Finite Group Databasebeta

← #18089002

Subgroups — #18089002

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926561C212yesmaximal
2#14572054C211yesmaximal, characteristic, complemented
3#14563368C211yesmaximal, characteristic, complemented
4C2×#11926304C212yesmaximal, complemented
5C19×#2297C211yesmaximal, characteristic
6C22×#64520C2212yes—
7C2×#10597372C2212yes—
8#11926561—24no—
9#11926561C418yescomplemented
10C2×#10597294—24no—
11#11926500—24no—
12C4×#64520—22no—
13#11926311—22no—
14#11926304—24no—
15C22×#41×C19C2211yescharacteristic
16C2×C19×#117C2211yescharacteristic
17C22×C42×C19C2211yescharacteristic
18C19×#391C412yescomplemented
19C19×#390C412yescomplemented
20C19×#386—22no—
21C4×C22⋊C4×C19—22no—
22C2×#41×C19—22no—
23C2×#41×C19—22no—
24C2×#41×C19—22no—
25C2×#41×C19—22no—
26C2×#41×C19—22no—
27C2×#41×C19C2×C414yes—
28C22×Q8×C19C2×C411yescharacteristic
29C22×D4×C19—21no—
30C22×D4×C19C2×C411yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C19×#117—22no—
35C19×#117—22no—
36C2×C4⋊C4×C19C2×C412yes—
37C2×C22⋊C4×C19—24no—
38C2×C22⋊C4×C19D412yes—
39C2×C42×C19—22no—
40C2×C42×C19—22no—
41C2×C42×C19—21no—
42C2×C42×C19C2×C412yes—
43C2×C42×C19D412yes—
44C2×C22⋊Dic19—22no—
45#10597372—22no—
46#10597372—22no—
47#10597372—22no—
48#10597372C2×C414yes—
49C2×C4⋊Dic19—22no—
50C2×C4×Dic19—22no—
51C2×#64520—22no—
52C2×#64520—22no—
53C2×#64520—22no—
54C2×#64520C2×C414yes—
55C2×#64520D414yes—
56C2×#64520D414yes—
57C22×C19⋊C8—22no—
58C19×#95—24no—
59#10597294—216no—
60#10597260—24no—
61C4×C19⋊C8—24no—
62C24×C19—21no—
63C24×C19C2×D411yescharacteristic
64#41×C19—24no—
65#41×C19—24no—
66#41×C19—24no—
67#41×C19—24no—
68#41×C19—42no—
69#41×C19—42no—
70#41×C19—42no—
71#41×C19—42no—
72C2×Q8×C19—21no—
73C2×Q8×C19—22no—
74C2×Q8×C19—22no—
75C2×Q8×C19C4212yes—
76C2×D4×C19—24no—
77C2×D4×C19—21no—
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—42no—
81C2×D4×C19—41no—
82C2×D4×C19—41no—
83C2×D4×C19C4212yes—
84C22×C4×C19—22no—
85C22×C4×C19—21no—
86C22×C4×C19—24no—
87C22×C4×C19—44no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—42no—
92C22×C4×C19—41no—
93C22×C4×C19C22⋊C414yes—
94C22×C4×C19C22×C412yes—
95C22×C4×C19C22×C411yescharacteristic
96C22×C4×C19C2×D412yes—
97C22×C4×C19C2×D412yes—
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4112yes—
100C22×C4×C19#4112yes—
101C22×C4×C19#4112yes—
102C22×Dic19—42no—
103C4⋊C4×C19—24no—
104C22⋊C4×C19—24no—
105C22⋊C4×C19—48no—
106C42×C19—22no—
107C42×C19—22no—
108C42×C19—24no—
109C42×C19—42no—
110C22⋊Dic19—24no—
111C22⋊Dic19—42no—
112C4⋊Dic19—24no—
113C4⋊Dic19—42no—
114C4×Dic19—24no—
115C4×Dic19—42no—
116#64520—24no—
117#64520—24no—
118#64520—24no—
119#64520C22⋊C418yescomplemented
120C2×C19⋊C8—24no—
121C2×C19⋊C8—24no—
122C2×C19⋊C8—24no—
123#10959—191nomaximal, Sylow
124C23×C19—22no—
125C23×C19—42no—
126C23×C19—44no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19C4×D412yes—
