Finite Group Databasebeta

← #18083022

Subgroups — #18083022

Order 4864.

888 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 101 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, complemented
2C2×#11926695C211yesmaximal, characteristic
3#14564620C211yesmaximal, characteristic, complemented
4#14563566C211yesmaximal, characteristic
5#14562207C211yesmaximal, characteristic, complemented
6#14561483C211yesmaximal, characteristic, complemented
7C19×#2435C211yesmaximal, characteristic
8C22×#64526—21no—
9C2×#10597370C2211yescharacteristic
10#11926879—21no—
11#11926877—21no—
12#11926783—22no—
13#11926700—21no—
14#11926699—21no—
15#11926695—22no—
16#11926695—22no—
17C2×#10597289—21no—
18C2×#10597289—22no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926404C2211yescharacteristic
22#11926310—22no—
23#11926281—22no—
24C23×D4×C19C2211yescharacteristic
25C2×C19×#124—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#394—22no—
28C19×#390—21no—
29C19×#379—22no—
30C4×C22⋊C4×C19C2211yescharacteristic
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
41C22×Dic38D411yescharacteristic
42C19×#124—44no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—24no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—24no—
52C2×C22⋊C4×C19D412yes—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—21no—
56C2×#64528—22no—
57C2×#64526—24no—
58C2×#64526—44no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19D411yescharacteristic
61#10597370—21no—
62#10597370—21no—
63#10597370—21no—
64#10597370—21no—
65C2×Dic19⋊C4—21no—
66C22×C19⋊C8—21no—
67C22×C19⋊C8D412yes—
68C19×#95—21no—
69#10597292—22no—
70#10597289—24no—
71#10597289—44no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77#10597267—22no—
78#10597264—22no—
79C24×C19—22no—
80C24×C19—44no—
81C24×C19—41no—
82C24×C19—41no—
83C24×C19—42no—
84C24×C19—42no—
85C24×C19—82no—
86C24×C19C2×D411yescharacteristic
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—42no—
90C2×D4×C19—24no—
91C2×D4×C19—24no—
92C2×D4×C19—24no—
93C2×D4×C19—22no—
94C2×D4×C19—22no—
95C2×D4×C19—42no—
96C2×D4×C19—42no—
97C2×D4×C19—42no—
98C2×D4×C19—44no—
99C2×D4×C19—44no—
100C2×D4×C19—44no—
101C2×D4×C19—41no—
102C2×D4×C19—41no—
103C22×C4×C19—22no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—42no—
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19#4111yescharacteristic
113C22×Dic19—21no—
114C22×Dic19—21no—
115C22×Dic19—41no—
116C2×Dic38—21no—
117C2×Dic38—21no—
118C2×Dic38—42no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—41no—
122C4⋊C4×C19—41no—
123C22⋊C4×C19—22no—
124C22⋊C4×C19—22no—
125C22⋊C4×C19—48no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—84no—
129C42×C19—42no—
130C22⋊Dic19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—42no—
133#64528—82no—
134#64526—48no—
135C4⋊Dic19—21no—
136C4⋊Dic19—21no—
137C4⋊Dic19—42no—
138Dic19⋊C4—41no—
139Dic19⋊C4—41no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—42no—
143C2×C19⋊C8—42no—
144#9955—191nomaximal, Sylow
145C23×C19—24no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—44no—
149C23×C19—44no—
150C23×C19—44no—
151C23×C19—42no—
152C23×C19—42no—
153C23×C19—44no—
154C23×C19—82no—
155C23×C19—82no—
156C23×C19—88no—
157C23×C19—88no—
158C23×C19—82no—
159C23×C19—81no—
160C23×C19—81no—
161C23×C19#12011yescharacteristic
162C23×C19#12111yescharacteristic
163C23×C19#12711yescharacteristic
164C23×C19#13512yes—
165C23×C19#13712yes—
166Q8×C19—42no—
167Q8×C19—81no—
168D4×C19—24no—
169D4×C19—24no—
170D4×C19—42no—
171D4×C19—42no—
172D4×C19—44no—
173D4×C19—44no—
174C2×C4×C19—22no—
175C2×C4×C19—22no—
176C2×C4×C19—22no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—42no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—42no—
187C2×C4×C19#12011yescharacteristic
188C2×C4×C19#12011yescharacteristic
189C2×C4×C19#12111yescharacteristic
190C2×C4×C19#12111yescharacteristic
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—81no—
194C2×Dic19—81no—
195C2×Dic19—81no—
196C2×Dic19—81no—
197C2×Dic19—81no—
198Dic38—42no—
199Dic38—42no—
200C19⋊C8—42no—
201C19⋊C8—42no—
202#3189—191no—
203C2×#450—191no—
204#2435D1911yescharacteristic
205#1996—191no—
206#1786—191no—
207#1520—191no—
208#1282—191no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—42no—
216C22×C19—42no—
217C22×C19—48no—
218C22×C19—44no—
219C22×C19—84no—
220C22×C19—84no—
221C22×C19—88no—
222C22×C19—84no—
223C22×C19—82no—
224C22×C19—82no—
225C22×C19#39211yescharacteristic
226C22×C19#45212yes—
227C22×C19#46412yes—
