Finite Group Databasebeta

← #18073886

Subgroups — #18073886

Order 4864.

1238 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#10597340C211yesmaximal, characteristic
2#14563544C212yesmaximal, complemented
3C2×#11926270C211yesmaximal, characteristic, complemented
4C2×#11926267C212yesmaximal, complemented
5C2×C19×#324C211yesmaximal, characteristic, complemented
6C23×D76C411yescharacteristic
7C23×C4×D19C2211yescharacteristic
8C2×#10597340—24no—
9C2×#10597340—24no—
10C2×#10597340—22no—
11C2×#10597340—22no—
12C22×Dic19⋊C4C411yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2212yes—
17C2×(C2×D19)⋊C8—24no—
18#11926270—22no—
19#11926267—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C2×C19×C22⋊C8C2212yes—
22C19×#324—22no—
23C24×D19C2×C411yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×D76—22no—
31C22×D76—22no—
32C22×D76—22no—
33C22×D76—44no—
34C22×C4×D19—21no—
35C22×C4×D19—22no—
36C22×C4×D19—21no—
37C22×C4×D19—44no—
38C22×C4×D19D414yes—
39C22×C8×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19D412yes—
43C2×C4⋊C4×C19D412yes—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4—22no—
53C2×(C2×D19)⋊C4D414yes—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C22×C19⋊C8—22no—
58#10597340—216no—
59#10597340—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64(C2×D19)⋊C8—48no—
65C24×C19C22×C411yescharacteristic
66C23×D19—21no—
67C23×D19—21no—
68C23×D19—24no—
69C23×D19—21no—
70C23×D19—21no—
71C23×D19—22no—
72C23×D19—22no—
73C23×D19—22no—
74C23×D19—22no—
75C23×D19—42no—
76C23×D19—42no—
77C23×D19—42no—
78C23×D19C22⋊C412yes—
79C23×D19C22⋊C412yes—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—42no—
87C22×C4×C19—42no—
88C22×C4×C19C22⋊C412yes—
89C22×C4×C19C22⋊C412yes—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D412yes—
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D411yescharacteristic
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—42no—
99C22×Dic19—42no—
100C22×Dic19C22⋊C412yes—
101C22×Dic19C22⋊C412yes—
102C2×D76—28no—
103C2×D76—48no—
104C2×D76—44no—
105C2×D76—48no—
106C2×D76—44no—
107C2×C4×D19—28no—
108C2×C4×D19—24no—
109C2×C4×D19—24no—
110C2×C4×D19—44no—
111C2×C4×D19—44no—
112C2×C4×D19—48no—
113C2×C4×D19—44no—
114C2×C8×C19—44no—
115C2×C8×C19—42no—
116C4⋊C4×C19—24no—
117C4⋊C4×C19—24no—
118(C2×D19)⋊C4—28no—
119(C2×D19)⋊C4—28no—
120(C2×D19)⋊C4—24no—
121(C2×D19)⋊C4—24no—
122Dic19⋊C4—28no—
123C2×C19⋊C8—44no—
124C2×C19⋊C8—42no—
125#8304—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—22no—
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19#13112yes—
132C23×C19#13112yes—
133C22×D19—24no—
134C22×D19—24no—
135C22×D19—22no—
136C22×D19—24no—
137C22×D19—22no—
138C22×D19—24no—
139C22×D19—22no—
140C22×D19—24no—
141C22×D19—48no—
142C22×D19—48no—
143C22×D19—42no—
144C22×D19—42no—
145C22×D19—42no—
146C22×D19—41no—
147C22×D19—41no—
148C22×D19—42no—
149C22×D19—42no—
150C22×D19—42no—
