Finite Group Databasebeta

← #18075310

Subgroups — #18075310

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563488C211yesmaximal, characteristic, complemented
2#14563488C211yesmaximal, characteristic, complemented
3C2×#11926284C212yesmaximal
4#14561516C212yesmaximal, complemented
5C4×C19×#124C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7C2×C4⋊(C19⋊C8)—21no—
8C2×#10597260C2212yes—
9C2×#10597260C2212yes—
10#11926299—21no—
11#11926299—21no—
12#11926284—24no—
13C2×C19×#124C2211yescharacteristic
14C2×C4×Q8×C19C411yescharacteristic
15C2×C4×D4×C19C411yescharacteristic
16C19×#391C411yescharacteristic
17C19×#390C411yescharacteristic
18C19×#388—21no—
19C19×#388—21no—
20C19×#382C2211yescharacteristic
21C4×C22⋊C4×C19—21no—
22C4×C22⋊C4×C19—21no—
23C43×C19C2211yescharacteristic
24C22×Q8×C19C2×C411yescharacteristic
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19—21no—
27C19×#124—21no—
28C19×#124—21no—
29C19×#124D412yes—
30C19×#124Q812yes—
31C4×Q8×C19—42no—
32C4×D4×C19—42no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C42×C19—21no—
42C2×C42×C19C2×C411yescharacteristic
43C2×C42×C19C2×C411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C42×C19D411yescharacteristic
46C2×C42×C19D411yescharacteristic
47C2×C42×C19D411yescharacteristic
48C2×C42×C19C2311yescharacteristic
49C22×C19⋊C8—22no—
50C22×C19⋊C8—22no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C4⋊(C19⋊C8)—24no—
56C4⋊(C19⋊C8)—24no—
57#10597260—22no—
58#10597260—22no—
59#10597260—22no—
60#10597260—22no—
61C24×C19—21no—
62C2×Q8×C19—21no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19C4⋊C412yes—
66C2×D4×C19—21no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C2×D4×C19C4⋊C412yes—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—42no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—42no—
86C22⋊C4×C19—22no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C42×C19—22no—
94C42×C19—22no—
95C42×C19—22no—
96C42×C19—41no—
97C42×C19—41no—
98C42×C19—41no—
99C42×C19—42no—
100C42×C19C2×D411yescharacteristic
101C42×C19C2×Q811yescharacteristic
102C42×C19#4111yescharacteristic
103C42×C19#4111yescharacteristic
104C2×C19⋊C8—24no—
105C2×C19⋊C8—24no—
106C2×C19⋊C8—42no—
107C2×C19⋊C8—42no—
108C2×C19⋊C8—42no—
109C2×C19⋊C8—42no—
110#8581—191nomaximal, Sylow
111C23×C19—22no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19C2×C22⋊C411yescharacteristic
119Q8×C19—42no—
120Q8×C19—42no—
121D4×C19—42no—
122D4×C19—42no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—22no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—84no—
148C2×C4×C19#10012yes—
149C2×C4×C19#10412yes—
150C2×C4×C19#10412yes—
151C2×C4×C19C2×C4⋊C411yescharacteristic
152C2×C4×C19#11711yescharacteristic
153C2×C4×C19#12111yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19C22⋊Q811yescharacteristic
156C2×C4×C19C22⋊Q811yescharacteristic
157C19⋊C8—44no—
158C19⋊C8—44no—
159C4×#124D1911yescharacteristic
160#1767—191no—
161#1767—191no—
162C2×#329—192no—
163#1295—192no—
164C22×C19—42no—
165C22×C19—42no—
166C22×C19—42no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19—81no—
170C22×C19—81no—
171C22×C19#38011yescharacteristic
172C22×C19C2×#10011yescharacteristic
173C22×C19#41311yescharacteristic
174C22×C19C2×#10411yescharacteristic
175C22×C19C2×#10411yescharacteristic
176C22×C19#42111yescharacteristic
177C22×C19#42111yescharacteristic
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—22no—
185C4×C19—22no—
186C4×C19—22no—
187C4×C19—42no—
188C4×C19—41no—
189C4×C19—81no—
190C4×C19—81no—
191C2×#124C2×D1911yescharacteristic
192C2×C4×Q8Dic1911yescharacteristic
