Finite Group Databasebeta

← #18078980

Subgroups — #18078980

Order 4864.

708 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11926702C211yesmaximal, characteristic
2#14566467C211yesmaximal, characteristic
3#14564619C211yesmaximal, characteristic
4#14563569C211yesmaximal, characteristic
5#14562206C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic
7C19×#1289C211yesmaximal, characteristic
8C23×Dic38C2211yescharacteristic
9C22×Dic76C412yescomplemented
10C2×#10597370C2211yescharacteristic
11C2×#10597333—21no—
12#11926702—21no—
13#11926702—22no—
14#11926702—21no—
15C2×#10597273C412yescomplemented
16C2×#10597267—22no—
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926449—21no—
19#11926448—22no—
20#11926402—21no—
21C22⋊C4×Dic19—21no—
22C4×C22⋊Dic19C2211yescharacteristic
23#11926310—21no—
24#11926310—21no—
25#11926280—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C19×#380C2211yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19—21no—
31C22×Dic38—21no—
32C22×Dic38—21no—
33C22×Dic38—21no—
34C22×Dic38—44no—
35C22×Dic38C2×C412yes—
36C22×Dic38C2×C411yescharacteristic
37C22×Dic38D411yescharacteristic
38C22×Dic38D412yes—
39C22×Dic38D411yescharacteristic
40C22×C8×C19C2×C412yes—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19D411yescharacteristic
47C2×C22⋊Dic19D411yescharacteristic
48C2×C4⋊Dic19C2×C411yescharacteristic
49#10597370—21no—
50#10597370—21no—
51#10597370—21no—
52#10597370—21no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—21no—
55C2×C4×Dic19—22no—
56C2×C4×Dic19—21no—
57C22×C19⋊C8—21no—
58C2×Dic76—22no—
59C2×Dic76—22no—
60C2×Dic76—44no—
61#10597333—44no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95—21no—
65C19×#95D412yes—
66C19⋊#95—22no—
67C19⋊#95—22no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71#10597273—22no—
72#10597273—22no—
73#10597267—44no—
74C24×C19C2×D411yescharacteristic
75C22×C4×C19—22no—
76C22×C4×C19—42no—
77C22×C4×C19—41no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—22no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—44no—
93C2×Dic38—21no—
94C2×Dic38—24no—
95C2×Dic38—24no—
96C2×Dic38—24no—
97C2×Dic38—22no—
98C2×Dic38—22no—
99C2×Dic38—21no—
100C2×Dic38—21no—
101C2×Dic38—21no—
102C2×Dic38—42no—
103C2×Dic38—42no—
104C2×Dic38—42no—
105C2×Dic38—44no—
106C2×Dic38—44no—
107C2×Dic38—44no—
108C2×Dic38—42no—
109C2×Dic38C22⋊C412yes—
110C2×Dic38C22⋊C412yes—
111C2×C8×C19—22no—
112C2×C8×C19—42no—
113C4⋊C4×C19—42no—
114C4⋊C4×C19—42no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊Dic19—21no—
120C22⋊Dic19—21no—
121C22⋊Dic19—21no—
122C22⋊Dic19—41no—
123C22⋊Dic19—41no—
124C22⋊Dic19Q1612yescomplemented
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127Dic19⋊C4—44no—
128Dic19⋊C4—41no—
129Dic19⋊C4—41no—
130C4×Dic19—44no—
131C4×Dic19—42no—
132C2×C19⋊C8—42no—
133C2×C19⋊C8—41no—
134Dic76—44no—
135Dic76—44no—
136#9258—191nomaximal, Sylow
137C23×C19—41no—
138C23×C19—41no—
139C23×C19C4×D411yescharacteristic
140C23×C19#12011yescharacteristic
141C23×C19#12111yescharacteristic
142C23×C19C2×Q1611yescharacteristic
143C23×C19#13511yescharacteristic
144C23×C19#13711yescharacteristic
145C23×C19#13711yescharacteristic
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19C2×C22⋊C411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12311yescharacteristic
162C2×Dic19—24no—
163C2×Dic19—22no—
164C2×Dic19—22no—
165C2×Dic19—22no—
166C2×Dic19—44no—
167C2×Dic19—44no—
168C2×Dic19—41no—
169C2×Dic19—42no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—81no—
177C2×Dic19—81no—
178Dic38—24no—
179Dic38—22no—
180Dic38—22no—
181Dic38—22no—
182Dic38—44no—
183Dic38—44no—
184Dic38—42no—
185Dic38—42no—
186Dic38—81no—
187Dic38#9914yes—
188C8×C19—42no—
189C19⋊C8—81no—
190C2×#451—191no—
191Q8×C22⋊C4—191no—
192#1996—191no—
193#1787—191no—
194#1520—191no—
195#1289D1911yescharacteristic
196#1282—191no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19—41no—
206C22×C19—41no—
207C22×C19#38611yescharacteristic
208C22×C19C4×Q1611yescharacteristic
209C22×C19#44111yescharacteristic
210C22×C19#45111yescharacteristic
211C22×C19#45211yescharacteristic
212C22×C19#46211yescharacteristic
213C22×C19#46411yescharacteristic
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—82no—
218C4×C19—161no—
219C4×C19C2×#9912yes—
220Dic19—24no—
221Dic19—42no—
222Dic19—42no—
223Dic19—81no—
224Dic19—81no—
225Dic19—81no—
226C23×Q8—191no—
