Finite Group Databasebeta

← #18075177

Subgroups — #18075177

Order 4864.

1166 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1166 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×#10597340C211yesmaximal, characteristic
2#14563715C211yesmaximal, characteristic, complemented
3#14561961C212yesmaximal, complemented
4#14561961C212yesmaximal, complemented
5C19×#1821C211yesmaximal, characteristic, complemented
6C23×D76C411yescharacteristic
7C23×C4×D19C411yescharacteristic
8C2×#10597340—24no—
9C2×#10597340—24no—
10C2×#10597340—22no—
11C2×#10597340—22no—
12C22×Dic19⋊C4C411yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C2211yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16#11926508C2212yes—
17#11926313—22no—
18#11926267—24no—
19#11926267—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#343—22no—
23C24×D19C2×C411yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×D76—22no—
31C22×D76—22no—
32C22×D76—22no—
33C22×D76—44no—
34C22×C4×D19—22no—
35C22×C4×D19—22no—
36C22×C4×D19—22no—
37C22×C4×D19—44no—
38C2×M16×C19—22no—
39C2×C4⋊C4×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19D412yes—
42C2×C4⋊C4×C19D412yes—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4D414yes—
53C2×(C2×D19)⋊C4D414yes—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C2×#64520—22no—
58#10597340—216no—
59#10597340—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64C24×C19C22×C411yescharacteristic
65C23×D19—21no—
66C23×D19—21no—
67C23×D19—24no—
68C23×D19—21no—
69C23×D19—21no—
70C23×D19—42no—
71C23×D19—42no—
72C23×D19—42no—
73C23×D19—42no—
74C23×D19—42no—
75C23×D19C22⋊C412yes—
76C23×D19C22⋊C412yes—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—42no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19C22⋊C412yes—
85C22×C4×C19C22⋊C412yes—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D412yes—
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—42no—
95C22×Dic19—42no—
96C22×Dic19C22⋊C412yes—
97C22×Dic19C22⋊C412yes—
98C2×D76—28no—
99C2×D76—48no—
100C2×D76—44no—
101C2×D76—48no—
102C2×D76—44no—
103C2×C4×D19—28no—
104C2×C4×D19—48no—
105C2×C4×D19—44no—
106C2×C4×D19—48no—
107C2×C4×D19—44no—
108M16×C19—44no—
109C2×C8×C19—42no—
110C4⋊C4×C19—24no—
111C4⋊C4×C19—24no—
112(C2×D19)⋊C4—28no—
113(C2×D19)⋊C4—24no—
114(C2×D19)⋊C4—24no—
115(C2×D19)⋊C4—24no—
116(C2×D19)⋊C4—24no—
117Dic19⋊C4—28no—
118#64520—44no—
119C2×C19⋊C8—42no—
120#8553—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19—22no—
123C23×C19—22no—
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19C2×C22⋊C411yescharacteristic
126C23×C19C2×C22⋊C411yescharacteristic
127C22×D19—24no—
128C22×D19—24no—
129C22×D19—22no—
130C22×D19—22no—
131C22×D19—22no—
132C22×D19—24no—
133C22×D19—416no—
134C22×D19—42no—
135C22×D19—42no—
136C22×D19—42no—
137C22×D19—42no—
138C22×D19—42no—
139C22×D19—42no—
140C22×D19—42no—
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—42no—
144C22×D19—42no—
145C22×D19—42no—
146C22×D19—42no—
147C22×D19—42no—
148C22×D19—88no—
149C22×D19#10014yes—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—42no—
162C2×C4×C19#12012yes—
163C2×C4×C19#12012yes—
164C2×Dic19—22no—
165C2×Dic19—22no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172D76—416no—
173C4×D19—416no—
174C8×C19—82no—
175C19⋊C8—82no—
176C22×#123—191no—
177#1821—191no—
178#1821D1911yescharacteristic, complemented
179#1462—192no—
180#1462—192no—
181C22×C19—28no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19#37911yescharacteristic
189C22×C19#41012yes—
190C22×C19C2×#10012yes—
191C22×C19#41312yes—
192C2×D19—24no—
193C2×D19—48no—
194C2×D19—44no—
195C2×D19—48no—
196C2×D19—42no—
197C2×D19—42no—
198C2×D19—44no—
199C2×D19—42no—
200C2×D19—42no—
201C2×D19—42no—
202C2×D19—84no—
203C2×D19—84no—
204C2×D19—84no—
205C4×C19—22no—
206C4×C19—22no—
207C4×C19—42no—
208C4×C19—42no—
209Dic19—42no—
210Dic19—42no—
211C23×D4—191no—
212C24×C4—191no—
213C2×#123—384no—
214C2×#123—384no—
215C2×#123—382no—
216C2×#123—382no—
217C22×C4⋊C4—191no—
