Finite Group Databasebeta

← #18078263

Subgroups — #18078263

Order 4864.

694 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571975C211yesmaximal, characteristic
2C2×#11926389C211yesmaximal, characteristic
3#14563701C211yesmaximal, characteristic
4C2×#11926282C211yesmaximal, characteristic
5C2×#11926280C211yesmaximal, characteristic
6#14561513C211yesmaximal, characteristic
7C19×#1294C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×C4×Dic19—21no—
10C22×C4×Dic19C2211yescharacteristic
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926449C412yescomplemented
13#11926443C412yescomplemented
14#11926429—22no—
15#11926419—21no—
16#11926405—21no—
17#11926389—22no—
18#11926389—22no—
19C2×C19⋊#95—21no—
20C2×C19⋊#95C2211yescharacteristic
21#11926298—22no—
22#11926282—22no—
23#11926280—22no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C2×C19×#95C2211yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C23×Dic19—21no—
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C22×Dic38C2×C411yescharacteristic
33C22×C8×C19—21no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊Dic19—21no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39#10597370—21no—
40#10597370—21no—
41#10597370—21no—
42#10597370—21no—
43C2×Dic19⋊C4—21no—
44C2×C4×Dic19—24no—
45C2×C4×Dic19—28no—
46C2×C4×Dic19—21no—
47C2×C4×Dic19—21no—
48C2×C4×Dic19—21no—
49C2×C4×Dic19—21no—
50C2×C4×Dic19C2×C412yes—
51C2×C4×Dic19D412yes—
52C22×C19⋊C8—21no—
53C19×C22⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19×#95D412yes—
58C19⋊#95—24no—
59C19⋊#95—21no—
60C19⋊#95—22no—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C24×C19C2×D411yescharacteristic
67C22×C4×C19—24no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—24no—
83C22×Dic19—24no—
84C22×Dic19—22no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—42no—
94C22×Dic19—41no—
95C22×Dic19—41no—
96C22×Dic19C22⋊C412yes—
97C22×Dic19C22⋊C412yes—
98C2×Dic38—21no—
99C2×Dic38—21no—
100C2×Dic38—42no—
101C2×C8×C19—42no—
102C2×C8×C19—41no—
103C4⋊C4×C19—42no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊Dic19—41no—
107C22⋊Dic19—41no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110C4⋊Dic19—44no—
111Dic19⋊C4—41no—
112Dic19⋊C4—41no—
113C4×Dic19—216no—
114C4×Dic19—22no—
115C4×Dic19—22no—
116C4×Dic19—22no—
117C4×Dic19—22no—
118C2×C19⋊C8—42no—
119C2×C19⋊C8—41no—
120#9145—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19—22no—
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19#12011yescharacteristic
125C23×C19#12311yescharacteristic
126C23×C19#13511yescharacteristic
127C23×C19#13511yescharacteristic
128C23×C19#13711yescharacteristic
129C23×C19#13711yescharacteristic
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—24no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—44no—
139C2×C4×C19—44no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19C4×D411yescharacteristic
145C2×C4×C19C4×D411yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×Dic19—24no—
149C2×Dic19—24no—
150C2×Dic19—22no—
151C2×Dic19—22no—
152C2×Dic19—24no—
153C2×Dic19—22no—
154C2×Dic19—22no—
155C2×Dic19—22no—
156C2×Dic19—42no—
157C2×Dic19—44no—
158C2×Dic19—44no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—42no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19#10414yes—
169Dic38—81no—
170Dic38—81no—
171C8×C19—81no—
172C19⋊C8—81no—
173#2855—191no—
174C2×#376—191no—
175#1817—191no—
176C2×#328—191no—
177C2×#328—191no—
178#1294—191no—
179#1294D1911yescharacteristic
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—22no—
185C22×C19—22no—
186C22×C19—22no—
187C22×C19—22no—
188C22×C19#38611yescharacteristic
189C22×C19#41012yes—
190C22×C19#41611yescharacteristic
191C22×C19#41911yescharacteristic
192C22×C19C2×#10412yes—
193C22×C19#45211yescharacteristic
194C22×C19#45211yescharacteristic
195C22×C19#48511yescharacteristic
196C22×C19#48511yescharacteristic
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—44no—
202C4×C19—82no—
203Dic19—24no—
204Dic19—44no—
205Dic19—42no—
206Dic19—81no—
207Dic19—81no—
208C2×C22⋊Q8—191no—
