Finite Group Databasebeta

← #18078589

Subgroups — #18078589

Order 4864.

612 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 105 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#14569442C211yesmaximal, characteristic
2#14566232C211yesmaximal, characteristic
3#14562207C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5#14561503C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1520C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4C2211yescharacteristic
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10#11926479C412yescomplemented
11#11926466—22no—
12#11926455C412yescomplemented
13#11926436—22no—
14#11926434—22no—
15#11926416—21no—
16#11926404C2211yescharacteristic
17#11926404C2211yescharacteristic
18#11926399—21no—
19#11926399—21no—
20C22⋊C4×Dic19—21no—
21#11926281—22no—
22#11926267—22no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#328—22no—
27C24×D19D411yescharacteristic
28C22×Q8×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×C8×C19—21no—
32C19×C22⋊Q8—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C2×C4⋊C4×C19—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×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—22no—
51C2×(C2×D19)⋊C4C2×C412yes—
52C2×(C2×D19)⋊C4D412yes—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×Dic19⋊C4—22no—
56C2×C4×Dic19—22no—
57C22×C19⋊C8—21no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95D412yes—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95C2×C412yes—
64C19⋊#95D412yes—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C24×C19C2×D411yescharacteristic
68C23×D19—21no—
69C23×D19—21no—
70C23×D19—21no—
71C23×D19—21no—
72C23×D19—21no—
73C23×D19—21no—
74C23×D19—81no—
75C23×D19—81no—
76C23×D19C22⋊C412yes—
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—81no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—22no—
83C22×C4×C19—81no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—22no—
94C22×Dic19—81no—
95C22×Dic19C22⋊C412yes—
96C2×C8×C19—41no—
97C2×C8×C19—81no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—81no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊Dic19—41no—
108C22⋊Dic19—41no—
109C22⋊Dic19—41no—
110C22⋊Dic19—41no—
111(C2×D19)⋊C4—22no—
112(C2×D19)⋊C4—22no—
113(C2×D19)⋊C4—22no—
114(C2×D19)⋊C4—22no—
115(C2×D19)⋊C4—82no—
116(C2×D19)⋊C4—82no—
117(C2×D19)⋊C4—82no—
118(C2×D19)⋊C4—82no—
119C4⋊Dic19—81no—
120C4⋊Dic19—81no—
121Dic19⋊C4—82no—
122C4×Dic19—82no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—81no—
125#9201—191nomaximal, Sylow
126C23×C19—41no—
127C23×C19—41no—
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19#12011yescharacteristic
130C23×C19#12311yescharacteristic
131C23×C19#13511yescharacteristic
132C23×C19#13511yescharacteristic
133C23×C19#13711yescharacteristic
134C23×C19#13711yescharacteristic
135C22×D19—22no—
136C22×D19—22no—
137C22×D19—22no—
138C22×D19—42no—
139C22×D19—42no—
140C22×D19—42no—
141C22×D19—42no—
142C22×D19—41no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—41no—
146C22×D19—81no—
147C22×D19—81no—
148C22×D19—82no—
149C22×D19—82no—
150C22×D19—82no—
151C22×D19—82no—
152Q8×C19—81no—
153Q8×C19—81no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—42no—
161C2×C4×C19—42no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—42no—
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19C4×D411yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#12111yescharacteristic
171C2×Dic19—22no—
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—
181C8×C19—81no—
182C19⋊C8—81no—
183#2626—191no—
184#2312—191no—
185#1520—191no—
186#1520D1911yescharacteristic, complemented
187C2×#323—191no—
188#1289—191no—
189#1289—191no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—41no—
197C22×C19—41no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19#38611yescharacteristic
201C22×C19#41611yescharacteristic
202C22×C19#41911yescharacteristic
203C22×C19#45211yescharacteristic
204C22×C19#45211yescharacteristic
205C22×C19#48511yescharacteristic
206C22×C19#48511yescharacteristic
207C2×D19—44no—
208C2×D19—42no—
209C2×D19—42no—
210C2×D19—42no—
211C2×D19—82no—
212C2×D19—82no—
213C2×D19—82no—
214C2×D19—82no—
215C2×D19—82no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—82no—
221C4×C19—81no—
222C4×C19—81no—
223Dic19—42no—
224Dic19—82no—
225Dic19—82no—
226C2×C22⋊Q8C2×D1911yescharacteristic
227C22×C22⋊C4—191no—
