Finite Group Databasebeta

← #18080189

Subgroups — #18080189

Order 4864.

770 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572080C211yesmaximal, characteristic, complemented
2#14563553C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal, complemented
4#14561488C212yesmaximal, complemented
5C19×#2431C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597291—21no—
8C2×#10597291—21no—
9#11926511—24no—
10#11926508—21no—
11#11926508C2212yes—
12#11926407C2212yes—
13#11926278—24no—
14C22×#41×C19C2211yescharacteristic
15C2×C19×#127C411yescharacteristic, complemented
16C2×C19×#124C411yescharacteristic, complemented
17C2×C19×#121C2211yescharacteristic
18C19×#392—21no—
19C19×#392—21no—
20C19×#391C411yescharacteristic, complemented
21C19×#390C411yescharacteristic, complemented
22C19×#386—21no—
23C19×#386—21no—
24C4×C22⋊C4×C19C2211yescharacteristic
25C2×#41×C19—22no—
26C2×#41×C19—22no—
27C2×#41×C19—42no—
28C2×#41×C19—42no—
29C22×Q8×C19C2×C411yescharacteristic
30C22×D4×C19—21no—
31C22×D4×C19—21no—
32C22×D4×C19—21no—
33C22×D4×C19C2×C411yescharacteristic
34C22×D4×C19C2×C411yescharacteristic
35C22×D4×C19D411yescharacteristic
36C22×D4×C19D411yescharacteristic
37C23×C4×C19D411yescharacteristic
38C23×C4×C19D411yescharacteristic
39C23×C4×C19C2311yescharacteristic
40C19×#127—42no—
41C19×#124—42no—
42C19×#121—22no—
43C19×#121—22no—
44C2×C4⋊C4×C19C2×C411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C42×C19C2×C411yescharacteristic
52C2×C42×C19C2×C411yescharacteristic
53C2×C22⋊Dic19—22no—
54C2×#64520—22no—
55C2×#64520—22no—
56C2×#64520—42no—
57C2×#64520—42no—
58C22×C19⋊C8—22no—
59C19×#95—21no—
60C19×#95—21no—
61C19×#95—21no—
62#10597291—42no—
63#10597291—42no—
64C19⋊#95—22no—
65C19⋊#95—22no—
66C22⋊(C19⋊C8)—24no—
67C22⋊(C19⋊C8)—22no—
68C22⋊(C19⋊C8)D414yescomplemented
69C24×C19—21no—
70C24×C19C22⋊C411yescharacteristic
71C24×C19C22⋊C411yescharacteristic
72C24×C19C2×D411yescharacteristic
73#41×C19—44no—
74#41×C19—44no—
75#41×C19—48no—
76C2×Q8×C19—22no—
77C2×Q8×C19—22no—
78C2×Q8×C19—41no—
79C2×D4×C19—22no—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—22no—
84C2×D4×C19—22no—
85C2×D4×C19—22no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—42no—
92C2×D4×C19—42no—
93C2×D4×C19—42no—
94C2×D4×C19—42no—
95C2×D4×C19—42no—
96C2×D4×C19—81no—
97C2×D4×C19—81no—
98C2×D4×C19—81no—
99C2×D4×C19—81no—
100C22×C4×C19—22no—
101C22×C4×C19—22no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—21no—
107C22×C4×C19—21no—
108C22×C4×C19—21no—
109C22×C4×C19—41no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19—41no—
113C22×C4×C19C22⋊C411yescharacteristic
114C22×C4×C19C22⋊C411yescharacteristic
115C22×C4×C19C22×C411yescharacteristic
116C22×C4×C19C2×D412yes—
117C22×C4×C19C2×D411yescharacteristic
118C22×C4×C19#4112yes—
119C22×Dic19—42no—
120C4⋊C4×C19—22no—
121C22⋊C4×C19—42no—
122C22⋊C4×C19—42no—
123C22⋊C4×C19—42no—
124C22⋊C4×C19—41no—
125C22⋊C4×C19—41no—
126C22⋊C4×C19—81no—
127C22⋊C4×C19—81no—
128C42×C19—41no—
129C42×C19—41no—
130C22⋊Dic19—42no—
131C22⋊Dic19—42no—
132#64520—44no—
133#64520—42no—
134#64520—42no—
135C2×C19⋊C8—24no—
136C2×C19⋊C8—44no—
137#9445—191nomaximal, Sylow
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—21no—
141C23×C19—21no—
142C23×C19—21no—
143C23×C19—21no—
144C23×C19—21no—
145C23×C19—41no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19#9912yes—
159C23×C19C2×C22⋊C411yescharacteristic
160C23×C19#12112yes—
161Q8×C19—44no—
162D4×C19—44no—
163D4×C19—44no—
164D4×C19—44no—
165D4×C19—82no—
166D4×C19—84no—
167D4×C19—84no—
168D4×C19—84no—
169C2×C4×C19—22no—
170C2×C4×C19—22no—
171C2×C4×C19—24no—
172C2×C4×C19—21no—
173C2×C4×C19—21no—
174C2×C4×C19—21no—
175C2×C4×C19—21no—
176C2×C4×C19—21no—
177C2×C4×C19—21no—
178C2×C4×C19—22no—
179C2×C4×C19—21no—
180C2×C4×C19—21no—
181C2×C4×C19—21no—
182C2×C4×C19—42no—
183C2×C4×C19—42no—
184C2×C4×C19—42no—
185C2×C4×C19—42no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—41no—
190C2×C4×C19—41no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19#9912yes—
195C2×C4×C19C4×D412yes—
196C2×C4×C19#12011yescharacteristic
197C2×C4×C19#12311yescharacteristic
198C2×Dic19—82no—
199C2×Dic19—82no—
200C2×Dic19—82no—
201C19⋊C8—44no—
202#2879—191no—
203#2431D1911yescharacteristic
204#1782—191no—
205#1510—192no—
206#1284—192no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—22no—
210C22×C19—22no—
211C22×C19—22no—
212C22×C19—22no—
213C22×C19—42no—
214C22×C19—42no—
215C22×C19—41no—
