Finite Group Databasebeta

← #18083833

Subgroups — #18083833

Order 4864.

648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11926906C211yesmaximal, characteristic, complemented
2#14571680C211yesmaximal, characteristic
3#14564609C211yesmaximal, characteristic, complemented
4C2×#11926284C211yesmaximal, characteristic, complemented
5C2×#11926283C211yesmaximal, characteristic, complemented
6#14561517C211yesmaximal, characteristic, complemented
7C2×C19×#497C211yesmaximal, characteristic, complemented
8C2×#10597321C2211yescharacteristic
9#11926906—22no—
10#11926906—22no—
11C2×#10597267—21no—
12C2×#10597266—21no—
13C2×#10597260C2211yescharacteristic
14C2×#10597260C2211yescharacteristic
15#11926460—22no—
16#11926456—21no—
17#11926455—21no—
18#11926453—21no—
19#11926452—21no—
20#11926410C2211yescharacteristic
21#11926306—22no—
22#11926284—22no—
23#11926283—22no—
24C22×Q16×C19—21no—
25C22×SD16×C19—21no—
26C2×C19×C4⋊Q8C2211yescharacteristic
27C2×C19×#124C2211yescharacteristic
28C19×#497—22no—
29C19×#497—22no—
30C2×C19×#97C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×Q8×C19D411yescharacteristic
33C22×D4×C19D411yescharacteristic
34C22×C22⋊D19—22no—
35C22×D76D411yescharacteristic
36C22×Dic38D411yescharacteristic
37C2×Q16×C19—24no—
38C2×Q16×C19—44no—
39C2×SD16×C19—24no—
40C2×SD16×C19—44no—
41C22×C8×C19—21no—
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8D412yescomplemented
46C19×#124—21no—
47C19×#124—21no—
48C19×#124—21no—
49C19×#124—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C22⋊C4×C19—21no—
54C2×C42×C19C2311yescharacteristic
55C2×C22⋊Dic19—22no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—22no—
59C2×C4⋊Dic19D412yes—
60C22×C19⋊C8—21no—
61C22×C19⋊C8—21no—
62#10597321—21no—
63#10597321—21no—
64#10597321—21no—
65#10597321—21no—
66C19×#97—21no—
67C19×#97D412yescomplemented
68C19⋊#95—22no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71#10597267—24no—
72#10597266—24no—
73#10597260—21no—
74#10597260—21no—
75#10597260—21no—
76#10597260D412yescomplemented
77C24×C19—21no—
78C23×D19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—22no—
81C2×Q8×C19—21no—
82C2×Q8×C19—42no—
83C2×Q8×C19—42no—
84C2×Q8×C19—42no—
85C2×Q8×C19—41no—
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—42no—
89C22×C4×C19—21no—
90C22×C4×C19—41no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C2×C22⋊D19—82no—
95C2×C22⋊D19—82no—
96C2×C22⋊D19—82no—
97C22×Dic19—21no—
98C22×Dic19—22no—
99C2×D76—21no—
100C2×D76—21no—
101C2×D76—42no—
102C2×Dic38—21no—
103C2×Dic38—21no—
104C2×Dic38—42no—
105Q16×C19—48no—
106SD16×C19—48no—
107C2×C8×C19—24no—
108C2×C8×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—22no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C42×C19C2×D411yescharacteristic
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19#4111yescharacteristic
121C22⋊Dic19—82no—
122(C2×D19)⋊C4—41no—
123(C2×D19)⋊C4—41no—
124(C2×D19)⋊C4—41no—
125(C2×D19)⋊C4—41no—
126(C2×D19)⋊C4—82no—
127C4⋊Dic19—42no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—42no—
132C2×C19⋊C8—41no—
133#10081—191nomaximal, Sylow
134C23×C19—41no—
135C23×C19—42no—
136C23×C19—42no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19#12011yescharacteristic
140C22×D19—41no—
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—41no—
144C22×D19—41no—
145Q8×C19—42no—
146Q8×C19—42no—
147Q8×C19—42no—
148Q8×C19—81no—
149Q8×C19—82no—
150D4×C19—42no—
151D4×C19—81no—
152C2×C4×C19—22no—
153C2×C4×C19—21no—
154C2×C4×C19—22no—
155C2×C4×C19—21no—
156C2×C4×C19—41no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—82no—
160C2×C4×C19#12011yescharacteristic
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12711yescharacteristic
166C22⋊D19—88no—
167C2×Dic19—41no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172D76—42no—
173D76—81no—
174Dic38—42no—
175Dic38—81no—
176C8×C19—24no—
177C19⋊C8—42no—
178C19⋊C8—42no—
179C2×#497D1911yescharacteristic, complemented
180C2×#489—191no—
181#2819—191no—
182#1993—191no—
183C2×#329—191no—
184C2×#329—191no—
185#1295—191no—
186C22×C19—82no—
187C22×C19—82no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19#39211yescharacteristic
192C22×C19#45312yes—
193C22×C19#45511yescharacteristic
194C22×C19#45512yes—
195C22×C19#45611yescharacteristic
196C2×D19—82no—
197C2×D19—82no—
198C2×D19—81no—
199C2×D19—81no—
200C2×D19—81no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—81no—
208C4×C19—82no—
209Dic19—82no—
