Finite Group Databasebeta

← #18080112

Subgroups — #18080112

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#14572631C211yesmaximal, characteristic
2#14562250C211yesmaximal, characteristic, complemented
3#14562199C211yesmaximal, characteristic, complemented
4#14562173C211yesmaximal, characteristic
5#14561534C211yesmaximal, characteristic, complemented
6#14561517C211yesmaximal, characteristic, complemented
7C19×#3181C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926601C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926500—21no—
16C2×#10597260C2211yescharacteristic
17#11926410C2211yescharacteristic
18#11926286—21no—
19#11926286—21no—
20#11926281—21no—
21#11926281—21no—
22#11926281—21no—
23#11926278—21no—
24C19×#533C2211yescharacteristic
25C19×#529C2211yescharacteristic
26C19×#501C411yescharacteristic, complemented
27C19×#497C411yescharacteristic, complemented
28C19×#491C411yescharacteristic, complemented
29C19×#489C411yescharacteristic, complemented
30C19×#467—21no—
31C19×#465—21no—
32C19×#441—21no—
33C19×#440—21no—
34C2×C19×#97C2211yescharacteristic
35C2×Q16×C19—21no—
36C2×SD16×C19—21no—
37C22×C8×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—
59C22×C19⋊C8—21no—
60C22×C19⋊C8—21no—
61C19×#107—21no—
62C19×#106—21no—
63C19×#103—21no—
64C19×#103—21no—
65C19×#103—21no—
66C19×#102—21no—
67C19×#97—21no—
68C19×#97C2×C411yescharacteristic
69C19×#97C2×C411yescharacteristic
70C19⋊#95—21no—
71C19⋊#95—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)D411yescharacteristic
76C22⋊(C19⋊C8)D411yescharacteristic
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81#10597260—21no—
82#10597260—21no—
83#10597260—21no—
84#10597260D411yescharacteristic
85#10597260D411yescharacteristic
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—
100C2×C8×C19—21no—
101C2×C8×C19—21no—
102C2×C8×C19—42no—
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—81no—
128#64520—42no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—42no—
134C2×C19⋊C8—42no—
135C2×C19⋊C8—41no—
136#9431—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—41no—
140Q8×C19—41no—
141Q8×C19—41no—
142Q8×C19—81no—
143D4×C19—41no—
144D4×C19—41no—
145D4×C19—41no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19C2×C22⋊C411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19#12011yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12311yescharacteristic
163C2×Dic19—81no—
164C2×Dic19—81no—
165C2×Dic19—81no—
166C8×C19—22no—
167C8×C19—41no—
168C19⋊C8—22no—
169C19⋊C8—41no—
170C19⋊C8—41no—
171C19⋊C8—41no—
172C19⋊C8—81no—
173#3181D1911yescharacteristic
174#2968—191no—
175#1531—191no—
176#1518—191no—
177#1512—191no—
178#1302—191no—
179#1295—191no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19#38611yescharacteristic
186C22×C19#47111yescharacteristic
187C22×C19#47311yescharacteristic
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19—81no—
198C4×C19—81no—
199Dic19—161no—
200#533C2×D1911yescharacteristic
201#529C2×D1911yescharacteristic
202#501Dic1911yescharacteristic, complemented
203#497Dic1911yescharacteristic, complemented
204#491Dic1911yescharacteristic, complemented
205#489Dic1911yescharacteristic, complemented
206#467—21no—
207#465—21no—
208#446—381no—
209#441—21no—
210#440—21no—
211#435—381no—
212#435—381no—
213C8×D4—381no—
214#433—381no—
215#432—191no—
216#431—191no—
217#405—381no—
218C2×#97—191no—
219C2×#97C2×D1911yescharacteristic
220#382—191no—
221#330—381no—
222#330—381no—
223#328—381no—
224#328—381no—
225#328—381no—
226#327—381no—
227C2×C19—21no—
228C2×C19—21no—
229C2×C19—81no—
230C2×C19#188411yescharacteristic
231C2×C19#190611yescharacteristic
232C2×C19#190811yescharacteristic
233C2×Q16—21no—
234C2×SD16—21no—
235C2×M16—381no—
236C22×C8—21no—
237C22×C8—381no—
238C22×C8—381no—
239C4⋊Q8C2×Dic1911yescharacteristic
240C4⋊Q8C2×Dic1911yescharacteristic
241#126—21no—
242#125—21no—
243#125C2×Dic1911yescharacteristic
244#124C2×Dic1911yescharacteristic
245#123—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8C22⋊D1911yescharacteristic
249#121C22⋊D1911yescharacteristic
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C22⋊D1911yescharacteristic
253C4×D4—21no—
254C4×D4C22⋊D1911yescharacteristic
255#117—21no—
256#117—21no—
257C2×C4⋊C4—381no—
258C2×C42C22×D1911yescharacteristic
259#107—21no—
260#106—21no—
261C4⋊C8—381no—
262C4⋊C8—381no—
263C4⋊C8—381no—
264C4⋊C8—381no—
265#103—21no—
266#103—21no—
267#103—21no—
268#102—21no—
269C22⋊C8—191no—
270C22⋊C8—191no—
271C22⋊C8—381no—
272C22⋊C8—381no—
273C22⋊C8—381no—
274#97—21no—
275#97—191no—
276#97—191no—
277#97—381no—
278#97—381no—
279#97—381no—
280#97C2×Dic1911yescharacteristic
281#97C2×Dic1911yescharacteristic
282C4×C8—381no—
283C4×C8—381no—
284#95—381no—
285#95—381no—
286C19#943111yescharacteristic, 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—762no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—42no—
303C2×C8—381no—
304C2×C8—381no—
305C2×C8—381no—
306C2×C8—381no—
307C2×C8—762no—
308C2×C8—762no—
309C2×C8—761no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—1521no—
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—
331C42D4×D1911yescharacteristic
332C42#6454311yescharacteristic
333C42C22×Dic1911yescharacteristic
334C42C2×C22⋊D1911yescharacteristic
335C23—21no—
336C23#1059738511yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—1521no—
356C2×C4—1521no—
357C2×C4—1521no—
358C2×C4D4×Dic1911yescharacteristic
359C2×C4D4×Dic1911yescharacteristic
360C2×C4#1059738111yescharacteristic
361C2×C4#1059738311yescharacteristic
362C2×C4#1059738511yescharacteristic
363C2×C4C2×C22⋊Dic1911yescharacteristic
364C8—22no—
365C8—41no—
366C8—382no—
367C8—761no—
368C8—761no—
369C8—761no—
370C8—1521no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#1192642411yescharacteristic
377C22#1192680911yescharacteristic
378C22#1192681711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—3041no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2#1456401911yescharacteristic
395C2#1456413811yescharacteristic
396C2#1456415211yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3181C2
socleC22×C19#386
prime radicalC19×#121D4
cosocleC2×C42×C19C23
hypercenter#3181D19
hypocenterC19#9431
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3181

Complements

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

NH ≅ G/Ntype
2. #14562250C2semidirect
3. #14562199C2semidirect
5. #14561534C2semidirect
6. #14561517C2semidirect
26. C19×#501C4semidirect
27. C19×#497C4semidirect
28. C19×#491C4semidirect
29. C19×#489C4semidirect
202. #501Dic19semidirect
203. #497Dic19semidirect
204. #491Dic19semidirect
205. #489Dic19semidirect
286. C19#9431semidirect

Maximal subgroups

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

subgroupindex
#145726312
#145622502
#145621992
#145621732
#145615342
#145615172
C19×#31812
#943119