Finite Group Databasebeta

← #18075064

Subgroups — #18075064

Order 4864.

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

normal subgroups only

This group has 720 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
1C2×#11927165C211yesmaximal, characteristic
2#14562351C212yesmaximal, complemented
3#14562258C212yesmaximal, complemented
4#14561969C211yesmaximal, characteristic, complemented
5C19×#1464C211yesmaximal, characteristic, complemented
6#11927165—24no—
7#11927165—24no—
8C2×#10597315C2211yescharacteristic
9C2×#10597344—21no—
10C2×#10597321C2211yescharacteristic
11C2×#10597331—21no—
12C2×#10597329—21no—
13C2×#10597370C411yescharacteristic
14C2×#10597342—21no—
15C2×#10597376C411yescharacteristic
16C2×C4×Dic38C411yescharacteristic
17C2×C4×D76C411yescharacteristic
18#11926601C2212yes—
19#11926289—24no—
20#11926283—24no—
21#11926270—21no—
22#11926268—21no—
23C2×C19×#117C2211yescharacteristic
24C19×#432C2212yes—
25C19×#324—21no—
26C19×#323—21no—
27C23×C4×C19C2×C411yescharacteristic
28C22×C22⋊D19—21no—
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×Dic38—21no—
32C22×Dic38C2×C411yescharacteristic
33C19×#117—22no—
34C19×#117—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C42×C19C2×C411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C2×C22⋊Dic19—21no—
42#10597376—22no—
43#10597376—22no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19C2×C411yescharacteristic
50C2×C4⋊Dic19C2×C411yescharacteristic
51#10597370—22no—
52#10597370—22no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—21no—
55C2×C4×Dic19—21no—
56#10597344—28no—
57#10597342—28no—
58#10597331—28no—
59#10597329—28no—
60#10597321—22no—
61#10597321D414yes—
62C4×D76—22no—
63C4×D76—22no—
64#10597315—22no—
65#10597315D414yes—
66C4×Dic38—22no—
67C4×Dic38—22no—
68C19×C4⋊C8—22no—
69C19×C22⋊C8—22no—
70C19×#97—22no—
71C22⋊(C19⋊C8)—22no—
72C4⋊(C19⋊C8)—22no—
73#10597260—22no—
74C24×C19C22⋊C411yescharacteristic
75C23×D19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—42no—
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C22×C411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C2×C22⋊D19—24no—
86C2×C22⋊D19—82no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C2×D76—21no—
91C2×D76—42no—
92C2×D76C22⋊C412yes—
93C2×C4×D19—24no—
94C2×C4×D19—82no—
95C2×Dic38—21no—
96C2×Dic38—24no—
97C2×Dic38—42no—
98C2×Dic38—82no—
99C2×Dic38C22⋊C412yes—
100C2×C8×C19—42no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19—22no—
105C42×C19—21no—
106C42×C19—21no—
107C42×C19C2×D412yes—
108C42×C19C2×D412yes—
109C22⋊Dic19—24no—
110(C2×D19)⋊C4—24no—
111(C2×D19)⋊C4—24no—
112(C2×D19)⋊C4—24no—
113(C2×D19)⋊C4—24no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—24no—
117C4⋊Dic19C22⋊C412yes—
118C4⋊Dic19C22⋊C412yes—
119Dic19⋊C4—24no—
120Dic19⋊C4—24no—
121C4×Dic19—24no—
122C2×C19⋊C8—42no—
123#8523—191nomaximal, Sylow
124C23×C19—21no—
125C23×C19—22no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19C2×C22⋊C411yescharacteristic
129C22×D19—22no—
130C22×D19—42no—
131C22×D19—42no—
132C22×D19—42no—
133C2×C4×C19—22no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—22no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19C2×C22⋊C411yescharacteristic
145C2×C4×C19C2×C22⋊C411yescharacteristic
146C2×C4×C19#12012yes—
147C2×C4×C19#12012yes—
148C22⋊D19—84no—
149C2×Dic19—22no—
150C2×Dic19—22no—
151C2×Dic19—22no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155D76—42no—
156D76—42no—
157C4×D19—84no—
158Dic38—42no—
159Dic38—42no—
160Dic38—84no—
161C8×C19—82no—
162C19⋊C8—82no—
163C2×#542—191no—
164#1556—192no—
165#1533—192no—
166#1464—191no—
167#1464D1911yescharacteristic, complemented
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—82no—
174C22×C19#37911yescharacteristic
175C22×C19#41312yes—
176C2×D19—42no—
177C2×D19—42no—
178C2×D19—42no—
179C2×D19—84no—
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19—41no—
187Dic19—42no—