210Dic19—81no—
211C22×Q16—21no—
212C22×SD16—21no—
213C2×C4⋊Q8C2×D1911yescharacteristic
214C2×#124—191no—
215C2×#124C2×D1911yescharacteristic
216#497—22no—
217#497—22no—
218#489—382no—
219#489—382no—
220C2×#103—381no—
221C2×#102—381no—
222C2×#97—191no—
223C2×#97—191no—
224C2×#97C2×D1911yescharacteristic
225#394—382no—
226#393—381no—
227#393—381no—
228#392—381no—
229#392—381no—
230#382—191no—
231#340—382no—
232#329—382no—
233#329—382no—
234C2×C19—161no—
235C2×C19#165912yes—
236C2×C19#166112yes—
237C2×C19#200211yescharacteristic
238C2×C19#200411yescharacteristic
239C2×C19#200711yescharacteristic
240D19—161no—
241C22×Q8—21no—
242C22×Q8—191no—
243C22×Q8C22⋊D1911yescharacteristic
244C22×D4—191no—
245C22×D4—382no—
246C22×D4C22⋊D1911yescharacteristic
247C2×Q16—24no—
248C2×Q16—44no—
249C2×SD16—24no—
250C2×SD16—44no—
251C22×C8—21no—
252C22×C8—381no—
253C22×C8—381no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8C22⋊D1912yescomplemented
258#124—21no—
259#124—21no—
260#124—21no—
261#124—21no—
262#124—381no—
263#124—381no—
264#124—381no—
265#124—381no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—192no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—381no—
272C2×C22⋊C4—381no—
273C2×C22⋊C4—382no—
274C2×C22⋊C4—382no—
275C2×C42C22×D1911yescharacteristic
276#103—384no—
277#102—384no—
278#97—21no—
279#97—192no—
280#97—381no—
281#97—381no—
282#97—381no—
283#97C22⋊D1912yescomplemented
284#95—382no—
285#95—381no—
286#95—381no—
287C19#1008111yescharacteristic, complemented, Sylow
288C24—21no—
289C24—381no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—42no—
294C2×Q8—42no—
295C2×Q8—42no—
296C2×Q8—41no—
297C2×Q8—381no—
298C2×Q8—381no—
299C2×Q8—762no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—42no—
303C2×D4—381no—
304C2×D4—381no—
305C2×D4—762no—
306C2×D4—1522no—
307C2×D4—1522no—
308C2×D4—1522no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—382no—
312C22×C4—381no—
313C22×C4D4×D1911yescharacteristic
314C22×C4D4×D1911yescharacteristic
315C22×C4C2×C22⋊D1911yescharacteristic
316Q16—48no—
317SD16—48no—
318C2×C8—24no—
319C2×C8—22no—
320C2×C8—382no—
321C2×C8—382no—
322C2×C8—761no—
323C2×C8—762no—
324C2×C8—761no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—762no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—761no—
338C22⋊C4—1522no—
339C22⋊C4—1522no—
340C42D4×D1911yescharacteristic
341C42#6454311yescharacteristic
342C42C2×C22⋊D1911yescharacteristic
343C42C2×C22⋊D1911yescharacteristic
344C23—41no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—761no—
350C23—762no—
351C23—762no—
352C23—761no—
353C23—761no—
354C23#1059738311yescharacteristic
355Q8—42no—
356Q8—42no—
357Q8—42no—
358Q8—81no—
359Q8—82no—
360Q8—762no—
361Q8—1521no—
362D4—42no—
363D4—81no—
364D4—762no—
365D4—1521no—
366D4—1528no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—761no—
376C2×C4—762no—
377C2×C4—762no—
378C2×C4—762no—
379C2×C4—762no—
380C2×C4#1059738311yescharacteristic
381C2×C4#1059738411yescharacteristic
382C2×C4#1059738511yescharacteristic
383C2×C4#1059738511yescharacteristic
384C2×C4#1059738611yescharacteristic
385C2×C4#1059739911yescharacteristic
386C8—24no—
387C8—762no—
388C8—762no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—82no—
393C22—82no—
394C22—1521no—
395C22—1521no—
396C22—1521no—
397C22—1522no—
398C22—1522no—
399C22#1192645211yescharacteristic
400C22#1192671112yes—
401C22#1192672012yes—
402C22#1192672011yescharacteristic
403C22#1192672511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—82no—
412C4—1521no—
413C4—1522no—
414C2—161no—
415C2—3041no—
416C2#1456293912yes—
417C2#1456294912yes—
418C2#1456465011yescharacteristic
419C2#1456466111yescharacteristic
420C2#1456468011yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#497C2
socleC23×C19#120
prime radical#14571680C2
hypercenterC2×#497D19
hypocenterC19#10081
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#11926906C2semidirect
3. #14564609C2semidirect
4. C2×#11926284C2semidirect
5. C2×#11926283C2semidirect
6. #14561517C2semidirect
7. C2×C19×#497C2semidirect
45. C19×C4⋊Q8D4semidirect
67. C19×#97D4semidirect
76. #10597260D4semidirect
179. C2×#497D19semidirect
257. C4⋊Q8C22⋊D19semidirect
283. #97C22⋊D19semidirect
287. C19#10081semidirect

Maximal subgroups

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

subgroupindex
C2×#119269062
#145716802
#145646092
C2×#119262842
C2×#119262832
#145615172
C2×C19×#4972
#1008119