Finite Group Databasebeta

← #18079736

Subgroups — #18079736

Order 4864.

542 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 93 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#14573576C211yesmaximal, characteristic
2#14566526C211yesmaximal, characteristic, complemented
3#14564471C211yesmaximal, characteristic
4#14563735C211yesmaximal, characteristic, complemented
5#14562150C211yesmaximal, characteristic
6#14561540C211yesmaximal, characteristic, complemented
7C19×#1297C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597372C2211yescharacteristic
10#11926869—22no—
11#11926863—21no—
12#11926858—21no—
13#11926586C412yescomplemented
14#11926550C412yescomplemented
15C2×#10597263—22no—
16#11926508C2211yescharacteristic
17#11926442—21no—
18#11926438—22no—
19#11926411—21no—
20#11926404C2211yescharacteristic
21C4×C4⋊Dic19—21no—
22#11926395—21no—
23#11926304—22no—
24#11926277—21no—
25#11926277—21no—
26C19×#407C2211yescharacteristic
27C4×C22⋊C4×C19C2211yescharacteristic
28C4×C22⋊C4×C19C2211yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—21no—
31C22×D76C2×C411yescharacteristic
32C2×M16×C19C2×C412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19—21no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19D412yes—
39#10597376—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376—21no—
43C2×(C2×D19)⋊C4—21no—
44#10597372—21no—
45#10597372—21no—
46#10597372C2×C412yes—
47#10597372D412yes—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19C2×C411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4⋊Dic19D411yescharacteristic
52C2×Dic19⋊C4—22no—
53C2×C4×Dic19—21no—
54C2×C4×Dic19—22no—
55C2×#64520—21no—
56C19×C22⋊C8—21no—
57C19×C22⋊C8—21no—
58C19×#95—21no—
59C19×#95D411yescharacteristic
60C19×#95D411yescharacteristic
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95—21no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66#10597278—22no—
67#10597278—22no—
68#10597275—22no—
69#10597274—22no—
70#10597263—44no—
71C24×C19C2×D411yescharacteristic
72C23×D19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—42no—
76C22×C4×C19—41no—
77C22×C4×C19C22×C411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C2×C22⋊D19—42no—
84C2×C22⋊D19—42no—
85C2×C22⋊D19—41no—
86C2×C22⋊D19—41no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—22no—
91C2×D76—21no—
92C2×D76—21no—
93C2×D76—42no—
94M16×C19—42no—
95C2×C8×C19—22no—
96C22⋊C4×C19—22no—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—41no—
99C42×C19—42no—
100C42×C19—42no—
101C22⋊Dic19—22no—
102C22⋊Dic19—22no—
103C22⋊Dic19—42no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—41no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110C4⋊Dic19—42no—
111C4⋊Dic19C22⋊C412yes—
112C4⋊Dic19C22⋊C412yes—
113Dic19⋊C4—44no—
114C4×Dic19—22no—
115C4×Dic19—22no—
116C4×Dic19—82no—
117#64520—42no—
118C2×C19⋊C8—41no—
119#9366—191nomaximal, Sylow
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19C4×D411yescharacteristic
125C23×C19#12011yescharacteristic
126C23×C19#12111yescharacteristic
127C22×D19—41no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19—81no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—42no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—81no—
145C2×C4×C19—81no—
146C2×C4×C19C2×C22⋊C411yescharacteristic
147C2×C4×C19C4×D411yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12311yescharacteristic
150C22⋊D19—82no—
151C22⋊D19—81no—
152C22⋊D19—81no—
153C2×Dic19—22no—
154C2×Dic19—22no—
155C2×Dic19—42no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—41no—
162C2×Dic19—42no—
163D76—42no—
164D76—81no—
165C8×C19—42no—
166C19⋊C8—81no—
167#3094—191no—
168#2347—191no—
169#1964—191no—
170#1826—191no—
171#1507—191no—
172#1305—191no—
173#1297D1911yescharacteristic, complemented
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19#38611yescharacteristic
185C22×C19#45311yescharacteristic
186C22×C19#45411yescharacteristic
187C2×D19—81no—
188C2×D19—81no—
189C2×D19—81no—
