Finite Group Databasebeta

← #18077442

Subgroups — #18077442

Order 4864.

452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572805C211yesmaximal, characteristic, complemented
2#14564468C211yesmaximal, characteristic, complemented
3#14562121C211yesmaximal, characteristic, complemented
4#14562104C211yesmaximal, characteristic, complemented
5#14561529C211yesmaximal, characteristic, complemented
6#14561525C211yesmaximal, characteristic, complemented
7C19×#3171C211yesmaximal, 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
17C2×#10597294—21no—
18C2×#10597294—21no—
19#11926390C2211yescharacteristic
20#11926281—21no—
21#11926278—21no—
22D4⋊(C19⋊C8)—21no—
23D4⋊(C19⋊C8)—21no—
24C19×#532C2211yescharacteristic
25C19×#529C2211yescharacteristic
26C19×#501C411yescharacteristic, complemented
27C19×#496C411yescharacteristic, complemented
28C19×#490C411yescharacteristic, complemented
29C19×#489C411yescharacteristic, complemented
30C19×#469—21no—
31C19×#468—21no—
32C4×SD16×C19—21no—
33C4×D8×C19—21no—
34C4×M16×C19C2211yescharacteristic
35C2×#41×C19—21no—
36C2×SD16×C19—21no—
37C2×D8×C19—21no—
38C2×M16×C19—21no—
39C19×C4⋊Q8C2×C411yescharacteristic
40C19×#127C2×C411yescharacteristic
41C19×#126—21no—
42C19×#125C2×C411yescharacteristic
43C19×#124—21no—
44C19×#124C2×C411yescharacteristic
45C19×#123—21no—
46C19×C22⋊Q8D411yescharacteristic
47C19×#121—21no—
48C19×#121—21no—
49C19×#121D411yescharacteristic
50C4×Q8×C19D411yescharacteristic
51C4×D4×C19—21no—
52C4×D4×C19—21no—
53C4×D4×C19—21no—
54C4×D4×C19D411yescharacteristic
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×#102—21no—
66C19×#102—21no—
67C19×#102—21no—
68C19×#97C2×C411yescharacteristic
69C19×#97C2×C411yescharacteristic
70C4×C8×C19—21no—
71#10597294—42no—
72#10597294—42no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4⋊(C19⋊C8)—21no—
83C4⋊(C19⋊C8)—21no—
84C4⋊(C19⋊C8)D411yescharacteristic
85C4⋊(C19⋊C8)D411yescharacteristic
86#10597260—21no—
87#10597260—21no—
88C4×C19⋊C8—21no—
89C4×C19⋊C8—21no—
90#41×C19—41no—
91#41×C19—41no—
92#41×C19—41no—
93#41×C19—41no—
94C2×Q8×C19—21no—
95C2×Q8×C19C22⋊C411yescharacteristic
96C2×D4×C19—21no—
97C2×D4×C19—21no—
98C2×D4×C19—21no—
99C2×D4×C19—21no—
100C2×D4×C19—41no—
101C2×D4×C19C22⋊C411yescharacteristic
102C22×C4×C19—21no—
103C22×C4×C19—41no—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×Dic19—41no—
108SD16×C19—42no—
109D8×C19—42no—
110M16×C19—42no—
111C2×C8×C19—21no—
112C2×C8×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19C22⋊C411yescharacteristic
120C4⋊C4×C19C22⋊C411yescharacteristic
121C22⋊C4×C19—21no—
122C22⋊C4×C19—21no—
123C22⋊C4×C19—21no—
124C22⋊C4×C19—21no—
125C22⋊C4×C19—21no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C42×C19—21no—
129C42×C19C22×C411yescharacteristic
130C42×C19C2×D411yescharacteristic
131C42×C19C2×D411yescharacteristic
132C42×C19#4111yescharacteristic
133C4×Dic19—22no—
134C4×Dic19—41no—
135#64520—41no—
136#64520—41no—
137#64520—81no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—81no—
144#8997—191nomaximal, Sylow
145C23×C19—21no—
146C23×C19—41no—
147C23×C19#12111yescharacteristic
148Q8×C19—41no—
149Q8×C19—41no—
150Q8×C19—41no—
151D4×C19—41no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—42no—
155D4×C19—41no—
156D4×C19—41no—
157D4×C19—81no—
158D4×C19—81no—
159D4×C19—81no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—21no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—81no—
171C2×C4×C19—81no—
172C2×C4×C19C2×C22⋊C411yescharacteristic
173C2×C4×C19C4×D411yescharacteristic
174C2×C4×C19C4×D411yescharacteristic
175C2×C4×C19#12011yescharacteristic
176C2×C4×C19#12111yescharacteristic
177C2×C4×C19#12311yescharacteristic
178C2×Dic19—42no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181C8×C19—22no—
182C8×C19—41no—
183C19⋊C8—41no—
184C19⋊C8—41no—
185C19⋊C8—41no—
186C19⋊C8—41no—
187C19⋊C8—81no—
188#3171D1911yescharacteristic
189#2995—191no—
190#1963—191no—
191#1500—191no—
192#1496—191no—
193#1300—191no—
194#1299—191no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19—41no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19#38611yescharacteristic
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—41no—
211C4×C19—41no—
212C4×C19—41no—
213C4×C19—81no—
214C4×C19#45311yescharacteristic
