Finite Group Databasebeta

← #18083657

Subgroups — #18083657

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926918C211yesmaximal, characteristic
2C2×#11926836C211yesmaximal, characteristic, complemented
3#14568637C211yesmaximal, characteristic
4C2×#11926287C211yesmaximal, characteristic
5C2×#11926274C211yesmaximal, characteristic, complemented
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1987C211yesmaximal, characteristic, complemented
8C22×#64527—22no—
9C2×#10597320C2211yescharacteristic
10C2×#10597321—21no—
11C2×C4×Dic38C2211yescharacteristic
12#11926918—22no—
13#11926918—22no—
14#11926836—22no—
15#11926836—22no—
16C2×#10597264—21no—
17C2×C4⋊(C19⋊C8)C2211yescharacteristic
18C2×#10597267—21no—
19C2×C4×C19⋊C8C2211yescharacteristic
20#11926462—22no—
21#11926446—21no—
22#11926445—22no—
23#11926287—22no—
24#11926274—22no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C4×C4⋊C4×C19C2211yescharacteristic
28C19×#340—22no—
29C22×Q8×C19—21no—
30C22×D76—21no—
31C22×D76—21no—
32C22×D76D412yes—
33C22×Dic38D411yescharacteristic
34C22×C8×C19—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8D412yes—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D412yes—
42C2×C42×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×#64527—28no—
45C2×#64527—48no—
46C2×(C2×D19)⋊C4—24no—
47C2×(C2×D19)⋊C4—24no—
48C2×C4⋊Dic19D411yescharacteristic
49C2×Dic19⋊C4—21no—
50C2×C4×Dic19—21no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—21no—
53#10597321—42no—
54#10597321—42no—
55#10597320—21no—
56#10597320—21no—
57#10597320—21no—
58#10597320—21no—
59C4×Dic38—21no—
60C4×Dic38—21no—
61C4×Dic38—21no—
62C4×Dic38—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×#95—21no—
66#10597267—24no—
67#10597264—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)D412yes—
70C4×C19⋊C8—21no—
71C4×C19⋊C8D412yes—
72C23×D19—22no—
73C2×Q8×C19—22no—
74C2×Q8×C19—44no—
75C2×Q8×C19—41no—
76C22×C4×C19—22no—
77C22×C4×C19—41no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—21no—
82C22×Dic19—21no—
83C2×D76—22no—
84C2×D76—22no—
85C2×D76—44no—
86C2×D76—41no—
87C2×D76—41no—
88C2×D76—41no—
89C2×D76—41no—
90C2×D76—41no—
91C2×D76—42no—
92C2×D76—41no—
93C2×D76—41no—
94C2×D76—42no—
95C2×D76—41no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×Dic38—21no—
99C2×Dic38—21no—
100C2×Dic38—21no—
101C2×Dic38SD1612yescomplemented
102C2×C8×C19—41no—
103C2×C8×C19—42no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C42×C19—41no—
111C42×C19—41no—
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19#4111yescharacteristic
116#64527—416no—
117(C2×D19)⋊C4—48no—
118(C2×D19)⋊C4—84no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
123C4×Dic19—41no—
124C4×Dic19—41no—
125C2×C19⋊C8—24no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130#10055—191nomaximal, Sylow
131C23×C19#12011yescharacteristic
132C22×D19—42no—
133C22×D19—42no—
134C22×D19—44no—
135C22×D19—42no—
136C22×D19—44no—
137Q8×C19—44no—
138Q8×C19—82no—
139C2×C4×C19—22no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—82no—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12711yescharacteristic
151C2×C4×C19C2×SD1611yescharacteristic
152C2×C4×C19#13512yes—
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C19#13712yes—
156C2×C4×C19#13711yescharacteristic
157C2×Dic19—22no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—42no—
162D76—44no—
163D76—82no—
164D76—81no—
165D76—81no—
166D76—82no—
167D76—81no—
168D76—81no—
169D76—81no—
170D76—81no—
171Dic38—22no—
172Dic38—22no—
173Dic38—41no—
174Dic38—41no—
175C8×C19—81no—
176C19⋊C8—24no—
177C19⋊C8—42no—
178C2×#492—191no—
179C2×#477—191no—
180#2548—191no—
181#1987D1911yescharacteristic, complemented
182C2×#331—191no—
183C2×Q8⋊C8—191no—
184#1279—191no—
185C22×C19#39211yescharacteristic
186C22×C19#45011yescharacteristic
187C22×C19#45212yes—
188C22×C19#45211yescharacteristic
189C22×C19#45312yes—
190C2×D19—84no—
191C2×D19—84no—
192C2×D19—82no—
193C2×D19—82no—
194C2×D19—82no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—82no—
198C4×C19—82no—
199C4×C19#44811yescharacteristic
200C4×C19#44911yescharacteristic
201C4×C19#46412yes—
202C4×C19#46511yescharacteristic
203C4×C19#46811yescharacteristic
204C4×C19#49511yescharacteristic
205C4×C19#49711yescharacteristic
206Dic19—42no—
207Dic19—81no—
208C22×SD16—382no—
209C2×C4⋊Q8C2×D1911yescharacteristic
210C2×#127—191no—
