Finite Group Databasebeta

← #18080198

Subgroups — #18080198

Order 4864.

568 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568602C211yesmaximal, characteristic
2#14562258C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic, complemented
4#14561490C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic, complemented
6C2×#10597386C411yescharacteristic
7C2×#10597321C2211yescharacteristic
8C2×#10597382C411yescharacteristic
9#11926601C2212yes—
10#11926460—21no—
11#11926460—21no—
12#11926449C411yescharacteristic
13#11926445C411yescharacteristic
14#11926423—21no—
15#11926423—21no—
16C4×C4⋊Dic19C2211yescharacteristic
17#11926283—24no—
18#11926268—21no—
19#11926268—21no—
20C2×C4×D4×C19C2211yescharacteristic
21C19×#435—24no—
22C19×#432C2212yes—
23C19×#407—21no—
24C2×C19×C22⋊C8—21no—
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C22×C22⋊D19—21no—
29C22×C22⋊D19—21no—
30C22×D76C2×C411yescharacteristic
31C22×Dic38C2×C411yescharacteristic
32C2×M16×C19—22no—
33C22×C8×C19—22no—
34C4×D4×C19—22no—
35C4×D4×C19—22no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C42×C19C2311yescharacteristic
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42#10597386—42no—
43#10597382—42no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19C2×C411yescharacteristic
50C2×C4×Dic19C2×C411yescharacteristic
51#10597321—22no—
52#10597321—22no—
53C19×C4⋊C8—22no—
54C19×C22⋊C8—22no—
55C19×C22⋊C8—22no—
56C19×C22⋊C8—22no—
57C19×#97D414yescomplemented
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C22⋊(C19⋊C8)—22no—
62C4⋊(C19⋊C8)—22no—
63#10597260—22no—
64C24×C19C22⋊C411yescharacteristic
65C24×C19C22⋊C411yescharacteristic
66C23×D19—21no—
67C2×D4×C19—22no—
68C2×D4×C19—22no—
69C2×D4×C19—41no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—81no—
75C22×C4×C19—81no—
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C2×C22⋊D19—42no—
82C2×C22⋊D19—42no—
83C2×C22⋊D19—42no—
84C2×C22⋊D19—42no—
85C2×C22⋊D19—81no—
86C2×C22⋊D19—81no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C2×D76—22no—
91C2×D76—41no—
92C2×D76—41no—
93C2×Dic38—22no—
94C2×Dic38—41no—
95C2×Dic38—41no—
96M16×C19—82no—
97C2×C8×C19—24no—
98C2×C8×C19—82no—
99C4⋊C4×C19—22no—
100C22⋊C4×C19—22no—
101C22⋊C4×C19—22no—
102C42×C19C2×D412yes—
103C42×C19#4112yes—
104C22⋊Dic19—42no—
105C22⋊Dic19—42no—
106(C2×D19)⋊C4—41no—
107(C2×D19)⋊C4—42no—
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—81no—
110(C2×D19)⋊C4—81no—
111C4⋊Dic19—42no—
112C4×Dic19—41no—
113C4×Dic19—41no—
114C2×C19⋊C8—42no—
115#9447—191nomaximal, Sylow
116C23×C19—21no—
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19#10012yes—
126C23×C19C2×C22⋊C411yescharacteristic
127C22×D19—41no—
128C22×D19—41no—
129C22×D19—41no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134D4×C19—44no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—81no—
146C2×C4×C19—81no—
147C2×C4×C19C4×D412yes—
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12112yes—
150C2×C4×C19#12311yescharacteristic
151C22⋊D19—84no—
152C22⋊D19—84no—
153C2×Dic19—22no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162D76—82no—
163Dic38—82no—
164C8×C19—44no—
165C19⋊C8—82no—
166#2973D1911yescharacteristic, complemented
167#2544—191no—
168#1533—192no—
169#1466—191no—
170#1285—192no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—22no—
174C22×C19—42no—
175C22×C19—42no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—81no—
182C22×C19—81no—
183C22×C19#38611yescharacteristic
184C22×C19C2×#10011yescharacteristic
185C22×C19#41311yescharacteristic
186C2×D19—81no—
187C2×D19—81no—
188C2×D19—81no—
189C2×D19—81no—
190C2×D19—81no—
191C2×D19—81no—
192C2×D19—81no—
193C4×C19—22no—
194C4×C19—22no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—41no—
198C4×C19—41no—
199Dic19—42no—
200Dic19—81no—
201Dic19—81no—
202C2×#127—191no—
203C2×#124—191no—
204C2×#124—191no—
