Finite Group Databasebeta

← #18078469

Subgroups — #18078469

Order 4864.

446 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566600C211yesmaximal, characteristic
2#14562199C211yesmaximal, characteristic
3#14562134C211yesmaximal, characteristic
4#14562030C211yesmaximal, characteristic
5#14561536C211yesmaximal, characteristic
6#14561495C211yesmaximal, characteristic
7C19×#3078C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9#11926597C2211yescharacteristic
10#11926451—21no—
11#11926430—22no—
12#11926412—21no—
13#11926410C2211yescharacteristic
14C4⋊C4×Dic19—21no—
15C4×C4⋊Dic19C2211yescharacteristic
16#11926390—21no—
17#11926281—21no—
18#11926281—21no—
19#11926281—22no—
20Q8⋊(C19⋊C8)—22no—
21C19×#533C2211yescharacteristic
22C2×C4×Q8×C19C2211yescharacteristic
23C19×#479—22no—
24C19×#477C412yescomplemented
25C19×#475C412yescomplemented
26C19×#428—21no—
27C19×#423C2211yescharacteristic
28C19×#419—21no—
29C22×Q8×C19D411yescharacteristic
30C2×M16×C19—21no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19C2×C412yes—
41C4×Q8×C19D412yes—
42C19×#117—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—22no—
50C2×C4×Dic19—21no—
51C19×#107—22no—
52C19×#106—22no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8C2×C412yes—
55C19×#103—22no—
56C19×#103—22no—
57C19⋊#95—22no—
58C19⋊#95—22no—
59C19⋊#95—22no—
60C19⋊#95—21no—
61C19⋊#95D411yescharacteristic
62C19⋊#95D411yescharacteristic
63C19⋊#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4×C19⋊C8—21no—
69C4×C19⋊C8—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19C22⋊C412yes—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×Dic19—21no—
84C22×Dic19—22no—
85C22×Dic19—21no—
86M16×C19—41no—
87M16×C19—41no—
88C2×C8×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19C22⋊C412yes—
99C22⋊C4×C19—41no—
100C42×C19—22no—
101C42×C19—22no—
102C42×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C42×C19#4111yescharacteristic
107C4⋊Dic19—42no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4×Dic19—44no—
111C4×Dic19—41no—
112C4×Dic19—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115#9178—191nomaximal, Sylow
116C23×C19#12011yescharacteristic
117Q8×C19—22no—
118Q8×C19—22no—
119Q8×C19—41no—
120Q8×C19—41no—
121Q8×C19—81no—
122Q8×C19—81no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12311yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13711yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—42no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—42no—
149C2×Dic19—41no—
150C2×Dic19—42no—
151C8×C19—42no—
152C19⋊C8—81no—
153C19⋊C8—81no—
154#3078D1911yescharacteristic
155#2356—191no—
156#1518—191no—
157#1503—191no—
158#1479—191no—
159#1303—191no—
160#1286—191no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19#38611yescharacteristic
164C22×C19#45211yescharacteristic
165C22×C19#45211yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—42no—
171C4×C19—42no—
172C4×C19—81no—
173C4×C19—81no—
174C4×C19#41611yescharacteristic
175C4×C19#41911yescharacteristic
176C4×C19#48511yescharacteristic
177C4×C19#48511yescharacteristic
178Dic19—42no—
179Dic19—81no—
180Dic19—82no—
181#533C2×D1911yescharacteristic
182C2×C4×Q8C2×D1911yescharacteristic
183#479—22no—
184#477Dic1912yescomplemented
185#475Dic1912yescomplemented
186#431—191no—
187#431—191no—
188#428—21no—
189#423C2×D1911yescharacteristic
190#419—21no—
191#391—381no—
192#387—382no—
193#383—381no—
194#382—191no—
195C4×C4⋊C4—191no—
196C4×C4⋊C4—381no—
197#376—381no—
198#328—381no—
199#328—381no—
200#328—382no—
201Q8⋊C8—382no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19#187311yescharacteristic
205C2×C19#190511yescharacteristic
206C2×C19#190611yescharacteristic
207C22×Q8C22⋊D1911yescharacteristic
208C2×M16—21no—
209C4⋊Q8C2×Dic1911yescharacteristic
210C4⋊Q8C2×Dic1911yescharacteristic
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8C2×Dic1912yes—
219C4×Q8C22⋊D1912yes—
220#117—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4C22⋊D1911yescharacteristic
225C2×C42—21no—
226C2×C42—382no—
227C2×C42—381no—
228C2×C42C22×D1911yescharacteristic
229#107—22no—
230#106—22no—
231C4⋊C8—21no—
232C4⋊C8—381no—
233C4⋊C8—381no—
234C4⋊C8C2×Dic1912yes—
235#103—22no—
236#103—22no—
237C22⋊C8—381no—
238C22⋊C8—381no—
239C4×C8—381no—
240C4×C8—381no—
241#95—191no—
242#95—191no—
243#95—192no—
244#95—382no—
245#95—382no—
246#95—382no—
247#95—381no—
248C19#917811yescharacteristic, complemented, Sylow
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8C22⋊Dic1912yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—381no—
260C22×C4—382no—
261C22×C4—381no—
262C22×C4D4×D1911yescharacteristic
263C22×C4D4×D1911yescharacteristic
264C22×C4C2×C22⋊D1911yescharacteristic
265M16—41no—
266M16—41no—
267C2×C8—22no—
268C2×C8—761no—
269C2×C8—761no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—762no—
280C4⋊C4—761no—
281C4⋊C4—761no—
282C4⋊C4C22⋊Dic1912yes—
283C22⋊C4—41no—
284C42—22no—
285C42—22no—
286C42—41no—
287C42—764no—
288C42—761no—
289C42—761no—
290C42#6454311yescharacteristic
291C42#6454311yescharacteristic
292C42C22×Dic1911yescharacteristic
293C42C2×C22⋊D1911yescharacteristic
294C23#1059738311yescharacteristic
295Q8—22no—
296Q8—22no—
297Q8—41no—
298Q8—41no—
299Q8—81no—
300Q8—81no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—382no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—762no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—762no—
317C2×C4—761no—
318C2×C4—762no—
319C2×C4D4×Dic1911yescharacteristic
320C2×C4D4×Dic1911yescharacteristic
321C2×C4#1059738111yescharacteristic
322C2×C4#1059738511yescharacteristic
323C2×C4#1059738511yescharacteristic
324C2×C4#1059738811yescharacteristic
325C2×C4#1059738811yescharacteristic
326C2×C4#1059739611yescharacteristic
327C2×C4#1059739611yescharacteristic
328C2×C4C2×C22⋊Dic1911yescharacteristic
329C8—42no—
330C8—1521no—
331C8—1521no—
332C22—21no—
333C22—21no—
334C22#1192642411yescharacteristic
335C22#1192670411yescharacteristic
336C22#1192670411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—81no—
344C4—81no—
345C4—762no—
346C4—1521no—
347C4—1522no—
348C4#1192654011yescharacteristic
349C4#1192655311yescharacteristic
350C4#1192688211yescharacteristic
351C4#1192688211yescharacteristic
352C2—21no—
353C2—21no—
354C2#1456394811yescharacteristic
355C2#1456413111yescharacteristic
356C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3078C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#3078D19
hypocenterC19#9178
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
24. C19×#477C4semidirect
25. C19×#475C4semidirect
184. #477Dic19semidirect
185. #475Dic19semidirect
248. C19#9178semidirect

Maximal subgroups

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

subgroupindex
#145666002
#145621992
#145621342
#145620302
#145615362
#145614952
C19×#30782
#917819