Finite Group Databasebeta

← #18082827

Subgroups — #18082827

Order 4864.

654 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#11926874C211yesmaximal, characteristic
2#14569451C211yesmaximal, characteristic
3C2×#11926475C211yesmaximal, characteristic
4C2×#11926282C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic
6#14561513C211yesmaximal, characteristic
7C19×#1823C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×Dic19⋊C4—21no—
10C22×Dic19⋊C4C2211yescharacteristic
11#11926874—22no—
12#11926874—22no—
13C2×#10597265—21no—
14C2×#10597267—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926484—21no—
17#11926475—22no—
18#11926475—22no—
19#11926474—22no—
20#11926465—21no—
21#11926419—21no—
22#11926405—21no—
23C2×C19⋊#95—21no—
24C2×C19⋊#95C2211yescharacteristic
25#11926282—22no—
26#11926269—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#340—22no—
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C23×Dic19—21no—
34C23×Dic19D411yescharacteristic
35C23×Dic19D411yescharacteristic
36C22×Dic38D411yescharacteristic
37C22×C8×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×C19—21no—
43C2×C4⋊C4×C19D412yes—
44C2×C4⋊C4×C19D412yes—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊Dic19—21no—
47C2×C4⋊Dic19—22no—
48C2×C4⋊Dic19D411yescharacteristic
49#10597370—21no—
50#10597370—21no—
51#10597370—21no—
52#10597370—21no—
53C2×Dic19⋊C4—24no—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—42no—
62C2×Dic19⋊C4—42no—
63C22×C19⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×#95—21no—
67C19⋊#95—24no—
68C19⋊#95—22no—
69C19⋊#95—22no—
70C19⋊#95—22no—
71C19⋊#95—21no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yes—
75#10597267—24no—
76#10597265—24no—
77C24×C19C2×D411yescharacteristic
78C22×C4×C19—22no—
79C22×C4×C19—22no—
80C22×C4×C19—42no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×Dic19—24no—
94C22×Dic19—22no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—42no—
107C22×Dic19—41no—
108C22×Dic19—41no—
109C22×Dic19—42no—
110C22×Dic19SD1612yes—
111C2×Dic38—21no—
112C2×Dic38—21no—
113C2×Dic38—42no—
114C2×C8×C19—42no—
115C2×C8×C19—41no—
116C4⋊C4×C19—22no—
117C4⋊C4×C19—22no—
118C4⋊C4×C19—42no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊Dic19—41no—
124C22⋊Dic19—41no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—82no—
128Dic19⋊C4—48no—
129Dic19⋊C4—41no—
130Dic19⋊C4—41no—
131Dic19⋊C4—41no—
132Dic19⋊C4—41no—
133Dic19⋊C4—41no—
134Dic19⋊C4—41no—
135C2×C19⋊C8—22no—
136C2×C19⋊C8—42no—
137#9927—191nomaximal, Sylow
138C23×C19—22no—
139C23×C19—22no—
140C23×C19#12011yescharacteristic
141C23×C19#12011yescharacteristic
142C23×C19#12111yescharacteristic
143C23×C19C2×SD1611yescharacteristic
144C23×C19#13511yescharacteristic
145C23×C19AGL(1,ℤ/8)11yescharacteristic
146C23×C19#13711yescharacteristic
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19#12011yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12711yescharacteristic
167C2×Dic19—24no—
168C2×Dic19—22no—
169C2×Dic19—22no—
170C2×Dic19—22no—
171C2×Dic19—44no—
172C2×Dic19—44no—
173C2×Dic19—42no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—42no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—42no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—42no—
184C2×Dic19—42no—
185C2×Dic19—42no—
186C2×Dic19—81no—
187Dic38—42no—
188Dic38—81no—
189C8×C19—81no—
190C19⋊C8—42no—
191C2×#483—191no—
192#2627—191no—
193C2×#398—191no—
194#1823D1911yescharacteristic
195C2×#328—191no—
196C2×#324—191no—
197#1294—191no—
198C22×C19—22no—
199C22×C19—22no—
200C22×C19—22no—
201C22×C19—22no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19#39211yescharacteristic
207C22×C19#44811yescharacteristic
208C22×C19#44911yescharacteristic
209C22×C19#45011yescharacteristic
210C22×C19#45211yescharacteristic
211C22×C19#45612yes—
212C22×C19#45812yes—
213C22×C19#46511yescharacteristic
214C22×C19#46811yescharacteristic
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—82no—
220C4×C19—82no—
221Dic19—44no—
222Dic19—42no—
223Dic19—81no—
224Dic19—81no—
225Dic19—81no—
226C2×C22⋊Q8—191no—
227C22×C4⋊C4—191no—
228C22×C4⋊C4—381no—
229C22×C4⋊C4C2×D1911yescharacteristic
230#483—382no—
231#483—382no—
