Finite Group Databasebeta

← #18074977

Subgroups — #18074977

Order 4864.

648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 131 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#14564617C211yesmaximal, characteristic, complemented
2#14562300C211yesmaximal, characteristic, complemented
3#14562121C212yesmaximal, complemented
4#14562100C212yesmaximal, complemented
5C19×#3531C211yesmaximal, characteristic
6#11926597C2212yes—
7#11926568C2211yescharacteristic
8#11926390C2211yescharacteristic
9#11926303—22no—
10#11926290—22no—
11#11926281—22no—
12#11926278—22no—
13Q8⋊(C19⋊C8)—22no—
14D4⋊(C19⋊C8)—22no—
15C19×#564C411yescharacteristic, complemented
16C19×#563—22no—
17C19×#563—22no—
18C19×#563C412yescomplemented
19C19×#562—22no—
20C19×#562C411yescharacteristic, complemented
21C19×#533—22no—
22C19×#533C2211yescharacteristic
23C19×#529—22no—
24C19×#529—22no—
25C19×#529C2212yes—
26C19×C4⋊Q8—22no—
27C19×C4⋊Q8—22no—
28C19×C4⋊Q8D412yes—
29C19×#126—22no—
30C19×#126—22no—
31C19×#126—22no—
32C19×#126—22no—
33C19×#126—22no—
34C19×#125—22no—
35C19×#125—22no—
36C19×#125—22no—
37C19×#125—22no—
38C19×#125C2×C412yes—
39C19×#125C2×C411yescharacteristic
40C19×#125C2×C411yescharacteristic
41C19×#124—22no—
42C19×#124—22no—
43C19×#124C2×C412yes—
44C19×#123—22no—
45C19×#123—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×#123—22no—
49C19×C22⋊Q8—22no—
50C19×C22⋊Q8—22no—
51C19×C22⋊Q8—22no—
52C19×C22⋊Q8—22no—
53C19×C22⋊Q8—22no—
54C19×C22⋊Q8—22no—
55C19×C22⋊Q8—22no—
56C19×C22⋊Q8D412yes—
57C19×#121—22no—
58C19×#121—22no—
59C19×#121D412yes—
60C4×Q8×C19—22no—
61C4×Q8×C19—22no—
62C4×Q8×C19D412yes—
63C4×D4×C19—22no—
64C4×D4×C19—22no—
65C4×D4×C19D412yes—
66C19×#117—22no—
67C19×#117—22no—
68C19×#117D412yes—
69C2×C42×C19—22no—
70C2×C42×C19C2311yescharacteristic
71C2×C4×Dic19—21no—
72C2×#64520—21no—
73C19⋊#95—22no—
74C22⋊(C19⋊C8)—22no—
75C4⋊(C19⋊C8)—22no—
76C4⋊(C19⋊C8)—22no—
77C4×C19⋊C8—22no—
78C2×Q8×C19—22no—
79C2×Q8×C19—22no—
80C2×Q8×C19C22⋊C412yes—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19C22⋊C412yes—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—22no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×Dic19—41no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19C22⋊C412yes—
104C4⋊C4×C19C22⋊C412yes—
105C4⋊C4×C19C22⋊C412yes—
106C4⋊C4×C19C22⋊C412yes—
107C22⋊C4×C19—22no—
108C22⋊C4×C19—22no—
109C22⋊C4×C19—22no—
110C22⋊C4×C19—22no—
111C22⋊C4×C19—22no—
112C22⋊C4×C19—22no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C22⋊C4×C19—22no—
117C42×C19—22no—
118C42×C19—22no—
119C42×C19—22no—
120C42×C19—22no—
121C42×C19C22×C411yescharacteristic
122C42×C19C2×D412yes—
123C42×C19C2×D411yescharacteristic
124C4×Dic19—22no—
125C4×Dic19—41no—
126#64520—42no—
127C2×C19⋊C8—42no—
128C2×C19⋊C8—41no—
129#8505—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19#12011yescharacteristic
132Q8×C19—42no—
133Q8×C19—82no—
134Q8×C19—82no—
135D4×C19—42no—
136D4×C19—82no—
137D4×C19—82no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—82no—
149C2×C4×C19—82no—
150C2×C4×C19C2×C22⋊C411yescharacteristic
151C2×C4×C19C2×C22⋊C412yes—
152C2×C4×C19#12012yes—
153C2×C4×C19#12011yescharacteristic
154C2×Dic19—42no—
155C2×Dic19—82no—
156C19⋊C8—82no—
157C19⋊C8—81no—
158#3531D1911yescharacteristic
159#1995—191no—
160#1544—191no—
161#1500—192no—
162#1495—192no—
163C22×C19—21no—
164C22×C19—22no—
165C22×C19—42no—
166C22×C19—42no—
167C22×C19—42no—
168C22×C19#37911yescharacteristic
169C4×C19—21no—
170C4×C19—22no—
171C4×C19—22no—
172C4×C19—42no—
173C4×C19—42no—
174C4×C19—42no—
175C4×C19—42no—
