Finite Group Databasebeta

← #18080412

Subgroups — #18080412

Order 4864.

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

normal subgroups only

This group has 522 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#14572718C211yesmaximal, characteristic, complemented
2#14568545C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic, complemented
4#14562061C211yesmaximal, characteristic
5#14562059C211yesmaximal, characteristic
6#14561493C211yesmaximal, characteristic, complemented
7C19×#1286C211yesmaximal, characteristic, complemented
8C2×#10597343—21no—
9C2×C4×Dic38C2211yescharacteristic
10C2×C4×D76C2211yescharacteristic
11#11926674—22no—
12#11926671—22no—
13#11926598—22no—
14#11926597C2211yescharacteristic
15#11926568C2211yescharacteristic
16C2×#10597281—21no—
17#11926476C412yes—
18#11926462C412yes—
19#11926436—22no—
20#11926401—21no—
21#11926312—21no—
22#11926273—22no—
23#11926271—22no—
24C19×#431C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C19×#382C2211yescharacteristic
27C22×D76C2×C411yescharacteristic
28C22×C4×D19—21no—
29C22×Dic38D411yescharacteristic
30C2×M16×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4C2×C412yes—
40C2×C4×Dic19D412yes—
41C2×#64520—21no—
42#10597343—42no—
43#10597343—42no—
44C4×D76—21no—
45C4×D76—21no—
46C4×D76—21no—
47C4×D76—21no—
48C4×Dic38—21no—
49C4×Dic38—21no—
50C4×Dic38—21no—
51C4×Dic38—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C22⋊C8—21no—
56C4×C8×C19D412yes—
57C19×#95—21no—
58C19×#95C2×C412yes—
59C19⋊#95—22no—
60C22⋊(C19⋊C8)—21no—
61#10597281—42no—
62#10597272—24no—
63Dic19⋊C8—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4×C19⋊C8D412yes—
68C23×D19—21no—
69C22×C4×C19—22no—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19C22⋊C412yes—
75C22×Dic19C22⋊C412yes—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76—42no—
79C2×C4×D19—41no—
80C2×C4×D19—41no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×C4×D19—41no—
84C2×C4×D19—41no—
85C2×Dic38—21no—
86C2×Dic38—21no—
87C2×Dic38—21no—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91M16×C19—41no—
92M16×C19—41no—
93C2×C8×C19—22no—
94C2×C8×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19#4111yescharacteristic
100C42×C19#4111yescharacteristic
101(C2×D19)⋊C4—44no—
102(C2×D19)⋊C4—44no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—41no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—44no—
110Dic19⋊C4—22no—
111Dic19⋊C4—22no—
112C4×Dic19—22no—
113C4×Dic19—22no—
114#64520—41no—
115#64520—41no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—41no—
118#9490—191nomaximal, Sylow
119C23×C19C2×C22⋊C411yescharacteristic
120C22×D19—22no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12311yescharacteristic
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—22no—
143C2×Dic19—22no—
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—42no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150D76—22no—
151D76—22no—
152D76—41no—
153D76—41no—
154C4×D19—81no—
155C4×D19—81no—
156C4×D19—81no—
157C4×D19—81no—
158Dic38—41no—
159Dic38—41no—
160Dic38—41no—
161Dic38—41no—
162C8×C19—42no—
163C8×C19—81no—
164C19⋊C8—42no—
165C19⋊C8—81no—
166#2983—191no—
167#2536—191no—
168#1801—191no—
169#1486—191no—
170#1486—191no—
171#1286—191no—
172#1286D1911yescharacteristic, complemented
173C22×C19—21no—
174C22×C19—21no—
175C22×C19#38611yescharacteristic
176C22×C19#41711yescharacteristic
177C22×C19#41811yescharacteristic
178C2×D19—42no—
179C2×D19—42no—
180C2×D19—42no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—82no—
190C4×C19#46811yescharacteristic
191C4×C19#46811yescharacteristic
192C4×C19#46911yescharacteristic
193C4×C19#46911yescharacteristic
194Dic19—42no—
195Dic19—42no—
196Dic19—81no—
197C2×C22⋊Q8—381no—
198C2×C4×Q8—191no—
199C2×C4×D4—191no—
200#446—382no—
201#446—382no—
202#432—382no—
203#431—191no—
204#431C2×D1911yescharacteristic
205#423—191no—
206#423C2×D1911yescharacteristic
207C2×#101—381no—
208#398—192no—
209#394—192no—
210#388—382no—