228C22×C19#49511yescharacteristic
229C22×C19#49711yescharacteristic
230C4×C19—21no—
231C4×C19—21no—
232C4×C19—21no—
233C4×C19—82no—
234C4×C19—81no—
235C4×C19—81no—
236C4×C19B(4,𝔽2)12yes—
237Dic19—81no—
238Dic19—81no—
239Dic19—161no—
240C23×D4C2×D1911yescharacteristic
241C22×SD16—381no—
242C2×#124—21no—
243C2×C22⋊Q8—191no—
244C2×C22⋊Q8C2×D1911yescharacteristic
245#484—381no—
246#484—381no—
247#467—382no—
248#451—381no—
249#451—381no—
250#450—382no—
251#450—382no—
252C2×#102—381no—
253C2×#102—382no—
254C2×C22⋊C8—191no—
255C2×C22⋊C8—191no—
256#394—22no—
257#390—21no—
258#380—191no—
259#379—22no—
260C4×C22⋊C4C2×D1911yescharacteristic
261#342—382no—
262#328—382no—
263C2×C19—21no—
264C2×C19—22no—
265C2×C19—22no—
266C2×C19—21no—
267C2×C19—84no—
268C2×C19#200811yescharacteristic
269C2×C19#201511yescharacteristic
270C2×C19#202111yescharacteristic
271C25—21no—
272C22×Q8—191no—
273C22×Q8C22⋊D1911yescharacteristic
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—44no—
280C22×D4C22⋊D1912yes—
281C23×C4C22×D1911yescharacteristic
282C2×Q16—382no—
283C2×SD16—384no—
284C2×SD16—764no—
285C22×C8—192no—
286C22×C8—381no—
287#124—44no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—381no—
293C22⋊Q8—381no—
294C22⋊Q8—381no—
295C22⋊Q8—381no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—191no—
298C2×C4⋊C4—381no—
299C2×C4⋊C4—381no—
300C2×C4⋊C4C22⋊D1911yescharacteristic
301C2×C22⋊C4—24no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—381no—
305C2×C22⋊C4—381no—
306C2×C22⋊C4C22⋊D1912yes—
307C2×C42—21no—
308#107—382no—
309#103—382no—
310#103—382no—
311#102—384no—
312#102—764no—
313C22⋊C8—192no—
314C22⋊C8—381no—
315C22⋊C8—381no—
316C22⋊C8—381no—
317#95—21no—
318#95—381no—
319C19#995511yescharacteristic, complemented, Sylow
320C24—22no—
321C24—44no—
322C24—41no—
323C24—41no—
324C24—42no—
325C24—42no—
326C24—82no—
327C24C2×C22⋊D1911yescharacteristic
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—42no—
331C2×Q8—381no—
332C2×Q8—381no—
333C2×Q8—762no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—44no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—761no—
354C22×C4D4×D1911yescharacteristic
355C22×C4D4×D1911yescharacteristic
356C22×C4D4×D1911yescharacteristic
357C22×C4#6454311yescharacteristic
358C22×C4C2×C22⋊D1911yescharacteristic
359C22×C4C2×C22⋊D1911yescharacteristic
360Q16—1522no—
361SD16—768no—
362C2×C8—382no—
363C2×C8—382no—
364C2×C8—762no—
365C2×C8—762no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—381no—
371C4⋊C4—381no—
372C4⋊C4—762no—
373C4⋊C4—761no—
374C4⋊C4—761no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—84no—
381C22⋊C4—761no—
382C22⋊C4—761no—
383C22⋊C4—762no—
384C42—42no—
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—42no—
392C23—44no—
393C23—42no—
394C23—82no—
395C23—82no—
396C23—88no—
397C23—88no—
398C23—81no—
399C23—81no—
400C23—82no—
401C23#1059738411yescharacteristic
402C23#1059738611yescharacteristic
403C23#1059739612yes—
404C23#1059739712yes—
405C23#1059739911yescharacteristic
406Q8—42no—
407Q8—81no—
408Q8—762no—
409Q8—762no—
410D4—24no—
411D4—24no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—44no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—761no—
430C2×C4—761no—
431C2×C4—1521no—
432C2×C4—1521no—
433C2×C4—1521no—
434C2×C4—1521no—
435C2×C4—1521no—
436C2×C4#1059738311yescharacteristic
437C2×C4#1059738311yescharacteristic
438C2×C4#1059738511yescharacteristic
439C2×C4#1059738511yescharacteristic
440C8—762no—
441C8—762no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—48no—
451C22—44no—
452C22—84no—
453C22—84no—
454C22—84no—
455C22—88no—
456C22—82no—
457C22—82no—
458C22#1192645211yescharacteristic
459C22#1192670612yes—
460C22#1192676312yes—
461C22#1192692611yescharacteristic
462C22#1192693911yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—3041no—
470C4—1521no—
471C4—1521no—
472C4#1192673012yes—
473C2—22no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—84no—
478C2#1456468811yescharacteristic
479C2#1456472911yescharacteristic
480C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2435C2
socleC22×C19#392
prime radicalC23×D4×C19C22
hypercenter#2435D19
hypocenterC19#9955
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. #14574407C2semidirect
3. #14564620C2semidirect
5. #14562207C2semidirect
6. #14561483C2semidirect
319. C19#9955semidirect

Maximal subgroups

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

subgroupindex
#145744072
C2×#119266952
#145646202
#145635662
#145622072
#145614832
C19×#24352
#995519