151C22×D19—41no—
152C22×D19—41no—
153C22×D19—42no—
154C22×D19—42no—
155C22×D19—42no—
156C22×D19—42no—
157C22×D19—84no—
158C22×D19—84no—
159C22×D19#9914yes—
160C2×C4×C19—24no—
161C2×C4×C19—22no—
162C2×C4×C19—22no—
163C2×C4×C19—22no—
164C2×C4×C19—22no—
165C2×C4×C19—41no—
166C2×C4×C19—42no—
167C2×C4×C19—41no—
168C2×C4×C19—42no—
169C2×C4×C19—42no—
170C2×C4×C19—42no—
171C2×C4×C19—42no—
172C2×C4×C19—42no—
173C2×C4×C19#12012yes—
174C2×C4×C19#12012yes—
175C2×Dic19—22no—
176C2×Dic19—22no—
177C2×Dic19—24no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183D76—416no—
184C4×D19—48no—
185C4×D19—48no—
186C8×C19—82no—
187C19⋊C8—82no—
188C22×#123—191no—
189#1779—192no—
190C2×#324—191no—
191C2×#324D1911yescharacteristic, complemented
192C2×#323—192no—
193C22×C19—24no—
194C22×C19—24no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19#37911yescharacteristic
200C22×C19#40812yes—
201C22×C19#40812yes—
202C22×C19#40811yescharacteristic
203C22×C19#40811yescharacteristic
204C22×C19C2×#9912yes—
205C22×C19#41312yes—
206C2×D19—28no—
207C2×D19—24no—
208C2×D19—48no—
209C2×D19—44no—
210C2×D19—44no—
211C2×D19—44no—
212C2×D19—42no—
213C2×D19—42no—
214C2×D19—42no—
215C2×D19—42no—
216C2×D19—42no—
217C2×D19—82no—
218C2×D19—82no—
219C2×D19—84no—
220C2×D19—84no—
221C4×C19—22no—
222C4×C19—22no—
223C4×C19—42no—
224C4×C19—42no—
225Dic19—42no—
226Dic19—42no—
227C23×D4—191no—
228C24×C4—191no—
229C2×#123—384no—
230C2×#123—384no—
231C2×#123—382no—
232C2×#123—382no—
233C22×C4⋊C4—191no—
234C22×C4⋊C4C2×D1911yescharacteristic
235C22×C22⋊C4—191no—
236C22×C22⋊C4—191no—
237C22×C22⋊C4—191no—
238C2×C22⋊C8—192no—
239C2×C22⋊C8—384no—
240C2×C22⋊C8C2×D1912yes—
241#324—22no—
242#324—382no—
243#323—384no—
244C2×C19—22no—
245C2×C19—21no—
246C2×C19—21no—
247C2×C19#146814yes—
248C2×C19#178011yescharacteristic
249C2×C19#178111yescharacteristic
250C2×C19#178511yescharacteristic
251D19—44no—
252D19—82no—
253C25—191no—
254C25—191no—
255C22×D4—382no—
256C22×D4—382no—
257C22×D4—382no—
258C22×D4—764no—
259C23×C4—191no—
260C23×C4—191no—
261C23×C4—194no—
262C23×C4—381no—
263C23×C4—382no—
264C23×C4—381no—
265C23×C4—764no—
266C23×C4C4×D1911yescharacteristic
267C23×C4C4×D1911yescharacteristic
268C23×C4C22×D1911yescharacteristic
269C22×C8—22no—
270C22×C8—382no—
271#123—3816no—
272#123—3816no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—382no—
276C2×C4⋊C4—382no—
277C2×C4⋊C4—382no—
278C2×C4⋊C4D7612yes—
279C2×C4⋊C4C22⋊D1912yes—
280C2×C22⋊C4—194no—
281C2×C22⋊C4—382no—
282C2×C22⋊C4—382no—
283C2×C22⋊C4—382no—
284C2×C22⋊C4—382no—
285C2×C22⋊C4—382no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—382no—
289C2×C22⋊C4—381no—
290C22⋊C8—22no—
291C22⋊C8—22no—
292C22⋊C8—382no—
293C22⋊C8—382no—
294C22⋊C8—768no—
295C19#830411yescharacteristic, complemented, Sylow
296C24—192no—
297C24—192no—
298C24—384no—
299C24—381no—
300C24—381no—
301C24—381no—
302C24—382no—
303C24—382no—
304C24—381no—
