Finite Group Databasebeta

← #18083042

Subgroups — #18083042

Order 4864.

594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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#14574388C211yesmaximal, characteristic
2C2×#11926877C211yesmaximal, characteristic, complemented
3#14568127C211yesmaximal, characteristic
4#14563723C211yesmaximal, characteristic, complemented
5#14562202C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic, complemented
7C19×#1996C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10#11926877—22no—
11#11926877—22no—
12#11926872—21no—
13#11926862—21no—
14#11926775—22no—
15#11926694—21no—
16#11926683—21no—
17C2×#10597264—21no—
18C2×#10597292—21no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926471—22no—
22#11926446—21no—
23#11926421—22no—
24#11926410—21no—
25#11926306—22no—
26#11926277—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#380C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C19×#342—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19—21no—
35C22×D76D411yescharacteristic
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19D412yes—
46C2×C42×C19—21no—
47C2×#64527—22no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—24no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19D411yescharacteristic
60C2×C4⋊Dic19D412yes—
61C22×C19⋊C8—21no—
62C22×C19⋊C8D412yes—
63C19×#95—21no—
64C19×#95—21no—
65#10597292—24no—
66#10597292—22no—
67C19⋊#95—24no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)D412yes—
72#10597266—22no—
73#10597265—22no—
74#10597264—24no—
75C24×C19C2×D411yescharacteristic
76C23×D19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—42no—
80C22×C4×C19—22no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—42no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C2×C22⋊D19—41no—
92C2×C22⋊D19—41no—
93C2×C22⋊D19—42no—
94C2×C22⋊D19—42no—
95C22×Dic19—22no—
96C22×Dic19—21no—
97C22×Dic19—41no—
98C22×Dic19—41no—
99C22×Dic19—82no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—42no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—42no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C22⋊C4×C19—22no—
109C22⋊C4×C19—22no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊C4×C19—42no—
113C42×C19—42no—
114#64527—82no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—84no—
118C4⋊Dic19—21no—
119C4⋊Dic19—22no—
120C4⋊Dic19—21no—
121C4⋊Dic19—22no—
122C4⋊Dic19—41no—
123C4⋊Dic19—41no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—42no—
127C2×C19⋊C8—42no—
128#9958—191nomaximal, Sylow
129C23×C19—41no—
130C23×C19—41no—
131C23×C19#12011yescharacteristic
132C23×C19#12111yescharacteristic
133C23×C19#12711yescharacteristic
134C23×C19#13512yes—
135C23×C19#13712yes—
136C22×D19—42no—
137C22×D19—42no—
138C22×D19—41no—
139C22×D19—42no—
140Q8×C19—42no—
141Q8×C19—42no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—81no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C22⋊D19—82no—
163C22⋊D19—81no—
164C22⋊D19—81no—
165C2×Dic19—44no—
166C2×Dic19—42no—
167C2×Dic19—41no—
168C2×Dic19—42no—
169C2×Dic19—82no—
170C2×Dic19—82no—
171D76—42no—
172D76—81no—
173C19⋊C8—42no—
174C19⋊C8—42no—
175#3187—191no—
176C2×#484—191no—
177#2504—191no—
178#1996D1911yescharacteristic, complemented
179#1824—191no—
180#1519—191no—
181#1282—191no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—42no—
189C22×C19—42no—
190C22×C19#39211yescharacteristic
191C22×C19#45212yes—
192C22×C19#46412yes—
193C22×C19#49511yescharacteristic
194C22×C19#49711yescharacteristic
195C2×D19—84no—
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—82no—
203C4×C19—81no—
204C4×C19—81no—
205C4×C19—161no—
206C4×C19#45812yes—
207Dic19—82no—
208Dic19—81no—
209C2×C22⋊Q8C2×D1911yescharacteristic
210C2×#121—191no—
211C22×C4⋊C4—191no—
212#484—382no—
