Finite Group Databasebeta

← #18085424

Subgroups — #18085424

Order 4864.

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

normal subgroups only

This group has 602 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#14574407C211yesmaximal, characteristic
2#14571974C211yesmaximal, characteristic
3#14563703C211yesmaximal, characteristic
4#14562207C211yesmaximal, characteristic
5#14562206C211yesmaximal, characteristic
6#14561502C211yesmaximal, characteristic
7C19×#2855C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926879—21no—
10#11926877—21no—
11#11926783—22no—
12#11926700—21no—
13#11926699—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926450—21no—
17#11926442—21no—
18#11926428—22no—
19#11926417—21no—
20#11926407—21no—
21#11926404C2211yescharacteristic
22#11926299—22no—
23#11926281—22no—
24#11926280—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C22×C42×C19C2211yescharacteristic
27C19×#391—21no—
28C19×#389—21no—
29C19×#387—22no—
30C19×#385—21no—
31C19×#381—21no—
32C19×#380C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×Dic38D411yescharacteristic
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C2×C4⋊C4×C19—22no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C42×C19—21no—
49C2×C42×C19—21no—
50C2×C42×C19—21no—
51C2×C42×C19—21no—
52C2×C42×C19—21no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—21no—
56C2×#64528—22no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19D411yescharacteristic
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62#10597370—21no—
63C2×Dic19⋊C4—22no—
64C2×Dic19⋊C4—21no—
65C22×C19⋊C8—21no—
66C22×C19⋊C8D412yes—
67C19×#95—22no—
68C19×#95—22no—
69C19×#95—22no—
70C19×#95D412yes—
71#10597292—22no—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80#10597267—22no—
81#10597264—22no—
82C24×C19C2×D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—42no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—22no—
97C22×C4×C19—21no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19Q1612yescomplemented
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×Dic19—21no—
108C22×Dic19—22no—
109C22×Dic19—21no—
110C2×Dic38—21no—
111C2×Dic38—21no—
112C2×Dic38—42no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—42no—
116C4⋊C4×C19—44no—
117C4⋊C4×C19—41no—
118C4⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C42×C19—41no—
124C42×C19—41no—
125C42×C19—41no—
126C42×C19—41no—
127C22⋊Dic19—41no—
128C22⋊Dic19—41no—
129C22⋊Dic19—41no—
130C22⋊Dic19—41no—
131#64528—82no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134C4⋊Dic19—42no—
135Dic19⋊C4—44no—
136Dic19⋊C4—41no—
137Dic19⋊C4—41no—
138C2×C19⋊C8—22no—
139C2×C19⋊C8—42no—
140C2×C19⋊C8—42no—
141C2×C19⋊C8—41no—
142#10325—191nomaximal, Sylow
143C23×C19—41no—
144C23×C19—41no—
145C23×C19#12011yescharacteristic
146C23×C19#12011yescharacteristic
147C23×C19#12111yescharacteristic
148C23×C19C2×Q1611yescharacteristic
149C23×C19#13511yescharacteristic
150C23×C19#13711yescharacteristic
151C23×C19#13711yescharacteristic
152Q8×C19—42no—
153Q8×C19—81no—
154C2×C4×C19—22no—
155C2×C4×C19—22no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—22no—
159C2×C4×C19—22no—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—22no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—42no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—42no—
181C2×C4×C19#12011yescharacteristic
182C2×C4×C19#12111yescharacteristic
183C2×C4×C19#12111yescharacteristic
184C2×C4×C19#12711yescharacteristic
185C2×Dic19—42no—
186C2×Dic19—42no—
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—41no—
190C2×Dic19—41no—
191C2×Dic19—42no—
192Dic38—42no—
193Dic38—81no—
194C19⋊C8—42no—
195C19⋊C8—81no—
196#3189—191no—
197#2855—191no—
198#2855D1911yescharacteristic
199#1817—191no—
200#1520—191no—
201#1520—191no—
202#1289—191no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—41no—
210C22×C19—41no—
211C22×C19—41no—
212C22×C19—41no—
213C22×C19#39211yescharacteristic
214C22×C19#45111yescharacteristic
215C22×C19#45111yescharacteristic
216C22×C19#45211yescharacteristic
217C22×C19#45211yescharacteristic
218C22×C19#46711yescharacteristic
219C22×C19#47011yescharacteristic
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—42no—
224C4×C19—42no—
225C4×C19—82no—
226C4×C19—81no—
227C4×C19—81no—
228C4×C19#45812yes—
