Finite Group Databasebeta

← #18083374

Subgroups — #18083374

Order 4864.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#14574841C211yesmaximal, characteristic
2#14573765C211yesmaximal, characteristic
3#14564578C211yesmaximal, characteristic
4#14562237C211yesmaximal, characteristic
5#14562082C211yesmaximal, characteristic
6#14561491C211yesmaximal, characteristic
7C19×#2584C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926954—21no—
10#11926914—21no—
11#11926879—21no—
12#11926874—21no—
13#11926874—21no—
14#11926848—22no—
15#11926829—21no—
16#11926754—21no—
17#11926700—21no—
18#11926649—22no—
19#11926601C2211yescharacteristic
20#11926601C2211yescharacteristic
21C4×#64520C2211yescharacteristic
22#11926304—22no—
23#11926286—22no—
24Q8⋊(C19⋊C8)—22no—
25C2×C19×#125C2211yescharacteristic
26C2×C4×Q8×C19C2211yescharacteristic
27C19×#398—21no—
28C19×#395—21no—
29C19×#389—21no—
30C19×#389—21no—
31C19×#389—22no—
32C4×C4⋊C4×C19C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C19×#125—21no—
35C19×#125—21no—
36C19×#125—21no—
37C19×#125—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C4×Q8×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—22no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C42×C19—21no—
52C2×C42×C19D412yes—
53C2×C42×C19C2311yescharacteristic
54C2×#64528—22no—
55#10597372—21no—
56#10597370—21no—
57#10597370—21no—
58C2×#64520—21no—
59#10597316—21no—
60#10597315D411yescharacteristic
61#10597315D411yescharacteristic
62C4×Dic38—21no—
63C4×Dic38—21no—
64C19×#95—22no—
65C19×#95—22no—
66C19×#95—21no—
67#10597292—22no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70#10597267—22no—
71#10597267—22no—
72#10597267—22no—
73#10597265—22no—
74#10597265—22no—
75#10597264—22no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)D412yes—
78#10597260—21no—
79#10597260—21no—
80#10597260D412yes—
81C4×C19⋊C8—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—42no—
85C22×C4×C19—21no—
86C22×C4×C19—22no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C2×Dic38—21no—
94C2×Dic38—21no—
95C4⋊C4×C19—24no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—44no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—82no—
110C42×C19—42no—
111C42×C19—41no—
112C42×C19—41no—
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117C22⋊Dic19—41no—
118#64528—44no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123Dic19⋊C4—41no—
124Dic19⋊C4—41no—
125C4×Dic19—41no—
126#64520—22no—
127#64520—41no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—41no—
131#10011—191nomaximal, Sylow
132C23×C19#12011yescharacteristic
133Q8×C19—22no—
134Q8×C19—22no—
135Q8×C19—41no—
136Q8×C19—41no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—22no—
140C2×C4×C19—24no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12011yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12711yescharacteristic
161C2×Dic19—41no—
162C2×Dic19—41no—
163Dic38—42no—
164Dic38—42no—
165C19⋊C8—42no—
166C19⋊C8—42no—
167C19⋊C8—42no—
168#3236—191no—
169#3113—191no—
170#2584D1911yescharacteristic
171#1986—191no—
172#1528—191no—
173#1491—191no—
174#1285—191no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19#39211yescharacteristic
178C22×C19#45511yescharacteristic
179C22×C19#45611yescharacteristic
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—44no—
186C4×C19—42no—
187C4×C19—81no—
188C4×C19—81no—
189C4×C19—81no—
190C4×C19#45612yes—
191Dic19—81no—
192Dic19—81no—
193#533—191no—
194C2×#125C2×D1911yescharacteristic
195C2×C4×Q8C2×D1911yescharacteristic
196#501—381no—
197#491—381no—
198#484—381no—
199#483—381no—
200#483—381no—
201#479—382no—
202#475—381no—
203#462—381no—
204#451—381no—
205#441—382no—
206#432—191no—
207#432—191no—
208C4×M16—191no—
209#398—21no—
210#395—21no—
211#389—21no—
212#389—21no—
213#389—22no—
214C4×C4⋊C4C2×D1911yescharacteristic
215#339—382no—
216#330—382no—
217Q8⋊C8—382no—
218C2×C19—21no—
219C2×C19—21no—
220C2×C19#200511yescharacteristic
221C2×C19#200711yescharacteristic
222C2×C19#201011yescharacteristic
223C22×Q8C22⋊D1911yescharacteristic
224C2×Q16—382no—
225C2×M16—381no—
226C4⋊Q8—191no—
227C4⋊Q8—191no—
228#125—21no—
229#125—21no—
230#125—21no—
231#125—21no—
232#125—381no—
233C22⋊Q8—381no—
234C22⋊Q8—381no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—381no—
240C4×Q8—381no—
241#117—381no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4C22⋊D1911yescharacteristic
249C2×C4⋊C4C22⋊D1911yescharacteristic
250C2×C4⋊C4C22⋊D1911yescharacteristic
251C2×C42—21no—
252C2×C42C22⋊D1912yes—
253C2×C42C22×D1911yescharacteristic
254#107—382no—
255#106—382no—
256#106—382no—
257C4⋊C8—192no—
258C4⋊C8—381no—
259#103—382no—
260#103—382no—
261#103—382no—
262#103—382no—
263C22⋊C8—381no—
264C22⋊C8—381no—
265#97—192no—
266#97—381no—
267#97—381no—
268C4×C8—381no—
269#95—22no—
270#95—22no—
271#95—21no—
272C19#1001111yescharacteristic, complemented, Sylow
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—381no—
277C2×Q8—381no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4C2×C22⋊D1911yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285C22×C4C2×C22⋊D1911yescharacteristic
286Q16—764no—
287M16—382no—
288M16—761no—
289C2×C8—382no—
290C2×C8—382no—
291C2×C8—761no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—82no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—761no—
312C4⋊C4—761no—
313C22⋊C4—761no—
314C42—42no—
315C42—41no—
316C42—41no—
317C42—761no—
318C42D4×D1911yescharacteristic
319C42D4×D1911yescharacteristic
320C42D4×D1911yescharacteristic
321C42#6454311yescharacteristic
322C23#1059739911yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—762no—
328Q8—762no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4#1059738311yescharacteristic
350C2×C4#1059738311yescharacteristic
351C2×C4#1059738411yescharacteristic
352C2×C4#1059738511yescharacteristic
353C2×C4#1059738511yescharacteristic
354C2×C4#1059738611yescharacteristic
355C8—762no—
356C8—762no—
357C8—762no—
358C22—21no—
359C22—21no—
360C22#1192645211yescharacteristic
361C22#1192672211yescharacteristic
362C22#1192672711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—1521no—
374C4—1521no—
375C4#1192672612yes—
376C2—21no—
377C2—21no—
378C2#1456467111yescharacteristic
379C2#1456468211yescharacteristic
380C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2584C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#2584D19
hypocenterC19#10011
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2584

Complements

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

NH ≅ G/Ntype
272. C19#10011semidirect

Maximal subgroups

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

subgroupindex
#145748412
#145737652
#145645782
#145622372
#145620822
#145614912
C19×#25842
#1001119