Finite Group Databasebeta

← #18083049

Subgroups — #18083049

Order 4864.

568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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#14574407C211yesmaximal, characteristic
2C2×#11926877C211yesmaximal, characteristic
3#14568113C211yesmaximal, characteristic
4#14563723C211yesmaximal, characteristic
5#14562206C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic
7C19×#1996C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10#11926879—21no—
11#11926877—21no—
12#11926877—22no—
13#11926877—22no—
14#11926783—22no—
15#11926700—21no—
16#11926699—21no—
17C2×#10597264—21no—
18C2×#10597292—21no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926476—22no—
22#11926450—21no—
23#11926419—22no—
24#11926414—21no—
25#11926306—22no—
26#11926280—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#380C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C19×#342—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C23×Dic19—21no—
34C22×Dic38D411yescharacteristic
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19D412yes—
45C2×C42×C19—21no—
46C2×C22⋊Dic19—21no—
47C2×#64528—22no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C2×C4⋊Dic19—24no—
54C2×C4⋊Dic19D411yescharacteristic
55C2×C4⋊Dic19D412yes—
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60C2×Dic19⋊C4—21no—
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#10597267—22no—
73#10597264—24no—
74#10597264—22no—
75C24×C19C2×D411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—42no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—42no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—41no—
94C22×Dic19—41no—
95C22×Dic19—82no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×Dic38—42no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—42no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C22⋊C4×C19—22no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—42no—
108C22⋊C4×C19Q1614yescomplemented
109C42×C19—42no—
110C22⋊Dic19—41no—
111C22⋊Dic19—41no—
112#64528—82no—
113C4⋊Dic19—21no—
114C4⋊Dic19—22no—
115C4⋊Dic19—21no—
116C4⋊Dic19—22no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119C4⋊Dic19—84no—
120Dic19⋊C4—41no—
121Dic19⋊C4—41no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—42no—
125C2×C19⋊C8—42no—
126#9959—191nomaximal, Sylow
127C23×C19—41no—
128C23×C19—41no—
129C23×C19#12011yescharacteristic
130C23×C19#12111yescharacteristic
131C23×C19#12711yescharacteristic
132C23×C19C2×Q1612yes—
133C23×C19#13712yes—
134Q8×C19—42no—
135Q8×C19—42no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—24no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—81no—
148C2×C4×C19—81no—
149C2×C4×C19—81no—
150C2×C4×C19—81no—
151C2×C4×C19—81no—
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12011yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×Dic19—42no—
157C2×Dic19—44no—
158C2×Dic19—42no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—42no—
162C2×Dic19—82no—
163C2×Dic19—82no—
164Dic38—42no—
165Dic38—81no—
166C19⋊C8—42no—
167C19⋊C8—42no—
168#3189—191no—
169C2×#484—191no—
170#2502—191no—
171#1996D1911yescharacteristic
172#1824—191no—
173#1520—191no—
174#1282—191no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19#39211yescharacteristic
184C22×C19#45112yes—
185C22×C19#46212yes—
186C22×C19#49411yescharacteristic
187C22×C19#49711yescharacteristic
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—44no—
192C4×C19—81no—
193C4×C19—81no—
194C4×C19—161no—
195C4×C19#45812yes—
196Dic19—81no—
197Dic19—82no—
198Dic19—81no—
199C2×C22⋊Q8—191no—
200C2×C22⋊Q8C2×D1911yescharacteristic
201C22×C4⋊C4—191no—
202#484—382no—
203#484—382no—
204#484—381no—
205#484—381no—
206#467—382no—
207#451—381no—
208#451—381no—
209C2×#107—381no—
210C2×#103—381no—
211C2×C22⋊C8—191no—
212C2×C22⋊C8—191no—
213#398—382no—
214#391—381no—
215#385—382no—
216#384—381no—
217#380C2×D1911yescharacteristic
218C4×C22⋊C4C2×D1911yescharacteristic
219#342—22no—
220#340—382no—
221#328—382no—
222C2×C19—22no—
223C2×C19—21no—
224C2×C19—22no—
225C2×C19—21no—
226C2×C19#200811yescharacteristic
227C2×C19#201611yescharacteristic
228C2×C19#202211yescharacteristic
229C22×Q8—191no—
230C22×Q8D7611yescharacteristic
231C23×C4—381no—
232C23×C4C22×D1911yescharacteristic
233C2×Q16—382no—
234C22×C8—192no—
235C22×C8—381no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—381no—
241C22⋊Q8—381no—
242C22⋊Q8—381no—
243C22⋊Q8—381no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—192no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—384no—
255C2×C4⋊C4D7611yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4C22⋊D1912yes—
260C2×C42—21no—
261#107—384no—
262#107—382no—
263#103—382no—
264#103—384no—
265#103—382no—
266C22⋊C8—192no—
267C22⋊C8—381no—
268C22⋊C8—381no—
269C22⋊C8—381no—
270#95—21no—
271#95—21no—
272#95—384no—
273C19#995911yescharacteristic, complemented, Sylow
274C24C2×C22⋊D1911yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—42no—
278C2×Q8—381no—
279C2×Q8—381no—
280C2×Q8—762no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—381no—
287C22×C4—382no—
288C22×C4—381no—
289C22×C4—761no—
290C22×C4—761no—
291C22×C4—1522no—
292C22×C4C2×D7611yescharacteristic
293C22×C4#6454111yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4D4×D1911yescharacteristic
298Q16—1522no—
299C2×C8—382no—
300C2×C8—382no—
301C2×C8—762no—
302C2×C8—762no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—382no—
309C4⋊C4—381no—
310C4⋊C4—382no—
311C4⋊C4—381no—
312C4⋊C4—761no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—1524no—
317C22⋊C4—22no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C22⋊C4#6452814yescomplemented
324C42—42no—
325C23—41no—
326C23—41no—
327C23#1059737611yescharacteristic
328C23#1059738311yescharacteristic
329C23#1059738611yescharacteristic
330C23C2×#6452812yes—
331C23#1059739712yes—
332Q8—42no—
333Q8—42no—
334Q8—762no—
335Q8—1521no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—762no—
353C2×C4—764no—
354C2×C4—762no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—762no—
358C2×C4—1522no—
359C2×C4—1522no—
360C2×C4#1059732811yescharacteristic
361C2×C4#1059732811yescharacteristic
362C2×C4#1059733011yescharacteristic
363C2×C4#1059733011yescharacteristic
364C8—762no—
365C8—762no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1192645311yescharacteristic
375C22#1192669912yes—
376C22#1192675412yes—
377C22#1192692311yescharacteristic
378C22#1192693911yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—81no—
384C4—81no—
385C4—161no—
386C4—1522no—
387C4—1521no—
388C4—1521no—
389C4#1192673512yes—
390C2—22no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2#1456468711yescharacteristic
395C2#1456473411yescharacteristic
396C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1996C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1996D19
hypocenterC19#9959
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
108. C22⋊C4×C19Q16semidirect
273. C19#9959semidirect
323. C22⋊C4#64528semidirect

Maximal subgroups

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

subgroupindex
#145744072
C2×#119268772
#145681132
#145637232
#145622062
#145614832
C19×#19962
#995919