Finite Group Databasebeta

← #18083092

Subgroups — #18083092

Order 4864.

1020 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#11926695C211yesmaximal, characteristic
2#14569751C211yesmaximal, characteristic, complemented
3C2×#11926282C211yesmaximal, characteristic, complemented
4C2×#11926281C211yesmaximal, characteristic, complemented
5#14561876C211yesmaximal, characteristic
6#14561477C211yesmaximal, characteristic, complemented
7C2×C19×#450C211yesmaximal, characteristic
8C22×#64526—21no—
9C2×#10597370C2211yescharacteristic
10C22×C22⋊Dic19—22no—
11#11926695—22no—
12#11926695—22no—
13C2×#10597289—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926475—21no—
16#11926474—21no—
17#11926464—21no—
18#11926463—21no—
19#11926402—22no—
20C2×C19⋊#95C2211yescharacteristic
21C2×C19⋊#95C2211yescharacteristic
22#11926282—22no—
23#11926281—22no—
24C23×D4×C19C2211yescharacteristic
25C22×SD16×C19—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#450—22no—
28C19×#450—22no—
29C2×C19×#102—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C25×C19—21no—
32C22×Q8×C19D411yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19—21no—
35C22×D4×C19—21no—
36C22×D4×C19—21no—
37C22×D4×C19—21no—
38C22×D4×C19—44no—
39C22×D4×C19D412yes—
40C23×C4×C19C2311yescharacteristic
41C23×Dic19—21no—
42C23×Dic19D412yes—
43C22×Dic38D411yescharacteristic
44C2×SD16×C19—24no—
45C2×SD16×C19—44no—
46C22×C8×C19—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8—21no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19D411yescharacteristic
53C2×C22⋊C4×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—44no—
56C2×C22⋊Dic19—44no—
57C2×C22⋊Dic19—44no—
58C2×#64526—24no—
59C2×#64526—44no—
60C2×C4⋊Dic19D411yescharacteristic
61#10597370—21no—
62#10597370—21no—
63#10597370—21no—
64#10597370—21no—
65C2×Dic19⋊C4—21no—
66C2×Dic19⋊C4—22no—
67C2×Dic19⋊C4—22no—
68C22×C19⋊C8—21no—
69C19×#102—24no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8D412yes—
72#10597289—24no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95—21no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)D412yes—
81C24×C19—24no—
82C24×C19—22no—
83C24×C19—42no—
84C24×C19—42no—
85C24×C19—42no—
86C24×C19—41no—
87C24×C19—41no—
88C24×C19—42no—
89C24×C19—42no—
90C24×C19C2×D411yescharacteristic
91C2×Q8×C19—21no—
92C2×Q8×C19—21no—
93C2×Q8×C19—42no—
94C2×D4×C19—24no—
95C2×D4×C19—24no—
96C2×D4×C19—22no—
97C2×D4×C19—22no—
98C2×D4×C19—42no—
99C2×D4×C19—42no—
100C2×D4×C19—44no—
101C2×D4×C19—44no—
102C2×D4×C19—44no—
103C2×D4×C19—44no—
104C2×D4×C19—41no—
105C2×D4×C19—41no—
106C22×C4×C19—21no—
107C22×C4×C19—21no—
108C22×C4×C19—42no—
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19#4111yescharacteristic
115C22×Dic19—22no—
116C22×Dic19—22no—
117C22×Dic19—22no—
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—42no—
121C22×Dic19—42no—
122C22×Dic19—42no—
123C22×Dic19—41no—
124C22×Dic19—41no—
125C22×Dic19—42no—
126C22×Dic19SD1614yescomplemented
127C2×Dic38—21no—
128C2×Dic38—21no—
129C2×Dic38—42no—
130SD16×C19—48no—
131C2×C8×C19—22no—
132C2×C8×C19—42no—
133C4⋊C4×C19—21no—
134C4⋊C4×C19—21no—
135C4⋊C4×C19—41no—
136C4⋊C4×C19—41no—
137C22⋊C4×C19—41no—
138C22⋊C4×C19—41no—
139C22⋊Dic19—416no—
140C22⋊Dic19—41no—
141C22⋊Dic19—41no—
142#64526—48no—
143C4⋊Dic19—21no—
144C4⋊Dic19—21no—
145Dic19⋊C4—41no—
146Dic19⋊C4—41no—
147Dic19⋊C4—82no—
148Dic19⋊C4—82no—
149C2×C19⋊C8—22no—
150C2×C19⋊C8—42no—
151#9966—191nomaximal, Sylow
152C23×C19—21no—
153C23×C19—21no—
154C23×C19—22no—
155C23×C19—24no—
156C23×C19—44no—
