Finite Group Databasebeta

← #18079688

Subgroups — #18079688

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572760C211yesmaximal, characteristic, complemented
2#14564476C211yesmaximal, characteristic, complemented
3#14562303C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic, complemented
5C19⋊#1309C211yesmaximal, characteristic, complemented
6#14561524C211yesmaximal, characteristic, complemented
7C19×#3038C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—22no—
10D4×C19⋊C8—21no—
11#11926601—21no—
12#11926597C2211yescharacteristic
13#11926568C2211yescharacteristic
14#11926568C2211yescharacteristic
15C2×C4⋊(C19⋊C8)—21no—
16C2×#10597290—22no—
17C4×#64520C2211yescharacteristic
18#11926288—21no—
19#11926288—21no—
20Q8⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C2×C19×AGL(1,ℤ/8)C412yes—
23C2×C19×#127C2211yescharacteristic
24C4×#41×C19C2211yescharacteristic
25C19×#460—21no—
26C19×#460—21no—
27C19×#459—21no—
28C19×#459—21no—
29C19×#423C2211yescharacteristic
30C19×#418C412yes—
31C2×#41×C19C2×C411yescharacteristic
32C22×D4×C19—21no—
33C22×D4×C19—21no—
34C22×D4×C19C2×C412yes—
35C19×AGL(1,ℤ/8)—44no—
36C2×SD16×C19—22no—
37C2×D8×C19—22no—
38C2×M16×C19C2×C412yes—
39C19×#127—21no—
40C19×#127—21no—
41C19×#127—21no—
42C19×#127—21no—
43C4×Q8×C19D411yescharacteristic
44C4×Q8×C19D411yescharacteristic
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19D411yescharacteristic
48C4×D4×C19D411yescharacteristic
49C19×#117—21no—
50C19×#117C2×C411yescharacteristic
51C2×C42×C19—21no—
52C2×C42×C19C2311yescharacteristic
53C2×#64520—21no—
54C2×#64520—21no—
55C2×#64520D412yes—
56C22×C19⋊C8—22no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59C19×#102—22no—
60C19×#102—22no—
61#10597290—44no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—22no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)D411yescharacteristic
70C4⋊(C19⋊C8)D411yescharacteristic
71#10597260—22no—
72#10597260—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C24×C19—22no—
76#41×C19—22no—
77#41×C19—41no—
78C2×Q8×C19C22⋊C411yescharacteristic
79C2×D4×C19—21no—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19—42no—
83C2×D4×C19—42no—
84C2×D4×C19—42no—
85C2×D4×C19—42no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—81no—
91C2×D4×C19—81no—
92C2×D4×C19C22⋊C411yescharacteristic
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19#4111yescharacteristic
99SD16×C19—44no—
100D8×C19—44no—
101M16×C19—42no—
102C2×C8×C19—22no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19C22⋊C411yescharacteristic
106C4⋊C4×C19C22⋊C411yescharacteristic
107C22⋊C4×C19—21no—
108C22⋊C4×C19—21no—
109C22⋊C4×C19—21no—
110C42×C19—21no—
111C42×C19—21no—
112C42×C19—21no—
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117#64520—22no—
118#64520—41no—
119#64520—42no—
120#64520—81no—
121C2×C19⋊C8—21no—
122C2×C19⋊C8—21no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—82no—
127#9359—191nomaximal, Sylow
128C23×C19—21no—
129C23×C19—44no—
130C23×C19—42no—
131C23×C19—82no—
132C23×C19—82no—
133C23×C19C4×D411yescharacteristic
134Q8×C19—21no—
135Q8×C19—21no—
136D4×C19—21no—
137D4×C19—42no—
138D4×C19—42no—
139D4×C19—42no—
140D4×C19—82no—
141D4×C19—82no—
142D4×C19—82no—
143D4×C19—81no—
144D4×C19—81no—
145D4×C19—81no—
146D4×C19—81no—
147D4×C19#10012yescomplemented
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—42no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C8×C19—42no—
169C19⋊C8—42no—
170C19⋊C8—41no—
171C19⋊C8—42no—
172C19⋊C8—41no—
173C19⋊C8—81no—
174#3038D1911yescharacteristic
175#2990—191no—
176#1965—191no—
177#1545—191no—
178#1489—191no—
179#1309—191no—
180#1299—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—22no—
184C22×C19—21no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19—82no—
188C22×C19—82no—
189C22×C19—82no—
190C22×C19—164no—
191C22×C19#38611yescharacteristic
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19—41no—
198C4×C19C2×#10011yescharacteristic
199C4×C19#41311yescharacteristic
200C4×C19#45311yescharacteristic
