Finite Group Databasebeta

← #18080495

Subgroups — #18080495

Order 4864.

544 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 95 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#14572662C211yesmaximal, characteristic
2#14567937C211yesmaximal, characteristic
3#14563715C211yesmaximal, characteristic, complemented
4#14561971C211yesmaximal, characteristic
5#14561542C211yesmaximal, characteristic, complemented
6#14561540C211yesmaximal, characteristic, complemented
7C19×#1821C211yesmaximal, characteristic, complemented
8C2×#10597375C412yes—
9C2×C4×C22⋊D19C2211yescharacteristic
10#11926618—22no—
11#11926613—22no—
12#11926598—21no—
13#11926508C2211yescharacteristic
14#11926508C2211yescharacteristic
15C22⋊C8×D19—21no—
16#11926475—21no—
17#11926470—21no—
18#11926440—21no—
19#11926407C412yes—
20#11926404C2211yescharacteristic
21#11926401—21no—
22#11926313—22no—
23#11926269—21no—
24#11926267—21no—
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#407C2211yescharacteristic
27C19×#407C2211yescharacteristic
28C19×#343—22no—
29C23×C4×C19C2×C412yes—
30C23×C4×C19C2311yescharacteristic
31C22×C22⋊D19C2×C411yescharacteristic
32C22×C4×D19D411yescharacteristic
33C2×M16×C19—21no—
34C2×M16×C19D412yes—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C22⋊Dic19C2×C411yescharacteristic
42C2×C22⋊Dic19C2×C412yes—
43#10597375—44no—
44C4×C22⋊D19—21no—
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47C4×C22⋊D19—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4D411yescharacteristic
50C2×C4⋊Dic19—21no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4D411yescharacteristic
53C2×C4×Dic19D411yescharacteristic
54C2×#64520—21no—
55C2×#64520D412yes—
56C2×C8×D19—22no—
57C19×C22⋊C8—21no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19⋊#95—21no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68(C2×D19)⋊C8—22no—
69#10597272—22no—
70Dic19⋊C8—22no—
71C24×C19C22×C411yescharacteristic
72C23×D19C22⋊C411yescharacteristic
73C22×C4×C19—22no—
74C22×C4×C19—22no—
75C22×C4×C19—22no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C2×C22⋊D19—21no—
86C2×C22⋊D19—21no—
87C2×C22⋊D19—22no—
88C2×C22⋊D19—41no—
89C22×Dic19—22no—
90C22×Dic19C22⋊C411yescharacteristic
91C22×Dic19C22⋊C411yescharacteristic
92C22×Dic19C22⋊C411yescharacteristic
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×C4×D19—42no—
96M16×C19—42no—
97M16×C19—42no—
98C2×C8×C19—22no—
99C2×C8×C19—41no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C22⋊Dic19—21no—
105C22⋊Dic19—21no—
106C22⋊Dic19—42no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—44no—
110C4⋊Dic19—42no—
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113Dic19⋊C4—44no—
114C4×Dic19—21no—
115C4×Dic19—21no—
116#64520—42no—
117#64520—42no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—41no—
120C8×D19—82no—
121#9507—191nomaximal, Sylow
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19C2×C22⋊C411yescharacteristic
127C23×C19C4×D411yescharacteristic
128C23×C19C4×D411yescharacteristic
129C22×D19—21no—
130C22×D19—21no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19#10012yes—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—82no—
144C2×C4×C19—82no—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12311yescharacteristic
149C22⋊D19—42no—
150C22⋊D19—42no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C4×D19—42no—
162C4×D19—81no—
163C8×C19—42no—
164C8×C19—81no—
165C19⋊C8—42no—
166C19⋊C8—81no—
167#2973—191no—
168#2486—191no—
169#1821—191no—
170#1821D1911yescharacteristic, complemented
171#1465—191no—
172#1305—191no—
173#1305—191no—
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—42no—
183C22×C19—42no—
184C22×C19#38611yescharacteristic
185C22×C19C2×#10011yescharacteristic
186C22×C19#41311yescharacteristic
187C2×D19—22no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—42no—
