Finite Group Databasebeta

← #18080460

Subgroups — #18080460

Order 4864.

660 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 93 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#14567913C211yesmaximal, characteristic
2#14566231C211yesmaximal, characteristic
3#14563709C211yesmaximal, characteristic
4#14563707C211yesmaximal, characteristic
5C19⋊#1304C211yesmaximal, characteristic
6C19⋊#1304C211yesmaximal, characteristic
7C19×#1819C211yesmaximal, characteristic
8C22×C22⋊Dic19C2211yescharacteristic
9#11926472—22no—
10#11926438—22no—
11#11926432—22no—
12#11926417C412yescomplemented
13#11926416—21no—
14#11926407C412yescomplemented
15#11926405—21no—
16#11926402—21no—
17#11926400C2211yescharacteristic
18#11926400C2211yescharacteristic
19#11926400C2211yescharacteristic
20C22⋊C4×Dic19—21no—
21#11926311—22no—
22#11926310—22no—
23C22×C22⋊C4×C19C2211yescharacteristic
24C19×#379C2211yescharacteristic
25C19×#379C2211yescharacteristic
26C19×#342—22no—
27C25×C19C2311yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2×C411yescharacteristic
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19D412yes—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19C2×C412yes—
56C2×C22⋊Dic19C2×C412yes—
57C2×C22⋊Dic19D412yes—
58C2×C22⋊Dic19D412yes—
59C2×Dic19⋊C4—22no—
60C2×Dic19⋊C4—22no—
61C2×C4×Dic19—22no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95—22no—
66C19⋊#95—22no—
67C24×C19—42no—
68C24×C19—42no—
69C24×C19—81no—
70C24×C19C22×C411yescharacteristic
71C24×C19C2×D411yescharacteristic
72C24×C19C2×D411yescharacteristic
73C24×C19C2×D411yescharacteristic
74C24×C19C2×D411yescharacteristic
75C24×C19#4111yescharacteristic
76C24×C19#4111yescharacteristic
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—42no—
85C22×C4×C19—41no—
86C22×C4×C19—81no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—22no—
92C22×Dic19—22no—
93C22×Dic19—42no—
94C22×Dic19—41no—
95C22×Dic19—81no—
96C22×Dic19C22⋊C412yes—
97C22×Dic19C22⋊C412yes—
98C22⋊C4×C19—42no—
99C22⋊C4×C19—41no—
100C22⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—42no—
104C22⋊C4×C19—42no—
105C22⋊C4×C19—42no—
106C22⋊C4×C19—81no—
107C22⋊C4×C19—81no—
108C22⋊Dic19—22no—
109C22⋊Dic19—22no—
110C22⋊Dic19—22no—
111C22⋊Dic19—22no—
112C22⋊Dic19—42no—
113C22⋊Dic19—42no—
114C22⋊Dic19—42no—
115C22⋊Dic19—42no—
116C22⋊Dic19—42no—
117C22⋊Dic19—42no—
118C22⋊Dic19—81no—
119C22⋊Dic19—81no—
120C22⋊Dic19—81no—
121Dic19⋊C4—82no—
122Dic19⋊C4—82no—
123C4×Dic19—82no—
124#9500—191nomaximal, Sylow
125C23×C19—22no—
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—22no—
129C23×C19—22no—
130C23×C19—22no—
131C23×C19—41no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19—41no—
145C23×C19—41no—
146C23×C19—88no—
147C23×C19C2×C22⋊C411yescharacteristic
148C23×C19C4×D411yescharacteristic
149C23×C19C4×D411yescharacteristic
150C23×C19#12011yescharacteristic
151C23×C19#12111yescharacteristic
152C23×C19#12111yescharacteristic
153C23×C19#12311yescharacteristic
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19—81no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×C4×C19—81no—
167C2×C4×C19—81no—
168C2×Dic19—22no—
169C2×Dic19—22no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—81no—
181C2×Dic19—81no—
182C2×Dic19—81no—
183C2×Dic19—81no—
184C2×Dic19—81no—
185#2483—191no—
186#2312—191no—
187#1819—191no—
188#1819—191no—
189#1819D1911yescharacteristic
190#1304—191no—
191#1304—191no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—44no—
212C22×C19—44no—
213C22×C19—82no—
214C22×C19—82no—
215C22×C19—82no—
216C22×C19—82no—
217C22×C19—82no—
218C22×C19#38611yescharacteristic
219C22×C19#41012yes—
220C22×C19#45812yes—
221C4×C19—82no—