215C4×C19#45411yescharacteristic
216Dic19—82no—
217#532C2×D1911yescharacteristic
218#529C2×D1911yescharacteristic
219#501Dic1911yescharacteristic, complemented
220#496Dic1911yescharacteristic, complemented
221#490Dic1911yescharacteristic, complemented
222#489Dic1911yescharacteristic, complemented
223#469—21no—
224#468—21no—
225#446—381no—
226C4×SD16—21no—
227C4×D8—21no—
228#436—381no—
229#435—381no—
230#435—381no—
231#433—381no—
232#432—191no—
233#431—191no—
234#424—381no—
235#423—191no—
236C2×#104—381no—
237C2×#104—381no—
238C4×M16C2×D1911yescharacteristic
239#376—191no—
240#328—381no—
241#327—381no—
242D4⋊C8—381no—
243D4⋊C8—381no—
244C2×C19—41no—
245C2×C19—81no—
246C2×C19—161no—
247C2×C19#188111yescharacteristic
248C2×C19#188311yescharacteristic
249C2×C19#188411yescharacteristic
250C2×#41—21no—
251C2×SD16—21no—
252C2×D8—21no—
253C2×M16—21no—
254C2×M16—191no—
255C2×M16—191no—
256C2×M16—381no—
257C22×C8—381no—
258C4⋊Q8C2×Dic1911yescharacteristic
259#127C2×Dic1911yescharacteristic
260#126—21no—
261#125C2×Dic1911yescharacteristic
262#124—21no—
263#124C2×Dic1911yescharacteristic
264#123—21no—
265C22⋊Q8C22⋊D1911yescharacteristic
266#121—21no—
267#121—21no—
268#121C22⋊D1911yescharacteristic
269C4×Q8C22⋊D1911yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4C22⋊D1911yescharacteristic
274#117—21no—
275C2×C42—381no—
276C2×C42C22×D1911yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—191no—
280C4⋊C8—191no—
281C4⋊C8—381no—
282C4⋊C8—381no—
283C4⋊C8—381no—
284C4⋊C8—381no—
285C4⋊C8—381no—
286#104—762no—
287#104—762no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294C22⋊C8—381no—
295C22⋊C8—381no—
296#97—381no—
297#97—381no—
298#97C2×Dic1911yescharacteristic
299#97C2×Dic1911yescharacteristic
300C4×C8—21no—
301C4×C8—381no—
302C4×C8—381no—
303#95—381no—
304#95—381no—
305C19#899711yescharacteristic, complemented, Sylow
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310C2×Q8—21no—
311C2×Q8C22⋊Dic1911yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4C22⋊Dic1911yescharacteristic
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—761no—
321C22×C4D4×D1911yescharacteristic
322C22×C4#6454311yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324SD16—42no—
325D8—42no—
326M16—42no—
327M16—761no—
328M16—761no—
329M16—1521no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—381no—
333C2×C8—381no—
334C2×C8—381no—
335C2×C8—381no—
336C2×C8—761no—
337C2×C8—1521no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4C22⋊Dic1911yescharacteristic
345C4⋊C4C22⋊Dic1911yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—21no—
354C42—382no—
355C42—761no—
356C42D4×D1911yescharacteristic
357C42#6454311yescharacteristic
358C42C22×Dic1911yescharacteristic
359C42C2×C22⋊D1911yescharacteristic
360C23—21no—
361C23—41no—
362C23#1059738511yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—762no—
388C2×C4—1521no—
389C2×C4—1521no—
390C2×C4D4×Dic1911yescharacteristic
391C2×C4D4×Dic1911yescharacteristic
392C2×C4#1059738111yescharacteristic
393C2×C4#1059738311yescharacteristic
394C2×C4#1059738511yescharacteristic
395C2×C4C2×C22⋊Dic1911yescharacteristic
396C8—22no—
397C8—41no—
398C8—761no—
399C8—761no—
400C8—761no—
401C8—761no—
402C8—1521no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1192642411yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—81no—
422C4—1522no—
423C4#1192671011yescharacteristic
424C4#1192671511yescharacteristic
425C2—41no—
426C2—81no—
427C2—161no—
428C2#1456399911yescharacteristic
429C2#1456401311yescharacteristic
430C2#1456401911yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3171C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3171D19
hypocenterC19#8997
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #14572805C2semidirect
2. #14564468C2semidirect
3. #14562121C2semidirect
4. #14562104C2semidirect
5. #14561529C2semidirect
6. #14561525C2semidirect
26. C19×#501C4semidirect
27. C19×#496C4semidirect
28. C19×#490C4semidirect
29. C19×#489C4semidirect
219. #501Dic19semidirect
220. #496Dic19semidirect
221. #490Dic19semidirect
222. #489Dic19semidirect
305. C19#8997semidirect

Maximal subgroups

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

subgroupindex
#145728052
#145644682
#145621212
#145621042
#145615292
#145615252
C19×#31712
#899719