Finite Group Databasebeta

← #18085124

Subgroups — #18085124

Order 4864.

542 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926895C211yesmaximal, characteristic
2C2×#11926830C211yesmaximal, characteristic
3C2×#11926755C211yesmaximal, characteristic
4#14564571C211yesmaximal, characteristic
5C2×#11926291C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C19×#1277C211yesmaximal, characteristic
8C22×Dic76—21no—
9C2×#10597315C2211yescharacteristic
10C2×#10597315C2211yescharacteristic
11C2×C4×Dic38C2211yescharacteristic
12#11926895—22no—
13#11926895—22no—
14#11926830—22no—
15#11926830—22no—
16#11926755—22no—
17#11926755—22no—
18C2×#10597274—21no—
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597273—21no—
21C2×#10597273—21no—
22C2×#10597273—22no—
23#11926298—22no—
24#11926291—22no—
25#11926289—22no—
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C4×C8×C19C2211yescharacteristic
29C22×Dic38—21no—
30C22×Dic38—21no—
31C22×Dic38D411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C22×C8×C19D412yes—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19D411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44C2×Dic76—24no—
45C2×Dic76—42no—
46C2×Dic76—42no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315D412yes—
54#10597315D412yes—
55C4×Dic38—21no—
56C4×Dic38—21no—
57C4×Dic38—21no—
58C4×Dic38—21no—
59C19×C4⋊C8—21no—
60C19×C4⋊C8—21no—
61C19×C4⋊C8D412yes—
62C19×C4⋊C8D412yes—
63C4×C8×C19—21no—
64C4×C8×C19—21no—
65#10597274—24no—
66#10597273—24no—
67#10597273—28no—
68#10597273—24no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—21no—
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×Dic38—22no—
84C2×Dic38—22no—
85C2×Dic38—41no—
86C2×Dic38—42no—
87C2×Dic38—41no—
88C2×Dic38—41no—
89C2×Dic38—42no—
90C2×Dic38—41no—
91C2×Dic38—41no—
92C2×Dic38—41no—
93C2×Dic38SD1612yes—
94C2×C8×C19—22no—
95C2×C8×C19—22no—
96C2×C8×C19—22no—
97C2×C8×C19—22no—
98C2×C8×C19—22no—
99C2×C8×C19—41no—
100C2×C8×C19—41no—
101C2×C8×C19—41no—
102C2×C8×C19—41no—
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C4⋊Dic19—21no—
108C4⋊Dic19—22no—
109C4⋊Dic19—22no—
110C4⋊Dic19—21no—
111C4⋊Dic19—22no—
112C4⋊Dic19—22no—
113C4⋊Dic19—41no—
114C4⋊Dic19—41no—
115C4⋊Dic19—41no—
116C4⋊Dic19—41no—
117Dic19⋊C4—41no—
118Dic19⋊C4—41no—
119C4×Dic19—41no—
120C4×Dic19—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—42no—
123Dic76—48no—
124#10272—191nomaximal, Sylow
125C23×C19#12111yescharacteristic
126C2×C4×C19—22no—
127C2×C4×C19#12011yescharacteristic
128C2×C4×C19#12011yescharacteristic
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12711yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19#13512yes—
135C2×C4×C19#13511yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19#13712yes—
138C2×C4×C19#13711yescharacteristic
139C2×Dic19—22no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—82no—
147C2×Dic19—81no—
148C2×Dic19—81no—
149Dic38—22no—
150Dic38—22no—
151Dic38—41no—
152Dic38—41no—
153Dic38—42no—
154Dic38—44no—
155Dic38—42no—
156Dic38—81no—
157Dic38—81no—
158Dic38—81no—
159Dic38—81no—
160C8×C19—42no—
161C8×C19—42no—
162C8×C19—42no—
163C19⋊C8—81no—
164C2×#487—191no—
165C2×#475—191no—
166C2×#462—191no—
167#1984—191no—
168C2×#332—191no—
169C2×#332—191no—
170#1277D1911yescharacteristic
171C22×C19#39211yescharacteristic
172C22×C19#46412yes—
173C22×C19#46511yescharacteristic
174C22×C19#46811yescharacteristic
175C22×C19#47312yes—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19#44811yescharacteristic
179C4×C19#44911yescharacteristic
180C4×C19#45011yescharacteristic
181C4×C19#45212yes—
182C4×C19#45211yescharacteristic
183C4×C19#49511yescharacteristic
184C4×C19#49711yescharacteristic
185Dic19—42no—
186Dic19—82no—
187Dic19—82no—
188Dic19—81no—
189C22×Q16—381no—
190C2×C4⋊Q8—191no—
191C2×C4⋊Q8—191no—
192C2×C4×Q8—191no—
193#487—382no—
194#487—382no—
195#475—382no—
196#475—382no—
197#462—382no—
198#462—382no—
199C2×#106—381no—
200C2×C4⋊C8—191no—