232C2×#106—381no—
233C2×#103—381no—
234C2×C22⋊C8—191no—
235C2×C22⋊C8C2×D1911yescharacteristic
236#400—381no—
237#398—382no—
238#398—382no—
239#398—382no—
240#395—381no—
241#385—381no—
242#381—381no—
243#380C2×D1911yescharacteristic
244C2×#95—191no—
245C2×#95—381no—
246#340—22no—
247#328—382no—
248#324—382no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19#160912yes—
254C2×C19#161112yes—
255C2×C19#200011yescharacteristic
256C2×C19#200511yescharacteristic
257C2×C19#202211yescharacteristic
258C22×Q8—191no—
259C23×C4—21no—
260C23×C4—191no—
261C23×C4—191no—
262C23×C4—381no—
263C23×C4C22×D1911yescharacteristic
264C22×C8—21no—
265C22×C8—381no—
266C22⋊Q8—381no—
267C22⋊Q8—381no—
268C22⋊Q8—381no—
269C22⋊Q8—381no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—191no—
276C2×C4⋊C4—384no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—381no—
280C2×C4⋊C4—381no—
281C2×C4⋊C4—381no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4—381no—
284C2×C4⋊C4—382no—
285C2×C4⋊C4—762no—
286C2×C4⋊C4—762no—
287C2×C4⋊C4D7612yes—
288C2×C4⋊C4C22⋊D1912yes—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—381no—
291#106—384no—
292#103—384no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—192no—
296C22⋊C8—381no—
297#95—21no—
298#95—192no—
299#95—384no—
300#95—382no—
301#95—382no—
302#95—382no—
303#95—381no—
304C19#992711yescharacteristic, complemented, Sylow
305C24D4×D1911yescharacteristic
306C2×Q8—381no—
307C2×Q8—381no—
308C2×Q8—762no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—192no—
319C22×C4—384no—
320C22×C4—381no—
321C22×C4—382no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—762no—
333C22×C4—761no—
334C22×C4—761no—
335C22×C4—762no—
336C22×C4C2×D7611yescharacteristic
337C22×C4#6454111yescharacteristic
338C22×C4D4×D1911yescharacteristic
339C22×C4D4×D1911yescharacteristic
340C22×C4D4×D1911yescharacteristic
341C22×C4C2×C22⋊D1911yescharacteristic
342C2×C8—42no—
343C2×C8—41no—
344C2×C8—382no—
345C2×C8—762no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—42no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—381no—
352C4⋊C4—381no—
353C4⋊C4—768no—
354C4⋊C4—761no—
355C4⋊C4—761no—
356C4⋊C4—761no—
357C4⋊C4—761no—
358C4⋊C4—761no—
359C4⋊C4—761no—
360C4⋊C4—1522no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—761no—
364C22⋊C4—761no—
365C23—22no—
366C23—22no—
367C23#1059732811yescharacteristic
368C23#1059733011yescharacteristic
369C23#1059735711yescharacteristic
370C23#1059735811yescharacteristic
371C23SD16×D1911yescharacteristic
372C23#1059736111yescharacteristic
373C23#1059738311yescharacteristic
374Q8—762no—
375Q8—1521no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—384no—
393C2×C4—382no—
394C2×C4—382no—
395C2×C4—382no—
396C2×C4—764no—
397C2×C4—764no—
398C2×C4—762no—
399C2×C4—761no—
400C2×C4—761no—
401C2×C4—762no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—762no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—762no—
409C2×C4—762no—
410C2×C4—762no—
411C2×C4—1521no—
412C2×C4#1059732811yescharacteristic
413C2×C4#1059733011yescharacteristic
414C2×C4#1059737611yescharacteristic
415C2×C4#1059738611yescharacteristic
416C8—81no—
417C8—762no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22#1192645311yescharacteristic
427C22#1192668111yescharacteristic
428C22#1192668611yescharacteristic
429C22#1192669611yescharacteristic
430C22#1192670711yescharacteristic
431C22#1192672512yes—
432C22#1192673312yes—
433C22#1192677211yescharacteristic
434C22#1192678911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—82no—
441C4—764no—
442C4—762no—
443C4—1521no—
444C4—1521no—
445C4—1521no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#1456262912yes—
451C2#1456264112yes—
452C2#1456463911yescharacteristic
453C2#1456467211yescharacteristic
454C2#1456476611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1823C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1823D19
hypocenterC19#9927
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
304. C19#9927semidirect

Maximal subgroups

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

subgroupindex
C2×#119268742
#145694512
C2×#119264752
C2×#119262822
C2×#119262692
#145615132
C19×#18232
#992719