Finite Group Databasebeta

← #18073897

Subgroups — #18073897

Order 4864.

1174 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#10597342C211yesmaximal, characteristic
2#14563544C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic, complemented
4C2×#11926269C212yesmaximal, complemented
5C2×C19×#324C211yesmaximal, characteristic, complemented
6C23×Dic38C411yescharacteristic
7C23×C4×D19C2211yescharacteristic
8C2×#10597342—24no—
9C2×#10597342—24no—
10C2×#10597342—22no—
11C2×#10597342—22no—
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C2211yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C411yescharacteristic
16C2×C22⋊(C19⋊C8)C2212yes—
17C2×(C2×D19)⋊C8—24no—
18#11926270—22no—
19#11926269—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C2×C19×C22⋊C8C2212yes—
22C19×#324—22no—
23C24×D19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×C4×D19—22no—
32C22×C4×D19—21no—
33C22×C4×D19—44no—
34C22×C4×D19D414yes—
35C22×Dic38—22no—
36C22×Dic38—22no—
37C22×Dic38—22no—
38C22×Dic38—44no—
39C22×C8×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19D412yes—
43C2×C4⋊C4×C19D412yes—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—22no—
50C2×Dic19⋊C4—22no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4D414yes—
57C22×C19⋊C8—22no—
58#10597342—216no—
59#10597342—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64(C2×D19)⋊C8—48no—
65C24×C19C22×C411yescharacteristic
66C23×D19—21no—
67C23×D19—21no—
68C23×D19—24no—
69C23×D19—22no—
70C23×D19—22no—
71C23×D19—42no—
72C23×D19C22⋊C412yes—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—22no—
78C22×C4×C19—22no—
79C22×C4×C19—42no—
80C22×C4×C19—42no—
81C22×C4×C19C22⋊C412yes—
82C22×C4×C19C22⋊C412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D412yes—
85C22×C4×C19C2×D412yes—
86C22×C4×C19C2×D411yescharacteristic
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—24no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—22no—
95C22×Dic19—22no—
96C22×Dic19—42no—
97C22×Dic19C22⋊C412yes—
98C22×Dic19C22⋊C412yes—
99C22×Dic19C22⋊C412yes—
100C2×C4×D19—24no—
101C2×C4×D19—24no—
102C2×C4×D19—28no—
103C2×C4×D19—44no—
104C2×C4×D19—44no—
105C2×C4×D19—48no—
106C2×C4×D19—44no—
107C2×Dic38—28no—
108C2×Dic38—48no—
109C2×Dic38—48no—
110C2×Dic38—44no—
111C2×Dic38—44no—
112C2×C8×C19—44no—
113C2×C8×C19—42no—
114C4⋊C4×C19—24no—
115C4⋊C4×C19—24no—
116(C2×D19)⋊C4—28no—
117(C2×D19)⋊C4—28no—
118Dic19⋊C4—28no—
119Dic19⋊C4—24no—
120Dic19⋊C4—24no—
121C2×C19⋊C8—44no—
122C2×C19⋊C8—42no—
123#8308—191nomaximal, Sylow
124C23×C19—22no—
125C23×C19—22no—
126C23×C19C2×C22⋊C411yescharacteristic
127C23×C19C2×C22⋊C411yescharacteristic
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19#13112yes—
130C23×C19#13112yes—
131C22×D19—24no—
132C22×D19—24no—
133C22×D19—22no—
134C22×D19—24no—
135C22×D19—24no—
136C22×D19—22no—
137C22×D19—48no—
138C22×D19—48no—
139C22×D19—42no—
140C22×D19—42no—
141C22×D19—42no—
142C22×D19—41no—
143C22×D19—41no—
144C22×D19#10114yes—
145C2×C4×C19—24no—
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19#12012yes—
159C2×C4×C19#12012yes—
160C2×Dic19—24no—
161C2×Dic19—24no—
162C2×Dic19—22no—
163C2×Dic19—22no—
164C2×Dic19—22no—
165C2×Dic19—22no—
166C2×Dic19—24no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19#9914yes—
174C4×D19—48no—
175C4×D19—48no—
176Dic38—416no—
177C8×C19—82no—
178C19⋊C8—82no—
179C22×C22⋊Q8—191no—
180#1779—192no—
181C2×#324—192no—
182C2×#324—191no—
183C2×#324D1911yescharacteristic, complemented
184C22×C19—24no—
185C22×C19—24no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19#37911yescharacteristic
191C22×C19#40812yes—
192C22×C19#40812yes—
193C22×C19#40811yescharacteristic
194C22×C19#40811yescharacteristic
195C22×C19C2×#9912yes—
196C22×C19C2×#10112yes—
197C2×D19—28no—
198C2×D19—24no—
199C2×D19—48no—
200C2×D19—44no—
201C2×D19—44no—
202C2×D19—44no—
203C2×D19—42no—
204C2×D19—42no—
205C4×C19—22no—
206C4×C19—22no—
207C4×C19—42no—
208C4×C19—42no—
209Dic19—24no—
210Dic19—42no—
211Dic19—42no—
212C23×Q8—191no—
213C24×C4—191no—
214C2×C22⋊Q8—384no—
215C2×C22⋊Q8—384no—
216C2×C22⋊Q8—382no—
217C2×C22⋊Q8—382no—