191C2×D19—81no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—82no—
196C4×C19#45812yes—
197Dic19—41no—
198Dic19—41no—
199Dic19—41no—
200Dic19—82no—
201C2×#123—192no—
202C2×C4×D4—191no—
203C22×C4⋊C4C2×D1911yescharacteristic
204#435—382no—
205#435—382no—
206#432—381no—
207#407—191no—
208#407—191no—
209#407C2×D1911yescharacteristic
210#407C2×D1911yescharacteristic
211C2×C22⋊C8—381no—
212#398—381no—
213#397—381no—
214#389—381no—
215#381—192no—
216#380—191no—
217#380—381no—
218#343—22no—
219#343—382no—
220#324—381no—
221#323—381no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19—41no—
225C2×C19—41no—
226C2×C19#189011yescharacteristic
227C2×C19#190011yescharacteristic
228C2×C19#191511yescharacteristic
229D19—42no—
230C22×D4—191no—
231C23×C4—191no—
232C23×C4C4×D1912yes—
233C23×C4C22×D1911yescharacteristic
234C2×M16—21no—
235C2×M16—192no—
236C2×M16—381no—
237C2×M16C22⋊D1912yes—
238C22×C8—382no—
239#123—764no—
240C4×D4—381no—
241C4×D4—381no—
242C4×D4—381no—
243C4×D4—381no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—191no—
251C2×C4⋊C4—382no—
252C2×C4⋊C4—381no—
253C2×C22⋊C4—191no—
254C2×C22⋊C4—191no—
255C2×C22⋊C4—192no—
256C2×C22⋊C4—382no—
257C2×C42—191no—
258C4⋊C8—382no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—382no—
264C22⋊C8—381no—
265C22⋊C8—381no—
266C22⋊C8—381no—
267C22⋊C8—381no—
268#97—382no—
269#95—382no—
270#95—382no—
271#95—381no—
272C19#950711yescharacteristic, complemented, Sylow
273C24—191no—
274C24C2×C4×D1911yescharacteristic
275C2×D4—382no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—761no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—191no—
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—382no—
291C22×C4—762no—
292C22×C4#6454111yescharacteristic
293C22×C4D4×D1911yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4#6454311yescharacteristic
297C22×C4C2×C22⋊D1911yescharacteristic
298M16—42no—
299M16—42no—
300M16—762no—
301M16—762no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—382no—
305C2×C8—761no—
306C2×C8—1522no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—762no—
314C4⋊C4—764no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—764no—
320C22⋊C4—762no—
321C42—381no—
322C42—381no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—192no—
328C23—381no—
329C23—381no—
330C23—761no—
331C23—761no—
332C23C22⋊C4×D1911yescharacteristic
333C23(C22⋊D19)⋊C411yescharacteristic
334C23C4×C22⋊D1911yescharacteristic
335D4—762no—
336D4—762no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—762no—
354C2×C4—761no—
355C2×C4—761no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—1521no—
360C2×C4#1059732911yescharacteristic
361C2×C4#1059733011yescharacteristic
362C2×C4#1059738311yescharacteristic
363C2×C4#1059738411yescharacteristic
364C8—42no—
365C8—81no—
366C8—762no—
367C8—1521no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—382no—
379C22—762no—
380C22—761no—
381C22—761no—
382C22—1521no—
383C22#1192642011yescharacteristic
384C22#100×D1911yescharacteristic
385C22#1192652511yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—761no—
391C4—761no—
392C4—761no—
393C4—1522no—
394C4#1192673312yes—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—762no—
400C2#1456404511yescharacteristic
401C2#1456409511yescharacteristic
402C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1821C2
socleC22×C19#386
prime radicalC22×C22⋊D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1821D19
hypocenterC19#9507
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
3. #14563715C2semidirect
5. #14561542C2semidirect
6. #14561540C2semidirect
7. C19×#1821C2semidirect
170. #1821D19semidirect
272. C19#9507semidirect

Maximal subgroups

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

subgroupindex
#145726622
#145679372
#145637152
#145619712
#145615422
#145615402
C19×#18212
#950719