Finite Group Databasebeta

← #18080544

Subgroups — #18080544

Order 4864.

626 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572676C211yesmaximal, characteristic, complemented
2#14561973C211yesmaximal, characteristic, complemented
3#14561962C212yesmaximal, complemented
4#14561541C212yesmaximal, complemented
5C19×#2534C211yesmaximal, characteristic
6#11926622—24no—
7#11926597—21no—
8#11926508—21no—
9#11926508C2212yes—
10#11926508C2212yes—
11#11926270—21no—
12#11926268—24no—
13#11926268—21no—
14C2×C19×#123C411yescharacteristic
15C2×C19×#120C411yescharacteristic
16C2×C4×D4×C19C2211yescharacteristic
17C22×C22⋊C4×C19C2211yescharacteristic
18C19×#396—21no—
19C19×#394—21no—
20C19×#388—21no—
21C19×#386—21no—
22C19×#381C411yescharacteristic
23C19×#380C2211yescharacteristic
24C19×#379C411yescharacteristic
25C25×C19C2×C411yescharacteristic
26C22×D4×C19—21no—
27C22×D4×C19C2×C411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C19×#123—42no—
32C19×#120—42no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—22no—
44C2×C22⋊C4×C19—22no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19C2×C411yescharacteristic
47C2×C22⋊C4×C19C2×C411yescharacteristic
48C2×C22⋊C4×C19C2×C411yescharacteristic
49C2×C22⋊C4×C19D411yescharacteristic
50C2×C42×C19D411yescharacteristic
51C2×#64520—22no—
52C2×#64520—22no—
53C2×#64520—22no—
54C19×#95—21no—
55C19×#95—21no—
56C19×#95—21no—
57C22⋊(C19⋊C8)—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)D414yescomplemented
62C4⋊(C19⋊C8)—22no—
63C4×C19⋊C8—22no—
64C24×C19—21no—
65C24×C19—22no—
66C24×C19—42no—
67C24×C19—41no—
68C24×C19—41no—
69C24×C19—81no—
70C24×C19C22⋊C411yescharacteristic
71C24×C19C22×C411yescharacteristic
72C2×D4×C19—22no—
73C2×D4×C19—22no—
74C2×D4×C19—41no—
75C2×D4×C19—42no—
76C2×D4×C19—42no—
77C2×D4×C19—81no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—22no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—81no—
87C22×C4×C19—81no—
88C22×C4×C19C22⋊C411yescharacteristic
89C22×C4×C19C22⋊C411yescharacteristic
90C22×C4×C19C22⋊C411yescharacteristic
91C22×C4×C19C2×D412yes—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4112yes—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—42no—
97C4⋊C4×C19—81no—
98C22⋊C4×C19—22no—
99C22⋊C4×C19—22no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—42no—
102C22⋊C4×C19—42no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19—42no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—81no—
109C42×C19—21no—
110C42×C19—21no—
111#64520—82no—
112#64520—82no—
113#64520—82no—
114C2×C19⋊C8—24no—
115C2×C19⋊C8—42no—
116#9516—191nomaximal, Sylow
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—22no—
120C23×C19—24no—
121C23×C19—21no—
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—42no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—82no—
136C23×C19—82no—
137C23×C19—84no—
138C23×C19—84no—
139C23×C19C2×C22⋊C411yescharacteristic
140C23×C19C4×D412yes—
141D4×C19—44no—
142D4×C19—84no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—81no—
164C2×C4×C19—82no—
165C2×C4×C19#10012yes—
166C2×C4×C19#12011yescharacteristic
167C2×C4×C19#12112yes—
168C2×C4×C19#12311yescharacteristic
169C19⋊C8—44no—
170C19⋊C8—82no—
171#2975—191no—
172#2534D1911yescharacteristic
173#1465—191no—
174#1462—192no—
175#1305—192no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—22no—
180C22×C19—22no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—42no—
184C22×C19—42no—
185C22×C19—42no—
186C22×C19—42no—
187C22×C19—41no—
188C22×C19—41no—
189C22×C19—41no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19—84no—
194C22×C19—84no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19#38611yescharacteristic
198C22×C19C2×#10011yescharacteristic
199C22×C19#41311yescharacteristic
200C4×C19—22no—
201C4×C19—21no—
