Finite Group Databasebeta

← #18078604

Subgroups — #18078604

Order 4864.

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

normal subgroups only

This group has 622 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
1#14569379C211yesmaximal, characteristic
2#14566252C211yesmaximal, characteristic, complemented
3#14562203C211yesmaximal, characteristic
4C2×#11926269C211yesmaximal, characteristic, complemented
5#14561503C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1519C211yesmaximal, characteristic
8C2×#10597381—21no—
9C2×#10597323—21no—
10C22×Dic19⋊C4C2211yescharacteristic
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926475C412yescomplemented
13#11926467—22no—
14#11926458C412yescomplemented
15#11926441—22no—
16#11926439—22no—
17#11926424—21no—
18#11926404C2211yescharacteristic
19#11926404C2211yescharacteristic
20#11926402—21no—
21#11926278—22no—
22#11926269—22no—
23C2×C19×#121C2211yescharacteristic
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#327—22no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C22×C8×C19—21no—
33C19×#121—21no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#121—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45#10597381—42no—
46#10597381—42no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—21no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4C2×C412yes—
57C2×Dic19⋊C4D412yes—
58C2×C4×Dic19—22no—
59C22×C19⋊C8—21no—
60#10597323—42no—
61#10597323—42no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95D412yes—
65C19⋊#95—22no—
66C19⋊#95—22no—
67C19⋊#95C2×C412yes—
68C19⋊#95D412yes—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C24×C19—21no—
72C24×C19C2×D411yescharacteristic
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C2×D4×C19—41no—
78C2×D4×C19—41no—
79C2×D4×C19—41no—
80C2×D4×C19—41no—
81C2×D4×C19—81no—
82C22×C4×C19—21no—
83C22×C4×C19—22no—
84C22×C4×C19—81no—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—22no—
98C22×Dic19—22no—
99C22×Dic19—81no—
100C22×Dic19C22⋊C412yes—
101C22×Dic19C22⋊C412yes—
102C22×Dic19D812yes—
103C22×Dic19SD1612yes—
104C2×C8×C19—41no—
105C2×C8×C19—81no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—81no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C22⋊Dic19—41no—
114C22⋊Dic19—41no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19—44no—
118C22⋊Dic19—82no—
119C4⋊Dic19—81no—
120C4⋊Dic19—81no—
121Dic19⋊C4—22no—
122Dic19⋊C4—22no—
123Dic19⋊C4—22no—
124Dic19⋊C4—22no—
125Dic19⋊C4—44no—
126Dic19⋊C4—44no—
127Dic19⋊C4—82no—
128C4×Dic19—44no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—81no—
131#9204—191nomaximal, Sylow
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—42no—
135C23×C19—42no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19C2×C22⋊C411yescharacteristic
140C23×C19#12011yescharacteristic
141C23×C19#12311yescharacteristic
142C23×C19C2×D811yescharacteristic
143C23×C19C2×SD1611yescharacteristic
144C23×C19AGL(1,ℤ/8)11yescharacteristic
145C23×C19#13711yescharacteristic
146D4×C19—81no—
147D4×C19—81no—
148D4×C19—81no—
149D4×C19—81no—
150D4×C19—81no—
151D4×C19—81no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12111yescharacteristic
168C2×Dic19—22no—
169C2×Dic19—22no—
170C2×Dic19—22no—
171C2×Dic19—22no—
172C2×Dic19—22no—
173C2×Dic19—22no—
174C2×Dic19—22no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—81no—
184C2×Dic19#10214yes—
185C8×C19—81no—
186C19⋊C8—81no—
187#2618—191no—
188#2316—191no—
189#1519—191no—
190#1519D1911yescharacteristic
191C2×#324—191no—
192#1289—191no—
193#1289—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—41no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—82no—
205C22×C19—82no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19#38611yescharacteristic
210C22×C19C2×#10211yescharacteristic
211C22×C19#41711yescharacteristic
212C22×C19#44711yescharacteristic
213C22×C19#44811yescharacteristic
214C22×C19#48011yescharacteristic
215C22×C19#48111yescharacteristic
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—82no—
221C4×C19—81no—
222Dic19—24no—
223Dic19—42no—
224Dic19—82no—
225Dic19—82no—
226C2×#123—381no—
227C2×#121C2×D1911yescharacteristic