131C23×C19#12112yes—
132C23×C19#12411yescharacteristic
133C23×C19#12711yescharacteristic
134Q8×C19—24no—
135Q8×C19—42no—
136D4×C19—24no—
137D4×C19—44no—
138D4×C19—44no—
139D4×C19—42no—
140C2×C4×C19—24no—
141C2×C4×C19—22no—
142C2×C4×C19—24no—
143C2×C4×C19—42no—
144C2×C4×C19—44no—
145C2×C4×C19—44no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—44no—
150C2×C4×C19—44no—
151C2×C4×C19—44no—
152C2×C4×C19C2×C4211yescharacteristic
153C2×C4×C19C2×C22⋊C412yes—
154C2×C4×C19#11712yes—
155C2×C4×C19#11711yescharacteristic
156C2×C4×C19C4×D412yes—
157C2×C4×C19C4×D412yes—
158C2×C4×C19C4×D412yes—
159C2×C4×C19C4×D412yes—
160C2×C4×C19C4×D412yes—
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12112yes—
163C2×C4×C19#12112yes—
164C2×C4×C19#12311yescharacteristic
165C2×C4×C19#12312yes—
166C2×C4×C19#12412yes—
167C2×C4×C19#12612yes—
168C2×Dic19—44no—
169C2×Dic19—84no—
170C19⋊C8—28no—
171C2×#421—192no—
172#2873—191no—
173#2297D1911yescharacteristic
174#1740—191no—
175C2×#339—192no—
176C22×C19—24no—
177C22×C19—22no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—42no—
181C22×C19—44no—
182C22×C19—42no—
183C22×C19—82no—
184C22×C19—82no—
185C22×C19C4×C22⋊C411yescharacteristic
186C22×C19#38611yescharacteristic
187C22×C19#38812yes—
188C22×C19#39012yes—
189C22×C19#39011yescharacteristic
190C4×C19—44no—
191C4×C19—44no—
192C4×C19—42no—
193C4×C19C4×C22⋊C412yes—
194C4×C19#38612yes—
195C4×C19#38812yes—
196C4×C19#38812yes—
197Dic19—84no—
198C22×#41C2×D1911yescharacteristic
199C22×M16—192no—
200C2×#117—192no—
201C2×#117C2×D1911yescharacteristic
202C22×C42C2×D1911yescharacteristic
203#421—198no—
204#421—384no—
205C2×#104—384no—
206#405—384no—
207C4×M16—382no—
208#391Dic1912yescomplemented
209#390Dic1912yescomplemented
210#386—22no—
211C4×C22⋊C4—22no—
212#342—382no—
213#339—384no—
214C2×C19—22no—
215C2×C19—21no—
216C2×C19—21no—
217C2×C19—22no—
218C2×C19—82no—
219C2×C19#143711yescharacteristic
220C2×C19#188412yes—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41C4×D1914yes—
227C22×Q8C2×Dic1911yescharacteristic
228C22×D4—21no—
229C22×D4C2×Dic1911yescharacteristic
230C23×C4—21no—
231C23×C4—21no—
232C23×C4C22×D1911yescharacteristic
233C2×M16—194no—
234C2×M16—194no—
235C2×M16—194no—
236C2×M16—382no—
237C2×M16—382no—
238C2×M16—382no—
239C22×C8—382no—
240#117—22no—
241#117—22no—
242#117—194no—
243#117—382no—
244#117—382no—
245#117—382no—
246C2×C4⋊C4—382no—
247C2×C4⋊C4C2×Dic1912yes—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—382no—
250C2×C22⋊C4C22⋊D1912yes—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—21no—
254C2×C42—382no—
255C2×C42C2×Dic1912yes—
256C2×C42C22⋊D1912yes—
257#104—3816no—
258#97—384no—
259C4×C8—384no—
260#95—24no—
261C19#1095911yescharacteristic, complemented, Sylow
262C24—21no—
263C24C2×C22⋊D1911yescharacteristic
264#41—24no—
265#41—24no—
266#41—24no—
267#41—24no—
268#41—42no—