157C23×C19—44no—
158C23×C19—42no—
159C23×C19—44no—
160C23×C19—44no—
161C23×C19—44no—
162C23×C19—44no—
163C23×C19—42no—
164C23×C19—44no—
165C23×C19—44no—
166C23×C19—82no—
167C23×C19—82no—
168C23×C19—82no—
169C23×C19—82no—
170C23×C19—82no—
171C23×C19—82no—
172C23×C19—81no—
173C23×C19—81no—
174C23×C19—81no—
175C23×C19—81no—
176C23×C19#12011yescharacteristic
177C23×C19#12111yescharacteristic
178C23×C19#12711yescharacteristic
179C23×C19C2×SD1612yes—
180C23×C19#13712yes—
181Q8×C19—42no—
182Q8×C19—81no—
183D4×C19—24no—
184D4×C19—24no—
185D4×C19—42no—
186D4×C19—42no—
187D4×C19—44no—
188D4×C19—44no—
189C2×C4×C19—22no—
190C2×C4×C19—22no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—41no—
198C2×C4×C19—41no—
199C2×C4×C19—42no—
200C2×C4×C19#12011yescharacteristic
201C2×C4×C19#12011yescharacteristic
202C2×C4×C19#12111yescharacteristic
203C2×C4×C19#12111yescharacteristic
204C2×Dic19—24no—
205C2×Dic19—42no—
206C2×Dic19—42no—
207C2×Dic19—44no—
208C2×Dic19—44no—
209C2×Dic19—42no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—42no—
215C2×Dic19—82no—
216C2×Dic19—82no—
217C2×Dic19—81no—
218C2×Dic19—81no—
219Dic38—42no—
220Dic38—81no—
221C8×C19—42no—
222C19⋊C8—42no—
223C2×#450—191no—
224C2×#450D1911yescharacteristic
225#2659—191no—
226C2×#328—191no—
227C2×#328—191no—
228#1438—191no—
229#1280—191no—
230C22×C19—22no—
231C22×C19—22no—
232C22×C19—22no—
233C22×C19—22no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—48no—
239C22×C19—44no—
240C22×C19—84no—
241C22×C19—84no—
242C22×C19—84no—
243C22×C19—84no—
244C22×C19—84no—
245C22×C19—82no—
246C22×C19—82no—
247C22×C19#39211yescharacteristic
248C22×C19#44812yes—
249C22×C19#45311yescharacteristic
250C22×C19#45411yescharacteristic
251C22×C19B(4,𝔽2)12yes—
252C22×C19#46112yes—
253C22×C19#49211yescharacteristic
254C22×C19#49711yescharacteristic
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—81no—
260C4×C19—81no—
261Dic19—44no—
262Dic19—82no—
263Dic19—81no—
264Dic19—81no—
265C23×D4C2×D1911yescharacteristic
266C22×SD16—21no—
267C22×SD16—381no—
268C2×C22⋊Q8—191no—
269C2×C22⋊Q8C2×D1911yescharacteristic
270C22×C22⋊C4—382no—
271#450—22no—
272#450—22no—
273#450—382no—
274#450—382no—
275C2×#102—21no—
276C2×#102—381no—
277C2×C22⋊C8—191no—
278C2×C22⋊C8C2×D1911yescharacteristic
279#398—381no—
280#398—381no—
281#395—381no—
282#395—381no—
283#380—382no—
284C2×#95—191no—
285C2×#95—191no—
286#328—382no—
287#328—382no—
288C2×C19—21no—
289C2×C19—22no—
290C2×C19—21no—
291C2×C19—84no—
292C2×C19#159612yes—
293C2×C19#159912yes—
294C2×C19#200611yescharacteristic
295C2×C19#201311yescharacteristic
296C2×C19#202111yescharacteristic
297C25—21no—
298C22×Q8—191no—
299C22×Q8C22⋊D1911yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—44no—
306C22×D4C22⋊D1912yes—
307C23×C4—192no—
308C23×C4—381no—
309C23×C4C22×D1911yescharacteristic
310C2×SD16—24no—
311C2×SD16—44no—
312C2×SD16—384no—
313C2×SD16—764no—
314C22×C8—21no—
315C22×C8—381no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—381no—
321C22⋊Q8—381no—
322C22⋊Q8—381no—
323C22⋊Q8—381no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—191no—
326C2×C4⋊C4—381no—
327C2×C4⋊C4—382no—
328C2×C4⋊C4—382no—
329C2×C4⋊C4C22⋊D1911yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—381no—
332C2×C22⋊C4—764no—
333C2×C22⋊C4—764no—
334C2×C22⋊C4—764no—
335#102—24no—
336#102—384no—
337C22⋊C8—21no—
338C22⋊C8—192no—
339C22⋊C8—381no—
340C22⋊C8C22⋊D1912yes—
341#95—382no—
342#95—382no—
343#95—381no—
344#95—381no—
345#95—381no—
346#95—381no—
347C19#996611yescharacteristic, complemented, Sylow