188Dic19—42no—
189Dic19—42no—
190#542—384no—
191#542—384no—
192C2×C4⋊Q8—191no—
193C2×#126—381no—
194C2×#124—191no—
195C2×#124—381no—
196C2×#123—381no—
197C2×C22⋊Q8—191no—
198C2×C22⋊Q8—381no—
199C2×#121—191no—
200C2×C4×Q8—191no—
201C2×C4×D4—191no—
202C2×#117C2×D1911yescharacteristic
203#432—192no—
204#432C2×D1912yes—
205#332—384no—
206#329—384no—
207#324—21no—
208#324—381no—
209#323—21no—
210#323—381no—
211C2×C19—22no—
212C2×C19—81no—
213C2×C19#178511yescharacteristic
214C2×C19#179511yescharacteristic
215C2×C19#179611yescharacteristic
216D19—82no—
217C22×Q8—191no—
218C22×Q8—381no—
219C22×D4—191no—
220C22×D4—381no—
221C23×C4—381no—
222C23×C4C4×D1911yescharacteristic
223C4⋊Q8—194no—
224C4⋊Q8—382no—
225#126—388no—
226#124—194no—
227#124—388no—
228#124—382no—
229#123—388no—
230C22⋊Q8—388no—
231C22⋊Q8—382no—
232C22⋊Q8—382no—
233#121—382no—
234#121—382no—
235C4×Q8—382no—
236C4×Q8—382no—
237C4×D4—382no—
238C4×D4—382no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4D7611yescharacteristic
247C2×C4⋊C4C22⋊D1911yescharacteristic
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—381no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4D7611yescharacteristic
254C2×C22⋊C4C22⋊D1911yescharacteristic
255C2×C42—381no—
256C2×C42C4×D1911yescharacteristic
257C2×C42C22×D1911yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—382no—
260C22⋊C8—22no—
261C22⋊C8—382no—
262#97—22no—
263#97—382no—
264C19#852311yescharacteristic, complemented, Sylow
265C24—381no—
266C24(C2×D19)⋊C411yescharacteristic
267C2×Q8—192no—
268C2×Q8—381no—
269C2×Q8—384no—
270C2×Q8—762no—
271C2×Q8—1522no—
272C2×D4—192no—
273C2×D4—384no—
274C2×D4—381no—
275C2×D4—762no—
276C2×D4—1522no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—384no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4—381no—
284C22×C4—1522no—
285C22×C4(C2×D19)⋊C411yescharacteristic
286C22×C4(C2×D19)⋊C411yescharacteristic
287C22×C4(C2×D19)⋊C411yescharacteristic
288C22×C4C2×C4×D1911yescharacteristic
289C22×C4C2×D7611yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291C2×C8—42no—
292C2×C8—762no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—192no—
296C4⋊C4—192no—
297C4⋊C4—384no—
298C4⋊C4—384no—
299C4⋊C4—384no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—384no—
305C22⋊C4—384no—
306C22⋊C4—384no—
307C22⋊C4—384no—
308C22⋊C4—384no—
309C42—21no—
310C42—21no—
311C42—384no—
312C42D4×D1912yes—
313C42D4×D1912yes—
314C23—21no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—382no—
319C23—762no—
320C23—762no—
321C23—762no—
322C23C2×(C2×D19)⋊C411yescharacteristic
323Q8—762no—
324Q8—762no—
325Q8—1524no—
326D4—762no—
327D4—762no—
328D4—1524no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—382no—
341C2×C4—382no—
342C2×C4—382no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4—762no—
346C2×C4—1524no—
347C2×C4C22⋊C4×D1911yescharacteristic
348C2×C4C22⋊C4×D1911yescharacteristic
349C2×C4#1059732812yes—
350C2×C4#1059738312yes—
351C8—82no—
352C8—1522no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—82no—
359C22—762no—
360C22—762no—
361C22—762no—
362C22—1524no—
363C22#1192639911yescharacteristic
364C22#1192652612yes—
365C4—22no—
366C4—22no—
367C4—21no—
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—762no—
373C4—762no—
374C4—762no—
375C2—22no—
376C2—81no—
377C2—1522no—
378C2#1456356111yescharacteristic
379C2#1456360611yescharacteristic
380C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1464C2
socleC22×C19#379
prime radicalC2×#10597376C4
cosocleC2×C42×C19C23
hypercenter#1464D19
hypocenterC19#8523
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #14562351C2semidirect
3. #14562258C2semidirect
4. #14561969C2semidirect
5. C19×#1464C2semidirect
167. #1464D19semidirect
264. C19#8523semidirect

Maximal subgroups

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

subgroupindex
C2×#119271652
#145623512
#145622582
#145619692
C19×#14642
#852319