Finite Group Databasebeta

← #18075175

Subgroups — #18075175

Order 4864.

1154 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×#10597331C211yesmaximal, characteristic
2#14563558C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561961C212yesmaximal, complemented
5C19×#1462C211yesmaximal, characteristic, complemented
6C23×Dic38C2211yescharacteristic
7C23×C22⋊D19C411yescharacteristic
8C2×#10597331—24no—
9C2×#10597331—24no—
10C2×#10597331—22no—
11C2×#10597331—22no—
12C22×C22⋊Dic19C411yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C2211yescharacteristic
15C22×C4×Dic19C411yescharacteristic
16C2×#10597281—24no—
17#11926508C2212yes—
18#11926268—22no—
19#11926267—24no—
20C22×C22⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#323—22no—
23C25×C19C2×C411yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C22×C22⋊D19—22no—
28C22×C22⋊D19—22no—
29C22×C22⋊D19—22no—
30C22×C22⋊D19—44no—
31C23×Dic19C2×C411yescharacteristic
32C23×Dic19C2×C411yescharacteristic
33C23×Dic19C2×C411yescharacteristic
34C22×Dic38—21no—
35C22×Dic38—22no—
36C22×Dic38—21no—
37C22×Dic38—44no—
38C22×Dic38D414yes—
39C2×M16×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19D412yes—
43C2×C22⋊C4×C19D412yes—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—22no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—22no—
53C2×(C2×D19)⋊C4D414yes—
54C2×C4×Dic19—22no—
55C2×C4×Dic19—22no—
56C2×C4×Dic19—22no—
57C2×#64520—22no—
58#10597331—216no—
59#10597331—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64#10597281—48no—
65C24×C19—21no—
66C24×C19—21no—
67C24×C19—42no—
68C24×C19—42no—
69C24×C19—42no—
70C24×C19C22⋊C412yes—
71C24×C19C22×C411yescharacteristic
72C23×D19—21no—
73C23×D19—21no—
74C23×D19—42no—
75C23×D19—42no—
76C23×D19—42no—
77C23×D19C22⋊C412yes—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—42no—
81C22×C4×C19—42no—
82C22×C4×C19C22⋊C412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D412yes—
85C22×C4×C19C2×D412yes—
86C22×C4×C19C2×D411yescharacteristic
87C2×C22⋊D19—28no—
88C2×C22⋊D19—48no—
89C2×C22⋊D19—48no—
90C2×C22⋊D19—44no—
91C2×C22⋊D19—44no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—24no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—42no—
100C22×Dic19—42no—
101C22×Dic19C22⋊C412yes—
102C22×Dic19C22⋊C412yes—
103C22×Dic19C22⋊C412yes—
104C2×Dic38—24no—
105C2×Dic38—24no—
106C2×Dic38—28no—
107C2×Dic38—44no—
108C2×Dic38—44no—
109C2×Dic38—48no—
110C2×Dic38—44no—
111M16×C19—44no—
112C2×C8×C19—42no—
113C22⋊C4×C19—24no—
114C22⋊C4×C19—24no—
115C22⋊Dic19—28no—
116(C2×D19)⋊C4—28no—
117(C2×D19)⋊C4—24no—
118(C2×D19)⋊C4—24no—
119C4×Dic19—28no—
120#64520—44no—
121C2×C19⋊C8—42no—
122#8552—191nomaximal, Sylow
123C23×C19—22no—
124C23×C19—22no—
125C23×C19—22no—
126C23×C19—22no—
127C23×C19—24no—
128C23×C19—42no—
129C23×C19—42no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19—42no—
134C23×C19—42no—
135C23×C19—42no—
136C23×C19—88no—
137C23×C19C2×C22⋊C411yescharacteristic
138C23×C19C2×C22⋊C411yescharacteristic
139C23×C19C2×C22⋊C411yescharacteristic
140C22×D19—22no—
141C22×D19—24no—
142C22×D19—42no—
143C22×D19—42no—
144C22×D19—42no—
145C22×D19—42no—
146C22×D19—42no—
147C22×D19—42no—
148C22×D19—42no—
149C22×D19—42no—
150C22×D19—88no—
151C2×C4×C19—24no—
152C2×C4×C19—22no—
153C2×C4×C19—41no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19#12012yes—
160C2×C4×C19#12012yes—
161C22⋊D19—416no—
162C2×Dic19—24no—
163C2×Dic19—24no—
164C2×Dic19—22no—
165C2×Dic19—22no—
166C2×Dic19—22no—
167C2×Dic19—22no—
168C2×Dic19—24no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C2×Dic19#9914yes—
175Dic38—48no—
176Dic38—48no—
177C8×C19—82no—
178C19⋊C8—82no—
179C22×#124—191no—
180#1784—192no—
181#1462—192no—
182#1462—191no—
183#1462D1911yescharacteristic, complemented
184C22×C19—28no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—42no—
192C22×C19—42no—
193C22×C19—42no—
194C22×C19—84no—
195C22×C19—84no—
196C22×C19—84no—
197C22×C19#37911yescharacteristic
198C22×C19C2×#9912yes—
199C22×C19#41312yes—
200C22×C19#41312yes—
201C2×D19—42no—
202C2×D19—42no—
203C2×D19—42no—
204C2×D19—84no—
205C2×D19—84no—
206C2×D19—84no—
207C4×C19—22no—
208C4×C19—22no—
