Finite Group Databasebeta

← #18082813

Subgroups — #18082813

Order 4864.

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

normal subgroups only

This group has 810 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
1C2×#11926700C211yesmaximal, characteristic
2#14569451C211yesmaximal, characteristic
3C2×#11926463C211yesmaximal, characteristic
4C2×#11926282C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic
6#14561513C211yesmaximal, characteristic
7C19×#1787C211yesmaximal, characteristic
8C22×#64528—21no—
9C2×#10597370C2211yescharacteristic
10C22×Dic19⋊C4—21no—
11C22×Dic19⋊C4C2211yescharacteristic
12#11926700—22no—
13#11926700—22no—
14C2×#10597292—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926484—21no—
17#11926474—22no—
18#11926465—21no—
19#11926463—22no—
20#11926463—22no—
21#11926419—21no—
22#11926405—21no—
23C2×C19⋊#95—21no—
24C2×C19⋊#95C2211yescharacteristic
25#11926282—22no—
26#11926269—22no—
27C23×Q8×C19C2211yescharacteristic
28C2×C19×#103—22no—
29C2×C19×C22⋊C8C2211yescharacteristic
30C19×#380C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×Q8×C19—21no—
33C22×Q8×C19—21no—
34C22×Q8×C19—21no—
35C22×Q8×C19—21no—
36C22×Q8×C19—44no—
37C22×Q8×C19D412yes—
38C23×C4×C19—21no—
39C23×C4×C19C2311yescharacteristic
40C23×Dic19—21no—
41C23×Dic19D411yescharacteristic
42C23×Dic19D411yescharacteristic
43C22×Dic38D411yescharacteristic
44C22×C8×C19—21no—
45C2×C4⋊C4×C19D412yes—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×#64528—24no—
49C2×#64528—44no—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19D411yescharacteristic
52#10597370—21no—
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56C2×Dic19⋊C4—24no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C2×Dic19⋊C4—44no—
65C22×C19⋊C8—21no—
66C19×#103—44no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×#95—21no—
70#10597292—24no—
71C19⋊#95—24no—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95—21no—
76C19⋊#95D412yes—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)D412yes—
79C24×C19C2×D411yescharacteristic
80C2×Q8×C19—24no—
81C2×Q8×C19—24no—
82C2×Q8×C19—22no—
83C2×Q8×C19—22no—
84C2×Q8×C19—44no—
85C2×Q8×C19—42no—
86C2×Q8×C19—42no—
87C2×Q8×C19—44no—
88C2×Q8×C19—44no—
89C2×Q8×C19—44no—
90C2×Q8×C19—41no—
91C2×Q8×C19—41no—
92C22×C4×C19—24no—
93C22×C4×C19—22no—
94C22×C4×C19—22no—
95C22×C4×C19—42no—
96C22×C4×C19—42no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×Dic19—24no—
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
115C22×Dic19—21no—
116C22×Dic19—21no—
117C22×Dic19—21no—
118C22×Dic19—42no—
119C22×Dic19—41no—
120C22×Dic19—41no—
121C22×Dic19—42no—
122C22×Dic19Q1612yescomplemented
123C2×Dic38—21no—
124C2×Dic38—21no—
125C2×Dic38—42no—
126C2×C8×C19—42no—
127C2×C8×C19—41no—
128C4⋊C4×C19—42no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133#64528—48no—
134C4⋊Dic19—21no—
135C4⋊Dic19—21no—
136C4⋊Dic19—82no—
137Dic19⋊C4—48no—
138Dic19⋊C4—41no—
139Dic19⋊C4—41no—
140Dic19⋊C4—41no—
141Dic19⋊C4—41no—
142Dic19⋊C4—41no—
143Dic19⋊C4—41no—
144C2×C19⋊C8—22no—
145C2×C19⋊C8—42no—
146#9925—191nomaximal, Sylow
147C23×C19—22no—
148C23×C19—22no—
149C23×C19#12011yescharacteristic
150C23×C19#12011yescharacteristic
151C23×C19#12111yescharacteristic