216C22×C19—41no—
217C22×C19—41no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—81no—
221C22×C19—81no—
222C22×C19—81no—
223C22×C19—81no—
224C22×C19—81no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19—81no—
228C22×C19—81no—
229C22×C19—81no—
230C22×C19—81no—
231C22×C19#38611yescharacteristic
232C22×C19C2×#9911yescharacteristic
233C22×C19C2×#9911yescharacteristic
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—22no—
237C4×C19—22no—
238C4×C19—42no—
239C4×C19—41no—
240C4×C19—81no—
241C4×C19—81no—
242Dic19—162no—
243C22×#41C2×D1911yescharacteristic
244C22×M16—381no—
245C2×#127Dic1911yescharacteristic, complemented
246C2×#124Dic1911yescharacteristic, complemented
247C2×#121C2×D1911yescharacteristic
248C2×#99—381no—
249C2×#99—381no—
250#408—384no—
251#407—192no—
252#407—381no—
253#392—21no—
254#392—21no—
255#391Dic1911yescharacteristic, complemented
256#390Dic1911yescharacteristic, complemented
257#386—21no—
258#386—21no—
259#381—192no—
260C4×C22⋊C4C2×D1911yescharacteristic
261#327—384no—
262C2×C19—21no—
263C2×C19—21no—
264C2×C19—42no—
265C2×C19—42no—
266C2×C19—81no—
267C2×C19—161no—
268C2×C19#188411yescharacteristic
269C2×C19#189811yescharacteristic
270C2×C19#191011yescharacteristic
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—42no—
274C2×#41—42no—
275C22×Q8C2×Dic1911yescharacteristic
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4C2×Dic1911yescharacteristic
280C22×D4C2×Dic1911yescharacteristic
281C22×D4C22⋊D1911yescharacteristic
282C22×D4C22⋊D1911yescharacteristic
283C23×C4C22⋊D1911yescharacteristic
284C23×C4C22⋊D1911yescharacteristic
285C23×C4C22×D1911yescharacteristic
286C2×M16—382no—
287C2×M16—382no—
288C2×M16—762no—
289C2×M16—762no—
290C22×C8—382no—
291#127—42no—
292#124—42no—
293#121—22no—
294#121—22no—
295C2×C4⋊C4C2×Dic1911yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—382no—
303C2×C42C2×Dic1911yescharacteristic
304C2×C42C2×Dic1911yescharacteristic
305#99—762no—
306#99—762no—
307C22⋊C8—194no—
308C22⋊C8—384no—
309C22⋊C8—382no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—382no—
314#95—382no—
315C19#944511yescharacteristic, complemented, Sylow
316C24—21no—
317C24C22⋊Dic1911yescharacteristic
318C24C22⋊Dic1911yescharacteristic
319C24C2×C22⋊D1911yescharacteristic
320#41—44no—
321#41—44no—
322#41—48no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4—81no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—762no—
361C22×C4C22⋊Dic1911yescharacteristic
362C22×C4C22⋊Dic1911yescharacteristic
363C22×C4D4×D1912yes—
364C22×C4#6454312yes—
365C22×C4C22×Dic1911yescharacteristic
366C22×C4C2×C22⋊D1911yescharacteristic
367M16—764no—
368M16—762no—
369M16—762no—
370C2×C8—384no—
371C2×C8—764no—
372C4⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—81no—
379C22⋊C4—81no—
380C22⋊C4—762no—
381C22⋊C4—762no—
382C42—41no—
383C42—41no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23#1059729112yes—
405C23#1059738512yes—
406C23C2×C22⋊Dic1911yescharacteristic
407Q8—44no—
408D4—44no—
409D4—44no—
410D4—44no—
411D4—82no—
412D4—84no—
413D4—84no—
414D4—84no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—1522no—
441C2×C4—1522no—
442C2×C4—1522no—
443C2×C4#1059729112yes—
444C2×C4D4×Dic1912yes—
445C2×C4#1059738111yescharacteristic
446C2×C4#1059738311yescharacteristic
447C8—764no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22#1192642411yescharacteristic
473C22C2×#1059729111yescharacteristic
474C22C2×#1059729111yescharacteristic
475C4—21no—
476C4—21no—
477C4—22no—
478C4—22no—
479C4—42no—
480C4—41no—
481C4—81no—
482C4—81no—
483C4—3042no—
484C2—21no—
485C2—21no—
486C2—42no—
487C2—42no—
488C2—81no—
489C2—161no—
490C2#1456401911yescharacteristic
491C2#1456408911yescharacteristic
492C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2431C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2431D19
hypocenterC19#9445
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. #14572080C2semidirect
2. #14563553C2semidirect
3. #14562164C2semidirect
4. #14561488C2semidirect
15. C2×C19×#127C4semidirect
16. C2×C19×#124C4semidirect
20. C19×#391C4semidirect
21. C19×#390C4semidirect
68. C22⋊(C19⋊C8)D4semidirect
245. C2×#127Dic19semidirect
246. C2×#124Dic19semidirect
255. #391Dic19semidirect
256. #390Dic19semidirect
315. C19#9445semidirect

Maximal subgroups

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

subgroupindex
#145720802
#145635532
#145621642
#145614882
C19×#24312
#944519