222C4×C19—81no—
223C4×C19—81no—
224C4×C19—161no—
225Dic19—42no—
226Dic19—42no—
227Dic19—82no—
228Dic19—82no—
229Dic19—161no—
230C22×C22⋊C4—191no—
231C22×C22⋊C4C2×D1911yescharacteristic
232#397—382no—
233#388—382no—
234#388—382no—
235#385—192no—
236#385—381no—
237#381—192no—
238#381—381no—
239#380—381no—
240#379—191no—
241#379—191no—
242#379—191no—
243#379C2×D1911yescharacteristic
244#379C2×D1911yescharacteristic
245C4×C22⋊C4—381no—
246#342—22no—
247#342—382no—
248#342—382no—
249C2×C19—22no—
250C2×C19—22no—
251C2×C19—41no—
252C2×C19—41no—
253C2×C19—41no—
254C2×C19—41no—
255C2×C19—41no—
256C2×C19#189011yescharacteristic
257C2×C19#189911yescharacteristic
258C2×C19#191311yescharacteristic
259C25C22×D1911yescharacteristic
260C23×C4—191no—
261C23×C4—191no—
262C23×C4C4×D1911yescharacteristic
263C23×C4C4×D1911yescharacteristic
264C2×C4⋊C4—382no—
265C2×C4⋊C4—382no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—192no—
278C2×C22⋊C4—192no—
279C2×C22⋊C4—192no—
280C2×C22⋊C4—192no—
281C2×C22⋊C4—381no—
282C2×C22⋊C4—381no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—381no—
289C2×C22⋊C4—381no—
290C2×C22⋊C4—381no—
291C2×C22⋊C4—381no—
292C2×C22⋊C4C22⋊D1912yes—
293C2×C42—382no—
294#95—382no—
295#95—382no—
296#95—382no—
297#95—382no—
298#95—382no—
299C19#950011yescharacteristic, complemented, Sylow
300C24—42no—
301C24—42no—
302C24—81no—
303C24C2×C4×D1911yescharacteristic
304C24#6454111yescharacteristic
305C24D4×D1911yescharacteristic
306C24D4×D1911yescharacteristic
307C24D4×D1911yescharacteristic
308C24#6454311yescharacteristic
309C24C2×C22⋊D1911yescharacteristic
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4—192no—
321C22×C4—192no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—382no—
327C22×C4—382no—
328C22×C4—762no—
329C22×C4—761no—
330C22×C4—1521no—
331C4⋊C4—1522no—
332C4⋊C4—1522no—
333C22⋊C4—42no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—382no—
344C22⋊C4—382no—
345C22⋊C4—382no—
346C22⋊C4—382no—
347C22⋊C4—762no—
348C22⋊C4—762no—
349C22⋊C4—762no—
350C22⋊C4—762no—
351C22⋊C4—762no—
352C22⋊C4—762no—
353C22⋊C4—1521no—
354C22⋊C4—1521no—
355C22⋊C4—1521no—
356C42—1522no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—88no—
379C23C22⋊C4×D1911yescharacteristic
380C23(C22⋊D19)⋊C411yescharacteristic
381C23#1059732911yescharacteristic
382C23#1059733011yescharacteristic
383C23C4×C22⋊D1911yescharacteristic
384C23#1059738311yescharacteristic
385C23#1059738411yescharacteristic
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—382no—
401C2×C4—382no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—762no—
409C2×C4—762no—
410C2×C4—762no—
411C2×C4—762no—
412C2×C4—1521no—
413C2×C4—1521no—
414C2×C4—1521no—
415C2×C4—1521no—
416C2×C4—1521no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—44no—
437C22—44no—
438C22—82no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22#1192642011yescharacteristic
444C22#1192651612yes—
445C22#1192673312yes—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—161no—
450C4—3041no—
451C4—762no—
452C4—762no—
453C4—1522no—
454C4—1522no—
455C2—22no—
456C2—22no—
457C2—41no—
458C2—41no—
459C2—41no—
460C2—41no—
461C2—41no—
462C2#1456404511yescharacteristic
463C2#1456409011yescharacteristic
464C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#1819C2
socleC22×C19#386
prime radical, cosocleC25×C19C23
hypercenter#1819D19
hypocenterC19#9500
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
12. #11926417C4semidirect
14. #11926407C4semidirect
299. C19#9500semidirect

Maximal subgroups

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

subgroupindex
#145679132
#145662312
#145637092
#145637072
C19⋊#13042
C19×#18192
#950019