Finite Group Databasebeta

← #18078666

Subgroups — #18078666

Order 4864.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572279C211yesmaximal, characteristic, complemented
2#14562227C211yesmaximal, characteristic, complemented
3#14562086C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic, complemented
5#14561526C211yesmaximal, characteristic, complemented
6#14561471C211yesmaximal, characteristic, complemented
7C19×#3106C211yesmaximal, characteristic
8#11926605—22no—
9#11926597—22no—
10#11926571—21no—
11#11926568C2211yescharacteristic
12#11926511—21no—
13C4×#64520C2211yescharacteristic
14C4×#64520C2211yescharacteristic
15C2×C4×C19⋊C8C2211yescharacteristic
16#11926284—22no—
17Q8⋊(C19⋊C8)—21no—
18D4⋊(C19⋊C8)—22no—
19D4⋊(C19⋊C8)—21no—
20C19×#532C2211yescharacteristic
21C4×#41×C19C2211yescharacteristic
22C19×#482—21no—
23C19×#477C411yescharacteristic
24C19×#476C411yescharacteristic
25C19×#460C411yescharacteristic
26C19×#459C411yescharacteristic
27C19×#449—21no—
28C4×SD16×C19—21no—
29C4×D8×C19—21no—
30C19×#431C2211yescharacteristic
31C2×#41×C19—21no—
32C2×#41×C19D411yescharacteristic
33C2×SD16×C19—21no—
34C2×D8×C19—21no—
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×#127C2×C411yescharacteristic
37C19×#124—21no—
38C19×#121—21no—
39C19×#121—21no—
40C4×Q8×C19C2×C411yescharacteristic
41C4×Q8×C19D411yescharacteristic
42C4×D4×C19—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19C2×C411yescharacteristic
47C4×D4×C19D411yescharacteristic
48C19×#117—21no—
49C19×#117D411yescharacteristic
50C2×C42×C19—21no—
51C2×C42×C19C2311yescharacteristic
52C2×#64520—21no—
53C2×#64520—21no—
54C2×#64520—21no—
55C22×C19⋊C8—21no—
56C19×#107—21no—
57C19×#106—21no—
58C19×C4⋊C8C2×C411yescharacteristic
59C19×C4⋊C8C2×C411yescharacteristic
60C19×#103—21no—
61C19×#102—21no—
62C19×#102—21no—
63C19×#102—21no—
64C19×C22⋊C8—21no—
65C4×C8×C19—21no—
66C22⋊(C19⋊C8)—24no—
67C4⋊(C19⋊C8)—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70#10597260—21no—
71#10597260D412yes—
72C4×C19⋊C8—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8D412yes—
76#41×C19—41no—
77#41×C19—41no—
78#41×C19—81no—
79#41×C19—81no—
80C2×Q8×C19—21no—
81C2×Q8×C19C22⋊C411yescharacteristic
82C2×D4×C19—21no—
83C2×D4×C19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C2×D4×C19C22⋊C411yescharacteristic
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—41no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×C4×C19#4111yescharacteristic
95SD16×C19—42no—
96D8×C19—42no—
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19C22⋊C411yescharacteristic
104C4⋊C4×C19C22⋊C411yescharacteristic
105C22⋊C4×C19—21no—
106C22⋊C4×C19—21no—
107C22⋊C4×C19—21no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C42×C19—21no—
111C42×C19—21no—
112C42×C19—21no—
113C42×C19C22×C411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19C2×D411yescharacteristic
117#64520—22no—
118#64520—41no—
119#64520—41no—
120#64520—41no—
121#64520—81no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128#9213—191nomaximal, Sylow
129C23×C19—21no—
130C23×C19—41no—
131C23×C19#12311yescharacteristic
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—81no—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—42no—
138D4×C19—41no—
139D4×C19—41no—
140D4×C19—41no—
141D4×C19—41no—
142D4×C19—81no—
143D4×C19—82no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19C2×C22⋊C411yescharacteristic
162C2×C4×C19C4×D411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C8×C19—41no—
168C8×C19—41no—
169C19⋊C8—42no—
170C19⋊C8—42no—
171C19⋊C8—42no—
172C19⋊C8—81no—
173#3106D1911yescharacteristic
174#2922—191no—
175#1525—191no—
176#1492—191no—
177#1489—191no—
178#1299—191no—
179#1278—191no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19—81no—
189C22×C19#38611yescharacteristic
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—81no—
197C4×C19#42111yescharacteristic
198C4×C19#42111yescharacteristic
199C4×C19#44311yescharacteristic
200C4×C19#44411yescharacteristic