201C4×C19#45411yescharacteristic
202C4×C19#47111yescharacteristic
203C4×C19#47211yescharacteristic
204C2×AGL(1,ℤ/8)Dic1912yes—
205C2×#127C2×D1911yescharacteristic
206C4×#41C2×D1911yescharacteristic
207#460—21no—
208#460—21no—
209#459—21no—
210#459—21no—
211#446—381no—
212#435—382no—
213C8×D4—381no—
214#432—381no—
215#431—191no—
216#423—191no—
217#423—191no—
218#423C2×D1911yescharacteristic
219C2×C4⋊C8—381no—
220#418Dic1912yes—
221C2×#100—382no—
222C4×M16—191no—
223#331—381no—
224#331—381no—
225Q8⋊C8—381no—
226D4⋊C8—381no—
227C2×C19—41no—
228C2×C19—42no—
229C2×C19—162no—
230C2×C19#188311yescharacteristic
231C2×C19#190011yescharacteristic
232C2×C19#190711yescharacteristic
233C2×#41C2×Dic1911yescharacteristic
234C22×D4—21no—
235C22×D4—21no—
236C22×D4C2×Dic1912yes—
237AGL(1,ℤ/8)—44no—
238C2×SD16—22no—
239C2×D8—22no—
240C2×M16—192no—
241C2×M16—381no—
242C2×M16—381no—
243C2×M16C2×Dic1912yes—
244C22×C8—382no—
245#127—21no—
246#127—21no—
247#127—21no—
248#127—21no—
249C4×Q8C22⋊D1911yescharacteristic
250C4×Q8C22⋊D1911yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C22⋊D1911yescharacteristic
254C4×D4C22⋊D1911yescharacteristic
255#117—21no—
256#117C2×Dic1911yescharacteristic
257C2×C42—21no—
258C2×C42C22×D1911yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—191no—
262C4⋊C8—191no—
263C4⋊C8—382no—
264C4⋊C8—381no—
265C4⋊C8—381no—
266C4⋊C8—381no—
267C4⋊C8—381no—
268#102—22no—
269#102—22no—
270#100—764no—
271C22⋊C8—382no—
272C22⋊C8—381no—
273#97—382no—
274#97—381no—
275C4×C8—381no—
276C4×C8—381no—
277C19#935911yescharacteristic, complemented, Sylow
278C24—22no—
279#41—22no—
280#41—41no—
281C2×Q8C22⋊Dic1911yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4C22⋊Dic1911yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4D4×D1911yescharacteristic
300C22×C4#6454311yescharacteristic
301C22×C4C22×Dic1911yescharacteristic
302SD16—44no—
303D8—44no—
304M16—42no—
305M16—382no—
306M16—761no—
307M16—762no—
308M16—1521no—
309C2×C8—22no—
310C2×C8—381no—
311C2×C8—381no—
312C2×C8—382no—
313C2×C8—761no—
314C2×C8—761no—
315C2×C8—1522no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4C22⋊Dic1911yescharacteristic
319C4⋊C4C22⋊Dic1911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42D4×D1911yescharacteristic
327C42#6454311yescharacteristic
328C42C2×C22⋊D1911yescharacteristic
329C42C2×C22⋊D1911yescharacteristic
330C23—21no—
331C23—44no—
332C23—42no—
333C23—82no—
334C23—82no—
335C23D4×Dic1911yescharacteristic
336Q8—21no—
337Q8—21no—
338D4—21no—
339D4—42no—
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4#1059729012yescomplemented
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4D4×Dic1911yescharacteristic
365C2×C4#1059738111yescharacteristic
366C2×C4#1059738311yescharacteristic
367C2×C4#1059738511yescharacteristic
368C2×C4#1059738511yescharacteristic
369C2×C4C2×C22⋊Dic1911yescharacteristic
370C8—42no—
371C8—762no—
372C8—761no—
373C8—762no—
374C8—761no—
375C8—1521no—
376C22—21no—
377C22—22no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—164no—
386C22#1192642411yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4C2×#1059729011yescharacteristic
394C4#1192652811yescharacteristic
395C4#1192671011yescharacteristic
396C4#1192671511yescharacteristic
397C4#1192680511yescharacteristic
398C4#1192681211yescharacteristic
399C2—41no—
400C2—42no—
401C2—162no—
402C2#1456401311yescharacteristic
403C2#1456409911yescharacteristic
404C2#1456414511yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3038C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3038D19
hypocenterC19#9359
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #14572760C2semidirect
2. #14564476C2semidirect
3. #14562303C2semidirect
4. #14562074C2semidirect
5. C19⋊#1309C2semidirect
6. #14561524C2semidirect
147. D4×C19#100semidirect
277. C19#9359semidirect
349. D4#10597290semidirect

Maximal subgroups

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

subgroupindex
#145727602
#145644762
#145623032
#145620742
C19⋊#13092
#145615242
C19×#30382
#935919