269#41—42no—
270#41—42no—
271#41—42no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8C4×Dic1912yes—
276C2×D4—24no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4C4×Dic1912yes—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—44no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—762no—
294C22×C4C22⋊Dic1914yes—
295C22×C4C2×C4×D1912yes—
296C22×C4#6454112yes—
297C22×C4D4×D1912yes—
298C22×C4D4×D1912yes—
299C22×C4#6454312yes—
300C22×C4#6454312yes—
301C22×C4C22×Dic1911yescharacteristic
302C22×C4C2×C22⋊D1911yescharacteristic
303M16—198no—
304M16—384no—
305M16—384no—
306M16—384no—
307C2×C8—384no—
308C2×C8—384no—
309C2×C8—384no—
310C4⋊C4—24no—
311C4⋊C4—384no—
312C4⋊C4—762no—
313C22⋊C4—24no—
314C22⋊C4—48no—
315C22⋊C4—384no—
316C22⋊C4—762no—
317C42—22no—
318C42—22no—
319C42—24no—
320C42—42no—
321C42—384no—
322C42—762no—
323C23—22no—
324C23—42no—
325C23—44no—
326C23—41no—
327C23—41no—
328C23C4×C22⋊D1912yes—
329C23#1059738211yescharacteristic
330C23#1059738512yes—
331C23#1059738611yescharacteristic
332C23C2×C22⋊Dic1911yescharacteristic
333Q8—24no—
334Q8—42no—
335D4—24no—
336D4—44no—
337D4—44no—
338D4—42no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—764no—
352C2×C4—1524no—
353C2×C4#1059732312yes—
354C2×C4#1059732512yes—
355C2×C4C22⋊C4×D1912yes—
356C2×C4(C22⋊D19)⋊C412yes—
357C2×C4(C22⋊D19)⋊C412yes—
358C2×C4#1059732912yes—
359C2×C4#1059733012yes—
360C2×C4#1059733112yes—
361C2×C4C2×C4×Dic1911yescharacteristic
362C2×C4#1059737211yescharacteristic
363C2×C4C4×C22⋊D1912yes—
364C2×C4D4×Dic1912yes—
365C2×C4D4×Dic1912yes—
366C2×C4#1059738111yescharacteristic
367C2×C4#1059738311yescharacteristic
368C2×C4#1059738412yes—
369C8—388no—
370C22—22no—
371C22—24no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—44no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22C4×C22⋊Dic1911yescharacteristic
380C22#1192642411yescharacteristic
381C22#1192643812yes—
382C22#1192644412yes—
383C22#1192644711yescharacteristic
384C4—44no—
385C4—42no—
386C4—44no—
387C4—1524no—
388C4C22⋊C4×Dic1912yes—
389C4#1192642012yes—
390C4#1192643212yes—
391C4#1192643712yes—
392C2—21no—
393C2—22no—
394C2—21no—
395C2—22no—
396C2—82no—
397C2#1456187211yescharacteristic
398C2#1456401912yes—
subgroupG/H
centerC2×C4#10597383
commutatorC2×C4×C19C2×C42
FrattiniC23×C4C22×D19
FittingC19×#2297C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#2297D19
hypocenterC19#10959
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. #14572054C2semidirect
3. #14563368C2semidirect
4. C2×#11926304C2semidirect
9. #11926561C4semidirect
18. C19×#391C4semidirect
19. C19×#390C4semidirect
119. #64520C22⋊C4semidirect
208. #391Dic19semidirect
209. #390Dic19semidirect
261. C19#10959semidirect

Maximal subgroups

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

subgroupindex
C2×#119265612
#145720542
#145633682
C2×#119263042
C19×#22972
#1095919