Finite Group Databasebeta

← #18083065

Subgroups — #18083065

Order 4864.

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

normal subgroups only

This group has 552 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#14574410C211yesmaximal, characteristic
2C2×#11926874C211yesmaximal, characteristic
3#14568116C211yesmaximal, characteristic
4#14564619C211yesmaximal, characteristic
5#14562206C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic
7C19×#1823C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×#10597370C2211yescharacteristic
10#11926880—21no—
11#11926880—21no—
12#11926874—22no—
13#11926874—22no—
14#11926785—22no—
15#11926702—21no—
16#11926702—21no—
17C2×#10597265—21no—
18C2×#10597267—21no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20#11926482—22no—
21#11926449—21no—
22#11926409—21no—
23#11926407—22no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926310—22no—
26#11926280—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#340—22no—
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×Dic38D411yescharacteristic
34C22×Dic38D411yescharacteristic
35C22×C8×C19D412yes—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19D412yes—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19D412yes—
47C2×C4⋊Dic19D411yescharacteristic
48C2×C4⋊Dic19D411yescharacteristic
49#10597370—21no—
50#10597370—21no—
51#10597370—21no—
52#10597370—21no—
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×C4×Dic19—21no—
60C22×C19⋊C8—21no—
61C2×Dic76—22no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95—21no—
65C19⋊#95—24no—
66C19⋊#95—24no—
67C19⋊#95—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)D412yes—
70#10597275—22no—
71#10597273—22no—
72#10597273—22no—
73#10597267—24no—
74#10597265—24no—
75C24×C19C2×D411yescharacteristic
76C22×C4×C19—22no—
77C22×C4×C19—42no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—42no—
81C22×C4×C19—42no—
82C22×C4×C19—41no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—22no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C2×Dic38—21no—
95C2×Dic38—21no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×Dic38—42no—
99C2×Dic38—42no—
100C2×C8×C19—22no—
101C2×C8×C19—42no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—42no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C22⋊C4×C19—42no—
108C22⋊Dic19—22no—
109C22⋊Dic19—22no—
110C22⋊Dic19—41no—
111C22⋊Dic19—41no—
112C22⋊Dic19—41no—
113C22⋊Dic19—41no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118Dic19⋊C4—41no—
119Dic19⋊C4—41no—
120Dic19⋊C4—41no—
121Dic19⋊C4—41no—
122C4×Dic19—42no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—42no—
125Dic76—82no—
126#9961—191nomaximal, Sylow
127C23×C19—41no—
128C23×C19—41no—
129C23×C19#12011yescharacteristic
130C23×C19#12111yescharacteristic
131C23×C19#12711yescharacteristic
132C23×C19#13512yes—
133C23×C19#13712yes—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—44no—
142C2×C4×C19—82no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19—81no—
146C2×C4×C19—81no—
147C2×C4×C19—81no—
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12011yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—42no—
161C2×Dic19—81no—
162C2×Dic19—81no—
163Dic38—42no—
164Dic38—42no—
165Dic38—42no—
166Dic38—81no—
167C8×C19—42no—
168C19⋊C8—42no—
169#3189—191no—
170C2×#483—191no—
171#2503—191no—
172#1996—191no—
173#1823D1911yescharacteristic
174#1520—191no—
175#1282—191no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—42no—
183C22×C19—42no—
184C22×C19#39211yescharacteristic
185C22×C19#45212yes—
186C22×C19#46412yes—
187C22×C19#49511yescharacteristic
188C22×C19#49711yescharacteristic
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—82no—
193C4×C19—161no—
194C4×C19#45812yes—
195Dic19—82no—
196Dic19—81no—
197Dic19—81no—
198Dic19—81no—
199Dic19—81no—
200C2×C22⋊Q8—191no—
201C2×C22⋊Q8—191no—
202C22×C4⋊C4C2×D1911yescharacteristic
203#484—381no—
204#484—381no—
205#483—382no—
206#483—382no—
207#467—382no—
208#451—381no—
209#451—381no—
210C2×#106—381no—
211C2×#103—381no—
212C2×C22⋊C8—191no—
213C2×C22⋊C8C2×D1911yescharacteristic
214#400—382no—
215#391—381no—
216#382—381no—
217#381—382no—
218#380C2×D1911yescharacteristic
219C4×C22⋊C4—191no—
220#342—382no—
221#340—22no—
222#328—382no—
223C2×C19—22no—
224C2×C19—21no—
225C2×C19—22no—
226C2×C19—21no—
227C2×C19#200911yescharacteristic
228C2×C19#201511yescharacteristic
229C2×C19#202211yescharacteristic
230C22×Q8—191no—
231C22×Q8—191no—
232C23×C4—21no—
233C23×C4C22×D1911yescharacteristic
234C2×Q16—382no—
235C22×C8—381no—
236C22×C8C22⋊D1912yes—
237C22⋊Q8—381no—
238C22⋊Q8—381no—
239C22⋊Q8—381no—
240C22⋊Q8—381no—
241C22⋊Q8—381no—
242C22⋊Q8—381no—
243C22⋊Q8—381no—
244C22⋊Q8—381no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—191no—
252C2×C4⋊C4—191no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4D7612yes—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—192no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4—381no—
260C2×C42—381no—
261#107—382no—
262#106—384no—
263#103—384no—
264#103—382no—
265#103—382no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—192no—
269C22⋊C8—381no—
270#95—21no—
271#95—384no—
272#95—384no—
273#95—381no—
274C19#996111yescharacteristic, complemented, Sylow
275C24D4×D1911yescharacteristic
276C2×Q8—381no—
277C2×Q8—381no—
278C2×Q8—381no—
279C2×Q8—381no—
280C2×Q8—762no—
281C2×Q8—762no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—382no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—381no—
293C22×C4—381no—
294C22×C4C2×D7611yescharacteristic
295C22×C4#6454111yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4D4×D1911yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300Q16—1522no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—382no—
304C2×C8—762no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—761no—
317C4⋊C4—761no—
318C22⋊C4—42no—
319C22⋊C4—382no—
320C22⋊C4—382no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C22⋊C4—761no—
324C22⋊C4—761no—
325C42—762no—
326C23—41no—
327C23—41no—
328C23#1059732811yescharacteristic
329C23#1059733011yescharacteristic
330C23#1059735812yes—
331C23#1059736112yes—
332C23#1059738611yescharacteristic
333Q8—762no—
334Q8—762no—
335Q8—762no—
336Q8—1521no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4—1521no—
361C2×C4—1521no—
362C2×C4#1059732811yescharacteristic
363C2×C4#1059733011yescharacteristic
364C2×C4#1059737611yescharacteristic
365C2×C4#1059738311yescharacteristic
366C8—42no—
367C8—762no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1192645311yescharacteristic
377C22#1192670712yes—
378C22#1192676512yes—
379C22#1192692711yescharacteristic
380C22#1192693511yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—161no—
386C4—1522no—
387C4—1521no—
388C4—1521no—
389C4—1521no—
390C4—1521no—
391C4#1192673312yes—
392C2—21no—
393C2—22no—
394C2—21no—
395C2—22no—
396C2#1456469711yescharacteristic
397C2#1456473111yescharacteristic
398C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1823C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1823D19
hypocenterC19#9961
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
274. C19#9961semidirect

Maximal subgroups

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

subgroupindex
#145744102
C2×#119268742
#145681162
#145646192
#145622062
#145614822
C19×#18232
#996119