Finite Group Databasebeta

← #18078357

Subgroups — #18078357

Order 4864.

472 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#14572655C211yesmaximal, characteristic, complemented
2#14563445C211yesmaximal, characteristic, complemented
3#14562227C211yesmaximal, characteristic, complemented
4#14562143C211yesmaximal, characteristic, complemented
5#14561527C211yesmaximal, characteristic, complemented
6#14561506C211yesmaximal, characteristic, complemented
7C19×#3115C211yesmaximal, characteristic
8Q8×C19⋊C8—21no—
9#11926622—22no—
10#11926622—21no—
11#11926601—21no—
12#11926601C2211yescharacteristic
13C2×#10597294—21no—
14C4×#64520—21no—
15C4×#64520C2211yescharacteristic
16C4×#64520C2211yescharacteristic
17#11926390C2211yescharacteristic
18#11926303—21no—
19#11926284—21no—
20#11926284—21no—
21#11926278—22no—
22C19×#532C2211yescharacteristic
23C4×#41×C19C2211yescharacteristic
24C19×#482—21no—
25C19×#475C411yescharacteristic, complemented
26C19×#474C411yescharacteristic, complemented
27C19×#460C411yescharacteristic, complemented
28C19×#459C411yescharacteristic, complemented
29C19×#449—21no—
30C19×#442—21no—
31C19×#440—21no—
32C19×#432C2211yescharacteristic
33C2×#41×C19—21no—
34C2×#41×C19D411yescharacteristic
35C2×SD16×C19—21no—
36C2×D8×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#127C2×C411yescharacteristic
39C19×#124—21no—
40C19×#121—21no—
41C19×#121—21no—
42C4×Q8×C19C2×C411yescharacteristic
43C4×Q8×C19D411yescharacteristic
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19—21no—
48C4×D4×C19C2×C411yescharacteristic
49C4×D4×C19D411yescharacteristic
50C19×#117—21no—
51C19×#117D411yescharacteristic
52C2×C42×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C4×Dic19—21no—
55C2×#64520—22no—
56C2×#64520—21no—
57C2×#64520—21no—
58C19×#107—21no—
59C19×#106—21no—
60C19×C4⋊C8C2×C411yescharacteristic
61C19×C4⋊C8C2×C411yescharacteristic
62C19×#103—21no—
63C19×#102—21no—
64C19×#102—21no—
65C19×#102—21no—
66C19×C22⋊C8—21no—
67C19×#97—21no—
68#10597294—24no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—22no—
72C22⋊(C19⋊C8)D412yes—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75#10597260—21no—
76#10597260—21no—
77#10597260D411yescharacteristic
78#10597260D411yescharacteristic
79C4×C19⋊C8—22no—
80C4×C19⋊C8—21no—
81C4×C19⋊C8—21no—
82#41×C19—22no—
83#41×C19—41no—
84#41×C19—82no—
85C2×Q8×C19—21no—
86C2×Q8×C19C22⋊C411yescharacteristic
87C2×D4×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—41no—
92C2×D4×C19C22⋊C411yescharacteristic
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—41no—
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×Dic19—41no—
101SD16×C19—42no—
102D8×C19—42no—
103C2×C8×C19—21no—
104C2×C8×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19C22⋊C411yescharacteristic
110C4⋊C4×C19C22⋊C411yescharacteristic
111C22⋊C4×C19—21no—
112C22⋊C4×C19—21no—
113C22⋊C4×C19—21no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C42×C19—21no—
117C42×C19—21no—
118C42×C19—21no—
119C42×C19C22×C411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19#4111yescharacteristic
123C4×Dic19—22no—
124C4×Dic19—41no—
125#64520—22no—
126#64520—42no—
127#64520—44no—
128#64520—41no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—22no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—41no—
133#9162—191nomaximal, Sylow
134C23×C19—21no—
135C23×C19—41no—
136C23×C19#12111yescharacteristic
137Q8×C19—21no—
138Q8×C19—81no—
139Q8×C19#10412yes—
140D4×C19—21no—
141D4×C19—21no—
142D4×C19—42no—
143D4×C19—41no—
144D4×C19—41no—
145D4×C19—81no—
146D4×C19—81no—
147D4×C19—82no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—41no—
158C2×C4×C19—81no—
159C2×C4×C19—82no—
160C2×C4×C19C2×C22⋊C411yescharacteristic
161C2×C4×C19C4×D411yescharacteristic
162C2×C4×C19C4×D411yescharacteristic
163C2×C4×C19#12011yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12311yescharacteristic
166C2×Dic19—42no—
167C2×Dic19—81no—
168C2×Dic19—81no—
169C8×C19—41no—
170C8×C19—41no—
171C19⋊C8—22no—
172C19⋊C8—42no—
173C19⋊C8—41no—
174C19⋊C8—42no—
175#3115D1911yescharacteristic
176#2971—191no—
177#1759—191no—
178#1525—191no—
179#1505—191no—
180#1300—191no—
181#1291—191no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19—41no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19#38611yescharacteristic