152C23×C19C2×Q1611yescharacteristic
153C23×C19#13511yescharacteristic
154C23×C19#13711yescharacteristic
155C23×C19#13711yescharacteristic
156Q8×C19—24no—
157Q8×C19—24no—
158Q8×C19—42no—
159Q8×C19—44no—
160Q8×C19—44no—
161Q8×C19—42no—
162C2×C4×C19—22no—
163C2×C4×C19—22no—
164C2×C4×C19—24no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—42no—
170C2×C4×C19—44no—
171C2×C4×C19—42no—
172C2×C4×C19—44no—
173C2×C4×C19—42no—
174C2×C4×C19—42no—
175C2×C4×C19—42no—
176C2×C4×C19#12011yescharacteristic
177C2×C4×C19#12111yescharacteristic
178C2×C4×C19#12111yescharacteristic
179C2×C4×C19#12711yescharacteristic
180C2×Dic19—24no—
181C2×Dic19—22no—
182C2×Dic19—22no—
183C2×Dic19—22no—
184C2×Dic19—42no—
185C2×Dic19—44no—
186C2×Dic19—44no—
187C2×Dic19—41no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—42no—
191C2×Dic19—41no—
192C2×Dic19—42no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—81no—
200Dic38—42no—
201Dic38—81no—
202C8×C19—81no—
203C19⋊C8—42no—
204C2×#451—191no—
205#2627—191no—
206C2×#395—191no—
207#1787D1911yescharacteristic
208C2×#328—191no—
209C2×#324—191no—
210#1294—191no—
211C22×C19—22no—
212C22×C19—22no—
213C22×C19—22no—
214C22×C19—22no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19#39211yescharacteristic
220C22×C19#45111yescharacteristic
221C22×C19#45111yescharacteristic
222C22×C19#45211yescharacteristic
223C22×C19#45211yescharacteristic
224C22×C19#45612yes—
225C22×C19B(4,𝔽2)12yes—
226C22×C19#46711yescharacteristic
227C22×C19#47011yescharacteristic
228C4×C19—21no—
229C4×C19—21no—
230C4×C19—21no—
231C4×C19—21no—
232C4×C19—44no—
233C4×C19—82no—
234Dic19—44no—
235Dic19—42no—
236Dic19—81no—
237Dic19—81no—
238Dic19—81no—
239C23×Q8C2×D1911yescharacteristic
240C22×Q16—381no—
241C2×C22⋊Q8—191no—
242C22×C4⋊C4—191no—
243C22×C4⋊C4—381no—
244#451—382no—
245#451—382no—
246C2×#103—22no—
247C2×#103—381no—
248C2×C22⋊C8—191no—
249C2×C22⋊C8C2×D1911yescharacteristic
250#400—381no—
251#398—382no—
252#395—381no—
253#395—382no—
254#395—382no—
255#385—381no—
256#381—381no—
257#380C2×D1911yescharacteristic
258C2×#95—191no—
259C2×#95—381no—
260#328—382no—
261#324—382no—
262C2×C19—21no—
263C2×C19—21no—
264C2×C19—21no—
265C2×C19—21no—
266C2×C19#160312yes—
267C2×C19#160512yes—
268C2×C19#200111yescharacteristic
269C2×C19#200511yescharacteristic
270C2×C19#202111yescharacteristic
271C22×Q8—21no—
272C22×Q8—21no—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—44no—
277C22×Q8—191no—
278C22×Q8D7612yes—
279C23×C4—21no—
280C23×C4—191no—
281C23×C4—191no—
282C23×C4—381no—
283C23×C4C22×D1911yescharacteristic
284C2×Q16—384no—
285C2×Q16—764no—
286C22×C8—21no—
287C22×C8—381no—
288C22⋊Q8—381no—
289C22⋊Q8—381no—
290C22⋊Q8—381no—
291C22⋊Q8—381no—
292C2×C4⋊C4—191no—
293C2×C4⋊C4—384no—
294C2×C4⋊C4—381no—
295C2×C4⋊C4—381no—
296C2×C4⋊C4—381no—
297C2×C4⋊C4—381no—
298C2×C4⋊C4—381no—
299C2×C4⋊C4—381no—
300C2×C4⋊C4—381no—
301C2×C4⋊C4—382no—
302C2×C4⋊C4—764no—
303C2×C4⋊C4C22⋊D1912yes—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—381no—
306#103—44no—
307#103—384no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—192no—
311C22⋊C8—381no—
312#95—21no—
313#95—192no—
314#95—384no—
315#95—382no—
316#95—382no—
317#95—382no—
318#95—381no—