201C4×C19#47111yescharacteristic
202C4×C19#47211yescharacteristic
203#532C2×D1911yescharacteristic
204C4×#41C2×D1911yescharacteristic
205#482—21no—
206#477Dic1911yescharacteristic
207#476Dic1911yescharacteristic
208#460Dic1911yescharacteristic
209#459Dic1911yescharacteristic
210#449—21no—
211C4×SD16—21no—
212C4×D8—21no—
213#433—382no—
214#431—382no—
215#431C2×D1911yescharacteristic
216#424—381no—
217#423—191no—
218#408—381no—
219C4×M16—191no—
220C4×M16—191no—
221C2×C4×C8—191no—
222#329—382no—
223Q8⋊C8—381no—
224D4⋊C8—382no—
225D4⋊C8—381no—
226C2×C19—41no—
227C2×C19—81no—
228C2×C19—161no—
229C2×C19#187611yescharacteristic
230C2×C19#189711yescharacteristic
231C2×C19#190711yescharacteristic
232C2×#41—21no—
233C2×#41C22⋊D1911yescharacteristic
234C2×SD16—21no—
235C2×D8—21no—
236C2×M16—381no—
237C2×M16—381no—
238C2×M16—381no—
239C22×C8—381no—
240C4⋊Q8C2×Dic1911yescharacteristic
241#127C2×Dic1911yescharacteristic
242#124—21no—
243#121—21no—
244#121—21no—
245C4×Q8C2×Dic1911yescharacteristic
246C4×Q8C22⋊D1911yescharacteristic
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C2×Dic1911yescharacteristic
252C4×D4C22⋊D1911yescharacteristic
253#117—21no—
254#117C22⋊D1911yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1911yescharacteristic
257#107—21no—
258#106—21no—
259C4⋊C8—384no—
260C4⋊C8—381no—
261C4⋊C8—381no—
262C4⋊C8C2×Dic1911yescharacteristic
263C4⋊C8C2×Dic1911yescharacteristic
264#103—21no—
265#102—21no—
266#102—21no—
267#102—21no—
268C22⋊C8—21no—
269C22⋊C8—384no—
270#97—192no—
271#97—381no—
272C4×C8—21no—
273C4×C8—192no—
274C4×C8—381no—
275C4×C8—381no—
276C4×C8—381no—
277C19#921311yescharacteristic, complemented, Sylow
278#41—41no—
279#41—41no—
280#41—81no—
281#41—81no—
282C2×Q8—21no—
283C2×Q8C22⋊Dic1911yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊Dic1911yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4#6454311yescharacteristic
295C22×C4#6454311yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297SD16—42no—
298D8—42no—
299M16—382no—
300M16—761no—
301M16—761no—
302M16—761no—
303M16—1521no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—382no—
307C2×C8—382no—
308C2×C8—761no—
309C2×C8—761no—
310C2×C8—761no—
311C2×C8—761no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4C22⋊Dic1911yescharacteristic
317C4⋊C4C22⋊Dic1911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42D4×D1911yescharacteristic
327C42D4×D1911yescharacteristic
328C42C22×Dic1911yescharacteristic
329C42C2×C22⋊D1911yescharacteristic
330C23—21no—
331C23—41no—
332C23#1059738111yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—81no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—82no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4D4×Dic1911yescharacteristic
363C2×C4D4×Dic1911yescharacteristic
364C2×C4#1059738311yescharacteristic
365C2×C4#1059738511yescharacteristic
366C2×C4#1059738511yescharacteristic
367C2×C4C2×C22⋊Dic1911yescharacteristic
368C8—41no—
369C8—41no—
370C8—762no—
371C8—762no—
372C8—762no—
373C8—1521no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#1192642411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4#1192656111yescharacteristic
392C4#1192656111yescharacteristic
393C4#1192666111yescharacteristic
394C4#1192666611yescharacteristic
395C4#1192680511yescharacteristic
396C4#1192681211yescharacteristic
397C2—41no—
398C2—81no—
399C2—161no—
400C2#1456396411yescharacteristic
401C2#1456408411yescharacteristic
402C2#1456414511yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3106C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3106D19
hypocenterC19#9213
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #14572279C2semidirect
2. #14562227C2semidirect
3. #14562086C2semidirect
4. #14562074C2semidirect
5. #14561526C2semidirect
6. #14561471C2semidirect
277. C19#9213semidirect

Maximal subgroups

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

subgroupindex
#145722792
#145622272
#145620862
#145620742
#145615262
#145614712
C19×#31062
#921319