227C22×Q16—192no—
228C2×C22⋊Q8—191no—
229C2×C4×Q8—381no—
230#451—381no—
231#451—382no—
232#451—381no—
233C2×#103—192no—
234C2×#103—382no—
235C2×C22⋊C8—191no—
236C2×C22⋊C8C2×D1911yescharacteristic
237#391—381no—
238#391—382no—
239#380—381no—
240#380C2×D1911yescharacteristic
241#380C2×D1911yescharacteristic
242C4×C22⋊C4—191no—
243C4×C22⋊C4—381no—
244#342—381no—
245#342—381no—
246#328—382no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19#187811yescharacteristic
254C2×C19#189811yescharacteristic
255C2×C19#190511yescharacteristic
256C22×Q8—192no—
257C22×Q8—191no—
258C22×Q8—191no—
259C22×Q8—192no—
260C22×Q8—191no—
261C22×Q8—381no—
262C22×Q8—381no—
263C22×Q8—381no—
264C22×Q8—764no—
265C23×C4—381no—
266C23×C4C22×D1911yescharacteristic
267C2×Q16—382no—
268C2×Q16—382no—
269C2×Q16—764no—
270C22×C8—381no—
271C22×C8C4×D1912yes—
272C22⋊Q8—381no—
273C22⋊Q8—381no—
274C22⋊Q8—381no—
275C22⋊Q8—381no—
276C4×Q8—764no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—191no—
280C2×C4⋊C4—382no—
281C2×C4⋊C4—381no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—191no—
285C2×C22⋊C4—191no—
286C2×C22⋊C4—381no—
287C2×C42—382no—
288C2×C42—381no—
289#103—382no—
290#103—382no—
291#103—764no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—381no—
295C22⋊C8—381no—
296#95—21no—
297#95—382no—
298#95—382no—
299#95—381no—
300#95D7612yes—
301C19#925811yescharacteristic, complemented, Sylow
302C24D4×D1911yescharacteristic
303C2×Q8—192no—
304C2×Q8—192no—
305C2×Q8—384no—
306C2×Q8—384no—
307C2×Q8—384no—
308C2×Q8—382no—
309C2×Q8—381no—
310C2×Q8—381no—
311C2×Q8—382no—
312C2×Q8—381no—
313C2×Q8—381no—
314C2×Q8—762no—
315C2×Q8—762no—
316C2×Q8—762no—
317C2×Q8—762no—
318C2×Q8—764no—
319C2×Q8—764no—
320C2×Q8—764no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—382no—
328C22×C4—382no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—764no—
333C22×C4C2×C4×D1911yescharacteristic
334C22×C4C2×D7611yescharacteristic
335C22×C4#6454111yescharacteristic
336C22×C4D4×D1911yescharacteristic
337C22×C4D4×D1911yescharacteristic
338C22×C4#6454511yescharacteristic
339Q16—764no—
340Q16—764no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—762no—
344C2×C8—761no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—381no—
348C4⋊C4—381no—
349C4⋊C4—764no—
350C4⋊C4—761no—
351C4⋊C4—761no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—192no—
357C22⋊C4—381no—
358C22⋊C4—381no—
359C22⋊C4—381no—
360C22⋊C4—761no—
361C22⋊C4—761no—
362C42—762no—
363C42—764no—
364C23—41no—
365C23—41no—
366C23#1059732811yescharacteristic
367C23#1059733011yescharacteristic
368C23#1059733911yescharacteristic
369C23#1059735811yescharacteristic
370C23#1059736111yescharacteristic
371C23#1059736111yescharacteristic
372C23Q16×D1911yescharacteristic
373Q8—194no—
374Q8—384no—
375Q8—382no—
376Q8—382no—
377Q8—382no—
378Q8—764no—
379Q8—764no—
380Q8—762no—
381Q8—762no—
382Q8—1521no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—384no—
396C2×C4—382no—
397C2×C4—382no—
398C2×C4—382no—
399C2×C4—764no—
400C2×C4—764no—
401C2×C4—761no—
402C2×C4—762no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—1521no—
410C2×C4—1521no—
411C2×C4C4×D7611yescharacteristic
412C2×C4C22⋊C4×D1911yescharacteristic
413C2×C4#1059734011yescharacteristic
414C2×C4#1059734111yescharacteristic
415C8—42no—
416C8—1521no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22#1192642211yescharacteristic
428C22#1192663811yescharacteristic
429C22#1192665011yescharacteristic
430C22#1192670111yescharacteristic
431C22#1192670711yescharacteristic
432C22#1192675311yescharacteristic
433C22#1192676511yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—82no—
438C4—161no—
439C4—384no—
440C4—762no—
441C4—762no—
442C4—1521no—
443C4—1521no—
444C4—1521no—
445C4#99×D1912yes—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2#1456397711yescharacteristic
453C2#1456408711yescharacteristic
454C2#1456413011yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1289C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1289D19
hypocenterC19#9258
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
9. C22×Dic76C4semidirect
15. C2×#10597273C4semidirect
124. C22⋊Dic19Q16semidirect
301. C19#9258semidirect

Maximal subgroups

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

subgroupindex
C2×#119267022
#145664672
#145646192
#145635692
#145622062
#145614822
C19×#12892
#925819