209C4×C19—42no—
210Dic19—24no—
211Dic19—42no—
212Dic19—42no—
213C23×Q8—191no—
214C23×D4—191no—
215C2×#124—384no—
216C2×#124—384no—
217C2×#124—382no—
218C2×#124—382no—
219C22×C22⋊C4—191no—
220C22×C22⋊C4—191no—
221C22×C22⋊C4—191no—
222C22×C22⋊C4C2×D1911yescharacteristic
223C22×C42—191no—
224C2×#101—384no—
225#407—192no—
226#407C2×D1912yes—
227#323—22no—
228#323—384no—
229#323—382no—
230C2×C19—22no—
231C2×C19—22no—
232C2×C19—22no—
233C2×C19—82no—
234C2×C19#178111yescharacteristic
235C2×C19#178511yescharacteristic
236C2×C19#178511yescharacteristic
237D19—82no—
238C25—191no—
239C25C4×D1911yescharacteristic
240C22×Q8—194no—
241C22×Q8—381no—
242C22×Q8—382no—
243C22×Q8—381no—
244C22×Q8—764no—
245C22×D4—382no—
246C22×D4—382no—
247C22×D4—382no—
248C22×D4—764no—
249C23×C4—191no—
250C23×C4—191no—
251C23×C4—191no—
252C23×C4C4×D1911yescharacteristic
253C23×C4C22×D1911yescharacteristic
254C2×M16—22no—
255C2×M16—382no—
256#124—3816no—
257#124—3816no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—194no—
261C2×C22⋊C4—382no—
262C2×C22⋊C4—382no—
263C2×C22⋊C4—382no—
264C2×C22⋊C4—382no—
265C2×C22⋊C4—382no—
266C2×C22⋊C4—382no—
267C2×C22⋊C4—381no—
268C2×C22⋊C4—382no—
269C2×C22⋊C4—381no—
270C2×C22⋊C4D7612yes—
271C2×C22⋊C4C22⋊D1912yes—
272C2×C42—382no—
273C2×C42—382no—
274C2×C42—382no—
275#101—768no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—382no—
279C22⋊C8—382no—
280C19#855211yescharacteristic, complemented, Sylow
281C24—21no—
282C24—21no—
283C24—42no—
284C24—42no—
285C24—42no—
286C24—192no—
287C24—381no—
288C24—381no—
289C24—762no—
290C24—762no—
291C24—762no—
292C24(C2×D19)⋊C412yes—
293C24C2×C4×D1911yescharacteristic
294C2×Q8—388no—
295C2×Q8—384no—
296C2×Q8—384no—
297C2×Q8—764no—
298C2×Q8—764no—
299C2×Q8—768no—
300C2×Q8—764no—
301C2×D4—388no—
302C2×D4—764no—
303C2×D4—768no—
304C2×D4—768no—
305C2×D4—764no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—192no—
311C22×C4—192no—
312C22×C4—192no—
313C22×C4—384no—
314C22×C4—381no—
315C22×C4—381no—
316C22×C4—381no—
317C22×C4—381no—
318C22×C4—381no—
319C22×C4—381no—
320C22×C4—762no—
321C22×C4—762no—
322C22×C4(C2×D19)⋊C412yes—
323C22×C4C2×D7611yescharacteristic
324C22×C4D4×D1912yes—
325C22×C4D4×D1912yes—
326C22×C4C2×C22⋊D1911yescharacteristic
327M16—44no—
328M16—764no—
329C2×C8—42no—
330C2×C8—762no—
331C22⋊C4—24no—
332C22⋊C4—24no—
333C22⋊C4—388no—
334C22⋊C4—388no—
335C22⋊C4—384no—
336C22⋊C4—384no—
337C42—388no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—88no—
352C23—382no—
353C23—384no—
354C23—762no—
355C23—762no—
356C23—762no—
357C23—762no—
358C23—762no—
359C23—762no—
360C23—762no—
361C23—762no—
362C23—1528no—
363C23C22⋊C4×D1911yescharacteristic
364C23C22⋊C4×D1911yescharacteristic
365C23C2×(C2×D19)⋊C411yescharacteristic
366Q8—768no—
367Q8—768no—
368D4—7616no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—194no—
378C2×C4—384no—
379C2×C4—384no—
380C2×C4—382no—
381C2×C4—382no—
382C2×C4—382no—
383C2×C4—382no—
384C2×C4—384no—
385C2×C4—762no—
386C2×C4—762no—
387C2×C4—762no—
388C2×C4—762no—
389C2×C4—762no—
390C2×C4#1059732812yes—
391C2×C4#1059738312yes—
392C8—82no—
393C8—1522no—
394C22—28no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—84no—
405C22—84no—
406C22—84no—
407C22—762no—
408C22—762no—
409C22—762no—
410C22—1524no—
411C22—1524no—
412C22—1524no—
413C22#1192639911yescharacteristic
414C22#99×D1912yes—
415C22#1192652512yes—
416C22#1192652612yes—
417C4—22no—
418C4—22no—
419C4—42no—
420C4—384no—
421C4—762no—
422C4—762no—
423C2—22no—
424C2—22no—
425C2—22no—
426C2—82no—
427C2—1522no—
428C2#1456354811yescharacteristic
429C2#1456356011yescharacteristic
430C2#1456356111yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1462C2
socleC22×C19#379
prime radicalC23×C22⋊D19C4
cosocleC23×C4×C19C23
hypercenter#1462D19
hypocenterC19#8552
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #14563558C2semidirect
3. #14561962C2semidirect
4. #14561961C2semidirect
5. C19×#1462C2semidirect
183. #1462D19semidirect
280. C19#8552semidirect

Maximal subgroups

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

subgroupindex
C22×#105973312
#145635582
#145619622
#145619612
C19×#14622
#855219