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—81no—
201C4×C19C2×#10411yescharacteristic
202C4×C19#42111yescharacteristic
203Dic19—82no—
204#532C2×D1911yescharacteristic
205C4×#41C2×D1911yescharacteristic
206#482—21no—
207#475Dic1911yescharacteristic, complemented
208#474Dic1911yescharacteristic, complemented
209#460Dic1911yescharacteristic, complemented
210#459Dic1911yescharacteristic, complemented
211#449—21no—
212C8×Q8—381no—
213#442—21no—
214#440—21no—
215#436—382no—
216#436—381no—
217#432—191no—
218#432—381no—
219#432C2×D1911yescharacteristic
220C2×#104—381no—
221C4×M16—191no—
222C4×M16—191no—
223C4×M16—381no—
224#376—191no—
225#339—381no—
226#329—381no—
227#329—381no—
228#327—382no—
229C2×C19—41no—
230C2×C19—81no—
231C2×C19—161no—
232C2×C19#187111yescharacteristic
233C2×C19#190311yescharacteristic
234C2×C19#190611yescharacteristic
235C2×#41—21no—
236C2×#41C22⋊D1911yescharacteristic
237C2×SD16—21no—
238C2×D8—21no—
239C2×M16—382no—
240C2×M16—381no—
241C2×M16—381no—
242C4⋊Q8C2×Dic1911yescharacteristic
243#127C2×Dic1911yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×Q8C2×Dic1911yescharacteristic
248C4×Q8C22⋊D1911yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C2×Dic1911yescharacteristic
254C4×D4C22⋊D1911yescharacteristic
255#117—21no—
256#117C22⋊D1911yescharacteristic
257C2×C42—21no—
258C2×C42—381no—
259C2×C42C22×D1911yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—382no—
263C4⋊C8—381no—
264C4⋊C8C2×Dic1911yescharacteristic
265C4⋊C8C2×Dic1911yescharacteristic
266#104—384no—
267#103—21no—
268#102—21no—
269#102—21no—
270#102—21no—
271C22⋊C8—21no—
272C22⋊C8—192no—
273C22⋊C8—382no—
274#97—21no—
275#97—191no—
276#97—191no—
277#97—381no—
278#97—381no—
279C4×C8—382no—
280C4×C8—381no—
281C4×C8—381no—
282#95—381no—
283#95—381no—
284C19#916211yescharacteristic, complemented, Sylow
285#41—22no—
286#41—41no—
287#41—82no—
288C2×Q8—21no—
289C2×Q8C22⋊Dic1911yescharacteristic
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4C22⋊Dic1911yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—761no—
301C22×C4D4×D1911yescharacteristic
302C22×C4#6454311yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304SD16—42no—
305D8—42no—
306M16—382no—
307M16—762no—
308M16—764no—
309M16—761no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—381no—
313C2×C8—381no—
314C2×C8—382no—
315C2×C8—761no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4C22⋊Dic1911yescharacteristic
321C4⋊C4C22⋊Dic1911yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42—382no—
331C42—761no—
332C42D4×D1911yescharacteristic
333C42#6454311yescharacteristic
334C42C22×Dic1911yescharacteristic
335C42C2×C22⋊D1911yescharacteristic
336C23—21no—
337C23—41no—
338C23#1059738511yescharacteristic
339Q8—21no—
340Q8—81no—
341Q8#1059729412yes—
342D4—21no—
343D4—21no—
344D4—42no—
345D4—41no—
346D4—41no—
347D4—81no—
348D4—81no—
349D4—82no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—762no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4D4×Dic1911yescharacteristic
366C2×C4D4×Dic1911yescharacteristic
367C2×C4#1059738111yescharacteristic
368C2×C4#1059738311yescharacteristic
369C2×C4#1059738511yescharacteristic
370C2×C4C2×C22⋊Dic1911yescharacteristic
371C8—41no—
372C8—41no—
373C8—382no—
374C8—761no—
375C8—762no—
376C8—762no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#1192642411yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—1522no—
397C4C2×#1059729411yescharacteristic
398C4#1192656111yescharacteristic
399C2—41no—
400C2—81no—
401C2—161no—
402C2#1456393811yescharacteristic
403C2#1456411711yescharacteristic
404C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3115C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3115D19
hypocenterC19#9162
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #14572655C2semidirect
2. #14563445C2semidirect
3. #14562227C2semidirect
4. #14562143C2semidirect
5. #14561527C2semidirect
6. #14561506C2semidirect
25. C19×#475C4semidirect
26. C19×#474C4semidirect
27. C19×#460C4semidirect
28. C19×#459C4semidirect
207. #475Dic19semidirect
208. #474Dic19semidirect
209. #460Dic19semidirect
210. #459Dic19semidirect
284. C19#9162semidirect

Maximal subgroups

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

subgroupindex
#145726552
#145634452
#145622272
#145621432
#145615272
#145615062
C19×#31152
#916219