229Dic19—82no—
230Dic19—81no—
231Dic19—81no—
232C2×C22⋊Q8—191no—
233C2×C22⋊Q8C2×D1911yescharacteristic
234C22×C42C2×D1911yescharacteristic
235#484—381no—
236#484—381no—
237#467—382no—
238#451—381no—
239#451—381no—
240C2×C22⋊C8—191no—
241C2×C22⋊C8—191no—
242#391—21no—
243#391—381no—
244#389—21no—
245#389—381no—
246#387—22no—
247#387—382no—
248#385—21no—
249#385—381no—
250#381—21no—
251#381—381no—
252#380—191no—
253#380C2×D1911yescharacteristic
254#336—382no—
255#328—382no—
256#328—382no—
257C2×C19—21no—
258C2×C19—21no—
259C2×C19—21no—
260C2×C19—21no—
261C2×C19—21no—
262C2×C19—21no—
263C2×C19#200111yescharacteristic
264C2×C19#201011yescharacteristic
265C2×C19#202211yescharacteristic
266C22×Q8—191no—
267C22×Q8C22⋊D1911yescharacteristic
268C23×C4C22⋊D1911yescharacteristic
269C23×C4C22⋊D1911yescharacteristic
270C23×C4C22×D1911yescharacteristic
271C2×Q16—382no—
272C22×C8—192no—
273C22×C8—381no—
274C22⋊Q8—21no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—381no—
279C22⋊Q8—381no—
280C22⋊Q8—381no—
281C22⋊Q8—381no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—191no—
286C2×C4⋊C4—382no—
287C2×C4⋊C4—381no—
288C2×C4⋊C4—381no—
289C2×C4⋊C4C22⋊D1911yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—381no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300#107—382no—
301#103—382no—
302#103—382no—
303C22⋊C8—381no—
304C22⋊C8—381no—
305C22⋊C8—381no—
306C22⋊C8—381no—
307#95—22no—
308#95—22no—
309#95—22no—
310#95—192no—
311#95—382no—
312#95—382no—
313#95—382no—
314#95C22⋊D1912yes—
315C19#1032511yescharacteristic, complemented, Sylow
316C24C2×C22⋊D1911yescharacteristic
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—42no—
320C2×Q8—381no—
321C2×Q8—381no—
322C2×Q8—762no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—382no—
338C22×C4—381no—
339C22×C4—381no—
340C22×C4#6452812yescomplemented
341C22×C4D4×D1911yescharacteristic
342C22×C4D4×D1911yescharacteristic
343C22×C4D4×D1911yescharacteristic
344C22×C4#6454311yescharacteristic
345C22×C4C2×C22⋊D1911yescharacteristic
346C22×C4C2×C22⋊D1911yescharacteristic
347Q16—1522no—
348C2×C8—382no—
349C2×C8—762no—
350C2×C8—762no—
351C2×C8—761no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—42no—
355C4⋊C4—44no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—381no—
359C4⋊C4—381no—
360C4⋊C4—764no—
361C4⋊C4—762no—
362C4⋊C4—761no—
363C4⋊C4—761no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—761no—
369C22⋊C4—761no—
370C22⋊C4—761no—
371C22⋊C4—761no—
372C42—41no—
373C42—41no—
374C42—41no—
375C42—41no—
376C23—41no—
377C23—41no—
378C23#1059738311yescharacteristic
379C23#1059738511yescharacteristic
380C23#1059738811yescharacteristic
381C23C2×#6452811yescharacteristic
382C23#1059739611yescharacteristic
383C23#1059739711yescharacteristic
384C23#1059739911yescharacteristic
385Q8—42no—
386Q8—81no—
387Q8—762no—
388Q8—1521no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—762no—
417C2×C4—762no—
418C2×C4—762no—
419C2×C4—762no—
420C2×C4—762no—
421C2×C4—761no—
422C2×C4—761no—
423C2×C4#1059738311yescharacteristic
424C2×C4#1059738411yescharacteristic
425C2×C4#1059738511yescharacteristic
426C2×C4#1059738611yescharacteristic
427C8—762no—
428C8—1521no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22#1192645211yescharacteristic
440C22#1192669911yescharacteristic
441C22#1192670011yescharacteristic
442C22#1192670411yescharacteristic
443C22#1192670611yescharacteristic
444C22#1192678311yescharacteristic
445C22#1192680011yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—42no—
451C4—82no—
452C4—81no—
453C4—81no—
454C4—1522no—
455C4—1521no—
456C4—1521no—
457C4#1192673312yes—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2#1456464311yescharacteristic
465C2#1456470011yescharacteristic
466C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2855C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#2855D19
hypocenterC19#10325
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2855

Complements

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

NH ≅ G/Ntype
100. C22×C4×C19Q16semidirect
315. C19#10325semidirect
340. C22×C4#64528semidirect

Maximal subgroups

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

subgroupindex
#145744072
#145719742
#145637032
#145622072
#145622062
#145615022
C19×#28552
#1032519