213#484—382no—
214#483—381no—
215#481—381no—
216#465—382no—
217#450—381no—
218#448—381no—
219C2×#107—381no—
220C2×#103—381no—
221C2×C22⋊C8—191no—
222C2×C22⋊C8—191no—
223#397—382no—
224#390—381no—
225#386—382no—
226#382—381no—
227#380C2×D1911yescharacteristic
228C4×C22⋊C4C2×D1911yescharacteristic
229#342—22no—
230#340—382no—
231#327—382no—
232C2×C19—22no—
233C2×C19—21no—
234C2×C19—22no—
235C2×C19—21no—
236C2×C19#200811yescharacteristic
237C2×C19#201511yescharacteristic
238C2×C19#202211yescharacteristic
239D19—161no—
240C22×Q8D7611yescharacteristic
241C22×D4—191no—
242C22×D4—381no—
243C23×C4—381no—
244C23×C4C22×D1911yescharacteristic
245C2×SD16—382no—
246C22×C8—192no—
247C22×C8—381no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252#121—381no—
253#121—381no—
254#121—381no—
255#121—381no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—192no—
259C2×C4⋊C4—191no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4—381no—
263C2×C4⋊C4—381no—
264C2×C4⋊C4—381no—
265C2×C4⋊C4D7611yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—384no—
270C2×C22⋊C4C22⋊D1912yes—
271C2×C42—21no—
272#107—384no—
273#106—382no—
274#103—384no—
275#103—382no—
276#102—382no—
277C22⋊C8—192no—
278C22⋊C8—381no—
279C22⋊C8—381no—
280C22⋊C8—381no—
281#95—21no—
282#95—21no—
283#95—384no—
284C19#995811yescharacteristic, complemented, Sylow
285C24—381no—
286C24C2×C22⋊D1911yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—762no—
293C2×D4—761no—
294C2×D4—761no—
295C2×D4—762no—
296C2×D4—762no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—381no—
303C22×C4—382no—
304C22×C4—761no—
305C22×C4—761no—
306C22×C4—1522no—
307C22×C4C2×D7611yescharacteristic
308C22×C4#6454111yescharacteristic
309C22×C4D4×D1911yescharacteristic
310C22×C4D4×D1911yescharacteristic
311C22×C4D4×D1911yescharacteristic
312C22×C4D4×D1911yescharacteristic
313SD16—1522no—
314C2×C8—382no—
315C2×C8—382no—
316C2×C8—762no—
317C2×C8—762no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—381no—
324C4⋊C4—382no—
325C4⋊C4—382no—
326C4⋊C4—381no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C22⋊C4—1524no—
337C42—42no—
338C23—41no—
339C23—41no—
340C23—762no—
341C23—762no—
342C23—762no—
343C23—761no—
344C23#1059737611yescharacteristic
345C23#1059738311yescharacteristic
346C23#1059738611yescharacteristic
347C23#1059738812yes—
348C23#1059739612yes—
349Q8—42no—
350Q8—42no—
351D4—762no—
352D4—1521no—
353D4—1521no—
354D4—1521no—
355D4—1522no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—764no—
373C2×C4—762no—
374C2×C4—761no—
375C2×C4—762no—
376C2×C4—1522no—
377C2×C4—1522no—
378C2×C4#1059732811yescharacteristic
379C2×C4#1059732811yescharacteristic
380C2×C4#1059733011yescharacteristic
381C2×C4#1059733011yescharacteristic
382C8—762no—
383C8—762no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—1524no—
393C22—1521no—
394C22—1521no—
395C22—1521no—
396C22#1192645311yescharacteristic
397C22#1192670412yes—
398C22#1192676612yes—
399C22#1192692611yescharacteristic
400C22#1192693611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—161no—
408C4—1522no—
409C4—1521no—
410C4#1192673512yes—
411C2—22no—
412C2—21no—
413C2—21no—
414C2—22no—
415C2—3041no—
416C2#1456468711yescharacteristic
417C2#1456472811yescharacteristic
418C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1996C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#1996D19
hypocenterC19#9958
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. C2×#11926877C2semidirect
4. #14563723C2semidirect
6. #14561483C2semidirect
7. C19×#1996C2semidirect
178. #1996D19semidirect
284. C19#9958semidirect

Maximal subgroups

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

subgroupindex
#145743882
C2×#119268772
#145681272
#145637232
#145622022
#145614832
C19×#19962
#995819