211C2×#124—381no—
212C2×C4×Q8—191no—
213#492—382no—
214#492—382no—
215#477—382no—
216#477—382no—
217C2×#107—381no—
218C2×C4⋊C8—191no—
219C2×C4⋊C8C2×D1911yescharacteristic
220C2×#103—381no—
221C2×C4×C8—191no—
222#394—382no—
223#390—381no—
224#390—382no—
225C4×C4⋊C4C2×D1911yescharacteristic
226#340—22no—
227#331—382no—
228Q8⋊C8—382no—
229C2×C19#163012yes—
230C2×C19#163112yes—
231C2×C19#200011yescharacteristic
232C2×C19#200211yescharacteristic
233C2×C19#201511yescharacteristic
234D19—162no—
235C22×Q8—21no—
236C22×Q8—191no—
237C22×D4—192no—
238C22×D4—381no—
239C22×D4—381no—
240C2×SD16—388no—
241C2×SD16—768no—
242C22×C8—21no—
243C22×C8—381no—
244C22×C8—381no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8D7612yes—
249#127—381no—
250#127—381no—
251#127—381no—
252#127—381no—
253#124—762no—
254#124—762no—
255C4×Q8—381no—
256C4×Q8—381no—
257C4×Q8—381no—
258C4×Q8—381no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—191no—
262C2×C4⋊C4—381no—
263C2×C4⋊C4C22⋊D1912yes—
264C2×C22⋊C4—384no—
265C2×C22⋊C4—384no—
266C2×C42—21no—
267C2×C42—381no—
268C2×C42C22×D1911yescharacteristic
269#107—384no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—192no—
273C4⋊C8—381no—
274#103—384no—
275C4×C8—192no—
276C4×C8—381no—
277#95—21no—
278C19#1005511yescharacteristic, complemented, Sylow
279C24—382no—
280C2×Q8—22no—
281C2×Q8—44no—
282C2×Q8—41no—
283C2×Q8—192no—
284C2×Q8—381no—
285C2×Q8—381no—
286C2×Q8—381no—
287C2×Q8—381no—
288C2×Q8—381no—
289C2×D4—382no—
290C2×D4—382no—
291C2×D4—764no—
292C2×D4—761no—
293C2×D4—761no—
294C2×D4—762no—
295C2×D4—762no—
296C2×D4—761no—
297C2×D4—761no—
298C2×D4—761no—
299C2×D4—761no—
300C2×D4—761no—
301C2×D4—761no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4D4×D1911yescharacteristic
307C22×C4D4×D1911yescharacteristic
308C22×C4C2×C22⋊D1911yescharacteristic
309SD16—7616no—
310C2×C8—41no—
311C2×C8—42no—
312C2×C8—384no—
313C2×C8—382no—
314C2×C8—382no—
315C2×C8—761no—
316C2×C8—761no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—761no—
326C4⋊C4—761no—
327C22⋊C4—768no—
328C22⋊C4—1524no—
329C42—41no—
330C42—41no—
331C42—761no—
332C42—761no—
333C42C2×D7611yescharacteristic
334C42#6454111yescharacteristic
335C42D4×D1911yescharacteristic
336C42D4×D1911yescharacteristic
337C23—762no—
338C23—764no—
339C23—762no—
340C23—762no—
341C23—764no—
342C23#1059738311yescharacteristic
343Q8—44no—
344Q8—82no—
345Q8—382no—
346Q8—382no—
347Q8—761no—
348Q8—761no—
349D4—764no—
350D4—1522no—
351D4—1521no—
352D4—1521no—
353D4—1521no—
354D4—1521no—
355D4—1521no—
356D4—1522no—
357D4—1521no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—382no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—762no—
369C2×C4#1059732811yescharacteristic
370C2×C4#1059732811yescharacteristic
371C2×C4#1059733011yescharacteristic
372C2×C4#1059733011yescharacteristic
373C2×C4SD16×D1911yescharacteristic
374C2×C4#1059736011yescharacteristic
375C2×C4#1059736411yescharacteristic
376C2×C4#1059736511yescharacteristic
377C2×C4#1059737611yescharacteristic
378C2×C4#1059738611yescharacteristic
379C2×C4#1059738812yes—
380C2×C4#1059739612yes—
381C8—81no—
382C8—384no—
383C8—762no—
384C22—1522no—
385C22—1522no—
386C22—1522no—
387C22—1524no—
388C22—1524no—
389C22#1192645311yescharacteristic
390C22#1192669311yescharacteristic
391C22#1192670412yes—
392C22#1192670511yescharacteristic
393C22#1192671012yes—
394C4—21no—
395C4—21no—
396C4—82no—
397C4—82no—
398C4—762no—
399C4—1521no—
400C4#1192668411yescharacteristic
401C4#1192669211yescharacteristic
402C4#1192676612yes—
403C4#1192677611yescharacteristic
404C4#1192679311yescharacteristic
405C4#1192692611yescharacteristic
406C4#1192693611yescharacteristic
407C2—3042no—
408C2#1456275512yes—
409C2#1456276112yes—
410C2#1456463711yescharacteristic
411C2#1456465111yescharacteristic
412C2#1456472811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1987C2
socleC23×C19#120
prime radicalC2×#10597320C22
hypercenter#1987D19
hypocenterC19#10055
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
2. C2×#11926836C2semidirect
5. C2×#11926274C2semidirect
6. #14561476C2semidirect
7. C19×#1987C2semidirect
101. C2×Dic38SD16semidirect
181. #1987D19semidirect
278. C19#10055semidirect

Maximal subgroups

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

subgroupindex
C2×#119269182
C2×#119268362
#145686372
C2×#119262872
C2×#119262742
#145614762
C19×#19872
#1005519