Finite Group Databasebeta

← #18085479

Subgroups — #18085479

Order 4864.

754 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 89 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#14574456C211yesmaximal, characteristic
2#14567275C211yesmaximal, characteristic
3#14563559C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic
5#14562154C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic
7C19×#2434C211yesmaximal, characteristic
8C2×#10597390—21no—
9C2×#10597370C2211yescharacteristic
10#11926874—21no—
11#11926872—21no—
12#11926800—22no—
13#11926700—21no—
14#11926699—21no—
15C2×#10597293—22no—
16#11926508C2211yescharacteristic
17#11926508C2211yescharacteristic
18#11926463—22no—
19#11926451—21no—
20#11926417—22no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926281—22no—
23#11926280—22no—
24C23×Q8×C19C2211yescharacteristic
25C2×C19×C4⋊Q8—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#395—22no—
28C19×#391—21no—
29C19×#385—22no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×Q8×C19—21no—
33C22×Q8×C19—21no—
34C22×Q8×C19—21no—
35C22×Q8×C19—21no—
36C22×Q8×C19—21no—
37C22×Q8×C19—44no—
38C22×Q8×C19D411yescharacteristic
39C23×C4×C19D412yes—
40C23×C4×C19C2311yescharacteristic
41C22×Dic38D411yescharacteristic
42C19×C4⋊Q8—44no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C2×C4⋊C4×C19—24no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C42×C19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55#10597390—44no—
56C2×#64528—22no—
57C2×C4⋊Dic19D411yescharacteristic
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62C2×Dic19⋊C4—24no—
63C2×Dic19⋊C4—21no—
64C2×C4×Dic19—21no—
65C2×#64520—21no—
66C2×#64520D412yes—
67C19×#95—24no—
68C19×#95D412yes—
69#10597293—44no—
70#10597292—22no—
71C19⋊#95—24no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77#10597267—22no—
78#10597265—22no—
79C24×C19C2×D411yescharacteristic
80C2×Q8×C19—24no—
81C2×Q8×C19—24no—
82C2×Q8×C19—24no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—42no—
86C2×Q8×C19—42no—
87C2×Q8×C19—42no—
88C2×Q8×C19—44no—
89C2×Q8×C19—44no—
90C2×Q8×C19—44no—
91C2×Q8×C19—42no—
92C2×Q8×C19—41no—
93C2×Q8×C19—41no—
94C2×Q8×C19—41no—
95C2×Q8×C19—41no—
96C22×C4×C19—22no—
97C22×C4×C19—22no—
98C22×C4×C19—22no—
99C22×C4×C19—22no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—44no—
103C22×C4×C19—42no—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C22×Dic19—22no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C2×Dic38—21no—
114C2×Dic38—21no—
115C2×Dic38—42no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—48no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C22⋊C4×C19—24no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C42×C19—42no—
125C22⋊Dic19—24no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128#64528—82no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131Dic19⋊C4—48no—
132Dic19⋊C4—41no—
133Dic19⋊C4—41no—
134C4×Dic19—42no—
135#64520—42no—
136#64520—42no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—41no—
139#10334—191nomaximal, Sylow
140C23×C19—22no—
141C23×C19—22no—
142C23×C19—41no—
143C23×C19#12011yescharacteristic
144C23×C19#12011yescharacteristic
145C23×C19#12111yescharacteristic
146Q8×C19—44no—
147Q8×C19—44no—
148Q8×C19—44no—
149Q8×C19—44no—
150Q8×C19—42no—
151Q8×C19—81no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—22no—
155C2×C4×C19—24no—
156C2×C4×C19—24no—
157C2×C4×C19—24no—
158C2×C4×C19—24no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—42no—
168C2×C4×C19—42no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—42no—
172C2×C4×C19#12011yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12111yescharacteristic
175C2×C4×C19#12711yescharacteristic
176C2×Dic19—24no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183Dic38—42no—
184Dic38—81no—
185C19⋊C8—42no—
186C19⋊C8—81no—
187#3195—191no—
188#2434—191no—
189#2434D1911yescharacteristic
190#1784—191no—
191#1508—191no—
192#1508—191no—
193#1297—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—44no—
202C22×C19#39211yescharacteristic