190C2×D19—162no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—42no—
195C4×C19—81no—
196C4×C19—82no—
197C4×C19#41012yes—
198Dic19—42no—
199Dic19—42no—
200Dic19—82no—
201Dic19—81no—
202C2×#121—191no—
203C2×#117—191no—
204#482—382no—
205#481—381no—
206#480—381no—
207#428—192no—
208#418—192no—
209C2×#99—382no—
210#407—191no—
211#407C2×D1911yescharacteristic
212#389—381no—
213#388—382no—
214#383—381no—
215#380—191no—
216C4×C4⋊C4—381no—
217C4×C4⋊C4—381no—
218C4×C22⋊C4C2×D1911yescharacteristic
219C4×C22⋊C4C2×D1911yescharacteristic
220#339—382no—
221#327—381no—
222#327—381no—
223C2×C19—21no—
224C2×C19—21no—
225C2×C19—41no—
226C2×C19—41no—
227C2×C19#188311yescharacteristic
228C2×C19#189911yescharacteristic
229C2×C19#190611yescharacteristic
230D19—161no—
231C22×D4—191no—
232C22×D4—381no—
233C23×C4C22×D1911yescharacteristic
234C2×M16—381no—
235C2×M16C4×D1912yes—
236#121—381no—
237#121—381no—
238#121—381no—
239#121—381no—
240#117—192no—
241#117—192no—
242#117—381no—
243#117—381no—
244C2×C4⋊C4—191no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—191no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4—381no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—192no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C42—21no—
255C2×C42—21no—
256C2×C42—381no—
257C2×C42—382no—
258#107—382no—
259#106—382no—
260#102—382no—
261#102—382no—
262#99—764no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—381no—
266C22⋊C8—381no—
267#95—21no—
268#95—382no—
269#95—382no—
270#95—381no—
271#95D7611yescharacteristic
272#95D7611yescharacteristic
273C19#936611yescharacteristic, complemented, Sylow
274C24—381no—
275C24D4×D1911yescharacteristic
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—762no—
279C2×D4—762no—
280C2×D4—762no—
281C2×D4—761no—
282C2×D4—761no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—382no—
290C22×C4—381no—
291C22×C4C2×C4×D1911yescharacteristic
292C22×C4C2×D7611yescharacteristic
293C22×C4#6454111yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4#6454511yescharacteristic
297M16—42no—
298M16—762no—
299C2×C8—22no—
300C2×C8—761no—
301C4⋊C4—192no—
302C4⋊C4—192no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4—764no—
308C4⋊C4—762no—
309C22⋊C4—22no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—382no—
313C22⋊C4—382no—
314C22⋊C4—761no—
315C22⋊C4—761no—
316C22⋊C4—762no—
317C42—42no—
318C42—42no—
319C42—382no—
320C42—382no—
321C42—1522no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—762no—
327C23—761no—
328C23—1521no—
329C23—1521no—
330C23#1059732811yescharacteristic
331C23#1059733011yescharacteristic
332C23#1059733911yescharacteristic
333D4—762no—
334D4—1521no—
335D4—1522no—
336D4—1521no—
337D4—1521no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—382no—
354C2×C4—382no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—761no—
362C2×C4—762no—
363C2×C4C4×D7611yescharacteristic
364C2×C4C22⋊C4×D1911yescharacteristic
365C2×C4#1059734011yescharacteristic
366C2×C4#1059734111yescharacteristic
367C8—42no—
368C8—1521no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—3042no—
380C22—1521no—
381C22—1521no—
382C22—1521no—
383C22#1192642211yescharacteristic
384C22#1192671311yescharacteristic
385C22#1192671811yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—82no—
392C4—762no—
393C4—762no—
394C4—1522no—
395C4—1521no—
396C4#1192651612yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—3041no—
402C2#1456401211yescharacteristic
403C2#1456409211yescharacteristic
404C2#1456413511yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1297D19
hypocenterC19#9366
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #14566526C2semidirect
4. #14563735C2semidirect
6. #14561540C2semidirect
7. C19×#1297C2semidirect
13. #11926586C4semidirect
14. #11926550C4semidirect
173. #1297D19semidirect
273. C19#9366semidirect

Maximal subgroups

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

subgroupindex
#145735762
#145665262
#145644712
#145637352
#145621502
#145615402
C19×#12972
#936619