Finite Group Databasebeta

← #18080397

Subgroups — #18080397

Order 4864.

518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 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#14572675C211yesmaximal, characteristic
2#14568994C211yesmaximal, characteristic
3#14563624C211yesmaximal, characteristic
4#14562065C211yesmaximal, characteristic, complemented
5#14562063C211yesmaximal, characteristic, complemented
6#14561493C211yesmaximal, characteristic, complemented
7C19×#1286C211yesmaximal, characteristic, complemented
8C2×C4×Dic38C2211yescharacteristic
9C2×C4×D76C2211yescharacteristic
10#11926623—22no—
11#11926621—22no—
12#11926597C2211yescharacteristic
13#11926568C2211yescharacteristic
14C2×#10597280—21no—
15#11926506—22no—
16#11926481C412yes—
17#11926457C412yes—
18#11926445—21no—
19#11926443—21no—
20#11926418—22no—
21#11926312—21no—
22#11926276—22no—
23#11926274—22no—
24C19×#431C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C19×#382C2211yescharacteristic
27C22×D76D411yescharacteristic
28C22×C4×D19D412yes—
29C22×Dic38C2×C411yescharacteristic
30C2×M16×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4C2×C412yes—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4—21no—
40C2×C4×Dic19—21no—
41C2×#64520—21no—
42C2×#64515—24no—
43C4×D76—21no—
44C4×D76—21no—
45C4×D76—21no—
46C4×D76—21no—
47C4×Dic38—21no—
48C4×Dic38—21no—
49C4×Dic38—21no—
50C4×Dic38—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C4×C8×C19D412yes—
56C19×#95—21no—
57C19×#95C2×C412yes—
58C19⋊#95—22no—
59C22⋊(C19⋊C8)—21no—
60#10597280—42no—
61(C2×D19)⋊C8—24no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4×C19⋊C8D412yes—
66C23×D19C22⋊C412yes—
67C22×C4×C19—22no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19C22⋊C412yes—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×C4×D19—22no—
81C2×C4×D19—22no—
82C2×C4×D19—82no—
83C2×Dic38—21no—
84C2×Dic38—21no—
85C2×Dic38—42no—
86M16×C19—41no—
87M16×C19—41no—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C42×C19C2×D411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19#4111yescharacteristic
95C42×C19#4111yescharacteristic
96(C2×D19)⋊C4—22no—
97(C2×D19)⋊C4—22no—
98(C2×D19)⋊C4—44no—
99(C2×D19)⋊C4—82no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19—82no—
105Dic19⋊C4—41no—
106Dic19⋊C4—41no—
107C4×Dic19—41no—
108C4×Dic19—41no—
109#64520—41no—
110#64520—41no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113#64515—84no—
114#9487—191nomaximal, Sylow
115C23×C19C2×C22⋊C411yescharacteristic
116C22×D19—22no—
117C22×D19—22no—
118C22×D19—22no—
119C22×D19—42no—
120C22×D19—42no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19#12011yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12311yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19#13711yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—42no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144D76—41no—
145D76—41no—
146D76—41no—
147D76—41no—
148C4×D19—44no—
149C4×D19—82no—
150Dic38—22no—
151Dic38—22no—
152Dic38—41no—
153Dic38—41no—
154C8×C19—42no—
155C8×C19—81no—
156C19⋊C8—42no—
157C19⋊C8—81no—
158#2975—191no—
159#2580—191no—
160#1800—191no—
161#1487—191no—
162#1487—191no—
163#1286—191no—
164#1286D1911yescharacteristic, complemented
165C22×C19—21no—
166C22×C19—21no—
167C22×C19#38611yescharacteristic
168C22×C19#41711yescharacteristic
169C22×C19#41911yescharacteristic
170C2×D19—44no—
171C2×D19—42no—
172C2×D19—42no—
173C2×D19—42no—
174C2×D19—82no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—82no—
180C4×C19#46811yescharacteristic
181C4×C19#46811yescharacteristic
182C4×C19#47011yescharacteristic
183C4×C19#47011yescharacteristic
184Dic19—42no—
185Dic19—42no—
186Dic19—81no—
187C2×C4×Q8—191no—
188C2×C4×D4—191no—
189#436—382no—
190#436—382no—
191#431—191no—
192#431C2×D1911yescharacteristic
193#423—191no—
194#423C2×D1911yescharacteristic
195C2×#100—381no—
196#407—382no—
197#399—192no—
