Finite Group Databasebeta

← #18073953

Subgroups — #18073953

Order 4864.

710 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564572C211yesmaximal, characteristic, complemented
2#14562022C212yesmaximal, complemented
3#14562017C212yesmaximal, complemented
4#14561959C211yesmaximal, characteristic, complemented
5C19×#3461C211yesmaximal, characteristic
6#11926597C2212yes—
7C2×C4⋊(C19⋊C8)C2211yescharacteristic
8C2×C4×C19⋊C8C2211yescharacteristic
9#11926299—22no—
10Q8⋊(C19⋊C8)—22no—
11Q8⋊(C19⋊C8)—22no—
12D4⋊(C19⋊C8)—22no—
13D4⋊(C19⋊C8)—22no—
14#11926270—22no—
15C19×#544C411yescharacteristic
16C19×#542—22no—
17C19×#541—22no—
18C19×#539—22no—
19C19×#537C411yescharacteristic
20C19×#536C412yes—
21C19×#533—22no—
22C19×#529—22no—
23C19×#529—22no—
24C4×#41×C19C2212yes—
25C2×C4×Q8×C19C2211yescharacteristic
26C2×#41×C19C2×C412yes—
27C22×Q8×C19C2×C411yescharacteristic
28C19×C4⋊Q8—22no—
29C19×C4⋊Q8—22no—
30C19×#126—24no—
31C19×#126—24no—
32C19×#125—22no—
33C19×#125—24no—
34C19×#125—22no—
35C19×#124—22no—
36C19×#124—22no—
37C19×#123—24no—
38C19×#123—24no—
39C19×C22⋊Q8—24no—
40C19×C22⋊Q8—22no—
41C19×C22⋊Q8—22no—
42C19×C22⋊Q8—22no—
43C19×C22⋊Q8—22no—
44C19×#121—22no—
45C19×#121—22no—
46C4×Q8×C19—22no—
47C4×Q8×C19—22no—
48C4×Q8×C19—22no—
49C4×Q8×C19D412yes—
50C4×Q8×C19D412yes—
51C4×D4×C19—22no—
52C4×D4×C19—22no—
53C4×D4×C19—22no—
54C4×D4×C19D412yes—
55C4×D4×C19D412yes—
56C19×#117—24no—
57C19×#117—22no—
58C19×#117C2×C412yes—
59C2×C4⋊C4×C19C2×C411yescharacteristic
60C2×C4⋊C4×C19D412yes—
61C2×C42×C19—22no—
62C2×C42×C19D412yes—
63C2×C42×C19C2311yescharacteristic
64C22×C19⋊C8—21no—
65C22×C19⋊C8—21no—
66C22⋊(C19⋊C8)—22no—
67C4⋊(C19⋊C8)—22no—
68C4⋊(C19⋊C8)—22no—
69C4×C19⋊C8—22no—
70C4×C19⋊C8—22no—
71#41×C19—28no—
72C2×Q8×C19—22no—
73C2×Q8×C19—22no—
74C2×Q8×C19—24no—
75C2×Q8×C19C22⋊C412yes—
76C2×D4×C19—22no—
77C2×D4×C19—22no—
78C2×D4×C19C22⋊C412yes—
79C22×C4×C19—22no—
80C22×C4×C19—22no—
81C22×C4×C19—22no—
82C22×C4×C19C22⋊C412yes—
83C22×C4×C19C22⋊C412yes—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C4⋊C4×C19—24no—
88C4⋊C4×C19—24no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—24no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—24no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19C22⋊C412yes—
97C4⋊C4×C19C22⋊C412yes—
98C22⋊C4×C19—24no—
99C22⋊C4×C19—24no—
100C22⋊C4×C19—24no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—22no—
103C22⋊C4×C19—22no—
104C42×C19—22no—
105C42×C19—22no—
106C42×C19—22no—
107C42×C19—22no—
108C42×C19—22no—
109C42×C19C2×D412yes—
110C42×C19C2×D412yes—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—42no—
115C2×C19⋊C8—42no—
116C2×C19⋊C8—41no—
117#8321—191nomaximal, Sylow
118C23×C19—22no—
119C23×C19C2×C22⋊C411yescharacteristic
120Q8×C19—24no—
121Q8×C19—44no—
122Q8×C19—82no—
123D4×C19—24no—
124D4×C19—44no—
125D4×C19—82no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—24no—
134C2×C4×C19—41no—
135C2×C4×C19—44no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—82no—
140C2×C4×C19C2×C22⋊C412yes—
141C2×C4×C19#12011yescharacteristic
142C2×C4×C19#12012yes—
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#13114yes—
145C19⋊C8—42no—
146C19⋊C8—82no—
147C19⋊C8—81no—
148#3461D1911yescharacteristic
149#1984—191no—
150#1477—192no—
151#1476—192no—
152#1461—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19—42no—
158C22×C19#37911yescharacteristic
159C22×C19#40812yes—
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—42no—
163C4×C19—42no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—42no—