209C22×C42—191no—
210C22×C42—381no—
211C2×C22⋊C8—191no—
212C2×C22⋊C8C2×D1911yescharacteristic
213#391—192no—
214#389—192no—
215#387—382no—
216#385—381no—
217#381—381no—
218#380C2×D1911yescharacteristic
219#376—382no—
220#376—382no—
221C2×#95—191no—
222C2×#95—381no—
223C2×#95C2×D1911yescharacteristic
224#336—382no—
225#328—382no—
226#328—382no—
227C2×C19—21no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19#150012yes—
232C2×C19#150612yes—
233C2×C19#187311yescharacteristic
234C2×C19#189611yescharacteristic
235C2×C19#189911yescharacteristic
236C22×Q8—191no—
237C23×C4—21no—
238C23×C4—191no—
239C23×C4—191no—
240C23×C4—381no—
241C23×C4C22×D1911yescharacteristic
242C22×C8—21no—
243C22×C8—381no—
244C22⋊Q8—381no—
245C22⋊Q8—381no—
246C22⋊Q8—381no—
247C22⋊Q8—381no—
248C2×C4⋊C4—191no—
249C2×C4⋊C4—382no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4C4×D1912yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—381no—
254C2×C42—192no—
255C2×C42—192no—
256C2×C42—384no—
257C2×C42—388no—
258C2×C42—381no—
259C2×C42—381no—
260C2×C42—381no—
261C2×C42—381no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—381no—
265C22⋊C8—381no—
266#95—21no—
267#95—21no—
268#95—192no—
269#95—382no—
270#95—382no—
271#95—382no—
272#95—384no—
273#95—381no—
274#95D7612yes—
275C19#914511yescharacteristic, complemented, Sylow
276C24D4×D1911yescharacteristic
277C2×Q8—381no—
278C2×Q8—381no—
279C2×Q8—762no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—192no—
288C22×C4—192no—
289C22×C4—384no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—384no—
293C22×C4—382no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—381no—
299C22×C4—381no—
300C22×C4—381no—
301C22×C4—381no—
302C22×C4—762no—
303C22×C4—761no—
304C22×C4—761no—
305C22×C4C2×C4×D1911yescharacteristic
306C22×C4C2×D7611yescharacteristic
307C22×C4#6454111yescharacteristic
308C22×C4D4×D1911yescharacteristic
309C22×C4D4×D1911yescharacteristic
310C22×C4#6454511yescharacteristic
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—762no—
314C2×C8—761no—
315C4⋊C4—42no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—764no—
319C4⋊C4—761no—
320C4⋊C4—761no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—761no—
324C22⋊C4—761no—
325C42—3816no—
326C42—382no—
327C42—382no—
328C42—382no—
329C42—382no—
330C23—22no—
331C23—22no—
332C23C22⋊C4×D1911yescharacteristic
333C23#1059732811yescharacteristic
334C23#1059734011yescharacteristic
335C23#1059735811yescharacteristic
336C23#1059736111yescharacteristic
337C23#1059736211yescharacteristic
338C23#1059736411yescharacteristic
339Q8—1521no—
340Q8—1521no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—194no—
356C2×C4—384no—
357C2×C4—384no—
358C2×C4—382no—
359C2×C4—382no—
360C2×C4—384no—
361C2×C4—382no—
362C2×C4—382no—
363C2×C4—382no—
364C2×C4—764no—
365C2×C4—764no—
366C2×C4—762no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—762no—
376C2×C4C4×D7611yescharacteristic
377C2×C4#1059733011yescharacteristic
378C2×C4#1059733911yescharacteristic
379C2×C4#1059734111yescharacteristic
380C8—81no—
381C8—1521no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22#1192642211yescharacteristic
391C22#1192651612yes—
392C22#1192653711yescharacteristic
393C22#1192655111yescharacteristic
394C22#104×D1912yes—
395C22#1192670711yescharacteristic
396C22#1192670911yescharacteristic
397C22#1192688711yescharacteristic
398C22#1192688811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—384no—
406C4—764no—
407C4—762no—
408C4—1521no—
409C4—1521no—
410C2—21no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2#1456211812yes—
415C2#1456214512yes—
416C2#1456394611yescharacteristic
417C2#1456407711yescharacteristic
418C2#1456409211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#9145
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
12. #11926449C4semidirect
13. #11926443C4semidirect
275. C19#9145semidirect

Maximal subgroups

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

subgroupindex
#145719752
C2×#119263892
#145637012
C2×#119262822
C2×#119262802
#145615132
C19×#12942
#914519