176C4×C19—42no—
177C4×C19#45411yescharacteristic
178C4×C19#45611yescharacteristic
179Dic19—82no—
180#564Dic1911yescharacteristic, complemented
181#563—22no—
182#563—22no—
183#563Dic1912yescomplemented
184#562—22no—
185#562Dic1911yescharacteristic, complemented
186#533—22no—
187#533C2×D1911yescharacteristic
188#529—22no—
189#529—22no—
190#529C2×D1912yes—
191#431—192no—
192#423—191no—
193#376—191no—
194#339—382no—
195#332—382no—
196#328—382no—
197#327—382no—
198Q8⋊C8—382no—
199D4⋊C8—382no—
200C2×C19—41no—
201C2×C19—82no—
202C2×C19#179311yescharacteristic
203C2×C19#179412yes—
204C2×M16—381no—
205C4⋊Q8—22no—
206C4⋊Q8—22no—
207C4⋊Q8C22⋊D1912yes—
208#126—22no—
209#126—22no—
210#126—22no—
211#126—22no—
212#126—22no—
213#125—22no—
214#125—22no—
215#125—22no—
216#125—22no—
217#125C2×Dic1912yes—
218#125C2×Dic1911yescharacteristic
219#125C2×Dic1911yescharacteristic
220#124—22no—
221#124—22no—
222#124C2×Dic1912yes—
223#123—22no—
224#123—22no—
225#123—22no—
226#123—22no—
227#123—22no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C22⋊Q8—22no—
235C22⋊Q8C22⋊D1912yes—
236#121—22no—
237#121—22no—
238#121C22⋊D1912yes—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8C22⋊D1912yes—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4C22⋊D1912yes—
245#117—22no—
246#117—22no—
247#117C22⋊D1912yes—
248C2×C42—22no—
249C2×C42—381no—
250C2×C42C22×D1911yescharacteristic
251C4⋊C8—382no—
252C4⋊C8—382no—
253C22⋊C8—382no—
254C4×C8—382no—
255#95—382no—
256C19#850511yescharacteristic, complemented, Sylow
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8C22⋊Dic1912yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4C22⋊Dic1912yes—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—761no—
267C22×C4C2×C22⋊D1911yescharacteristic
268C22×C4C2×C22⋊D1912yes—
269M16—762no—
270C2×C8—762no—
271C2×C8—761no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4C22⋊Dic1912yes—
286C4⋊C4C22⋊Dic1912yes—
287C4⋊C4C22⋊Dic1912yes—
288C4⋊C4C22⋊Dic1912yes—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—382no—
304C42—761no—
305C42C22×Dic1911yescharacteristic
306C42C2×C22⋊D1911yescharacteristic
307C42C2×C22⋊D1912yes—
308C23—22no—
309C23#1059739911yescharacteristic
310Q8—42no—
311Q8—82no—
312Q8—82no—
313D4—42no—
314D4—82no—
315D4—82no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—762no—
329C2×C4—1522no—
330C2×C4C2×C22⋊Dic1911yescharacteristic
331C2×C4C2×C22⋊Dic1912yes—
332C2×C4#1059739912yes—
333C2×C4#1059739911yescharacteristic
334C8—1522no—
335C8—1521no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22#1192640011yescharacteristic
342C4—21no—
343C4—22no—
344C4—22no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4—1522no—
351C4#1192671711yescharacteristic
352C4#1192672711yescharacteristic
353C2—41no—
354C2—82no—
355C2#1456359411yescharacteristic
356C2#1456359912yes—
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3531C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3531D19
hypocenterC19#8505
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3531

Complements

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

NH ≅ G/Ntype
1. #14564617C2semidirect
2. #14562300C2semidirect
3. #14562121C2semidirect
4. #14562100C2semidirect
15. C19×#564C4semidirect
18. C19×#563C4semidirect
20. C19×#562C4semidirect
180. #564Dic19semidirect
183. #563Dic19semidirect
185. #562Dic19semidirect
256. C19#8505semidirect

Maximal subgroups

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

subgroupindex
#145646172
#145623002
#145621212
#145621002
C19×#35312
#850519