193C2×C4×D4Dic1911yescharacteristic
194C2×C4⋊C8—381no—
195C2×C4⋊C8—381no—
196C2×#97—192no—
197C2×#97—192no—
198#391Dic1911yescharacteristic
199#390Dic1911yescharacteristic
200#388—21no—
201#388—21no—
202#382C2×D1911yescharacteristic
203C4×C22⋊C4—21no—
204C4×C22⋊C4—21no—
205C43C2×D1911yescharacteristic
206#336—381no—
207#336—381no—
208#329—384no—
209C2×C19—82no—
210C2×C19#152411yescharacteristic
211C2×C19#152711yescharacteristic
212C2×C19#153011yescharacteristic
213C2×C19#153511yescharacteristic
214C2×C19#180011yescharacteristic
215C2×C19#180611yescharacteristic
216C2×C19#180611yescharacteristic
217C22×Q8C2×Dic1911yescharacteristic
218C22×D4C2×Dic1911yescharacteristic
219C23×C4—21no—
220C22×C8—382no—
221C22×C8—382no—
222#124—21no—
223#124—21no—
224#124Dic3812yes—
225#124D7612yes—
226C4×Q8—42no—
227C4×D4—42no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C2×Dic1911yescharacteristic
230C2×C4⋊C4C2×Dic1911yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C2×C42C2×Dic1911yescharacteristic
238C2×C42C2×Dic1911yescharacteristic
239C2×C42C22⋊D1911yescharacteristic
240C2×C42C22⋊D1911yescharacteristic
241C2×C42C22⋊D1911yescharacteristic
242C2×C42C22⋊D1911yescharacteristic
243C2×C42C22×D1911yescharacteristic
244C4⋊C8—384no—
245C4⋊C8—384no—
246#97—382no—
247#97—382no—
248#97—382no—
249#97—382no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C19#858111yescharacteristic, complemented, Sylow
255C24—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8C4⋊Dic1912yes—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4C4⋊Dic1912yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C22⋊Dic1911yescharacteristic
271C22×C4C22⋊Dic1911yescharacteristic
272C22×C4C22⋊Dic1911yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C22×C4C22×Dic1911yescharacteristic
275C22×C4C2×C22⋊D1911yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277C2×C8—384no—
278C2×C8—384no—
279C2×C8—762no—
280C2×C8—762no—
281C2×C8—762no—
282C2×C8—762no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42C2×Dic3811yescharacteristic
301C42C2×D7611yescharacteristic
302C42#6454111yescharacteristic
303C42#6454111yescharacteristic
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C22⋊Dic1911yescharacteristic
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4#1059729012yes—
342C2×C4#1059729412yes—
343C2×C4#1059729412yes—
344C2×C4#1059737011yescharacteristic
345C2×C4#1059737011yescharacteristic
346C2×C4C2×C4⋊Dic1911yescharacteristic
347C2×C4#1059737211yescharacteristic
348C2×C4#1059737611yescharacteristic
349C2×C4#1059737611yescharacteristic
350C8—764no—
351C8—764no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#1192640411yescharacteristic
360C22C2×#1059729011yescharacteristic
361C22#1192652811yescharacteristic
362C22C2×#1059729411yescharacteristic
363C22C2×#1059729411yescharacteristic
364C22#1192656111yescharacteristic
365C22#1192656111yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—81no—
378C4—81no—
379C2—82no—
380C2#1456222311yescharacteristic
381C2#1456223311yescharacteristic
382C2#1456224611yescharacteristic
383C2#1456226611yescharacteristic
384C2#1456362711yescharacteristic
385C2#1456365511yescharacteristic
386C2#1456365511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#124C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#124D19
hypocenterC19#8581
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #14563488C2semidirect
2. #14563488C2semidirect
4. #14561516C2semidirect
254. C19#8581semidirect

Maximal subgroups

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

subgroupindex
#145634882
C2×#119262842
#145615162
C4×C19×#1242
#858119