348C24—24no—
349C24—22no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—41no—
354C24—41no—
355C24—42no—
356C24—42no—
357C24D4×D1911yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—42no—
361C2×Q8—381no—
362C2×Q8—381no—
363C2×Q8—762no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—44no—
371C2×D4—44no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—41no—
375C2×D4—41no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—194no—
380C22×C4—382no—
381C22×C4—382no—
382C22×C4—382no—
383C22×C4—381no—
384C22×C4—381no—
385C22×C4—762no—
386C22×C4—762no—
387C22×C4—762no—
388C22×C4—761no—
389C22×C4—761no—
390C22×C4—762no—
391C22×C4D4×D1911yescharacteristic
392C22×C4D4×D1911yescharacteristic
393C22×C4#6454311yescharacteristic
394C22×C4C2×C22⋊D1911yescharacteristic
395C22×C4C2×C22⋊D1911yescharacteristic
396C22×C4C2×C22⋊D1911yescharacteristic
397SD16—48no—
398SD16—768no—
399C2×C8—22no—
400C2×C8—42no—
401C2×C8—382no—
402C2×C8—762no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—381no—
408C4⋊C4—381no—
409C4⋊C4—761no—
410C4⋊C4—761no—
411C4⋊C4—1522no—
412C4⋊C4—1522no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—7616no—
416C22⋊C4—761no—
417C22⋊C4—761no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23—24no—
422C23—44no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—42no—
430C23—44no—
431C23—44no—
432C23—82no—
433C23—82no—
434C23—82no—
435C23—82no—
436C23—82no—
437C23—81no—
438C23—81no—
439C23—82no—
440C23—81no—
441C23—81no—
442C23SD16×D1912yes—
443C23#1059736112yes—
444C23#1059738311yescharacteristic
445C23#1059738511yescharacteristic
446C23#1059738611yescharacteristic
447Q8—42no—
448Q8—81no—
449Q8—762no—
450Q8—1521no—
451D4—24no—
452D4—24no—
453D4—42no—
454D4—42no—
455D4—44no—
456D4—44no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—384no—
469C2×C4—762no—
470C2×C4—762no—
471C2×C4—764no—
472C2×C4—764no—
473C2×C4—762no—
474C2×C4—761no—
475C2×C4—761no—
476C2×C4—761no—
477C2×C4—761no—
478C2×C4—762no—
479C2×C4—1522no—
480C2×C4—1522no—
481C2×C4—1521no—
482C2×C4—1521no—
483C2×C4#1059738311yescharacteristic
484C2×C4#1059738411yescharacteristic
485C2×C4#1059738511yescharacteristic
486C2×C4#1059739911yescharacteristic
487C8—42no—
488C8—762no—
489C22—22no—
490C22—22no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—22no—
496C22—22no—
497C22—48no—
498C22—44no—
499C22—84no—
500C22—84no—
501C22—84no—
502C22—84no—
503C22—82no—
504C22—82no—
505C22—84no—
506C22#1192645211yescharacteristic
507C22#1192668112yes—
508C22#1192671011yescharacteristic
509C22#1192671511yescharacteristic
510C22#1192673012yes—
511C22#1192674712yes—
512C22#1192691511yescharacteristic
513C22#1192693511yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—764no—
521C4—1522no—
522C4—1521no—
523C4—1521no—
524C2—21no—
525C2—22no—
526C2—21no—
527C2—84no—
528C2#1456255612yes—
529C2#1456257312yes—
530C2#1456467511yescharacteristic
531C2#1456471611yescharacteristic
532C2#1456475811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#450C2
socleC23×C19#120
prime radicalC23×D4×C19C22
hypercenterC2×#450D19
hypocenterC19#9966
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. #14569751C2semidirect
3. C2×#11926282C2semidirect
4. C2×#11926281C2semidirect
6. #14561477C2semidirect
126. C22×Dic19SD16semidirect
347. C19#9966semidirect

Maximal subgroups

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

subgroupindex
C2×#119266952
#145697512
C2×#119262822
C2×#119262812
#145618762
#145614772
C2×C19×#4502
#996619