Finite Group Databasebeta

← #18083788

Subgroups — #18083788

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926821C211yesmaximal, characteristic
2#14568631C211yesmaximal, characteristic
3#14564559C211yesmaximal, characteristic, complemented
4C2×#11926290C211yesmaximal, characteristic, complemented
5C2×#11926273C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic, complemented
7C2×C19×#498C211yesmaximal, characteristic, complemented
8C2×#10597393—21no—
9C2×C4×D76C2211yescharacteristic
10#11926821—22no—
11#11926821—22no—
12C2×#10597264—21no—
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×#10597292—22no—
16C2×#10597266—21no—
17#11926470—22no—
18#11926451—21no—
19#11926401—22no—
20C4×C4⋊Dic19C2211yescharacteristic
21#11926290—22no—
22#11926273—22no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×C4⋊Q8C2211yescharacteristic
25C19×#498—22no—
26C19×#498—22no—
27C2×C19×#106—22no—
28C2×C4×C8×C19C2211yescharacteristic
29C22×Q8×C19—21no—
30C22×Q8×C19—21no—
31C22×D76D411yescharacteristic
32C22×C4×D19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8—21no—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8—21no—
41C19×C4⋊Q8D412yes—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D412yes—
46C2×C42×C19C2311yescharacteristic
47#10597393—42no—
48#10597393—42no—
49C2×(C2×D19)⋊C4—24no—
50C2×(C2×D19)⋊C4—21no—
51C2×C4⋊Dic19D412yes—
52C2×C4⋊Dic19D411yescharacteristic
53C2×C4×Dic19—21no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56C4×D76—21no—
57C4×D76—21no—
58C4×D76—21no—
59C4×D76—21no—
60C19×#106—28no—
61C4×C8×C19—21no—
62C4×C8×C19D412yes—
63#10597292—44no—
64C19⋊#95—24no—
65C19⋊#95—21no—
66#10597266—24no—
67#10597264—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)D412yes—
72C23×D19—21no—
73C2×Q8×C19—22no—
74C2×Q8×C19—41no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—42no—
82C2×Q8×C19—42no—
83C22×C4×C19—22no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×Dic19—21no—
89C22×Dic19—22no—
90C2×D76—21no—
91C2×D76—21no—
92C2×D76—21no—
93C2×D76—21no—
94C2×D76—21no—
95C2×D76SD1612yes—
96C2×C4×D19—41no—
97C2×C4×D19—41no—
98C2×C4×D19—42no—
99C2×C4×D19—42no—
100C2×C8×C19—24no—
101C2×C8×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19#4111yescharacteristic
114(C2×D19)⋊C4—48no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—22no—
120C4⋊Dic19—22no—
121C4×Dic19—41no—
122C4×Dic19—41no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—42no—
128#10074—191nomaximal, Sylow
129C23×C19#12011yescharacteristic
130C22×D19—22no—
131C22×D19—41no—
132C22×D19—42no—
133C22×D19—41no—
134C22×D19—42no—
135Q8×C19—44no—
136Q8×C19—81no—
137Q8×C19—81no—
138Q8×C19—81no—
139Q8×C19—81no—
140Q8×C19—81no—
141Q8×C19—81no—
142C2×C4×C19—22no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—82no—
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12011yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×C4×C19#12711yescharacteristic
154C2×C4×C19C2×SD1611yescharacteristic
155C2×C4×C19#13511yescharacteristic
156C2×C4×C19#13512yes—
157C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C19AGL(1,ℤ/8)12yes—
159C2×C4×C19#13711yescharacteristic
160C2×Dic19—41no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165D76—22no—
166D76—22no—
167D76—41no—
168D76—41no—
169C4×D19—82no—
170C4×D19—81no—
171C4×D19—81no—
172C8×C19—24no—
173C19⋊C8—42no—
174C19⋊C8—81no—
175C2×#498D1911yescharacteristic, complemented
176C2×#474—191no—
177#2547—191no—
178#1981—191no—
179C2×#332—191no—
180C2×D4⋊C8—191no—
181#1279—191no—
182C22×C19#39211yescharacteristic
183C22×C19#44912yes—
184C22×C19#45011yescharacteristic
185C22×C19#45211yescharacteristic
186C22×C19#45612yes—
187C2×D19—44no—
188C2×D19—42no—
189C2×D19—82no—
190C2×D19—81no—
191C2×D19—81no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—82no—
195C4×C19—82no—
196C4×C19#44811yescharacteristic
197C4×C19#44911yescharacteristic
198C4×C19#46312yes—
199C4×C19#46511yescharacteristic
200C4×C19#46811yescharacteristic
201C4×C19#49511yescharacteristic
202C4×C19#49611yescharacteristic
203Dic19—82no—
204Dic19—81no—
205C2×C4⋊Q8C2×D1911yescharacteristic