319C19#992511yescharacteristic, complemented, Sylow
320C24D4×D1911yescharacteristic
321C2×Q8—24no—
322C2×Q8—24no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—44no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—44no—
329C2×Q8—44no—
330C2×Q8—44no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—381no—
334C2×Q8—381no—
335C2×Q8—762no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—192no—
344C22×C4—384no—
345C22×C4—381no—
346C22×C4—382no—
347C22×C4—381no—
348C22×C4—381no—
349C22×C4—381no—
350C22×C4—381no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—381no—
354C22×C4—381no—
355C22×C4—381no—
356C22×C4—381no—
357C22×C4—762no—
358C22×C4—761no—
359C22×C4—761no—
360C22×C4—762no—
361C22×C4C2×D7611yescharacteristic
362C22×C4#6454111yescharacteristic
363C22×C4D4×D1911yescharacteristic
364C22×C4D4×D1911yescharacteristic
365C22×C4D4×D1911yescharacteristic
366C22×C4C2×C22⋊D1911yescharacteristic
367Q16—768no—
368C2×C8—42no—
369C2×C8—41no—
370C2×C8—382no—
371C2×C8—762no—
372C4⋊C4—42no—
373C4⋊C4—381no—
374C4⋊C4—381no—
375C4⋊C4—768no—
376C4⋊C4—761no—
377C4⋊C4—761no—
378C4⋊C4—761no—
379C4⋊C4—761no—
380C4⋊C4—761no—
381C4⋊C4—761no—
382C4⋊C4—1522no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—761no—
386C22⋊C4—761no—
387C23—22no—
388C23—22no—
389C23#1059732811yescharacteristic
390C23#1059733011yescharacteristic
391C23#1059736111yescharacteristic
392C23#1059736211yescharacteristic
393C23Q16×D1911yescharacteristic
394C23#1059736411yescharacteristic
395C23#1059738311yescharacteristic
396Q8—24no—
397Q8—24no—
398Q8—44no—
399Q8—42no—
400Q8—42no—
401Q8—44no—
402Q8—762no—
403Q8—1521no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—384no—
419C2×C4—382no—
420C2×C4—382no—
421C2×C4—382no—
422C2×C4—762no—
423C2×C4—764no—
424C2×C4—764no—
425C2×C4—761no—
426C2×C4—761no—
427C2×C4—761no—
428C2×C4—761no—
429C2×C4—762no—
430C2×C4—762no—
431C2×C4—761no—
432C2×C4—761no—
433C2×C4—761no—
434C2×C4—762no—
435C2×C4—762no—
436C2×C4—762no—
437C2×C4—1521no—
438C2×C4#1059732811yescharacteristic
439C2×C4#1059733011yescharacteristic
440C2×C4#1059737611yescharacteristic
441C2×C4#1059738611yescharacteristic
442C8—81no—
443C8—762no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22#1192645311yescharacteristic
453C22#1192669811yescharacteristic
454C22#1192670111yescharacteristic
455C22#1192670311yescharacteristic
456C22#1192670911yescharacteristic
457C22#1192672512yes—
458C22#1192673012yes—
459C22#1192678411yescharacteristic
460C22#1192680111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—82no—
467C4—764no—
468C4—762no—
469C4—1521no—
470C4—1521no—
471C4—1521no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#1456259512yes—
477C2#1456260712yes—
478C2#1456464411yescharacteristic
479C2#1456467211yescharacteristic
480C2#1456476111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1787C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1787D19
hypocenterC19#9925
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
122. C22×Dic19Q16semidirect
319. C19#9925semidirect

Maximal subgroups

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

subgroupindex
C2×#119267002
#145694512
C2×#119264632
C2×#119262822
C2×#119262692
#145615132
C19×#17872
#992519