Finite Group Databasebeta

← #18075879

Subgroups — #18075879

Order 4864.

830 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926403C211yesmaximal, characteristic
2#14563544C212yesmaximal
3#14561478C211yesmaximal, characteristic, complemented
4#14561477C212yesmaximal, complemented
5C19×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D19C2211yescharacteristic
7C22×Dic19⋊C4C412yes—
8C22×(C2×D19)⋊C4C412yes—
9C2×C22⋊(C19⋊C8)C2212yes—
10C2×(C2×D19)⋊C8—22no—
11C2×(C2×D19)⋊C8—22no—
12#11926403—22no—
13#11926403—22no—
14C2×C19⋊#95C2211yescharacteristic
15C2×C19×C22⋊C8C2212yes—
16C2×C19×#95C2211yescharacteristic
17C24×D19C2×C411yescharacteristic
18C23×C4×C19C2×C412yes—
19C23×C4×C19C2311yescharacteristic
20C23×Dic19C2×C411yescharacteristic
21C23×Dic19C2×C412yes—
22C22×C4×D19—22no—
23C22×C4×D19—21no—
24C22×C4×D19—21no—
25C22×C4×D19—44no—
26C22×C4×D19D412yes—
27C22×C4×D19D412yes—
28C22×C8×C19—22no—
29C2×(C2×D19)⋊C4—22no—
30C2×(C2×D19)⋊C4—22no—
31C2×(C2×D19)⋊C4—44no—
32C2×Dic19⋊C4—22no—
33C2×Dic19⋊C4—22no—
34C2×Dic19⋊C4—44no—
35C22×C19⋊C8—22no—
36C19×C22⋊C8—22no—
37C19×C22⋊C8—22no—
38C19×#95—22no—
39C19⋊#95—22no—
40C22⋊(C19⋊C8)—22no—
41C22⋊(C19⋊C8)—22no—
42(C2×D19)⋊C8—44no—
43(C2×D19)⋊C8—44no—
44C24×C19C22×C411yescharacteristic
45C23×D19—21no—
46C23×D19—21no—
47C23×D19—22no—
48C23×D19—22no—
49C23×D19—22no—
50C23×D19—22no—
51C23×D19—42no—
52C23×D19C22⋊C411yescharacteristic
53C23×D19C22⋊C411yescharacteristic
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—42no—
58C22×C4×C19—42no—
59C22×C4×C19—42no—
60C22×C4×C19C2×D412yes—
61C22×C4×C19#4112yes—
62C22×C4×C19#4111yescharacteristic
63C22×C4×C19#4111yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—24no—
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C22×Dic19—42no—
71C22×Dic19—42no—
72C22×Dic19C22⋊C412yes—
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—22no—
76C2×C4×D19—22no—
77C2×C4×D19—24no—
78C2×C4×D19—24no—
79C2×C4×D19—42no—
80C2×C4×D19—42no—
81C2×C4×D19—48no—
82C2×C4×D19—44no—
83C2×C4×D19—44no—
84C2×C8×C19—42no—
85C2×C8×C19—42no—
86C2×C8×C19—42no—
87(C2×D19)⋊C4—44no—
88(C2×D19)⋊C4—44no—
89Dic19⋊C4—44no—
90Dic19⋊C4—44no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94#8704—191nomaximal, Sylow
95C23×C19—22no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19C2×C22⋊C411yescharacteristic
99C23×C19#11711yescharacteristic
100C23×C19#11711yescharacteristic
101C23×C19#13112yes—
102C23×C19#13112yes—
103C22×D19—24no—
104C22×D19—24no—
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—22no—
110C22×D19—22no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—44no—
114C22×D19—44no—
115C22×D19—44no—
116C22×D19—44no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—41no—
120C22×D19—42no—
121C22×D19—41no—
122C22×D19#10012yes—
123C22×D19#10112yes—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—82no—
133C2×C4×C19—82no—
134C2×C4×C19#12312yes—
135C2×C4×C19#12312yes—
136C2×Dic19—24no—
137C2×Dic19—24no—
138C2×Dic19—22no—
139C2×Dic19—22no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—82no—
144C2×Dic19—82no—
145C2×Dic19#9914yes—
146C4×D19—44no—
147C4×D19—44no—
148C4×D19—44no—
149C4×D19—44no—
150C8×C19—82no—
151C19⋊C8—82no—
152C2×#380—191no—
153#1779—192no—
154#1280—192no—
155#1280—191no—
156#1280D1911yescharacteristic, complemented
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19#38111yescharacteristic
166C22×C19#40812yes—
167C22×C19C2×#9912yes—
168C22×C19C2×#10011yescharacteristic
169C22×C19C2×#10111yescharacteristic
170C22×C19#43311yescharacteristic
171C22×C19#43312yes—
172C22×C19#43311yescharacteristic
173C2×D19—22no—
174C2×D19—22no—
175C2×D19—24no—
176C2×D19—24no—
177C2×D19—44no—
178C2×D19—48no—
179C2×D19—44no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—42no—
185C2×D19—42no—
186C4×C19—22no—