206C2×C4⋊Q8C2×D1911yescharacteristic
207C2×#124—381no—
208C2×C4×D4—191no—
209#498—22no—
210#498—22no—
211#474—382no—
212#474—382no—
213C2×#107—381no—
214C2×#106—22no—
215C2×C4⋊C8—191no—
216C2×C4⋊C8—191no—
217C2×#103—382no—
218C2×#102—381no—
219C2×C4×C8C2×D1911yescharacteristic
220#397—382no—
221#391—381no—
222#380—382no—
223C4×C4⋊C4—191no—
224#332—382no—
225D4⋊C8—382no—
226C2×C19#165212yes—
227C2×C19#165412yes—
228C2×C19#200011yescharacteristic
229C2×C19#200511yescharacteristic
230C2×C19#201211yescharacteristic
231D19—82no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×D4—191no—
235C23×C4—381no—
236C22×C8—21no—
237C22×C8—381no—
238C22×C8—381no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8C22⋊D1912yes—
247#124—762no—
248#124—762no—
249C4×D4—381no—
250C4×D4—381no—
251C4×D4—381no—
252C4×D4—381no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—191no—
257C2×C4⋊C4—192no—
258C2×C4⋊C4C22⋊D1912yes—
259C2×C22⋊C4—384no—
260C2×C22⋊C4—381no—
261C2×C42—381no—
262C2×C42C22×D1911yescharacteristic
263#107—384no—
264#106—28no—
265C4⋊C8—192no—
266C4⋊C8—381no—
267C4⋊C8—381no—
268C4⋊C8—381no—
269#103—764no—
270#102—384no—
271C4×C8—21no—
272C4×C8C22⋊D1912yes—
273#95—384no—
274#95—381no—
275C19#1007411yescharacteristic, complemented, Sylow
276C24—381no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×D4—192no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—381no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—381no—
296C22×C4—382no—
297C22×C4—761no—
298C22×C4—761no—
299C22×C4—762no—
300C22×C4—762no—
301C22×C4D4×D1911yescharacteristic
302C22×C4D4×D1911yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304C2×C8—24no—
305C2×C8—22no—
306C2×C8—382no—
307C2×C8—761no—
308C2×C8—761no—
309C2×C8—761no—
310C2×C8—762no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—381no—
320C4⋊C4—381no—
321C4⋊C4—382no—
322C4⋊C4—382no—
323C22⋊C4—768no—
324C22⋊C4—761no—
325C22⋊C4—761no—
326C42—761no—
327C42—761no—
328C42D4×D1911yescharacteristic
329C42#6454311yescharacteristic
330C42C2×C22⋊D1911yescharacteristic
331C42C2×C22⋊D1911yescharacteristic
332C23—382no—
333C23—762no—
334C23—761no—
335C23—761no—
336C23—762no—
337C23#1059738311yescharacteristic
338Q8—44no—
339Q8—81no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—382no—
346D4—382no—
347D4—761no—
348D4—761no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—761no—
359C2×C4—762no—
360C2×C4—1521no—
361C2×C4—1521no—
362C2×C4—1522no—
363C2×C4SD16×D1911yescharacteristic
364C2×C4#1059736011yescharacteristic
365C2×C4#1059736012yes—
366C2×C4#1059736111yescharacteristic
367C2×C4#1059736212yes—
368C2×C4#1059736211yescharacteristic
369C2×C4#1059738311yescharacteristic
370C2×C4#1059738411yescharacteristic
371C2×C4#1059738511yescharacteristic
372C2×C4#1059738511yescharacteristic
373C2×C4#1059738611yescharacteristic
374C2×C4#1059739911yescharacteristic
375C8—24no—
376C8—762no—
377C8—1521no—
378C22—762no—
379C22—764no—
380C22—1521no—
381C22—1522no—
382C22—1521no—
383C22#1192645211yescharacteristic
384C22#1192668812yes—
385C22#1192669311yescharacteristic
386C22#1192670311yescharacteristic
387C22#1192672612yes—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—82no—
392C4—1522no—
393C4—1521no—
394C4#1192668111yescharacteristic
395C4#1192668811yescharacteristic
396C4#1192676112yes—
397C4#1192677011yescharacteristic
398C4#1192678711yescharacteristic
399C4#1192692511yescharacteristic
400C4#1192693011yescharacteristic
401C2—1522no—
402C2#1456290212yes—
403C2#1456291612yes—
404C2#1456463511yescharacteristic
405C2#1456467111yescharacteristic
406C2#1456470911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#498C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenterC2×#498D19
hypocenterC19#10074
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #14564559C2semidirect
4. C2×#11926290C2semidirect
6. #14561475C2semidirect
7. C2×C19×#498C2semidirect
175. C2×#498D19semidirect
275. C19#10074semidirect

Maximal subgroups

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

subgroupindex
C2×#119268212
#145686312
#145645592
C2×#119262902
C2×#119262732
#145614752
C2×C19×#4982
#1007419