201C2×C4⋊C8C2×D1911yescharacteristic
202C2×C4⋊C8C2×D1911yescharacteristic
203C2×#103—381no—
204C2×#103—381no—
205C2×#103—382no—
206C2×C4×C8C2×D1911yescharacteristic
207#336—382no—
208#332—382no—
209#332—382no—
210C2×C19#168012yes—
211C2×C19#170012yes—
212C2×C19#200011yescharacteristic
213C2×C19#201511yescharacteristic
214C2×C19#202011yescharacteristic
215C22×Q8—191no—
216C22×Q8—381no—
217C22×Q8—381no—
218C2×Q16—384no—
219C2×Q16—762no—
220C2×Q16—762no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—381no—
224C22×C8D7612yes—
225C4⋊Q8—192no—
226C4⋊Q8—192no—
227C4⋊Q8—381no—
228C4⋊Q8—381no—
229C4⋊Q8—381no—
230C4⋊Q8—381no—
231C4⋊Q8—381no—
232C4⋊Q8—381no—
233C4×Q8—381no—
234C4×Q8—381no—
235C4×Q8—381no—
236C4×Q8—381no—
237C2×C4⋊C4—191no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4—381no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C42—381no—
244C2×C42C22×D1911yescharacteristic
245#106—384no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—381no—
249C4⋊C8—381no—
250C4⋊C8D7612yes—
251C4⋊C8D7612yes—
252#103—384no—
253#103—384no—
254#103—388no—
255C4×C8—21no—
256C4×C8—21no—
257C19#1027211yescharacteristic, complemented, Sylow
258C2×Q8—192no—
259C2×Q8—381no—
260C2×Q8—381no—
261C2×Q8—381no—
262C2×Q8—382no—
263C2×Q8—382no—
264C2×Q8—381no—
265C2×Q8—381no—
266C2×Q8—761no—
267C2×Q8—761no—
268C2×Q8—762no—
269C2×Q8—762no—
270C2×Q8—761no—
271C2×Q8—761no—
272C2×Q8—761no—
273C2×Q8—761no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—761no—
277C22×C4—761no—
278C22×C4C2×D7611yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4#6454511yescharacteristic
281Q16—768no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—761no—
292C2×C8—762no—
293C4⋊C4—381no—
294C4⋊C4—382no—
295C4⋊C4—382no—
296C4⋊C4—381no—
297C4⋊C4—382no—
298C4⋊C4—382no—
299C4⋊C4—761no—
300C4⋊C4—761no—
301C4⋊C4—761no—
302C4⋊C4—761no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C42—761no—
306C42—761no—
307C42C2×D7611yescharacteristic
308C42C2×D7611yescharacteristic
309C42D4×D1911yescharacteristic
310C42D4×D1911yescharacteristic
311C23#1059734111yescharacteristic
312Q8—382no—
313Q8—382no—
314Q8—761no—
315Q8—761no—
316Q8—762no—
317Q8—764no—
318Q8—762no—
319Q8—1521no—
320Q8—1521no—
321Q8—1521no—
322Q8—1521no—
323C2×C4—22no—
324C2×C4—382no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—762no—
328C2×C4—761no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—1521no—
332C2×C4—1522no—
333C2×C4—1521no—
334C2×C4#1059732011yescharacteristic
335C2×C4#1059732811yescharacteristic
336C2×C4#1059732811yescharacteristic
337C2×C4#1059732811yescharacteristic
338C2×C4#1059734111yescharacteristic
339C2×C4#1059734111yescharacteristic
340C2×C4#1059735012yes—
341C2×C4#1059735512yes—
342C2×C4#1059735711yescharacteristic
343C2×C4SD16×D1911yescharacteristic
344C2×C4#1059736211yescharacteristic
345C2×C4#1059736411yescharacteristic
346C8—42no—
347C8—42no—
348C8—42no—
349C8—1521no—
350C22#1192645411yescharacteristic
351C22#1192676712yes—
352C22#1192677411yescharacteristic
353C22#1192679111yescharacteristic
354C22#1192682012yes—
355C4—21no—
356C4—21no—
357C4—762no—
358C4—1522no—
359C4—1522no—
360C4—1521no—
361C4#1192668411yescharacteristic
362C4#1192669011yescharacteristic
363C4#1192669611yescharacteristic
364C4#1192670812yes—
365C4#1192670911yescharacteristic
366C4#1192692811yescharacteristic
367C4#1192693811yescharacteristic
368C2#1456306612yes—
369C2#1456319012yes—
370C2#1456464111yescharacteristic
371C2#1456473211yescharacteristic
372C2#1456475711yescharacteristic
subgroupG/H
centerC23#10597341
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socle, prime radicalC23×C19#121
hypercenter#1277D19
hypocenterC19#10272
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
257. C19#10272semidirect

Maximal subgroups

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

subgroupindex
C2×#119268952
C2×#119268302
C2×#119267552
#145645712
C2×#119262912
C2×#119262892
C19×#12772
#1027219