187C4×C19—22no—
188C4×C19—82no—
189Dic19—24no—
190Dic19—82no—
191C24×C4—191no—
192C22×C4⋊C4—192no—
193C22×C22⋊C4—192no—
194C2×C22⋊C8—192no—
195C2×C22⋊C8—382no—
196C2×C22⋊C8—382no—
197C2×C22⋊C8C2×D1912yes—
198#380—382no—
199#380—382no—
200C2×#95—191no—
201C2×#95C2×D1911yescharacteristic
202C2×C19—21no—
203C2×C19—22no—
204C2×C19—21no—
205C2×C19#147112yes—
206C2×C19#147212yes—
207C2×C19#181811yescharacteristic
208C2×C19#181911yescharacteristic
209C2×C19#182111yescharacteristic
210D19—42no—
211D19—42no—
212C25—191no—
213C23×C4—191no—
214C23×C4—192no—
215C23×C4—192no—
216C23×C4—192no—
217C23×C4—382no—
218C23×C4—381no—
219C23×C4—381no—
220C23×C4—764no—
221C23×C4C4×D1912yes—
222C23×C4C22×D1911yescharacteristic
223C22×C8—22no—
224C22×C8—382no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—382no—
227C2×C4⋊C4—764no—
228C2×C22⋊C4—382no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4—764no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235C22⋊C8—764no—
236C22⋊C8—764no—
237#95—22no—
238#95—382no—
239C19#870411yescharacteristic, complemented, Sylow
240C24—191no—
241C24—191no—
242C24—382no—
243C24—382no—
244C24—381no—
245C24—381no—
246C24—382no—
247C24—382no—
248C24—762no—
249C24C2×C4×D1911yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—192no—
257C22×C4—384no—
258C22×C4—384no—
259C22×C4—384no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—382no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—382no—
268C22×C4—382no—
269C22×C4—762no—
270C22×C4—762no—
271C22×C4—768no—
272C22×C4—764no—
273C22×C4—764no—
274C22×C4—762no—
275C22×C4—762no—
276C22×C4#6454112yes—
277C22×C4D4×D1912yes—
278C22×C4#6454311yescharacteristic
279C22×C4#6454511yescharacteristic
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—762no—
284C2×C8—762no—
285C2×C8—762no—
286C4⋊C4—764no—
287C4⋊C4—764no—
288C22⋊C4—764no—
289C22⋊C4—764no—
290C23—22no—
291C23—21no—
292C23—21no—
293C23—192no—
294C23—192no—
295C23—384no—
296C23—384no—
297C23—381no—
298C23—381no—
299C23—382no—
300C23—382no—
301C23—382no—
302C23—382no—
303C23—381no—
304C23—381no—
305C23—764no—
306C23—764no—
307C23—764no—
308C23—764no—
309C23—762no—
310C23—762no—
311C23—761no—
312C23—762no—
313C23—761no—
314C23#1059731811yescharacteristic
315C23C22⋊C4×D1911yescharacteristic
316C23#1059733811yescharacteristic
317C23#1059734712yes—
318C23#1059735312yes—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—194no—
330C2×C4—384no—
331C2×C4—384no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—764no—
335C2×C4—764no—
336C2×C4—764no—
337C2×C4—764no—
338C2×C4—762no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—1522no—
342C2×C4—1522no—
343C2×C4#1059732912yes—
344C2×C4#1059734012yes—
345C8—82no—
346C8—1522no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—382no—
356C22—382no—
357C22—384no—
358C22—384no—
359C22—764no—
360C22—768no—
361C22—764no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—762no—
367C22—762no—
368C22#1192640611yescharacteristic
369C22#1192650912yes—
370C22#99×D1912yes—
371C22#100×D1911yescharacteristic
372C22#101×D1911yescharacteristic
373C22#1192660311yescharacteristic
374C22#1192660412yes—
375C22#1192660611yescharacteristic
376C4—22no—
377C4—22no—
378C4—82no—
379C4—384no—
380C4—1522no—
381C2—21no—
382C2—22no—
383C2—21no—
384C2—762no—
385C2—762no—
386C2#1456199312yes—
387C2#1456199712yes—
388C2#1456370511yescharacteristic
389C2#1456370811yescharacteristic
390C2#1456371411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1280D19
hypocenterC19#8704
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #14561478C2semidirect
4. #14561477C2semidirect
5. C19×#1280C2semidirect
156. #1280D19semidirect
239. C19#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#119264032
#145635442
#145614782
#145614772
C19×#12802
#870419