Finite Group Databasebeta

← #18077449

Subgroups — #18077449

Order 4864.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572805C211yesmaximal, characteristic
2#14564617C211yesmaximal, characteristic, complemented
3#14562121C211yesmaximal, characteristic
4#14562108C211yesmaximal, characteristic, complemented
5#14561529C211yesmaximal, characteristic, complemented
6#14561525C211yesmaximal, characteristic, complemented
7C19×#3172C211yesmaximal, characteristic
8#11926675—21no—
9#11926622—21no—
10#11926616—21no—
11#11926616—21no—
12#11926605—21no—
13#11926601C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926571—21no—
16#11926568C2211yescharacteristic
17#11926390C2211yescharacteristic
18#11926303—21no—
19#11926303—21no—
20#11926281—21no—
21#11926278—21no—
22Q8⋊(C19⋊C8)—21no—
23Q8⋊(C19⋊C8)—21no—
24C19×#533C2211yescharacteristic
25C19×#529C2211yescharacteristic
26C19×#501C411yescharacteristic, complemented
27C19×#497C411yescharacteristic, complemented
28C19×#491C411yescharacteristic, complemented
29C19×#489C411yescharacteristic, complemented
30C19×#470—21no—
31C19×#468—21no—
32C4×Q16×C19—21no—
33C4×SD16×C19—21no—
34C4×M16×C19C2211yescharacteristic
35C2×Q16×C19—21no—
36C2×SD16×C19—21no—
37C2×M16×C19—21no—
38C19×C4⋊Q8C2×C411yescharacteristic
39C19×C4⋊Q8C2×C411yescharacteristic
40C19×#126—21no—
41C19×#125—21no—
42C19×#125C2×C411yescharacteristic
43C19×#124C2×C411yescharacteristic
44C19×#123—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8D411yescharacteristic
48C19×#121D411yescharacteristic
49C4×Q8×C19—21no—
50C4×Q8×C19—21no—
51C4×Q8×C19D411yescharacteristic
52C4×D4×C19—21no—
53C4×D4×C19D411yescharacteristic
54C19×#117—21no—
55C19×#117—21no—
56C2×C42×C19C2311yescharacteristic
57C2×C4×Dic19—21no—
58C2×#64520—21no—
59C2×#64520D411yescharacteristic
60C2×#64520D411yescharacteristic
61C22×C19⋊C8—21no—
62C19×#107—21no—
63C19×#106—21no—
64C19×#103—21no—
65C19×#103—21no—
66C19×#103—21no—
67C19×#102—21no—
68C19×#97C2×C411yescharacteristic
69C19×#97C2×C411yescharacteristic
70C4×C8×C19—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4⋊(C19⋊C8)D411yescharacteristic
83C4⋊(C19⋊C8)D411yescharacteristic
84#10597260—21no—
85#10597260—21no—
86C4×C19⋊C8—21no—
87C4×C19⋊C8—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19C22⋊C411yescharacteristic
91C2×D4×C19—21no—
92C2×D4×C19C22⋊C411yescharacteristic
93C22×C4×C19—21no—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—41no—
98Q16×C19—42no—
99SD16×C19—42no—
100M16×C19—42no—
101C2×C8×C19—21no—
102C2×C8×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19C22⋊C411yescharacteristic
114C4⋊C4×C19C22⋊C411yescharacteristic
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—21no—
120C22⋊C4×C19—41no—
121C42×C19—21no—
122C42×C19—41no—
123C42×C19C22×C411yescharacteristic
124C42×C19C2×D411yescharacteristic
125C42×C19C2×D411yescharacteristic
126C42×C19#4111yescharacteristic
127C4×Dic19—22no—
128C4×Dic19—41no—
129#64520—41no—
130#64520—41no—
131#64520—81no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—81no—
138#8998—191nomaximal, Sylow
139C23×C19—21no—
140C23×C19#12111yescharacteristic
141Q8×C19—41no—
142Q8×C19—41no—
143Q8×C19—41no—
144Q8×C19—42no—
145D4×C19—41no—
146D4×C19—81no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19C2×C22⋊C411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12311yescharacteristic
164C2×Dic19—42no—
165C2×Dic19—81no—
166C2×Dic19—81no—
167C8×C19—22no—
168C8×C19—41no—
169C19⋊C8—41no—
170C19⋊C8—41no—
171C19⋊C8—41no—
172C19⋊C8—41no—
173C19⋊C8—81no—
174#3172D1911yescharacteristic
175#2995—191no—
176#1995—191no—
177#1500—191no—
178#1497—191no—
179#1300—191no—
180#1299—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19#38611yescharacteristic
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—81no—
197C4×C19—81no—
198C4×C19#45511yescharacteristic
199C4×C19#45611yescharacteristic
200Dic19—82no—
201#533C2×D1911yescharacteristic
202#529C2×D1911yescharacteristic
203#501Dic1911yescharacteristic, complemented