202C4×C19—22no—
203C4×C19—21no—
204C4×C19—41no—
205C4×C19—41no—
206C4×C19—81no—
207C4×C19—81no—
208C4×C19—81no—
209C2×#123Dic1911yescharacteristic
210C2×#120Dic1911yescharacteristic
211C2×C4×D4C2×D1911yescharacteristic
212C22×C22⋊C4C2×D1911yescharacteristic
213#436—384no—
214#431—381no—
215#407—192no—
216#407—192no—
217#407—381no—
218#396—21no—
219#394—21no—
220#388—21no—
221#386—21no—
222#381Dic1911yescharacteristic
223#380C2×D1911yescharacteristic
224#379Dic1911yescharacteristic
225#324—381no—
226#323—384no—
227#323—381no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—42no—
231C2×C19—81no—
232C2×C19—82no—
233C2×C19#189111yescharacteristic
234C2×C19#190011yescharacteristic
235C2×C19#191311yescharacteristic
236C25C2×Dic1911yescharacteristic
237C22×D4—21no—
238C22×D4C2×Dic1911yescharacteristic
239C23×C4C2×Dic1911yescharacteristic
240C23×C4C22⋊D1911yescharacteristic
241C23×C4C22×D1911yescharacteristic
242C2×M16—382no—
243C2×M16—382no—
244C2×M16—382no—
245#123—42no—
246#120—42no—
247C4×D4—22no—
248C4×D4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C22⋊D1911yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4C2×Dic1911yescharacteristic
261C2×C22⋊C4C2×Dic1911yescharacteristic
262C2×C22⋊C4C2×Dic1911yescharacteristic
263C2×C22⋊C4C22⋊D1911yescharacteristic
264C2×C42C22⋊D1911yescharacteristic
265C4⋊C8—382no—
266C22⋊C8—194no—
267C22⋊C8—382no—
268C22⋊C8—382no—
269C22⋊C8—382no—
270C22⋊C8—382no—
271C4×C8—382no—
272#95—21no—
273#95—21no—
274#95—21no—
275C19#951611yescharacteristic, complemented, Sylow
276C24—21no—
277C24—22no—
278C24—42no—
279C24—41no—
280C24—41no—
281C24—81no—
282C24C22⋊Dic1911yescharacteristic
283C24C22×Dic1911yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—81no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4C22⋊Dic1911yescharacteristic
301C22×C4C22⋊Dic1911yescharacteristic
302C22×C4C22⋊Dic1911yescharacteristic
303C22×C4D4×D1912yes—
304C22×C4#6454312yes—
305C22×C4C2×C22⋊D1911yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307M16—1522no—
308M16—1522no—
309M16—1522no—
310C2×C8—384no—
311C2×C8—762no—
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—81no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C42—21no—
327C42—21no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—24no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—42no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—82no—
347C23—82no—
348C23—84no—
349C23—84no—
350C23D4×Dic1912yes—
351C23C2×C22⋊Dic1911yescharacteristic
352D4—44no—
353D4—84no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4#1059729012yes—
377C2×C4#1059738111yescharacteristic
378C2×C4#1059738311yescharacteristic
379C2×C4#1059738512yes—
380C8—764no—
381C8—1522no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—84no—
400C22—84no—
401C22—81no—
402C22—81no—
403C22#1192642411yescharacteristic
404C22C2×#1059729011yescharacteristic
405C22#1192652811yescharacteristic
406C4—22no—
407C4—21no—
408C4—22no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4—81no—
414C4—81no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—81no—
419C2—82no—
420C2#1456405411yescharacteristic
421C2#1456409911yescharacteristic
422C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2534C2
socleC22×C19#386
prime radicalC2×C19×#120C4
cosocleC23×C4×C19C23
hypercenter#2534D19
hypocenterC19#9516
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2534

Complements

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

NH ≅ G/Ntype
1. #14572676C2semidirect
2. #14561973C2semidirect
3. #14561962C2semidirect
4. #14561541C2semidirect
61. C22⋊(C19⋊C8)D4semidirect
275. C19#9516semidirect

Maximal subgroups

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

subgroupindex
#145726762
#145619732
#145619622
#145615412
C19×#25342
#951619