Finite Group Databasebeta

← #18077619

Subgroups — #18077619

Order 4864.

670 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#14572664C211yesmaximal, characteristic, complemented
2C4×#10597290C211yesmaximal, characteristic, complemented
3#14562078C212yesmaximal, complemented
4#14561528C212yesmaximal, complemented
5C19×#2397C211yesmaximal, characteristic
6#11926616—24no—
7#11926601C2212yes—
8C2×#10597290—21no—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11C4×#64520C2212yes—
12#11926313—21no—
13D4⋊(C19⋊C8)—24no—
14C2×C4×D4×C19—21no—
15C2×C4×D4×C19—21no—
16C2×C4×D4×C19C2211yescharacteristic
17C2×C4×D4×C19C2211yescharacteristic
18C19×#399—21no—
19C19×#399C411yescharacteristic
20C19×#399C411yescharacteristic
21C19×#392—21no—
22C19×#392C411yescharacteristic
23C19×#392C411yescharacteristic
24C19×#376C2211yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19—21no—
27C22×D4×C19C2×C411yescharacteristic
28C22×D4×C19D411yescharacteristic
29C23×C4×C19—21no—
30C23×C4×C19D411yescharacteristic
31C23×C4×C19D411yescharacteristic
32C4×D4×C19—22no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C4×D4×C19—22no—
36C4×D4×C19—44no—
37C4×D4×C19—44no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19C2×C411yescharacteristic
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19C2×C411yescharacteristic
48C2×C22⋊C4×C19C2×C411yescharacteristic
49C2×C42×C19—21no—
50C2×C42×C19C2311yescharacteristic
51C2×#64520—22no—
52C2×#64520—22no—
53C22×C19⋊C8—22no—
54C19×#95—21no—
55C19×#95C2×C411yescharacteristic
56C19×#95C2×C411yescharacteristic
57#10597290—24no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)D414yescomplemented
62#10597260—22no—
63#10597260—22no—
64C4×C19⋊C8—22no—
65C24×C19—21no—
66C24×C19C22⋊C411yescharacteristic
67C24×C19C22⋊C411yescharacteristic
68C2×D4×C19—22no—
69C2×D4×C19—22no—
70C2×D4×C19—22no—
71C2×D4×C19—41no—
72C2×D4×C19—42no—
73C2×D4×C19—42no—
74C2×D4×C19—42no—
75C2×D4×C19—42no—
76C2×D4×C19—42no—
77C2×D4×C19—42no—
78C2×D4×C19—42no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—42no—
87C22×C4×C19—42no—
88C22×C4×C19—42no—
89C22×C4×C19—42no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19C22⋊C411yescharacteristic
93C22×C4×C19C22⋊C411yescharacteristic
94C22×C4×C19C22×C411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—42no—
100C4⋊C4×C19—42no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—22no—
103C22⋊C4×C19—42no—
104C22⋊C4×C19—42no—
105C22⋊C4×C19—42no—
106C22⋊C4×C19—42no—
107C22⋊C4×C19—42no—
108C42×C19—24no—
109C42×C19C2×D412yes—
110C42×C19#4112yes—
111#64520—24no—
112#64520—42no—
113#64520—82no—
114C2×C19⋊C8—24no—
115C2×C19⋊C8—42no—
116C2×C19⋊C8—82no—
117#9031—191nomaximal, Sylow
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—22no—
121C23×C19—21no—
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—41no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19#10412yes—
135C23×C19C2×C22⋊C411yescharacteristic
136D4×C19—24no—
137D4×C19—44no—
138D4×C19—42no—
139D4×C19—48no—
140D4×C19—48no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19—82no—
163C2×C4×C19—82no—
164C2×C4×C19C4×D412yes—
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12112yes—
167C2×C4×C19#12311yescharacteristic
168C19⋊C8—44no—
169C19⋊C8—44no—
170#2973—191no—
171#2397D1911yescharacteristic
172C4×#100—191no—
173#1490—192no—
174#1300—192no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—22no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—42no—
187C22×C19—41no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19—81no—
