no—
107C2×C8×C19D812yescomplemented
108C4⋊C4×C19—21no—
109C4⋊C4×C19C22⋊C412yes—
110C22⋊C4×C19—22no—
111C22⋊C4×C19—22no—
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19#4111yescharacteristic
116#64525—44no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126#9049—191nomaximal, Sylow
127C23×C19—22no—
128C23×C19C4×D411yescharacteristic
129C22×D19—22no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136Q8×C19—41no—
137Q8×C19—41no—
138D4×C19—42no—
139D4×C19—42no—
140D4×C19—42no—
141D4×C19—41no—
142D4×C19—41no—
143D4×C19—81no—
144C2×C4×C19—22no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19C2×C22⋊C411yescharacteristic
150C2×C4×C19C4×D411yescharacteristic
151C2×C4×C19#12011yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×C4×C19#12111yescharacteristic
154C2×C4×C19#12311yescharacteristic
155C2×C4×C19C2×D811yescharacteristic
156C2×C4×C19#13511yescharacteristic
157C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162D76—22no—
163D76—22no—
164D76—41no—
165D76—41no—
166C4×D19—81no—
167C4×D19—81no—
168C4×D19—81no—
169C4×D19—81no—
170C8×C19—22no—
171C8×C19—42no—
172C8×C19—41no—
173C19⋊C8—42no—
174C19⋊C8—81no—
175C19⋊C8—81no—
176#3100—191no—
177#2932D1911yescharacteristic, complemented
178#1955—191no—
179#1540—191no—
180#1486—191no—
181#1301—191no—
182#1281—191no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—42no—
186C22×C19—42no—
187C22×C19—42no—
188C22×C19#38611yescharacteristic
189C22×C19C4×D811yescharacteristic
190C22×C19#44211yescharacteristic
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—42no—
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—81no—
197C2×D19—81no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—42no—
203C4×C19#44711yescharacteristic
204C4×C19#44911yescharacteristic
205C4×C19#45911yescharacteristic
206C4×C19#46311yescharacteristic
207Dic19—81no—
208C2×#131—21no—
209#532C2×D1911yescharacteristic
210C2×C4×D4—191no—
211#480—192no—
212#474—381no—
213#459—381no—
214#447—192no—
215C4×D8—382no—
216#435—22no—
217#435—22no—
218#431—191no—
219#431—191no—
220#423C2×D1911yescharacteristic
221C2×C4⋊C8—191no—
222#408—21no—
223C2×C22⋊C8—381no—
224C2×C22⋊C8—381no—
225C2×#97C2×D1911yescharacteristic
226#332—381no—
227#331—381no—
228D4⋊C8—382no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19—82no—
232C2×C19#187911yescharacteristic
233C2×C19#188111yescharacteristic
234C2×C19#189111yescharacteristic
235D19—82no—
236C2×#41—21no—
237C22×D4—191no—
238C23×C4—381no—
239C2×D8—382no—
240#131—42no—
241#131—42no—
242C2×M16—22no—
243C2×M16—21no—
244C22×C8—22no—
245C22×C8—381no—
246C22×C8C22⋊D1911yescharacteristic
247C22×C8C22⋊D1911yescharacteristic
248C4⋊Q8D7611yescharacteristic
249#127D7611yescharacteristic
250#124—21no—
251#121—21no—
252#121C4×D1912yes—
253C4×D4—21no—
254C4×D4—381no—
255C4×D4—381no—
256C4×D4—381no—
257C4×D4—381no—
258C4×D4C22⋊D1912yes—
259C2×C4⋊C4—191no—
260C2×C22⋊C4—381no—
261C2×C42C22×D1911yescharacteristic
262#107—382no—
263C4⋊C8—21no—
264C4⋊C8—381no—
265C4⋊C8—381no—
266C4⋊C8—381no—
267C4⋊C8—381no—
268C4⋊C8C22⋊D1912yes—
269#102—382no—
270#102—382no—
271C22⋊C8—24no—
272C22⋊C8—192no—
273C22⋊C8—381no—
274C22⋊C8—762no—
275C22⋊C8—762no—
276#97—21no—
277#97—21no—
278C4×C8—381no—
279C4×C8—381no—
280C19#904911yescharacteristic, complemented, Sylow
281C24—381no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—762no—
293C2×D4(C2×D19)⋊C412yes—
294C22×C4—22no—
295C22×C4—381no—
296C22×C4—761no—
297C22×C4—761no—
298C22×C4—761no—
299C22×C4—761no—
300C22×C4—761no—
301C22×C4—761no—
302C22×C4C2×C4×D1911yescharacteristic
303C22×C4#6454111yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305D8—764no—
306M16—44no—
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—44no—
316C2×C8—382no—
317C2×C8—761no—
318C2×C8—761no—
319C2×C8—761no—
320C2×C8—761no—
321C2×C8#6452512yescomplemented
322C4⋊C4—21no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4(C2×D19)⋊C412yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—761no—
329C22⋊C4—761no—
330C42C2×D7611yescharacteristic
331C42#6454111yescharacteristic
332C42C2×C22⋊D1911yescharacteristic
333C42C2×C22⋊D1911yescharacteristic
334C23—22no—
335C23—382no—
336C23—761no—
337C23—761no—
338C23—761no—
339C23—761no—
340C23—761no—
341C23—761no—
342C23C4×C22⋊D1911yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—42no—
346D4—42no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—382no—
352D4—382no—
353D4—761no—
354D4—761no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4—1521no—
366C2×C4—1521no—
367C2×C4C2×(C2×D19)⋊C411yescharacteristic
368C2×C4C4×C22⋊D1911yescharacteristic
369C2×C4#1059737511yescharacteristic
370C2×C4#1059737611yescharacteristic
371C2×C4#1059737611yescharacteristic
372C2×C4C2×#6452511yescharacteristic
373C2×C4#1059737811yescharacteristic
374C2×C4#1059739511yescharacteristic
375C2×C4#1059739611yescharacteristic
376C2×C4#1059739911yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—762no—
381C8—1521no—
382C8—1521no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—762no—
389C22—762no—
390C22—762no—
391C22—1521no—
392C22—1521no—
393C22—1521no—
394C22—1521no—
395C22#1192642311yescharacteristic
396C22C4×#6452511yescharacteristic
397C22#1192665411yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—1521no—
404C4#1192667811yescharacteristic
405C4#1192668911yescharacteristic
406C4#1192673911yescharacteristic
407C4#1192675911yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—1522no—
412C2#1456398311yescharacteristic
413C2#1456399711yescharacteristic
414C2#1456405311yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2932C2
socleC22×C19#386
prime radical#14573631C2
cosocleC2×C42×C19C23
hypercenter#2932D19
hypocenterC19#9049
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #14564433C2semidirect
3. #14562284C2semidirect
4. #14562059C2semidirect
5. #14561530C2semidirect
6. #14561480C2semidirect
7. C19×#2932C2semidirect
107. C2×C8×C19D8semidirect
177. #2932D19semidirect
280. C19#9049semidirect
321. C2×C8#64525semidirect

Maximal subgroups

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

subgroupindex
#145736312
#145644332
#145622842
#145620592
#145615302
#145614802
C19×#29322
#904919