205C2×C4×D4C2×D1911yescharacteristic
206#435—24no—
207#432—192no—
208#432C2×D1912yes—
209#407—21no—
210C2×C22⋊C8—21no—
211#394—381no—
212#394—381no—
213#391—191no—
214#390—191no—
215#386—381no—
216#386—381no—
217C4×C4⋊C4—191no—
218#329—384no—
219#323—381no—
220#323—381no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19—42no—
224C2×C19—81no—
225C2×C19#188411yescharacteristic
226C2×C19#190011yescharacteristic
227C2×C19#191111yescharacteristic
228D19—161no—
229C22×Q8—191no—
230C22×D4—191no—
231C22×D4—381no—
232C22×D4—381no—
233C22×D4C4×D1911yescharacteristic
234C23×C4C22⋊D1911yescharacteristic
235C23×C4C22⋊D1911yescharacteristic
236C2×M16—22no—
237C22×C8—22no—
238#127—762no—
239#124—382no—
240#124—382no—
241#124—762no—
242C4×D4—22no—
243C4×D4—22no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4C4×D1911yescharacteristic
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—381no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4D7611yescharacteristic
253C2×C22⋊C4D7611yescharacteristic
254C2×C42—191no—
255C2×C42—191no—
256C2×C42C22×D1911yescharacteristic
257C4⋊C8—22no—
258C4⋊C8—382no—
259C22⋊C8—22no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8—382no—
263#97—382no—
264#97C22⋊D1914yescomplemented
265#95—381no—
266#95—381no—
267#95—381no—
268C19#944711yescharacteristic, complemented, Sylow
269C24—381no—
270C24(C2×D19)⋊C411yescharacteristic
271C24(C2×D19)⋊C411yescharacteristic
272C2×Q8—382no—
273C2×Q8—761no—
274C2×Q8—761no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—382no—
279C2×D4—761no—
280C2×D4—761no—
281C2×D4—762no—
282C2×D4—762no—
283C2×D4—762no—
284C2×D4—762no—
285C2×D4—1521no—
286C2×D4—1521no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4(C2×D19)⋊C411yescharacteristic
297C22×C4(C2×D19)⋊C411yescharacteristic
298C22×C4C2×C4×D1911yescharacteristic
299C22×C4C2×D7611yescharacteristic
300C22×C4C2×C22⋊D1911yescharacteristic
301M16—82no—
302C2×C8—24no—
303C2×C8—82no—
304C2×C8—762no—
305C4⋊C4—22no—
306C4⋊C4—762no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—762no—
310C22⋊C4—762no—
311C22⋊C4—762no—
312C22⋊C4—761no—
313C22⋊C4—761no—
314C22⋊C4—1521no—
315C22⋊C4—1521no—
316C42—761no—
317C42—761no—
318C42#6454112yes—
319C42C2×C22⋊D1912yes—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—761no—
330C23—761no—
331C23—761no—
332C23—761no—
333C23—761no—
334C23—761no—
335C23—761no—
336C23#1059728012yes—
337C23C2×(C2×D19)⋊C411yescharacteristic
338Q8—1522no—
339D4—44no—
340D4—1522no—
341D4—1524no—
342D4—1524no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—382no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—761no—
364C2×C4C4×C22⋊D1912yes—
365C2×C4#1059737511yescharacteristic
366C2×C4#1059737612yes—
367C2×C4#1059739911yescharacteristic
368C8—44no—
369C8—1522no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—1521no—
383C22—1521no—
384C22—1521no—
385C22—1521no—
386C22—1521no—
387C22—1521no—
388C22—1521no—
389C22#1192642311yescharacteristic
390C22C2×#1059728011yescharacteristic
391C22#1192652611yescharacteristic
392C4—22no—
393C4—21no—
394C4—21no—
395C4—22no—
396C4—41no—
397C4—41no—
398C4—762no—
399C4—1521no—
400C4—1521no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—3041no—
406C2#1456401811yescharacteristic
407C2#1456409811yescharacteristic
408C2#1456416711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radicalC2×#10597386C4
cosocleC2×C42×C19C23
hypercenter#2973D19
hypocenterC19#9447
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14562258C2semidirect
3. #14561976C2semidirect
4. #14561490C2semidirect
5. C19×#2973C2semidirect
57. C19×#97D4semidirect
166. #2973D19semidirect
264. #97C22⋊D19semidirect
268. C19#9447semidirect

Maximal subgroups

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

subgroupindex
#145686022
#145622582
#145619762
#145614902
C19×#29732
#944719