Finite Group Databasebeta

← #18083099

Subgroups — #18083099

Order 4864.

804 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11926702C211yesmaximal, characteristic
2C2×#11926699C211yesmaximal, characteristic
3#14569751C211yesmaximal, characteristic
4C2×#11926280C211yesmaximal, characteristic
5#14561905C211yesmaximal, characteristic
6#14561477C211yesmaximal, characteristic
7C2×C19×#328C211yesmaximal, characteristic
8C23×Dic38C2211yescharacteristic
9C22×Dic76—21no—
10C22×#64528—21no—
11C2×#10597370C2211yescharacteristic
12#11926702—22no—
13#11926702—22no—
14#11926699—22no—
15#11926699—22no—
16C2×#10597273—21no—
17C2×#10597267—21no—
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19#11926475—21no—
20#11926474—21no—
21#11926464—21no—
22#11926463—21no—
23#11926402—22no—
24C2×C19⋊#95—22no—
25C2×C19⋊#95C2211yescharacteristic
26#11926280—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C23×Dic19—21no—
35C23×Dic19D412yes—
36C22×Dic38—21no—
37C22×Dic38—21no—
38C22×Dic38—21no—
39C22×Dic38—21no—
40C22×Dic38—21no—
41C22×Dic38—44no—
42C22×Dic38D411yescharacteristic
43C22×Dic38D412yes—
44C22×C8×C19—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C22⋊C4×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×#64528—24no—
54C2×#64528—44no—
55C2×C4⋊Dic19D411yescharacteristic
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—22no—
62C2×Dic19⋊C4—22no—
63C22×C19⋊C8—21no—
64C2×Dic76—24no—
65C2×Dic76—44no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8D412yes—
68C19×#95—21no—
69C19×#95—21no—
70C19⋊#95—22no—
71C19⋊#95—22no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—44no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77#10597273—24no—
78#10597267—24no—
79C24×C19C2×D411yescharacteristic
80C2×Q8×C19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—42no—
83C22×C4×C19—22no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—42no—
87C22×C4×C19—41no—
88C22×C4×C19—42no—
89C22×C4×C19—41no—
90C22×C4×C19—42no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—24no—
98C22×Dic19—22no—
99C22×Dic19—22no—
100C22×Dic19—22no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—42no—
104C22×Dic19—41no—
105C22×Dic19—41no—
106C22×Dic19—42no—
107C22×Dic19—42no—
108C22×Dic19Q1614yescomplemented
109C2×Dic38—24no—
110C2×Dic38—24no—
111C2×Dic38—22no—
112C2×Dic38—22no—
113C2×Dic38—21no—
114C2×Dic38—21no—
115C2×Dic38—44no—
116C2×Dic38—44no—
117C2×Dic38—44no—
118C2×Dic38—44no—
119C2×Dic38—42no—
120C2×Dic38—42no—
121C2×Dic38—41no—
122C2×Dic38—41no—
123C2×Dic38—42no—
124C2×C8×C19—22no—
125C2×C8×C19—42no—
126C4⋊C4×C19—21no—
127C4⋊C4×C19—21no—
128C4⋊C4×C19—41no—
129C4⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊C4×C19—41no—
132C22⋊Dic19—41no—
133C22⋊Dic19—41no—
134#64528—48no—
135C4⋊Dic19—21no—
136C4⋊Dic19—21no—
137Dic19⋊C4—41no—
138Dic19⋊C4—41no—
139Dic19⋊C4—82no—
140Dic19⋊C4—82no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—42no—
143Dic76—48no—
144#9967—191nomaximal, Sylow
145C23×C19—21no—
146C23×C19—21no—
147C23×C19—22no—
148C23×C19#12011yescharacteristic
149C23×C19#12111yescharacteristic
150C23×C19#12711yescharacteristic
151C23×C19C2×Q1612yes—
152C23×C19#13712yes—
153Q8×C19—42no—
154Q8×C19—81no—
155C2×C4×C19—22no—
156C2×C4×C19—22no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—44no—
162C2×C4×C19—42no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—42no—
168C2×C4×C19—82no—
169C2×C4×C19—81no—
170C2×C4×C19—81no—
171C2×C4×C19#12011yescharacteristic
172C2×C4×C19#12011yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12111yescharacteristic
175C2×Dic19—24no—
176C2×Dic19—24no—
177C2×Dic19—42no—
178C2×Dic19—44no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—44no—
183C2×Dic19—44no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—41no—
187C2×Dic19—41no—
188C2×Dic19—42no—
189C2×Dic19—82no—
190Dic38—24no—
191Dic38—24no—
192Dic38—42no—
193Dic38—42no—
194Dic38—44no—
195Dic38—44no—
196Dic38—42no—
197Dic38—81no—
198C8×C19—42no—
199C19⋊C8—42no—
200C2×#451—191no—
201C2×#451—191no—
202#2659—191no—
203C2×#328—191no—
204C2×#328D1911yescharacteristic
205#1446—191no—
206#1280—191no—
207C22×C19—22no—
208C22×C19—22no—
209C22×C19—22no—
210C22×C19—22no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19#39211yescharacteristic
216C22×C19#45112yes—
217C22×C19#45511yescharacteristic
218C22×C19#45611yescharacteristic
219C22×C19B(4,𝔽2)12yes—
220C22×C19#46212yes—
221C22×C19#49411yescharacteristic
222C22×C19#49711yescharacteristic
223C4×C19—21no—
224C4×C19—21no—
225C4×C19—21no—
226C4×C19—21no—
227C4×C19—82no—