203C22×C19#45612yes—
204C22×C19#45612yes—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—44no—
209C4×C19—44no—
210C4×C19—81no—
211C4×C19—81no—
212C4×C19B(4,𝔽2)12yes—
213Dic19—44no—
214Dic19—81no—
215Dic19—81no—
216C23×Q8C2×D1911yescharacteristic
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—381no—
219C2×C22⋊Q8—191no—
220C2×C22⋊Q8C2×D1911yescharacteristic
221#483—381no—
222#483—381no—
223#470—382no—
224#451—381no—
225#451—381no—
226C2×#101—382no—
227#407—191no—
228#407—191no—
229#395—22no—
230#395—382no—
231#391—21no—
232#391—381no—
233#385—22no—
234#385—382no—
235C4×C22⋊C4—191no—
236C4×C22⋊C4C2×D1911yescharacteristic
237#328—382no—
238#328—382no—
239C2×C19—22no—
240C2×C19—22no—
241C2×C19—41no—
242C2×C19#200511yescharacteristic
243C2×C19#200511yescharacteristic
244C2×C19#202111yescharacteristic
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—44no—
252C22×Q8—191no—
253C22×Q8C22⋊D1911yescharacteristic
254C23×C4C22⋊D1912yes—
255C23×C4C22×D1911yescharacteristic
256C2×Q16—382no—
257C2×M16—192no—
258C2×M16—381no—
259C4⋊Q8—44no—
260C4⋊Q8—764no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—381no—
266C22⋊Q8—381no—
267C22⋊Q8—381no—
268C22⋊Q8—381no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—384no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4C22⋊D1911yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4—381no—
279C2×C42—21no—
280C2×C42—381no—
281#106—382no—
282#103—382no—
283#103—382no—
284#101—764no—
285C22⋊C8—381no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289#95—24no—
290#95—192no—
291#95—384no—
292#95C22⋊D1912yes—
293C19#1033411yescharacteristic, complemented, Sylow
294C24C2×C22⋊D1911yescharacteristic
295C2×Q8—24no—
296C2×Q8—24no—
297C2×Q8—24no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—44no—
304C2×Q8—44no—
305C2×Q8—44no—
306C2×Q8—42no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—381no—
312C2×Q8—381no—
313C2×Q8—762no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—44no—
321C22×C4—42no—
322C22×C4—382no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4D4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4D4×D1911yescharacteristic
328C22×C4#6454311yescharacteristic
329C22×C4C2×C22⋊D1911yescharacteristic
330C22×C4C2×C22⋊D1911yescharacteristic
331Q16—1522no—
332M16—762no—
333M16—762no—
334C2×C8—382no—
335C2×C8—761no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—48no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—381no—
342C4⋊C4—381no—
343C4⋊C4—768no—
344C4⋊C4—761no—
345C4⋊C4—761no—
346C22⋊C4—24no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—384no—
350C22⋊C4—761no—
351C22⋊C4—761no—
352C42—42no—
353C42—762no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23#1059738311yescharacteristic
358C23#1059738511yescharacteristic
359C23#1059739911yescharacteristic
360Q8—44no—
361Q8—44no—
362Q8—44no—
363Q8—44no—
364Q8—42no—
365Q8—81no—
366Q8—762no—
367Q8—1521no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—384no—
389C2×C4—762no—
390C2×C4—762no—
391C2×C4—762no—
392C2×C4—761no—
393C2×C4—761no—
394C2×C4—762no—
395C2×C4#1059738311yescharacteristic
396C2×C4#1059738411yescharacteristic
397C2×C4#1059738511yescharacteristic
398C2×C4#1059738611yescharacteristic
399C8—762no—
400C8—1521no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—44no—
409C22#1192645211yescharacteristic
410C22#1192672612yes—
411C22#1192672712yes—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—44no—
416C4—44no—
417C4—81no—
418C4—81no—
419C4—764no—
420C4—1521no—
421C4—1521no—
422C4#1192673012yes—
423C2—22no—
424C2—22no—
425C2—41no—
426C2#1456466911yescharacteristic
427C2#1456467111yescharacteristic
428C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2434C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#2434D19
hypocenterC19#10334
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
293. C19#10334semidirect

Maximal subgroups

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

subgroupindex
#145744562
#145672752
#145635592
#145621552
#145621542
#145615212
C19×#24342
#1033419