218C22×C4⋊C4C2×D1911yescharacteristic
219C22×C22⋊C4—191no—
220C22×C22⋊C4—191no—
221C22×C22⋊C4—191no—
222#407—192no—
223#407C2×D1912yes—
224#343—22no—
225#343—382no—
226#323—384no—
227#323—384no—
228C2×C19—22no—
229C2×C19—22no—
230C2×C19—22no—
231C2×C19#178211yescharacteristic
232C2×C19#178311yescharacteristic
233C2×C19#178511yescharacteristic
234D19—44no—
235D19—82no—
236C25—191no—
237C25—191no—
238C22×D4—382no—
239C22×D4—382no—
240C22×D4—382no—
241C22×D4—764no—
242C23×C4—191no—
243C23×C4—191no—
244C23×C4—382no—
245C23×C4—382no—
246C23×C4—382no—
247C23×C4—764no—
248C23×C4C4×D1911yescharacteristic
249C23×C4C4×D1911yescharacteristic
250C23×C4C22×D1911yescharacteristic
251C2×M16—22no—
252C2×M16—382no—
253#123—3816no—
254#123—3816no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—382no—
258C2×C4⋊C4—382no—
259C2×C4⋊C4—382no—
260C2×C4⋊C4D7612yes—
261C2×C4⋊C4C22⋊D1912yes—
262C2×C22⋊C4—194no—
263C2×C22⋊C4—194no—
264C2×C22⋊C4—382no—
265C2×C22⋊C4—382no—
266C2×C22⋊C4—382no—
267C2×C22⋊C4—381no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—382no—
270C2×C22⋊C4—382no—
271C2×C22⋊C4—381no—
272C2×C22⋊C4—381no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8—382no—
276C22⋊C8—382no—
277C19#855311yescharacteristic, complemented, Sylow
278C24—192no—
279C24—192no—
280C24—384no—
281C24—381no—
282C24—381no—
283C24—381no—
284C24—381no—
285C24—762no—
286C24—762no—
287C24—762no—
288C24—762no—
289C24—762no—
290C24C2×C4×D1911yescharacteristic
291C2×D4—388no—
292C2×D4—764no—
293C2×D4—768no—
294C2×D4—764no—
295C2×D4—768no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—192no—
304C22×C4—192no—
305C22×C4—388no—
306C22×C4—381no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—764no—
311C22×C4—768no—
312C22×C4—764no—
313C22×C4—768no—
314C22×C4—762no—
315C22×C4—762no—
316C22×C4(C2×D19)⋊C412yes—
317C22×C4(C2×D19)⋊C412yes—
318C22×C4C2×D7611yescharacteristic
319C22×C4D4×D1912yes—
320C22×C4D4×D1912yes—
321C22×C4C2×C22⋊D1911yescharacteristic
322M16—44no—
323M16—764no—
324C2×C8—42no—
325C2×C8—762no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—388no—
329C22⋊C4—388no—
330C22⋊C4—384no—
331C22⋊C4—384no—
332C22⋊C4—384no—
333C22⋊C4—384no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—194no—
338C23—384no—
339C23—384no—
340C23—382no—
341C23—382no—
342C23—382no—
343C23—384no—
344C23—762no—
345C23—762no—
346C23—7616no—
347C23—762no—
348C23—762no—
349C23—762no—
350C23—762no—
351C23—762no—
352C23—762no—
353C23—762no—
354C23—762no—
355C23—762no—
356C23—762no—
357C23—762no—
358C23—762no—
359C23—1528no—
360C23C22⋊C4×D1911yescharacteristic
361C23C22⋊C4×D1911yescharacteristic
362C23C2×(C2×D19)⋊C411yescharacteristic
363D4—7616no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—382no—
377C2×C4—382no—
378C2×C4—7616no—
379C2×C4—762no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—762no—
384C2×C4—762no—
385C2×C4#1059732812yes—
386C2×C4#1059738312yes—
387C8—82no—
388C8—1522no—
389C22—28no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—384no—
397C22—764no—
398C22—768no—
399C22—764no—
400C22—768no—
401C22—762no—
402C22—762no—
403C22—762no—
404C22—762no—
405C22—762no—
406C22—1524no—
407C22—1524no—
408C22—1524no—
409C22#1192639911yescharacteristic
410C22#1192651712yes—
411C22#100×D1912yes—
412C22#1192652712yes—
413C4—22no—
414C4—22no—
415C4—42no—
416C4—42no—
417C4—762no—
418C4—762no—
419C2—22no—
420C2—22no—
421C2—22no—
422C2—764no—
423C2—1522no—
424C2#1456355211yescharacteristic
425C2#1456355411yescharacteristic
426C2#1456356211yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1821C2
socleC22×C19#379
prime radicalC23×D76C4
cosocleC23×C4×C19C23
hypercenter#1821D19
hypocenterC19#8553
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #14563715C2semidirect
3. #14561961C2semidirect
4. #14561961C2semidirect
5. C19×#1821C2semidirect
178. #1821D19semidirect
277. C19#8553semidirect

Maximal subgroups

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

subgroupindex
C22×#105973402
#145637152
#145619612
C19×#18212
#855319