228C2×#117—381no—
229C22×C4⋊C4—191no—
230C2×C22⋊C8—191no—
231C2×C22⋊C8C2×D1911yescharacteristic
232#398—192no—
233#396—382no—
234#394—192no—
235#389—382no—
236#389—382no—
237#386—381no—
238#380—191no—
239#380—191no—
240#380—381no—
241#380C2×D1911yescharacteristic
242#327—22no—
243#327—382no—
244#324—382no—
245C2×C19—21no—
246C2×C19—21no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—161no—
252C2×C19#187411yescharacteristic
253C2×C19#191211yescharacteristic
254C2×C19#191311yescharacteristic
255C22×D4—21no—
256C22×D4C4×D1911yescharacteristic
257C23×C4—191no—
258C23×C4—191no—
259C23×C4C22×D1911yescharacteristic
260C22×C8—21no—
261C22×C8—381no—
262#123—762no—
263#123—762no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#117—762no—
269#117—762no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—192no—
272C2×C4⋊C4—192no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4—382no—
278C2×C4⋊C4—382no—
279C2×C4⋊C4—382no—
280C2×C4⋊C4—381no—
281C2×C4⋊C4—381no—
282C2×C4⋊C4C4×D1911yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—382no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—382no—
289C2×C42—382no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294#95—192no—
295#95—192no—
296#95—382no—
297#95—382no—
298#95C22⋊D1912yes—
299C19#920411yescharacteristic, complemented, Sylow
300C24—21no—
301C24D4×D1911yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—81no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—81no—
314C22×C4—192no—
315C22×C4—192no—
316C22×C4—192no—
317C22×C4—192no—
318C22×C4—381no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—382no—
325C22×C4—382no—
326C22×C4—1521no—
327C22×C4C2×C4×D1911yescharacteristic
328C22×C4#6454111yescharacteristic
329C22×C4D4×D1911yescharacteristic
330C22×C4D4×D1911yescharacteristic
331C22×C4#6454311yescharacteristic
332C22×C4C2×C22⋊D1911yescharacteristic
333C2×C8—41no—
334C2×C8—81no—
335C2×C8—761no—
336C2×C8—1521no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—81no—
340C4⋊C4—382no—
341C4⋊C4—382no—
342C4⋊C4—382no—
343C4⋊C4—382no—
344C4⋊C4—764no—
345C4⋊C4—764no—
346C4⋊C4—1522no—
347C4⋊C4—1521no—
348C4⋊C4—1521no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—764no—
354C22⋊C4—761no—
355C22⋊C4—761no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—1522no—
359C42—764no—
360C23—41no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C22⋊C4×D1911yescharacteristic
368C23#1059732911yescharacteristic
369C23D8×D1911yescharacteristic
370C23#1059735711yescharacteristic
371C23SD16×D1911yescharacteristic
372C23#1059736111yescharacteristic
373C23#1059738311yescharacteristic
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—194no—
393C2×C4—382no—
394C2×C4—382no—
395C2×C4—382no—
396C2×C4—382no—
397C2×C4—382no—
398C2×C4—382no—
399C2×C4—382no—
400C2×C4—762no—
401C2×C4—762no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—1521no—
409C2×C4(C22⋊D19)⋊C411yescharacteristic
410C2×C4#1059733011yescharacteristic
411C2×C4C4×C22⋊D1911yescharacteristic
412C2×C4#1059738411yescharacteristic
413C8—81no—
414C8—1521no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22#1192642011yescharacteristic
431C22#102×D1911yescharacteristic
432C22#1192654211yescharacteristic
433C22#1192667611yescharacteristic
434C22#1192668111yescharacteristic
435C22#1192685611yescharacteristic
436C22#1192686111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—384no—
444C4—762no—
445C4—1522no—
446C4—1522no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—161no—
454C2#1456394911yescharacteristic
455C2#1456416911yescharacteristic
456C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1519C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#1519D19
hypocenterC19#9204
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #14566252C2semidirect
4. C2×#11926269C2semidirect
5. #14561503C2semidirect
6. #14561502C2semidirect
12. #11926475C4semidirect
14. #11926458C4semidirect
299. C19#9204semidirect

Maximal subgroups

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

subgroupindex
#145693792
#145662522
#145622032
C2×#119262692
#145615032
#145615022
C19×#15192
#920419