Finite Group Databasebeta

← #18080199

Subgroups — #18080199

Order 4864.

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

normal subgroups only

This group has 568 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#14572664C211yesmaximal, characteristic, complemented
2#14562259C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic, complemented
4#14561491C212yesmaximal, complemented
5C19×#2544C211yesmaximal, characteristic
6#11926616—24no—
7#11926601C2212yes—
8#11926601C2212yes—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11#11926284—24no—
12#11926268—21no—
13#11926268—21no—
14C2×C19×#127C411yescharacteristic
15C2×C19×#124C411yescharacteristic
16C2×C19×#124C2211yescharacteristic
17C2×C4×D4×C19C2211yescharacteristic
18C19×#394—21no—
19C19×#394—21no—
20C19×#391C411yescharacteristic
21C19×#390C411yescharacteristic
22C19×#386—21no—
23C19×#386—21no—
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19—21no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C411yescharacteristic
29C22×D4×C19C2×C411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C23×C4×C19D411yescharacteristic
32C19×#127—42no—
33C19×#124—22no—
34C19×#124—22no—
35C19×#124—42no—
36C4×D4×C19—22no—
37C4×D4×C19—22no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19D411yescharacteristic
47C2×C22⋊C4×C19D411yescharacteristic
48C2×C42×C19C2×C411yescharacteristic
49C2×C42×C19C2×C411yescharacteristic
50C2×C42×C19C2311yescharacteristic
51C2×#64520—22no—
52C22×C19⋊C8—22no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95—21no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C4⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)—22no—
62#10597260—22no—
63#10597260D414yescomplemented
64C24×C19—21no—
65C24×C19C22⋊C411yescharacteristic
66C24×C19C22⋊C411yescharacteristic
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×D4×C19—22no—
71C2×D4×C19—22no—
72C2×D4×C19—22no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—42no—
77C2×D4×C19—42no—
78C2×D4×C19—42no—
79C2×D4×C19—42no—
80C2×D4×C19—81no—
81C2×D4×C19—81no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—81no—
90C22×C4×C19—81no—
91C22×C4×C19C22⋊C411yescharacteristic
92C22×C4×C19C22⋊C411yescharacteristic
93C22×C4×C19C22×C411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C4⋊C4×C19—22no—
97C4⋊C4×C19—42no—
98C22⋊C4×C19—22no—
99C22⋊C4×C19—22no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—42no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—42no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—81no—
106C22⋊C4×C19—81no—
107C42×C19—41no—
108C42×C19—41no—
109C42×C19C2×D412yes—
110C42×C19#4112yes—
111#64520—82no—
112C2×C19⋊C8—24no—
113C2×C19⋊C8—42no—
114C2×C19⋊C8—82no—
115#9447—191nomaximal, Sylow
116C23×C19—21no—
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—41no—
132C23×C19#10012yes—
133C23×C19C2×C22⋊C411yescharacteristic
134Q8×C19—82no—
135D4×C19—44no—
136D4×C19—82no—
137D4×C19—84no—
138D4×C19—84no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—22no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
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—81no—
159C2×C4×C19—81no—
160C2×C4×C19C4×D412yes—
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12112yes—
163C2×C4×C19#12311yescharacteristic
164C19⋊C8—44no—
165C19⋊C8—82no—
166#2973—191no—
167#2544D1911yescharacteristic
168#1533—192no—
169#1466—191no—
170#1285—192no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—22no—
174C22×C19—42no—
175C22×C19—42no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—81no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19#38611yescharacteristic
191C22×C19C2×#10011yescharacteristic
192C22×C19#41311yescharacteristic
193C4×C19—22no—
194C4×C19—22no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—42no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—81no—
201C4×C19—81no—
202C2×#127Dic1911yescharacteristic
203C2×#124Dic1911yescharacteristic
204C2×#124C2×D1911yescharacteristic
205C2×C4×D4C2×D1911yescharacteristic
206#435—384no—
207#432—192no—
208#432—192no—
209#407—381no—
210C2×C22⋊C8—381no—
211#394—21no—
212#394—21no—
213#391Dic1911yescharacteristic
214#390Dic1911yescharacteristic
215#386—21no—
216#386—21no—
217C4×C4⋊C4C2×D1911yescharacteristic
218#329—384no—
219#323—381no—
220#323—381no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19—42no—
224C2×C19—81no—
225C2×C19—161no—
226C2×C19#188411yescharacteristic
227C2×C19#190011yescharacteristic
228C2×C19#191111yescharacteristic
229C22×Q8C2×Dic1911yescharacteristic
230C22×D4—21no—
231C22×D4—21no—
232C22×D4C2×Dic1911yescharacteristic
233C22×D4C2×Dic1911yescharacteristic
234C23×C4C22⋊D1911yescharacteristic
235C23×C4C22⋊D1911yescharacteristic
236C2×M16—382no—
237C22×C8—382no—
238#127—42no—
239#124—22no—
240#124—22no—
241#124—42no—
242C4×D4—22no—
243C4×D4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×Dic1911yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4C22⋊D1911yescharacteristic
253C2×C22⋊C4C22⋊D1911yescharacteristic
254C2×C42C2×Dic1911yescharacteristic
255C2×C42C2×Dic1911yescharacteristic
256C2×C42C22×D1911yescharacteristic
257C4⋊C8—382no—
258C4⋊C8—382no—
259C22⋊C8—382no—
260C22⋊C8—382no—
261C22⋊C8—382no—
262C22⋊C8—382no—
263#97—194no—
264#97—382no—
265#95—21no—
266#95—21no—
267#95—21no—
268C19#944711yescharacteristic, complemented, Sylow
269C24—21no—
270C24C22⋊Dic1911yescharacteristic
271C24C22⋊Dic1911yescharacteristic
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—81no—
286C2×D4—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4C22⋊Dic1911yescharacteristic
297C22×C4C22⋊Dic1911yescharacteristic
298C22×C4C22×Dic1911yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300C22×C4C2×C22⋊D1911yescharacteristic
301M16—1522no—
302C2×C8—384no—
303C2×C8—762no—
304C2×C8—1522no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—81no—
315C22⋊C4—81no—
316C42—41no—
317C42—41no—
318C42D4×D1912yes—
319C42#6454312yes—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#1059729012yes—
337C23C2×C22⋊Dic1911yescharacteristic
338Q8—82no—
339D4—44no—
340D4—82no—
341D4—84no—
342D4—84no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4D4×Dic1912yes—
365C2×C4#1059738111yescharacteristic
366C2×C4#1059738311yescharacteristic
367C2×C4#1059738512yes—
368C8—764no—
369C8—1522no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#1192642411yescharacteristic
390C22C2×#1059729011yescharacteristic
391C22#1192652811yescharacteristic
392C4—22no—
393C4—21no—
394C4—21no—
395C4—22no—
396C4—42no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—161no—
406C2#1456401911yescharacteristic
407C2#1456409911yescharacteristic
408C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2544C2
socleC22×C19#386
prime radicalC2×C19×#127C4
cosocleC2×C42×C19C23
hypercenter#2544D19
hypocenterC19#9447
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. #14572664C2semidirect
2. #14562259C2semidirect
3. #14561976C2semidirect
4. #14561491C2semidirect
63. #10597260D4semidirect
268. C19#9447semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145622592
#145619762
#145614912
C19×#25442
#944719