198#393—192no—
199#390—381no—
200#389—381no—
201#385—382no—
202#382C2×D1911yescharacteristic
203#343—381no—
204Q8⋊C8—382no—
205Q8⋊C8—382no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19#189111yescharacteristic
209C2×C19#189411yescharacteristic
210C2×C19#191111yescharacteristic
211D19—82no—
212C22×Q8—191no—
213C22×D4—191no—
214C23×C4—192no—
215C2×M16—21no—
216C2×M16—384no—
217C2×M16—381no—
218C4×Q8—381no—
219C4×Q8—381no—
220C4×Q8—381no—
221C4×Q8—381no—
222C4×D4—381no—
223C4×D4—381no—
224C4×D4—381no—
225C4×D4—381no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—191no—
228C2×C4⋊C4—191no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—382no—
231C2×C22⋊C4—192no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4—382no—
234C2×C42—381no—
235C2×C42C22×D1911yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—381no—
240C4⋊C8—381no—
241C4⋊C8—381no—
242#100—762no—
243C22⋊C8—21no—
244C22⋊C8—384no—
245C22⋊C8—381no—
246C4×C8—192no—
247C4×C8D7612yes—
248#95—21no—
249#95—382no—
250#95C4×D1912yes—
251C19#948711yescharacteristic, complemented, Sylow
252C24—192no—
253C2×Q8—381no—
254C2×Q8—381no—
255C2×Q8—762no—
256C2×D4—381no—
257C2×D4—381no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C22×C4—22no—
263C22×C4—192no—
264C22×C4—381no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—381no—
268C22×C4—1522no—
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4D4×D1911yescharacteristic
271C22×C4D4×D1911yescharacteristic
272M16—41no—
273M16—41no—
274M16—761no—
275M16—761no—
276M16—1524no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—382no—
280C2×C8—761no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—381no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—1522no—
290C22⋊C4—382no—
291C22⋊C4—382no—
292C22⋊C4—764no—
293C22⋊C4—1522no—
294C42—761no—
295C42—761no—
296C42C2×D7611yescharacteristic
297C42#6454111yescharacteristic
298C42D4×D1911yescharacteristic
299C42#6454511yescharacteristic
300C23—382no—
301C23—382no—
302C23—382no—
303C23—762no—
304C23—762no—
305C23C22⋊C4×D1911yescharacteristic
306Q8—382no—
307Q8—382no—
308Q8—761no—
309Q8—761no—
310D4—761no—
311D4—761no—
312D4—761no—
313D4—761no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—382no—
320C2×C4—382no—
321C2×C4—764no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—762no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—1522no—
329C2×C4C4×D7611yescharacteristic
330C2×C4#1059732811yescharacteristic
331C2×C4#1059733011yescharacteristic
332C2×C4#1059733911yescharacteristic
333C2×C4#1059734011yescharacteristic
334C2×C4#1059734111yescharacteristic
335C2×C4#1059735711yescharacteristic
336C2×C4#1059736111yescharacteristic
337C2×C4#1059736111yescharacteristic
338C2×C4#1059736411yescharacteristic
339C8—42no—
340C8—81no—
341C8—762no—
342C8—1521no—
343C22—21no—
344C22—21no—
345C22—764no—
346C22—762no—
347C22—762no—
348C22—762no—
349C22—1522no—
350C22#1192642211yescharacteristic
351C22#1192654211yescharacteristic
352C22#1192655111yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—82no—
358C4—762no—
359C4—762no—
360C4—1521no—
361C4#1192678911yescharacteristic
362C4#1192679111yescharacteristic
363C4#1192680111yescharacteristic
364C4#1192680311yescharacteristic
365C2—21no—
366C2—21no—
367C2—1522no—
368C2#1456405211yescharacteristic
369C2#1456406711yescharacteristic
370C2#1456416611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1286C2
socleC22×C19#386
prime radicalC22×D76D4
cosocleC2×C42×C19C23
hypercenter#1286D19
hypocenterC19#9487
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
4. #14562065C2semidirect
5. #14562063C2semidirect
6. #14561493C2semidirect
7. C19×#1286C2semidirect
164. #1286D19semidirect
251. C19#9487semidirect

Maximal subgroups

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

subgroupindex
#145726752
#145689942
#145636242
#145620652
#145620632
#145614932
C19×#12862
#948719