194C22×C19#38611yescharacteristic
195C22×C19C2×#10411yescharacteristic
196C22×C19#42111yescharacteristic
197C4×C19—22no—
198C4×C19—21no—
199C4×C19—22no—
200C4×C19—42no—
201C4×C19—42no—
202C4×C19—41no—
203C4×C19—41no—
204C4×C19—81no—
205C4×C19#45312yes—
206C2×C4×D4—21no—
207C2×C4×D4—21no—
208C2×C4×D4C2×D1911yescharacteristic
209C2×C4×D4C2×D1911yescharacteristic
210#435—384no—
211#432—192no—
212C2×#100—381no—
213#407—381no—
214C2×C22⋊C8—381no—
215C4×M16—192no—
216#399—21no—
217#399Dic1911yescharacteristic
218#399Dic1911yescharacteristic
219#392—21no—
220#392Dic1911yescharacteristic
221#392Dic1911yescharacteristic
222#376C2×D1911yescharacteristic
223#343—381no—
224D4⋊C8—384no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—42no—
228C2×C19—81no—
229C2×C19—82no—
230C2×C19#187111yescharacteristic
231C2×C19#188711yescharacteristic
232C2×C19#189111yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C2×Dic1911yescharacteristic
236C22×D4C22⋊D1911yescharacteristic
237C23×C4—21no—
238C23×C4C22⋊D1911yescharacteristic
239C23×C4C22⋊D1911yescharacteristic
240C2×M16—382no—
241C2×M16—382no—
242C22×C8—382no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—22no—
247C4×D4—44no—
248C4×D4—44no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×Dic1911yescharacteristic
252C2×C4⋊C4C22⋊D1911yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4C2×Dic1911yescharacteristic
259C2×C22⋊C4C2×Dic1911yescharacteristic
260C2×C42—21no—
261C2×C42C22×D1911yescharacteristic
262C4⋊C8—194no—
263#100—384no—
264C22⋊C8—382no—
265C22⋊C8—382no—
266C22⋊C8—382no—
267#97—382no—
268#97—382no—
269C4×C8—382no—
270#95—21no—
271#95C2×Dic1911yescharacteristic
272#95C2×Dic1911yescharacteristic
273C19#903111yescharacteristic, complemented, Sylow
274C24—21no—
275C24C22⋊Dic1911yescharacteristic
276C24C22⋊Dic1911yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C22⋊Dic1911yescharacteristic
302C22×C4C22⋊Dic1911yescharacteristic
303C22×C4C22×Dic1911yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305C22×C4C2×C22⋊D1911yescharacteristic
306M16—384no—
307M16—762no—
308M16—1522no—
309C2×C8—384no—
310C2×C8—762no—
311C2×C8—1522no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C42—24no—
324C42D4×D1912yes—
325C42#6454312yes—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#1059729412yes—
343C23C2×C22⋊Dic1911yescharacteristic
344D4—24no—
345D4—44no—
346D4—42no—
347D4—48no—
348D4—48no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4D4×Dic1912yes—
373C2×C4#1059738111yescharacteristic
374C2×C4#1059738311yescharacteristic
375C2×C4#1059738512yes—
376C8—764no—
377C8—764no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22#1192642411yescharacteristic
398C22C2×#1059729411yescharacteristic
399C22#1192656111yescharacteristic
400C4—22no—
401C4—21no—
402C4—22no—
403C4—42no—
404C4—42no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4#1192671112yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—82no—
414C2#1456393811yescharacteristic
415C2#1456403411yescharacteristic
416C2#1456405411yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2397C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#2397D19
hypocenterC19#9031
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #14572664C2semidirect
2. C4×#10597290C2semidirect
3. #14562078C2semidirect
4. #14561528C2semidirect
61. C4⋊(C19⋊C8)D4semidirect
273. C19#9031semidirect

Maximal subgroups

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

subgroupindex
#145726642
C4×#105972902
#145620782
#145615282
C19×#23972
#903119