218C22×C4⋊C4—191no—
219C22×C4⋊C4—191no—
220C22×C4⋊C4C2×D1911yescharacteristic
221C22×C22⋊C4—191no—
222C22×C22⋊C4—191no—
223C2×C22⋊C8—192no—
224C2×C22⋊C8—384no—
225C2×C22⋊C8C2×D1912yes—
226#324—22no—
227#324—384no—
228#324—382no—
229C2×C19—22no—
230C2×C19—21no—
231C2×C19—21no—
232C2×C19#147214yes—
233C2×C19#178011yescharacteristic
234C2×C19#178111yescharacteristic
235C2×C19#178411yescharacteristic
236D19—44no—
237C25—191no—
238C22×Q8—382no—
239C22×Q8—382no—
240C22×Q8—382no—
241C22×Q8—764no—
242C23×C4—191no—
243C23×C4—191no—
244C23×C4—191no—
245C23×C4—194no—
246C23×C4—381no—
247C23×C4—382no—
248C23×C4—381no—
249C23×C4—764no—
250C23×C4C4×D1911yescharacteristic
251C23×C4C4×D1911yescharacteristic
252C23×C4C22×D1911yescharacteristic
253C22×C8—22no—
254C22×C8—382no—
255C22⋊Q8—3816no—
256C22⋊Q8—3816no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—194no—
260C2×C4⋊C4—382no—
261C2×C4⋊C4—382no—
262C2×C4⋊C4—382no—
263C2×C4⋊C4—381no—
264C2×C4⋊C4—382no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4D7612yes—
267C2×C4⋊C4C22⋊D1912yes—
268C2×C22⋊C4—382no—
269C2×C22⋊C4—382no—
270C2×C22⋊C4—382no—
271C2×C22⋊C4—382no—
272C2×C22⋊C4—382no—
273C2×C22⋊C4—382no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—382no—
277C22⋊C8—382no—
278C22⋊C8—768no—
279C19#830811yescharacteristic, complemented, Sylow
280C24—192no—
281C24—384no—
282C24—381no—
283C24—381no—
284C24—382no—
285C24—382no—
286C24—762no—
287C24C2×C4×D1911yescharacteristic
288C2×Q8—388no—
289C2×Q8—764no—
290C2×Q8—768no—
291C2×Q8—764no—
292C2×Q8—768no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—192no—
302C22×C4—192no—
303C22×C4—192no—
304C22×C4—388no—
305C22×C4—384no—
306C22×C4—381no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—382no—
311C22×C4—382no—
312C22×C4—381no—
313C22×C4—381no—
314C22×C4—384no—
315C22×C4—384no—
316C22×C4—764no—
317C22×C4—764no—
318C22×C4—768no—
319C22×C4—764no—
320C22×C4—762no—
321C22×C4(C2×D19)⋊C412yes—
322C22×C4(C2×D19)⋊C412yes—
323C22×C4C2×D7611yescharacteristic
324C22×C4D4×D1912yes—
325C22×C4D4×D1912yes—
326C22×C4C2×C22⋊D1911yescharacteristic
327C2×C8—44no—
328C2×C8—42no—
329C2×C8—764no—
330C2×C8—762no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—388no—
334C4⋊C4—384no—
335C4⋊C4—384no—
336C22⋊C4—388no—
337C22⋊C4—388no—
338C23—22no—
339C23—22no—
340C23—194no—
341C23—384no—
342C23—384no—
343C23—382no—
344C23—384no—
345C23—384no—
346C23—382no—
347C23—768no—
348C23—768no—
349C23—762no—
350C23—762no—
351C23—762no—
352C23—761no—
353C23—761no—
354C23C22⋊C4×D1911yescharacteristic
355C23C22⋊C4×D1911yescharacteristic
356C23#1059734712yes—
357C23#1059735312yes—
358C23C2×(C2×D19)⋊C411yescharacteristic
359Q8—7616no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—194no—
374C2×C4—384no—
375C2×C4—384no—
376C2×C4—382no—
377C2×C4—382no—
378C2×C4—382no—
379C2×C4—382no—
380C2×C4—384no—
381C2×C4—768no—
382C2×C4—768no—
383C2×C4—762no—
384C2×C4—762no—
385C2×C4—761no—
386C2×C4—761no—
387C2×C4—762no—
388C2×C4—762no—
389C2×C4#1059732812yes—
390C2×C4#1059738312yes—
391C8—82no—
392C8—1522no—
393C22—24no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—388no—
400C22—384no—
401C22—768no—
402C22—764no—
403C22—764no—
404C22—764no—
405C22—762no—
406C22—762no—
407C22#1192639911yescharacteristic
408C22#1192650912yes—
409C22#1192650912yes—
410C22#1192651011yescharacteristic
411C22#1192651211yescharacteristic
412C22#99×D1912yes—
413C22#101×D1912yes—
414C4—22no—
415C4—22no—
416C4—42no—
417C4—42no—
418C4—384no—
419C4—762no—
420C4—762no—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—764no—
425C2#1456199714yes—
426C2#1456354611yescharacteristic
427C2#1456354811yescharacteristic
428C2#1456355711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#8308
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. C2×#11926270C2semidirect
4. C2×#11926269C2semidirect
5. C2×C19×#324C2semidirect
183. C2×#324D19semidirect
279. C19#8308semidirect

Maximal subgroups

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

subgroupindex
C22×#105973422
#145635442
C2×#119262702
C2×#119262692
C2×C19×#3242
#830819