305C24—382no—
306C24—382no—
307C24—762no—
308C24—762no—
309C24—762no—
310C24C2×C4×D1911yescharacteristic
311C2×D4—388no—
312C2×D4—764no—
313C2×D4—768no—
314C2×D4—764no—
315C2×D4—768no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—192no—
325C22×C4—192no—
326C22×C4—388no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—384no—
332C22×C4—384no—
333C22×C4—764no—
334C22×C4—764no—
335C22×C4—768no—
336C22×C4—764no—
337C22×C4—762no—
338C22×C4—762no—
339C22×C4(C2×D19)⋊C412yes—
340C22×C4(C2×D19)⋊C412yes—
341C22×C4C2×D7611yescharacteristic
342C22×C4D4×D1912yes—
343C22×C4D4×D1912yes—
344C22×C4C2×C22⋊D1911yescharacteristic
345C2×C8—44no—
346C2×C8—42no—
347C2×C8—764no—
348C2×C8—762no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—388no—
352C22⋊C4—388no—
353C22⋊C4—388no—
354C22⋊C4—384no—
355C22⋊C4—384no—
356C23—22no—
357C23—22no—
358C23—194no—
359C23—384no—
360C23—384no—
361C23—382no—
362C23—384no—
363C23—382no—
364C23—384no—
365C23—382no—
366C23—384no—
367C23—768no—
368C23—768no—
369C23—762no—
370C23—762no—
371C23—762no—
372C23—762no—
373C23—762no—
374C23—762no—
375C23—762no—
376C23—761no—
377C23—761no—
378C23—762no—
379C23—761no—
380C23—761no—
381C23—762no—
382C23—762no—
383C23—1524no—
384C23—1524no—
385C23C22⋊C4×D1911yescharacteristic
386C23C22⋊C4×D1911yescharacteristic
387C23#1059734712yes—
388C23#1059735312yes—
389C23C2×(C2×D19)⋊C411yescharacteristic
390D4—7616no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—382no—
405C2×C4—382no—
406C2×C4—384no—
407C2×C4—768no—
408C2×C4—768no—
409C2×C4—762no—
410C2×C4—762no—
411C2×C4—762no—
412C2×C4—762no—
413C2×C4—762no—
414C2×C4#1059732812yes—
415C2×C4#1059738312yes—
416C8—82no—
417C8—1522no—
418C22—24no—
419C22—24no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—388no—
425C22—384no—
426C22—768no—
427C22—764no—
428C22—764no—
429C22—764no—
430C22—762no—
431C22—762no—
432C22—762no—
433C22—762no—
434C22—762no—
435C22—1524no—
436C22—1522no—
437C22—1522no—
438C22—1524no—
439C22#1192639911yescharacteristic
440C22#1192650912yes—
441C22#1192650912yes—
442C22#1192651011yescharacteristic
443C22#1192651211yescharacteristic
444C22#99×D1912yes—
445C22#1192652712yes—
446C4—22no—
447C4—22no—
448C4—42no—
449C4—42no—
450C4—762no—
451C4—762no—
452C2—22no—
453C2—21no—
454C2—21no—
455C2—764no—
456C2—1522no—
457C2#1456198214yes—
458C2#1456354611yescharacteristic
459C2#1456354811yescharacteristic
460C2#1456356211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D76C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#8304
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #14563544C2semidirect
3. C2×#11926270C2semidirect
4. C2×#11926267C2semidirect
5. C2×C19×#324C2semidirect
191. C2×#324D19semidirect
295. C19#8304semidirect

Maximal subgroups

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

subgroupindex
C22×#105973402
#145635442
C2×#119262702
C2×#119262672
C2×C19×#3242
#830419