228C2×C22⋊C8—191no—
229C2×C22⋊C8C2×D1911yescharacteristic
230#399—192no—
231#396—382no—
232#393—192no—
233#388—382no—
234#388—382no—
235#385—381no—
236#380—191no—
237#380—191no—
238#380C2×D1911yescharacteristic
239#379—381no—
240#379—381no—
241C4×C22⋊C4—381no—
242#328—22no—
243#328—382no—
244#323—382no—
245C2×C19—21no—
246C2×C19—21no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19#187311yescharacteristic
252C2×C19#191111yescharacteristic
253C2×C19#191311yescharacteristic
254D19—82no—
255C25—191no—
256C22×Q8C4×D1911yescharacteristic
257C23×C4—191no—
258C23×C4C22×D1911yescharacteristic
259C22×C8—21no—
260C22×C8—381no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—382no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4C4×D1911yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—192no—
274C2×C22⋊C4—192no—
275C2×C22⋊C4—381no—
276C2×C22⋊C4—381no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—382no—
282C2×C22⋊C4—382no—
283C2×C22⋊C4—382no—
284C2×C22⋊C4—382no—
285C2×C42—382no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—381no—
289C22⋊C8—381no—
290#95—192no—
291#95—192no—
292#95—382no—
293#95—382no—
294#95C22⋊D1912yes—
295C19#920111yescharacteristic, complemented, Sylow
296C24—192no—
297C24—381no—
298C24—381no—
299C24—381no—
300C24—381no—
301C24—381no—
302C24—381no—
303C24—1521no—
304C24—1521no—
305C24D4×D1911yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—81no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—81no—
313C22×C4—192no—
314C22×C4—381no—
315C22×C4—381no—
316C22×C4—382no—
317C22×C4—382no—
318C22×C4—1521no—
319C22×C4C2×C4×D1911yescharacteristic
320C22×C4#6454111yescharacteristic
321C22×C4D4×D1911yescharacteristic
322C22×C4D4×D1911yescharacteristic
323C22×C4#6454311yescharacteristic
324C22×C4C2×C22⋊D1911yescharacteristic
325C2×C8—41no—
326C2×C8—81no—
327C2×C8—761no—
328C2×C8—1521no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C4⋊C4—1522no—
335C4⋊C4—1521no—
336C4⋊C4—1521no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—382no—
342C22⋊C4—382no—
343C22⋊C4—382no—
344C22⋊C4—382no—
345C22⋊C4—761no—
346C22⋊C4—761no—
347C22⋊C4—761no—
348C22⋊C4—761no—
349C22⋊C4—1522no—
350C22⋊C4—1522no—
351C22⋊C4—1522no—
352C22⋊C4—1522no—
353C42—1522no—
354C23—41no—
355C23—41no—
356C23—382no—
357C23—382no—
358C23—382no—
359C23—762no—
360C23—762no—
361C23—762no—
362C23—762no—
363C23—761no—
364C23—761no—
365C23—761no—
366C23—761no—
367C23—1521no—
368C23—1521no—
369C23—1522no—
370C23—1522no—
371C23—1522no—
372C23—1522no—
373C23C22⋊C4×D1911yescharacteristic
374C23#1059732911yescharacteristic
375C23#1059736111yescharacteristic
376C23#1059736211yescharacteristic
377C23#1059736411yescharacteristic
378C23#1059736511yescharacteristic
379C23#1059738311yescharacteristic
380Q8—81no—
381Q8—81no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—382no—
396C2×C4—762no—
397C2×C4—762no—
398C2×C4—762no—
399C2×C4—762no—
400C2×C4—762no—
401C2×C4—762no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—1521no—
405C2×C4(C22⋊D19)⋊C411yescharacteristic
406C2×C4#1059733011yescharacteristic
407C2×C4C4×C22⋊D1911yescharacteristic
408C2×C4#1059738411yescharacteristic
409C8—81no—
410C8—1521no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—764no—
422C22—762no—
423C22—762no—
424C22—762no—
425C22—1522no—
426C22—1522no—
427C22—1522no—
428C22—1522no—
429C22—1522no—
430C22#1192642011yescharacteristic
431C22#1192653911yescharacteristic
432C22#1192655111yescharacteristic
433C22#1192670311yescharacteristic
434C22#1192670511yescharacteristic
435C22#1192688311yescharacteristic
436C22#1192688411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—762no—
445C4—1522no—
446C4—1522no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—1522no—
454C2#1456394411yescharacteristic
455C2#1456416411yescharacteristic
456C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#386
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1520D19
hypocenterC19#9201
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
3. #14562207C2semidirect
5. #14561503C2semidirect
6. #14561502C2semidirect
7. C19×#1520C2semidirect
10. #11926479C4semidirect
12. #11926455C4semidirect
186. #1520D19semidirect
295. C19#9201semidirect

Maximal subgroups

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

subgroupindex
#145694422
#145662322
#145622072
C2×#119262672
#145615032
#145615022
C19×#15202
#920119