228C4×C19—81no—
229C4×C19—81no—
230Dic19—44no—
231Dic19—44no—
232Dic19—81no—
233Dic19—81no—
234C23×Q8—191no—
235C22×Q16—381no—
236C22×Q16—381no—
237C2×C22⋊Q8—191no—
238C2×C22⋊Q8C2×D1911yescharacteristic
239#451—382no—
240#451—382no—
241#451—382no—
242#451—382no—
243C2×#103—381no—
244C2×#103—381no—
245C2×C22⋊C8—191no—
246C2×C22⋊C8C2×D1911yescharacteristic
247#398—381no—
248#398—381no—
249#395—381no—
250#395—381no—
251#380—382no—
252C2×#95—191no—
253C2×#95—382no—
254C2×#95C2×D1911yescharacteristic
255#328—22no—
256#328—382no—
257C2×C19—21no—
258C2×C19—22no—
259C2×C19—21no—
260C2×C19#160212yes—
261C2×C19#160512yes—
262C2×C19#200711yescharacteristic
263C2×C19#201611yescharacteristic
264C2×C19#202111yescharacteristic
265C22×Q8—191no—
266C22×Q8—192no—
267C22×Q8—381no—
268C22×Q8—381no—
269C22×Q8—381no—
270C22×Q8—381no—
271C22×Q8—381no—
272C22×Q8—764no—
273C22×Q8D7611yescharacteristic
274C23×C4—21no—
275C23×C4—192no—
276C23×C4—381no—
277C23×C4C22×D1911yescharacteristic
278C2×Q16—384no—
279C2×Q16—384no—
280C2×Q16—764no—
281C2×Q16—764no—
282C22×C8—21no—
283C22×C8—381no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—381no—
289C22⋊Q8—381no—
290C22⋊Q8—381no—
291C22⋊Q8—381no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—191no—
294C2×C4⋊C4—381no—
295C2×C4⋊C4—382no—
296C2×C4⋊C4—382no—
297C2×C4⋊C4D7611yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—381no—
300#103—384no—
301#103—384no—
302C22⋊C8—21no—
303C22⋊C8—192no—
304C22⋊C8—381no—
305C22⋊C8C22⋊D1912yes—
306#95—21no—
307#95—21no—
308#95—382no—
309#95—382no—
310#95—381no—
311#95—381no—
312#95—764no—
313C19#996711yescharacteristic, complemented, Sylow
314C24D4×D1911yescharacteristic
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—42no—
318C2×Q8—384no—
319C2×Q8—384no—
320C2×Q8—382no—
321C2×Q8—381no—
322C2×Q8—382no—
323C2×Q8—381no—
324C2×Q8—762no—
325C2×Q8—762no—
326C2×Q8—762no—
327C2×Q8—764no—
328C2×Q8—764no—
329C2×Q8—764no—
330C2×Q8—764no—
331C2×Q8—761no—
332C2×Q8—761no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—194no—
342C22×C4—384no—
343C22×C4—382no—
344C22×C4—382no—
345C22×C4—382no—
346C22×C4—381no—
347C22×C4—381no—
348C22×C4—762no—
349C22×C4—761no—
350C22×C4—761no—
351C22×C4—762no—
352C22×C4—762no—
353C22×C4C2×D7611yescharacteristic
354C22×C4#6454111yescharacteristic
355C22×C4D4×D1911yescharacteristic
356C22×C4D4×D1911yescharacteristic
357C22×C4D4×D1911yescharacteristic
358C22×C4C2×C22⋊D1911yescharacteristic
359Q16—768no—
360Q16—768no—
361C2×C8—22no—
362C2×C8—42no—
363C2×C8—382no—
364C2×C8—762no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—381no—
370C4⋊C4—381no—
371C4⋊C4—761no—
372C4⋊C4—761no—
373C4⋊C4—1522no—
374C4⋊C4—1522no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—761no—
378C22⋊C4—761no—
379C23—21no—
380C23—21no—
381C23—22no—
382C23#1059732811yescharacteristic
383C23#1059733011yescharacteristic
384C23#1059736112yes—
385C23Q16×D1912yes—
386C23#1059738611yescharacteristic
387Q8—42no—
388Q8—81no—
389Q8—384no—
390Q8—384no—
391Q8—762no—
392Q8—762no—
393Q8—764no—
394Q8—764no—
395Q8—762no—
396Q8—1521no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—384no—
414C2×C4—384no—
415C2×C4—764no—
416C2×C4—762no—
417C2×C4—762no—
418C2×C4—762no—
419C2×C4—762no—
420C2×C4—764no—
421C2×C4—764no—
422C2×C4—761no—
423C2×C4—761no—
424C2×C4—761no—
425C2×C4—761no—
426C2×C4—762no—
427C2×C4—1522no—
428C2×C4#1059732811yescharacteristic
429C2×C4#1059733011yescharacteristic
430C2×C4#1059737611yescharacteristic
431C2×C4#1059738311yescharacteristic
432C8—42no—
433C8—762no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22#1192645311yescharacteristic
443C22#1192670112yes—
444C22#1192672311yescharacteristic
445C22#1192672811yescharacteristic
446C22#1192673212yes—
447C22#1192675312yes—
448C22#1192692211yescharacteristic
449C22#1192693511yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—82no—
455C4—81no—
456C4—81no—
457C4—764no—
458C4—764no—
459C4—1521no—
460C4—1521no—
461C2—21no—
462C2—21no—
463C2—22no—
464C2#1456259312yes—
465C2#1456261012yes—
466C2#1456468311yescharacteristic
467C2#1456473611yescharacteristic
468C2#1456476011yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#328C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenterC2×#328D19
hypocenterC19#9967
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
108. C22×Dic19Q16semidirect
313. C19#9967semidirect

Maximal subgroups

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

subgroupindex
C2×#119267022
C2×#119266992
#145697512
C2×#119262802
#145619052
#145614772
C2×C19×#3282
#996719