204#497Dic1911yescharacteristic, complemented
205#491Dic1911yescharacteristic, complemented
206#489Dic1911yescharacteristic, complemented
207#470—21no—
208#468—21no—
209#446—381no—
210C4×Q16—21no—
211C4×SD16—21no—
212#436—381no—
213#435—381no—
214#435—381no—
215#433—381no—
216#432—191no—
217#431—191no—
218#424—381no—
219#423—191no—
220C4×M16C2×D1911yescharacteristic
221#376—191no—
222#339—381no—
223#339—381no—
224#328—381no—
225#327—381no—
226Q8⋊C8—381no—
227Q8⋊C8—381no—
228C2×C19—41no—
229C2×C19—81no—
230C2×C19#188111yescharacteristic
231C2×C19#188211yescharacteristic
232C2×C19#188411yescharacteristic
233C2×Q16—21no—
234C2×SD16—21no—
235C2×M16—21no—
236C2×M16—191no—
237C2×M16—191no—
238C2×M16—381no—
239C22×C8—381no—
240C4⋊Q8C2×Dic1911yescharacteristic
241C4⋊Q8C2×Dic1911yescharacteristic
242#126—21no—
243#125—21no—
244#125C2×Dic1911yescharacteristic
245#124C2×Dic1911yescharacteristic
246#123—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8C22⋊D1911yescharacteristic
250#121C22⋊D1911yescharacteristic
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8C22⋊D1911yescharacteristic
254C4×D4—21no—
255C4×D4C22⋊D1911yescharacteristic
256#117—21no—
257#117—21no—
258C2×C42—381no—
259C2×C42C22×D1911yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—191no—
263C4⋊C8—191no—
264C4⋊C8—381no—
265C4⋊C8—381no—
266C4⋊C8—381no—
267C4⋊C8—381no—
268C4⋊C8—381no—
269#103—21no—
270#103—21no—
271#103—21no—
272#102—21no—
273C22⋊C8—381no—
274C22⋊C8—381no—
275C22⋊C8—381no—
276C22⋊C8—381no—
277#97—381no—
278#97—381no—
279#97C2×Dic1911yescharacteristic
280#97C2×Dic1911yescharacteristic
281C4×C8—21no—
282C4×C8—381no—
283C4×C8—381no—
284#95—381no—
285#95—381no—
286C19#899811yescharacteristic, complemented, Sylow
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊Dic1911yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊Dic1911yescharacteristic
292C22×C4—21no—
293C22×C4—761no—
294C22×C4D4×D1911yescharacteristic
295C22×C4#6454311yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300M16—761no—
301M16—761no—
302M16—1521no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—381no—
306C2×C8—381no—
307C2×C8—381no—
308C2×C8—381no—
309C2×C8—761no—
310C2×C8—1521no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4C22⋊Dic1911yescharacteristic
322C4⋊C4C22⋊Dic1911yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—41no—
331C42—382no—
332C42—761no—
333C42D4×D1911yescharacteristic
334C42#6454311yescharacteristic
335C42C22×Dic1911yescharacteristic
336C42C2×C22⋊D1911yescharacteristic
337C23—21no—
338C23#1059738511yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—762no—
357C2×C4—1521no—
358C2×C4—1521no—
359C2×C4D4×Dic1911yescharacteristic
360C2×C4D4×Dic1911yescharacteristic
361C2×C4#1059738111yescharacteristic
362C2×C4#1059738311yescharacteristic
363C2×C4#1059738511yescharacteristic
364C2×C4C2×C22⋊Dic1911yescharacteristic
365C8—22no—
366C8—41no—
367C8—761no—
368C8—761no—
369C8—761no—
370C8—761no—
371C8—1521no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1192642411yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C4—1522no—
390C4#1192672011yescharacteristic
391C4#1192672511yescharacteristic
392C2—41no—
393C2—81no—
394C2#1456399911yescharacteristic
395C2#1456400611yescharacteristic
396C2#1456401911yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3172C2
socleC22×C19#386
prime radicalC19×#121D4
cosocleC2×C42×C19C23
hypercenter#3172D19
hypocenterC19#8998
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #14564617C2semidirect
4. #14562108C2semidirect
5. #14561529C2semidirect
6. #14561525C2semidirect
26. C19×#501C4semidirect
27. C19×#497C4semidirect
28. C19×#491C4semidirect
29. C19×#489C4semidirect
203. #501Dic19semidirect
204. #497Dic19semidirect
205. #491Dic19semidirect
206. #489Dic19semidirect
286. C19#8998semidirect

Maximal subgroups

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

subgroupindex
#145728052
#145646172
#145621212
#145621082
#145615292
#145615252
C19×#31722
#899819