167C4×C19#40814yes—
168C4×C19#45411yescharacteristic
169C4×C19#45611yescharacteristic
170#544Dic1911yescharacteristic
171#542—22no—
172#541—22no—
173#539—22no—
174#537Dic1911yescharacteristic
175#536Dic1912yes—
176#533—22no—
177#529—22no—
178#529—22no—
179C4×#41C2×D1912yes—
180C2×C4×Q8C2×D1911yescharacteristic
181#431—192no—
182C2×C4⋊C8—191no—
183C2×C4×C8—191no—
184#336—382no—
185Q8⋊C8—382no—
186Q8⋊C8—382no—
187D4⋊C8—382no—
188D4⋊C8—382no—
189#324—382no—
190C2×C19—22no—
191C2×C19—82no—
192C2×C19#178011yescharacteristic
193C2×C19#179311yescharacteristic
194C2×C19#179411yescharacteristic
195C2×#41C2×Dic1912yes—
196C22×Q8C2×Dic1911yescharacteristic
197C22×C8—381no—
198C22×C8—381no—
199C4⋊Q8—22no—
200C4⋊Q8—22no—
201#126—24no—
202#126—24no—
203#125—22no—
204#125—24no—
205#125—22no—
206#124—22no—
207#124—22no—
208#123—24no—
209#123—24no—
210C22⋊Q8—24no—
211C22⋊Q8—22no—
212C22⋊Q8—22no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215#121—22no—
216#121—22no—
217C4×Q8—22no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8C22⋊D1912yes—
221C4×Q8C22⋊D1912yes—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—22no—
225C4×D4C22⋊D1912yes—
226C4×D4C22⋊D1912yes—
227#117—24no—
228#117—22no—
229#117C2×Dic1912yes—
230C2×C4⋊C4C2×Dic1911yescharacteristic
231C2×C4⋊C4C22⋊D1912yes—
232C2×C42—22no—
233C2×C42C22⋊D1912yes—
234C2×C42C22×D1911yescharacteristic
235C4⋊C8—382no—
236C4⋊C8—382no—
237C22⋊C8—382no—
238C4×C8—382no—
239C4×C8—382no—
240C19#832111yescharacteristic, complemented, Sylow
241#41—28no—
242C2×Q8—22no—
243C2×Q8—24no—
244C2×Q8—22no—
245C2×Q8C22⋊Dic1912yes—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4C22⋊Dic1912yes—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4C22⋊Dic1912yes—
253C22×C4C22⋊Dic1912yes—
254C22×C4C22×Dic1911yescharacteristic
255C22×C4C2×C22⋊D1911yescharacteristic
256C22×C4C2×C22⋊D1911yescharacteristic
257C2×C8—382no—
258C2×C8—761no—
259C2×C8—761no—
260C2×C8—762no—
261C2×C8—762no—
262C2×C8—761no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—22no—
269C4⋊C4—24no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4C22⋊Dic1912yes—
273C4⋊C4C22⋊Dic1912yes—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42C2×C22⋊D1912yes—
286C42C2×C22⋊D1912yes—
287C23—22no—
288C23C2×C22⋊Dic1911yescharacteristic
289Q8—24no—
290Q8—44no—
291Q8—82no—
292D4—24no—
293D4—44no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—82no—
309C2×C4#1059739414yes—
310C2×C4C2×C22⋊Dic1912yes—
311C2×C4#1059739911yescharacteristic
312C2×C4#1059739912yes—
313C2×C4#1059739911yescharacteristic
314C8—762no—
315C8—1522no—
316C8—1521no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22#1192640011yescharacteristic
323C22#1192651112yes—
324C4—21no—
325C4—22no—
326C4—42no—
327C4—42no—
328C4—42no—
329C4—42no—
330C4—42no—
331C4#1192651114yes—
332C4#1192671711yescharacteristic
333C4#1192672711yescharacteristic
334C2—22no—
335C2—82no—
336C2#1456354711yescharacteristic
337C2#1456359411yescharacteristic
338C2#1456359911yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3461C2
socleC22×C19#379
prime radicalC19×#537C4
cosocleC2×C42×C19C23
hypercenter#3461D19
hypocenterC19#8321
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #14564572C2semidirect
2. #14562022C2semidirect
3. #14562017C2semidirect
4. #14561959C2semidirect
240. C19#8321semidirect

Maximal subgroups

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

subgroupindex
#145645722
#145620222
#145620172
#145619592
C19×#34612
#832119