211#382C2×D1911yescharacteristic
212#380—381no—
213#343—381no—
214D4⋊C8—382no—
215D4⋊C8—382no—
216C2×C19—21no—
217C2×C19—21no—
218C2×C19#189111yescharacteristic
219C2×C19#189511yescharacteristic
220C2×C19#191211yescharacteristic
221D19—82no—
222C22×Q8—191no—
223C22×D4—191no—
224C23×C4—381no—
225C2×M16—21no—
226C2×M16—381no—
227C22⋊Q8—762no—
228C22⋊Q8—762no—
229C4×Q8—381no—
230C4×Q8—381no—
231C4×Q8—381no—
232C4×Q8—381no—
233C4×D4—381no—
234C4×D4—381no—
235C4×D4—381no—
236C4×D4—381no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—192no—
239C2×C4⋊C4—191no—
240C2×C4⋊C4—191no—
241C2×C4⋊C4—382no—
242C2×C22⋊C4—382no—
243C2×C22⋊C4—382no—
244C2×C22⋊C4—381no—
245C2×C42—192no—
246C2×C42C22×D1911yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—384no—
251C4⋊C8—381no—
252C4⋊C8—381no—
253C4⋊C8—381no—
254#101—762no—
255C22⋊C8—21no—
256C22⋊C8—381no—
257#97—384no—
258C4×C8—192no—
259C4×C8D7612yes—
260#95—21no—
261#95—382no—
262#95C4×D1912yes—
263C19#949011yescharacteristic, complemented, Sylow
264C24—381no—
265C2×Q8—381no—
266C2×Q8—381no—
267C2×Q8—381no—
268C2×Q8—381no—
269C2×Q8—381no—
270C2×Q8—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—762no—
274C22×C4—22no—
275C22×C4—192no—
276C22×C4—192no—
277C22×C4—381no—
278C22×C4—761no—
279C22×C4—761no—
280C22×C4—761no—
281C22×C4—761no—
282C22×C4—761no—
283C22×C4—761no—
284C22×C4C2×C4×D1911yescharacteristic
285C22×C4D4×D1911yescharacteristic
286C22×C4D4×D1911yescharacteristic
287M16—41no—
288M16—41no—
289M16—761no—
290M16—761no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—382no—
294C2×C8—761no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—382no—
298C4⋊C4—381no—
299C4⋊C4—382no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C4⋊C4—381no—
303C4⋊C4—764no—
304C22⋊C4—764no—
305C22⋊C4—764no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C42—382no—
309C42—382no—
310C42C2×D7611yescharacteristic
311C42#6454111yescharacteristic
312C42D4×D1911yescharacteristic
313C42#6454511yescharacteristic
314C23—382no—
315C23—761no—
316C23—761no—
317C23—761no—
318C23—761no—
319C23—761no—
320C23—761no—
321C23C22⋊C4×D1911yescharacteristic
322Q8—761no—
323Q8—761no—
324Q8—761no—
325Q8—761no—
326D4—382no—
327D4—382no—
328D4—761no—
329D4—761no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—382no—
336C2×C4—382no—
337C2×C4—382no—
338C2×C4—382no—
339C2×C4—762no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—1521no—
344C2×C4—1521no—
345C2×C4—1521no—
346C2×C4—1521no—
347C2×C4C4×D7611yescharacteristic
348C2×C4#1059732811yescharacteristic
349C2×C4#1059733011yescharacteristic
350C2×C4#1059733911yescharacteristic
351C2×C4#1059734011yescharacteristic
352C2×C4#1059734111yescharacteristic
353C2×C4#1059735711yescharacteristic
354C2×C4#1059736011yescharacteristic
355C2×C4#1059736011yescharacteristic
356C2×C4#1059736411yescharacteristic
357C8—42no—
358C8—81no—
359C8—762no—
360C8—1521no—
361C22—21no—
362C22—21no—
363C22—762no—
364C22—762no—
365C22—762no—
366C22—1521no—
367C22—1521no—
368C22—1521no—
369C22—1521no—
370C22#1192642211yescharacteristic
371C22#1192654411yescharacteristic
372C22#1192654711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—762no—
379C4—762no—
380C4—1521no—
381C4#1192679111yescharacteristic
382C4#1192679311yescharacteristic
383C4#1192679611yescharacteristic
384C4#1192679811yescharacteristic
385C2—21no—
386C2—21no—
387C2—1522no—
388C2#1456405211yescharacteristic
389C2#1456407211yescharacteristic
390C2#1456417111yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1286C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1286D19
hypocenterC19#9490
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
1. #14572718C2semidirect
3. #14563628C2semidirect
6. #14561493C2semidirect
7. C19×#1286C2semidirect
172. #1286D19semidirect
263. C19#9490semidirect

Maximal subgroups

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

subgroupindex
#145727182
#145685452
#145636282
#145620612
#145620592
#145614932
C19×#12862
#949019